From d08decfdf74f33807b4845a5ffca465dc0aca49c Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 15:07:55 -0400 Subject: [PATCH 01/26] Begin direct overlapping-rank compiler with explicit integer width bounds --- research/direct-mixed-flow/.gitattributes | 1 + research/direct-mixed-flow/README.md | 406 +++++++ research/direct-mixed-flow/RESULT.json | 492 +++++++++ research/direct-mixed-flow/SOURCES.json | 18 + research/direct-mixed-flow/TASK.json | 124 +++ research/direct-mixed-flow/VENDOR.json | 61 ++ research/direct-mixed-flow/VERIFY.json | 28 + research/direct-mixed-flow/flow.py | 198 ++++ .../vendor/FINITE-PRECOMPILATION.md | 313 ++++++ .../direct-mixed-flow/vendor/SUSSMAN-LICENSE | 201 ++++ .../direct-mixed-flow/vendor/SUSSMAN-NOTICE | 994 ++++++++++++++++++ .../vendor/higher-moment-README.md | 416 ++++++++ .../vendor/higher-moment-RESULT.json | 384 +++++++ .../direct-mixed-flow/vendor/p7-RESULT.json | 296 ++++++ .../direct-mixed-flow/vendor/theorem-1g.md | 264 +++++ .../direct-mixed-flow/vendor/tree_flow.py | 167 +++ research/direct-mixed-flow/verify.py | 232 ++++ 17 files changed, 4595 insertions(+) create mode 100644 research/direct-mixed-flow/.gitattributes create mode 100644 research/direct-mixed-flow/README.md create mode 100644 research/direct-mixed-flow/RESULT.json create mode 100644 research/direct-mixed-flow/SOURCES.json create mode 100644 research/direct-mixed-flow/TASK.json create mode 100644 research/direct-mixed-flow/VENDOR.json create mode 100644 research/direct-mixed-flow/VERIFY.json create mode 100644 research/direct-mixed-flow/flow.py create mode 100644 research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md create mode 100644 research/direct-mixed-flow/vendor/SUSSMAN-LICENSE create mode 100644 research/direct-mixed-flow/vendor/SUSSMAN-NOTICE create mode 100644 research/direct-mixed-flow/vendor/higher-moment-README.md create mode 100644 research/direct-mixed-flow/vendor/higher-moment-RESULT.json create mode 100644 research/direct-mixed-flow/vendor/p7-RESULT.json create mode 100644 research/direct-mixed-flow/vendor/theorem-1g.md create mode 100644 research/direct-mixed-flow/vendor/tree_flow.py create mode 100644 research/direct-mixed-flow/verify.py diff --git a/research/direct-mixed-flow/.gitattributes b/research/direct-mixed-flow/.gitattributes new file mode 100644 index 0000000000..2435bfdf63 --- /dev/null +++ b/research/direct-mixed-flow/.gitattributes @@ -0,0 +1 @@ +vendor/** -text -whitespace diff --git a/research/direct-mixed-flow/README.md b/research/direct-mixed-flow/README.md new file mode 100644 index 0000000000..65da945a22 --- /dev/null +++ b/research/direct-mixed-flow/README.md @@ -0,0 +1,406 @@ +# Direct mixed flow and explicit compiler size: a partial research checkpoint + +**Local work for user review. Do not push or submit a PR yet.** + +The target is a structural successor to +[PR4433](https://github.com/CrocSwap/integer-mult-bounds/pull/4433): remove the +tensor/padding step needed by overlapping ranks and control the complete +finite compiler's size. The user requested a significance target twice the +previous contribution. That is an ambitious scope target, not a numerical +measurement or a claim that it has been achieved. + +Two results are established under the source native-word hypotheses: + +1. A **finite chronological integer flow** works when paid ranks overlap + target ranks, provided `max paid < ambient`. It retains and pays every + unmatched job as an exit. All recursive ranks decrease. This gives a + finite uniform compiler, **without a proved near-root saving**. +2. Choosing **nested divisible widths** gives `B_N <= exp(O(N log N))`. + Exact rank-one accounting also bounds raw instances, owned centers and + routing slots. This batching choice preserves the normalized leaf cost + and therefore applies to the already supported PR4433 supplier. + +The main exponent target remains open. Exact compilation at rank 1,000 on +the raw p7 profile fails the desired saving. That finite failure is not an +asymptotic obstruction, and it does not invalidate PR4433's separated recipe. +No new κ, selected frontier, native admission or physical runtime is claimed. + +## 1. Source boundary and decision + +The starting point is Jacob Alan Sussman's multinomial lockstep construction, +retained by PR4359. Its separated proof requires `r_max < k_min` so every +parent output is consumed. PR4416 and PR4433 instead repair the raw p7 +overlap by chronological products, paid completion and splitting. + +Retain the four native hypotheses of +[FINITE-PRECOMPILATION.md](vendor/FINITE-PRECOMPILATION.md): a correct +all-column arbitrary-input word, disjoint splitting with complete spectators, +permitted and priced whole-job adapters, and finite-program closure with +owned initialization/erasure. Equal rank alone does not supply an adapter. +Changed finite combinatorics do not independently admit those hypotheses. + +**Continue, with two separate gates.** The finite-flow gate is now proved and +checked. The exponent gate requires a new uniform estimate on the complete +complement-plus-exit recurrence. Do not expand a search solely because a +moment root is favorable. The size theorem is useful independently, since +the predecessor leaves productive width and owned-instance counts implicit. + +| Obligation | Evidence / remaining work | +| --- | --- | +| Integer matching with overlapping ranks | Proved below; literal and merged replays agree | +| Chronological return and strictly smaller exits | Proved under `r_max < m`; no cross-round matching | +| Source complements and full uniform output | Source integer-batch induction, with nested divisible widths | +| Direct near-root saving | **Open**; rank 1,000 fails; no global conclusion | +| Productive width, rank-one leaves, raw instances, owned centers | Explicit bounds below, with exact finite controls | +| Routing slots and encoded adapter/move records | Counted in the stated macro grammar; physical implementations retain their own tariffs | +| Native all-column, physical, analytic, precision and recovery premises | Inherited; no full replay or new admission | + +## 2. Partially matched integer lockstep flow + +Let positive integer target multiplicities be W_k, chronological paid rounds +have ranks r_j, and let + +``` +2 <= k_min <= m=max(k), 1 <= r_max < m. +``` + +The paid word may have `r_max >= k_min`. At a fixed integer top rank n>=m, +put + +``` +c(a) = product_k k^a_k, +u(a) = multinomial(|a|;a) product_k W_k^a_k, +R(rho) = {a : m*rho*c(a) <= n}, +G = floor(log_(k_min)(floor(n/m))). +``` + +For every paid-round path s of length d<=G with multiplier rho_s, instantiate +u(a) units at column rho_s*c(a), for every point a in R(rho_s) of degree +G−d. This is the source class construction. For a parent class with +multiplier rho, its rank-r round supplies u(b) jobs at point b when b is +present. The child demand at that point is + +``` +D(b) = sum over eligible (b−e_k) of W_k*u(b−e_k). +``` + +The complete Pascal sum is u(b). Therefore: + +- If the parent point b exists, `0 <= D(b) <= u(b)`. Route D(b) of the + **whole** issued jobs to the child. Complete the remaining u(b)−D(b) + jobs as paid exits, at their actual rank `e=r*rho*c(b)`. +- If the parent point is absent, supply the child demand with new distinct + top input arrays. These are source jobs, not copies of issued data. +- At depth G, every point has degree zero; all paid jobs are exits. + +No fractional jobs, cloned productive inputs or uncharged discarded requests +are introduced. Within each point, choose a fixed enumeration of parent +jobs and target slots and match their first D(b) elements. The rest have +explicit endpoints and remain on their actual owners. + +### Sources and exits + +At the root, every demanded point has degree G+1, so it is outside R(1). +Its rank s is in `(n/m,n]`. A non-root source has no parent point, hence +`m*rho_parent*c(b)>n`; its rank is `r*rho_parent*c(b)>r*n/m>=n/m`. +Its eligible child target ensures s<=n. Thus every source is a positive +job in `(n/m,n]`. + +Every exit belongs to an actual parent unit, so + +``` +e <= r_max*n/m < n. +``` + +This holds for the new premature exits as well as leaf exits. A premature +exit has at least one omitted Pascal term, with +`m*r*rho*c(b)/k > n`; consequently `e > k_min*n/m`. These are large exits +near the upper boundary. They cannot be assigned the old bound +`r_max*(n/m)^theta` with theta<1. That lost estimate is the exponent issue. + +### Chronology and arbitrary inputs + +Run all scalar steps of a class in their specified order. At paid position +j, issue that position for every unit, partition its whole issued jobs into +matched and unmatched slots, finish all unmatched exits and the entire child +class, restore adapters, and only then resume position j+1. The child takes +incoming jobs from this one parent round plus its new top sources. It never +waits for a later round of a suspended parent. The finite class depth is G; +all complement and exit calls have rank below n, so their uniform programs +are already available by strong induction. + +Distinct slots in one class have distinct physical fields. Routing fewer +parent slots than the original full-Pascal construction preserves this +property. Arbitrary-input native correctness permits correlated values, +including current owned-center contents; it does not permit field aliasing +or extra productive credit. Each unit has its own owned identities and +retains them until its word clears them. These requirements are unchanged. + +### Exact potential and count identities + +Let S_s and E_e be integer source and exit inventories, U the unit count, +and Qcol the sum of the units' positive integer column multiplicities. +Cancellation of matched jobs gives, exactly at rank one, + +``` +sum_s S_s*s − sum_e E_e*e = Delta * Qcol, +Delta = sum_k W_k*k − sum_j r_j. +``` + +At any real exponent t, the corresponding identity is + +``` +sum_s S_s*s^t − sum_e E_e*e^t + = (T_t−P_t) * sum_units column^t. +``` + +Thus a favorable raw t-moment survives as a superpotential. It does **not** +by itself pay the source complements. Writing W=sum W_k and P=number of +paid rounds, complete untruncated layer counts give + +``` +U <= sum_(d=0..G) P^d W^(G−d) <= (W+P+1)^(G+1), +S := sum_s S_s <= W*U, +sum_e E_e <= P*U. +``` + +The source package's separated case is unchanged: no premature exits occur. +The verifier compares it with the byte-identical predecessor literal replay. + +## 3. Nested divisible widths and complete count bounds + +Use the ordinary base B_n=1, P_n=n below m, with B_0=1 and P_0=0. For n>=m +choose the replication factor and productive width + +``` +a_n = B_(n−1), B_n = a_n*S_n. +``` + +Every earlier width B_e divides B_(n−1), by induction. Therefore every +source-complement batch and exit batch is an integer number of smaller +uniform programs. This is a concrete choice within the source compiler's +existing denominator-clearing freedom; no optimum is claimed. Its previous +option to use an LCM is retained as predecessor context. + +As in the source compiler, each of the a_n*S_n original arrays first gets +its disjoint complementary job, then its one source job through the flow. +All exits are completed by smaller uniform programs. The result is a full +rank-n transform on every original array. Owned storage is excluded from B_n. + +The normalized leaf count satisfies the **same exact recurrence** for any +valid replication choice: + +``` +L(n) = (1/S_n) * [sum_s S_s L(n−s) + sum_e E_e L(e)]. +``` + +Changing the replication factors changes width and total counts equally. +It does not spend supplier saving or alter any outer parameter. + +For a fixed final N and h=G(N), all n<=N satisfy + +``` +S_n <= C_N := W*(W+P+1)^(h+1), +B_N = product_(n=m..N) S_n <= C_N^N. +``` + +Since h=O(log N), **log B_N=O(N log N)** for a fixed mixed rule. Repeatedly +multiplying all previous widths is unnecessary. This bounds one explicit +realization; the original compiler did not require that inefficient choice. + +If Delta>0, telescope rank-one mass over the fully expanded uniform program: + +``` +B_N*N − P_N = Delta * Qcol_N, +U_N <= Qcol_N <= B_N*N/Delta. +``` + +All raw columns are positive integers, which gives the middle inequality. +Thus paid leaves and raw instances have the same `exp(O(N log N))` bound. +With one owned center per raw unit, the center count is at most U_N. A rule +with O_local distinct owned banks per invocation instead gets O_local*U_N. +Extra router scratch must be counted separately. + +### Routing and word description + +Count one routing slot for every source, every exit, every unit target slot +and every unit paid position. At one flow its count is at most +`2*(W+P)*U`. The same bound telescopes over all recursive calls, because +each call contributes its own local unit instances. Exact compilation checks +this identity alongside widths and leaves. + +In the macro grammar that records a whole-job adapter, inverse adapter or +whole-field move as one record, a slot can be handled with at most eight +records: up to two whole-job conjugations and their inverses, and park/load/ +return/reorder moves. Allocate separate owned scratch for those moves when +needed; no zero-cost routing or free copying is assumed. If A is the complete +fixed unit's nonrecursive record allowance, including its owned operations, +the final macro word satisfies the conservative bound + +``` +R_macro <= A*U_N + 16*(W+P)*U_N + P_N + <= (A+16*(W+P)+1)*B_N*N, for Delta>=1. +``` + +This is a **description/record bound**, not a new tariff for executing a +general matrix or permutation. A dense binary address matrix and quadratic +phase have O(N^2) descriptor bits. Explicit role indices add O(log B_N) +bits. Thus an encoding of this finite word still has +`exp(O(N log N))` bits for a fixed unit and its finite coefficient alphabet. +If physical expansion of one adapter needs F(N) native records, multiply +the routing term by its actual F(N). That physical implementation, coefficient +heights and tape costs remain separately priced native obligations. They +are not set to zero by the macro bound. + +## 4. Applying the size result to PR4433 + +The new nested widths may be used in the separated compiler of PR4433. +Its normalized L(n), ambient N, uniform saving and outer ledger remain +unchanged. Therefore this application does not need the still-open direct +exponent lemma. + +With `v=150`, `H=349300000000`, `N=2^H`, the completed mixed rule has + +``` +W = 7688^150 < 2^1950, +P <= 131115^150 + 7688^150*15^150 < 2^2701, +W+P+1 < 2^2702. +``` + +The bound on P counts every original and completion call by its positive +rank mass; splitting preserves that mass. Since k_min>=2, h<=H. Set + +``` +D = 1950 + 2702*(H+1) = 943808600004652. +``` + +There is consequently a realization of the same proposed conditional +κ=0.00268647 supplier satisfying + +``` +B_N < 2^(D * 2^H), +P_N < B_N * 2^H. +``` + +More finely, after expanding every product, padding, split and compiler call +back to the raw p7 word, that word has surplus 608. Product/completion/split +boundaries cancel, so + +``` +B_N*N − P_N = 608 * sum_raw_p7_instances column, +U_raw <= (B_N*N − P_N)/608. +``` + +This is also an explicit bound on raw p7 center banks under the safe +one-center-per-instance allocation. These are large upper bounds, not +emitted words, smallest widths or practical precision estimates. They replace +one implicit part of the source finite-constant prescription. The native +adapter bodies, analytic transfer and physical costs retain their original +conditions; full numerical precision and tape thresholds are not closed here. + +## 5. Exact finite checks and the open exponent gate + +The verifier uses no floating-point acceptance tests. It checks: + +- Nine literal/merged flows at ranks 20, 40 and 80: a separated control, + strict overlap `{2:1,5:1} <- {1:2,4:1}`, and Sussman's open equality + example `{2:4,3:1} <- {1:6,2:2}`. Every whole input and exit agrees. +- The separated control agrees with the unchanged Sussman literal replay. +- Complete nested-width compilations through rank 100 on both overlap + examples, checking every recursive batch, routing count and rank identity. +- Raw p7 through rank 1,000: **880 exact nonbase compilations**. B_1000 has + 17,504 bits; the saved receipt binds all large computed integers by their + unsigned big-endian hashes, avoiding enormous decimal dumps. +- Removing premature exits violates mass conservation. Removing batch + replication fails integer divisibility. Allowing a paid rank equal to + the ambient rank is rejected because strict rank descent is unavailable. + +For raw p7 at rank 1,000, exact arithmetic gives + +``` +L(1000) > 990 > 1000^(1−0.00268647). +``` + +The second comparison is elementary and exact: `ln(2)>2/3` from its first +atanh term and `1000>2^9` give `ln(1000)>6`. Then +`1000^κ > 1+6κ > 100/99`. No log approximation is used in this rejection. +This checks one finite failure and keeps it distinct from the infinite-rank +question. + +The missing lemma is a uniform bound on the **whole** recurrence. For some +fixed p and sufficiently large n, one would need, for example, + +``` +sum_e E_e e^t (1+log2(e))^p + + sum_s S_s (n−s)^t (1+log2(n−s))^p + <= S_n n^t (1+log2(n))^p, +``` + +with zero-rank terms defined separately and a correctly funded base range. +The premature exits have rank proportional to n. Their logarithmic factors +cannot use the old fixed theta<1 power contraction. A raw moment advantage +alone does not prove this inequality. + +Exploratory `approximate_leaves` in flow.py evaluates the recurrence in +floating point and is deliberately excluded from verification. A bounded +run through 20,000 ranks found saving about 0.000827 for the default height; +varying the height did not approach 0.00268647 there. This is local search +evidence, not a lower bound or a reason to enlarge the same scan. A better +boundary estimate or a changed flow is the next research obligation. + +## 6. Reproduction and provenance + +Python 3.12, standard library only: + +```sh +python3.12 -B research/direct-mixed-flow/verify.py +python3.12 -B scripts/research_package.py --package research/direct-mixed-flow --check-only +python3.12 -B scripts/research_package.py --package research/direct-mixed-flow +``` + +Use `verify.py --out /absolute/new/result.json` for a fresh receipt. +[RESULT.json](RESULT.json) contains exact flows, integer compilation hashes, +symbolic size bounds and negative controls. `flow.py` is the new algorithm; +the verifier independently compares its merged and literal traversal outputs. +Those are two internal implementations, not an independent mathematical review. + +Canonical base is `12fa8c5c844be21bfefb38a19503fbd867a11244`, priority revision +7. SOURCES.json pins orientation metadata. VENDOR.json separately binds eight +unchanged exports by commit, full path, Git blob and SHA256. Their bytes and +notices are preserved; direct replay needs no foreign Git objects. The source +theorem and earlier finite compiler remain attributed hypotheses, not new work. + +The overlap refresh at 18:48 UTC covered 538 open PR bodies and 3,280 +discussion/comment records, with complete reported pagination. Specific +searches for direct overlapping-rank compilers, Pascal matching and nested +widths found no matching public item in that scope; this is not a novelty +certificate. Existing PR4433 supplies the fixed-rank application, and the +source theorem explicitly leaves the unseparated exponent open. No Discussion +claim or PR has been posted for this partial checkpoint. + +## Open next questions + +1. **Close or refute the direct exponent gate for this capped flow.** Start + with a proved bound on premature-exit potential relative to the actual + complement capacity. This decides whether the flow can replace the + tensor/padding layer. A larger rank scan is not a uniform proof. +2. **Finish physical word and precision bounds.** Bind the macro-record + allowance A and each adapter's actual implementation to the fixed native + caller; insert their coefficient heights, routing scratch and movement + counts into the source precision/stock formulas. Macro description size + is not a physical execution tariff. +3. **Tighten the constructive width.** The nested product is an explicit + upper bound, not an optimized LCM. A useful next step would control prime + valuations of the actual source counts; another arbitrary batching choice + would not by itself establish a smaller physical supplier. + +Prepared by zxv with substantial OpenAI Codex assistance in research, code +and writing. No subagents or independent human mathematical review were +used. New material is Apache-2.0. The integer lockstep/Pascal construction +and original open unseparated question are Jacob Alan Sussman's work, retained +at upstream `wht-power-saving-lean` commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a`; its LICENSE and NOTICE are included. +PR4359 supplies the native finite-precompilation bridge and p7 predecessor +lineage. PR4416's p7 product/padding is @1337isnot1337's work. PR4433 supplies +the unchanged sufficient rank. Their original contributor credit remains +in the authenticated exports. diff --git a/research/direct-mixed-flow/RESULT.json b/research/direct-mixed-flow/RESULT.json new file mode 100644 index 0000000000..e2f0b121eb --- /dev/null +++ b/research/direct-mixed-flow/RESULT.json @@ -0,0 +1,492 @@ +{ + "direct_exponent_theorem_established": false, + "exact_p7_direct_compilation": { + "column_mass": { + "bits": 17497, + "unsigned_big_endian_sha256": "0f2b521412ca3f565d734c244b1cf42b8c7d49ef1e61af197ec97b2605078a3c" + }, + "leaves_per_array": { + "lower": "24890741110487842821/25000000000000000", + "upper": "995629644419513712841/1000000000000000000" + }, + "n": 1000, + "nested_batch_checks": 880, + "paid_above_99_percent_linear": true, + "paid_rank_one_leaves": { + "bits": 17514, + "unsigned_big_endian_sha256": "1f28a559d21f0df473b67fef0c37eb57144955250234a44c998bd837d1e8f3d6" + }, + "productive_width": { + "bits": 17504, + "unsigned_big_endian_sha256": "49727d4435d62a4a84b79cf2451d374a5bb98234cbe460ec0b0ef3da77c8c9e6" + }, + "rank_one_surplus": 608, + "raw_instances": { + "bits": 17497, + "unsigned_big_endian_sha256": "0f5ce7310a89be0835b71681538c3e2e57134d2690ff663b8bc1cd10938b9c7f" + }, + "routing_slots": { + "bits": 17514, + "unsigned_big_endian_sha256": "98bde80b4a7bc886645e82f3b9e730545da94beddcbec4e98ce88e1c44a39242" + }, + "source_count_upper": 31182789153672, + "target_failure": { + "kappa": "268647/100000000", + "proved": "L(1000) > 990 > 1000^(1-kappa)", + "scope": "This particular finite rank fails; no asymptotic impossibility claim." + }, + "width_exponent_envelope": 45000 + }, + "exact_toy_compilations": [ + { + "column_mass": { + "bits": 438, + "unsigned_big_endian_sha256": "f469278cd8f6190ffe6a1ae190299a8d183d1675d4280087d107e5d7016aee25" + }, + "leaves_per_array": { + "lower": "63955485748643768733/1000000000000000000", + "upper": "31977742874321884367/500000000000000000" + }, + "n": 100, + "nested_batch_checks": 96, + "paid_above_99_percent_linear": false, + "paid_rank_one_leaves": { + "bits": 439, + "unsigned_big_endian_sha256": "7df4f5875466fa21b225c2b60317e60536fdededbe8473d18fe5fb3fb057bb6f" + }, + "productive_width": { + "bits": 433, + "unsigned_big_endian_sha256": "35f12bcc6000b703565e2f120e8077641f744909e8ec163921775b2b0c139254" + }, + "rank_one_surplus": 1, + "raw_instances": { + "bits": 436, + "unsigned_big_endian_sha256": "12b6d174870cd23fd40ad1f4ff56df629ed813fabbbfcf143a914bfdd875609d" + }, + "routing_slots": { + "bits": 439, + "unsigned_big_endian_sha256": "4034ff94efe1f1ab70575b300eebbd2469e9065861c4f2570a59256c47170f74" + }, + "source_count_upper": 15552, + "width_exponent_envelope": 1400 + }, + { + "column_mass": { + "bits": 1007, + "unsigned_big_endian_sha256": "f04dcf1684cd1a5f5708102f230375fb43cd08135626ac91b22478876e21c63e" + }, + "leaves_per_array": { + "lower": "65003740439870989333/1000000000000000000", + "upper": "32501870219935494667/500000000000000000" + }, + "n": 100, + "nested_batch_checks": 98, + "paid_above_99_percent_linear": false, + "paid_rank_one_leaves": { + "bits": 1008, + "unsigned_big_endian_sha256": "1302eac01cf514d2855c821612c64c9d38a6c9ff55f12115f72bf34a9906b9d5" + }, + "productive_width": { + "bits": 1002, + "unsigned_big_endian_sha256": "398043f007044ec4c1ba14eda89bf66b48733ce7a22bb855a3bc17a4665b5952" + }, + "rank_one_surplus": 1, + "raw_instances": { + "bits": 1006, + "unsigned_big_endian_sha256": "ebd327c71dde99fefa5afb70ef8ad5b207723935abb8bed0473a95d67e73fbe7" + }, + "routing_slots": { + "bits": 1010, + "unsigned_big_endian_sha256": "23f8f6398dbe8fe43a321ff79a6c52edfee5c4de97ff2852a6cdcc6c127e7cd7" + }, + "source_count_upper": 37647680, + "width_exponent_envelope": 2600 + } + ], + "existing_supplier_size_bounds": { + "D": 943808600004652, + "H": 349300000000, + "N": "2^349300000000", + "kappa": "268647/100000000", + "owned_p7_center_bound": "one per raw instance; <= B_N * 2^H / 608", + "paid_leaf_bound": "P_N < B_N * 2^H", + "physical_scope": "Encoded whole-job adapter/move records. Their permitted physical implementation and tariffs remain inherited, separately priced premises.", + "raw_p7_instance_bound": "U_raw <= (B_N * 2^H - P_N)/608", + "routing_macro_record_bound": "R <= (A + 16*(W+P) + 1) * B_N * N; A is the complete fixed-unit record allowance", + "routing_slot_bound": "slots <= 2*(W+P)*V, V completed-unit instances", + "width_bound": "B_N < 2^(D * 2^H)", + "winning_uniform_word_materialized": false + }, + "finite_flows": [ + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 18, + "exits": { + "1": 16, + "2": 16, + "4": 4 + }, + "height": 1, + "matched_jobs": 18, + "minimum_source": 9, + "n": 20, + "rank_one_surplus": 2, + "source_count": 9, + "sources": { + "12": 4, + "16": 1, + "9": 4 + }, + "unit_count_upper": 9, + "units": 9 + }, + "literal_classes": 7, + "paid": { + "1": 4, + "2": 2 + }, + "rule": "separated-control", + "targets": { + "3": 2, + "4": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 180, + "exits": { + "1": 64, + "2": 96, + "4": 48, + "8": 8 + }, + "height": 2, + "matched_jobs": 132, + "minimum_source": 12, + "n": 40, + "rank_one_surplus": 2, + "source_count": 42, + "sources": { + "12": 16, + "16": 4, + "24": 8, + "27": 8, + "32": 2, + "36": 4 + }, + "unit_count_upper": 63, + "units": 58 + }, + "literal_classes": 43, + "paid": { + "1": 4, + "2": 2 + }, + "rule": "separated-control", + "targets": { + "3": 2, + "4": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 244, + "exits": { + "1": 64, + "2": 96, + "4": 48, + "8": 8 + }, + "height": 2, + "matched_jobs": 162, + "minimum_source": 27, + "n": 80, + "rank_one_surplus": 2, + "source_count": 27, + "sources": { + "27": 8, + "36": 12, + "48": 6, + "64": 1 + }, + "unit_count_upper": 63, + "units": 63 + }, + "literal_classes": 43, + "paid": { + "1": 4, + "2": 2 + }, + "rule": "separated-control", + "targets": { + "3": 2, + "4": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": { + "16": 1 + }, + "column_mass": 28, + "exits": { + "1": 8, + "16": 5, + "4": 12 + }, + "height": 2, + "matched_jobs": 8, + "minimum_source": 5, + "n": 20, + "rank_one_surplus": 1, + "source_count": 14, + "sources": { + "10": 2, + "20": 5, + "5": 4, + "8": 3 + }, + "unit_count_upper": 19, + "units": 11 + }, + "literal_classes": 13, + "paid": { + "1": 2, + "4": 1 + }, + "rule": "strict-overlap", + "targets": { + "2": 1, + "5": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": { + "32": 5 + }, + "column_mass": 132, + "exits": { + "1": 16, + "16": 12, + "32": 5, + "4": 32 + }, + "height": 3, + "matched_jobs": 40, + "minimum_source": 10, + "n": 40, + "rank_one_surplus": 1, + "source_count": 30, + "sources": { + "10": 8, + "16": 3, + "20": 10, + "25": 4, + "40": 5 + }, + "unit_count_upper": 65, + "units": 35 + }, + "literal_classes": 40, + "paid": { + "1": 2, + "4": 1 + }, + "rule": "strict-overlap", + "targets": { + "2": 1, + "5": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": { + "40": 4, + "64": 5 + }, + "column_mass": 872, + "exits": { + "1": 32, + "16": 80, + "4": 80, + "40": 4, + "64": 29 + }, + "height": 4, + "matched_jobs": 132, + "minimum_source": 20, + "n": 80, + "rank_one_surplus": 1, + "source_count": 106, + "sources": { + "20": 36, + "25": 8, + "32": 15, + "40": 10, + "50": 8, + "80": 29 + }, + "unit_count_upper": 211, + "units": 119 + }, + "literal_classes": 121, + "paid": { + "1": 2, + "4": 1 + }, + "rule": "strict-overlap", + "targets": { + "2": 1, + "5": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 322, + "exits": { + "1": 216, + "2": 216, + "4": 72, + "8": 8 + }, + "height": 2, + "matched_jobs": 512, + "minimum_source": 8, + "n": 20, + "rank_one_surplus": 1, + "source_count": 128, + "sources": { + "12": 48, + "18": 10, + "8": 64, + "9": 6 + }, + "unit_count_upper": 129, + "units": 128 + }, + "literal_classes": 73, + "paid": { + "1": 6, + "2": 2 + }, + "rule": "source-open-equality", + "targets": { + "2": 4, + "3": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 4362, + "exits": { + "1": 1296, + "16": 16, + "2": 1728, + "4": 864, + "8": 192 + }, + "height": 3, + "matched_jobs": 5040, + "minimum_source": 16, + "n": 40, + "rank_one_surplus": 1, + "source_count": 670, + "sources": { + "16": 256, + "18": 84, + "24": 256, + "27": 6, + "36": 68 + }, + "unit_count_upper": 1157, + "units": 1142 + }, + "literal_classes": 585, + "paid": { + "1": 6, + "2": 2 + }, + "rule": "source-open-equality", + "targets": { + "2": 4, + "3": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 55372, + "exits": { + "1": 7776, + "16": 480, + "2": 12960, + "32": 32, + "4": 8640, + "8": 2880 + }, + "height": 4, + "matched_jobs": 45088, + "minimum_source": 27, + "n": 80, + "rank_one_surplus": 1, + "source_count": 3572, + "sources": { + "27": 36, + "32": 1024, + "36": 744, + "48": 1280, + "54": 96, + "72": 392 + }, + "unit_count_upper": 9881, + "units": 9732 + }, + "literal_classes": 4681, + "paid": { + "1": 6, + "2": 2 + }, + "rule": "source-open-equality", + "targets": { + "2": 4, + "3": 1 + } + } + ], + "new_code_sha256": { + "flow.py": "460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a", + "verify.py": "8104bbaac3afb1910290f97965503564f4299f3d6008af0b043742e9baffcead" + }, + "rejected_mutations": [ + "whole integer subprogram batches", + "finite direct-flow rank contract" + ], + "schema": "partial-direct-mixed-flow-and-finite-size/1", + "scope": "New finite matching/scheduling and batching/size bounds. The direct near-root exponent is open. Existing conditional endpoint and native/physical hypotheses remain inherited; no new kappa.", + "source_sha256": { + "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e", + "research/direct-mixed-flow/vendor/higher-moment-README.md": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", + "research/direct-mixed-flow/vendor/higher-moment-RESULT.json": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156", + "research/direct-mixed-flow/vendor/p7-RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab", + "research/direct-mixed-flow/vendor/theorem-1g.md": "c4a96c55c2509ff36e8bc6bddaaf6a8b1a34a5d794e4e09ac5214c82b51510e6", + "research/direct-mixed-flow/vendor/tree_flow.py": "750782f6d1cc0a9fff8a768899f3f4c62a7efdf0696d8b5a5d640b1836f5ab72" + }, + "status": "PASS_PARTIAL_DIRECT_FLOW_AND_SIZE_BOUNDS" +} diff --git a/research/direct-mixed-flow/SOURCES.json b/research/direct-mixed-flow/SOURCES.json new file mode 100644 index 0000000000..fcfba8aa31 --- /dev/null +++ b/research/direct-mixed-flow/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + } + ] +} diff --git a/research/direct-mixed-flow/TASK.json b/research/direct-mixed-flow/TASK.json new file mode 100644 index 0000000000..5522334d94 --- /dev/null +++ b/research/direct-mixed-flow/TASK.json @@ -0,0 +1,124 @@ +{ + "schema_version": 1, + "task_id": "supplier-boundary-audit", + "priority_revision": 7, + "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "original_card": { + "id": "supplier-boundary-audit", + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ], + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "existing_checks": [ + { + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3801: successor scatter-boundary decision package.", + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "status": "author-checked", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Target a direct chronological integer compiler for overlapping paid/productive ranks, without tensor power or paid padding, and explicit width/word/owned-storage bounds.", + "scope_change_reason": "User requests the next contribution target twice the significance of the higher-moment strictification. Raise the target from quantitative bounds inside that mechanism to removing its separation layer and controlling the full finite word. This is an ambitious target, not a claimed numerical significance measurement.", + "bottleneck_link": "Raw p7 has paid rank 48 above productive minimum 5. Existing compiler proofs require strict separation and the winning words lack explicit productive-width bounds. Partial matching may retain all unmatched jobs as priced exits; nested widths may avoid repeated products of batching denominators.", + "budget_minutes": 60, + "stop_rule": "First prove exact whole-integer matching, chronological return, top sources and smaller exits. Then test whether the complete recurrence supports the desired exponent. Do not infer exponent admission from moment balance. If it fails, preserve the first counterexample or missing lemma and the explicit-size result; no broader census or new kappa claim.", + "outcome": "partial", + "evidence": "README.md proves the finite partially matched direct compiler and exp(O(N log N)) productive-width bound. RESULT.json checks nine literal/merged flows, two full overlap compilations through rank 100, 880 exact p7 nonbase compilations through rank 1000, global surplus and routing-slot bounds. The direct exponent target remains open; rank 1000 fails.", + "author": "zxv, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance; no subagents.", + "open_questions": [ + { + "question": "Does the capped, partially matched direct flow close the target-saving induction?", + "why_it_matters": "A finite acyclic flow is insufficient if its boundary exits consume all complement capacity.", + "first_step": "Reconstruct every unmatched whole job and evaluate the complete complement-plus-exit recurrence on the source first examples and p7.", + "blocked_by": "No uniform boundary-exit bound or direct exponent proof yet." + }, + { + "question": "Can nested divisible widths and rank-one potential bound the whole expanded program?", + "why_it_matters": "It would control widths, owned centers and precision constants beyond ambient rank.", + "first_step": "Choose B_n=S_n B_(n-1), prove every smaller width divides it, and telescope the exact rank-one surplus over all raw instances.", + "blocked_by": "Full route/record counting and endpoint binding remain to be written." + } + ], + "publication_policy": "LOCAL ONLY until user review. Do not push, submit another PR or post Discussions.", + "significance_target": { + "relative_to": "PR4433 higher-moment strictification", + "requested_multiplier": 2, + "meaning": "Structural removal of tensor/padding plus full finite-program size control; aspirational scope, not a numerical guarantee." + }, + "upstream_checkpoint": { + "commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "priority_revision": 7, + "checked_at_utc": "2026-10-21T18:47:25Z" + }, + "scope_decision": "Continue toward the direct exponent gate; retain a separate complete count/batching theorem that already applies to PR4433. No further scan expansion without a new boundary estimate.", + "overlap": { + "checked_at_utc": "2026-10-21T18:48:25Z", + "open_prs": 538, + "discussion_records": 3280, + "complete_pagination": true, + "terms": [ + "direct mixed compiler", + "overlapping ranks", + "Pascal matching", + "nested widths", + "batch denominators", + "unmatched jobs" + ], + "specific_matches": "No matching public scope found; the later search matches this local task itself. This is not proof of novelty.", + "limits": "Open bodies, discussions and local notes; no arbitrary remote code-diff or remote closed-body search." + } +} diff --git a/research/direct-mixed-flow/VENDOR.json b/research/direct-mixed-flow/VENDOR.json new file mode 100644 index 0000000000..b05d41179f --- /dev/null +++ b/research/direct-mixed-flow/VENDOR.json @@ -0,0 +1,61 @@ +{ + "schema": "byte-identical-source-exports/1", + "files": [ + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/research/record-track/proofs/theorem-1g.md", + "path": "research/direct-mixed-flow/vendor/theorem-1g.md", + "git_blob": "36d2399f3538c34e4b1567a15b4a5dfe77ffc7ad", + "sha256": "c4a96c55c2509ff36e8bc6bddaaf6a8b1a34a5d794e4e09ac5214c82b51510e6" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/research/record-track/programs/theorem-1g/tree_flow.py", + "path": "research/direct-mixed-flow/vendor/tree_flow.py", + "git_blob": "31a9c1ae4d116b12e8db7d8e06f723f10425068d", + "sha256": "750782f6d1cc0a9fff8a768899f3f4c62a7efdf0696d8b5a5d640b1836f5ab72" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/LICENSE", + "path": "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/NOTICE", + "path": "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE", + "git_blob": "0b06967886fab2628afc0b881c884161bbf5e430", + "sha256": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md", + "path": "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "git_blob": "4badb40f0919c515823cb07e44c6470d4d6469ca", + "sha256": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8" + }, + { + "commit": "b84060c9c", + "original_path": "research/higher-moment-strictification/README.md", + "path": "research/direct-mixed-flow/vendor/higher-moment-README.md", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "commit": "b84060c9c", + "original_path": "research/higher-moment-strictification/RESULT.json", + "path": "research/direct-mixed-flow/vendor/higher-moment-RESULT.json", + "git_blob": "e66b39c674028adfd22f0de3170555dccda52f6a", + "sha256": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156" + }, + { + "commit": "e9058860b5c850760fdf970e796a96aefcdb1d98", + "original_path": "research/pr4359-p7-padding/RESULT.json", + "path": "research/direct-mixed-flow/vendor/p7-RESULT.json", + "git_blob": "ebb30a9b3b94fb159a316350f7da57bde4a30c25", + "sha256": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab" + } + ] +} diff --git a/research/direct-mixed-flow/VERIFY.json b/research/direct-mixed-flow/VERIFY.json new file mode 100644 index 0000000000..690caa1ac7 --- /dev/null +++ b/research/direct-mixed-flow/VERIFY.json @@ -0,0 +1,28 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/direct-mixed-flow/vendor/theorem-1g.md", + "research/direct-mixed-flow/vendor/tree_flow.py", + "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE", + "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE", + "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "research/direct-mixed-flow/vendor/higher-moment-README.md", + "research/direct-mixed-flow/vendor/higher-moment-RESULT.json", + "research/direct-mixed-flow/vendor/p7-RESULT.json", + "research/direct-mixed-flow/VENDOR.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact partially matched whole-job flows, chronological literal/merged controls, nested batching through p7 rank 1000, telescoped size bounds and rejected omissions. No direct exponent theorem." + } + ] +} diff --git a/research/direct-mixed-flow/flow.py b/research/direct-mixed-flow/flow.py new file mode 100644 index 0000000000..07175cd6e1 --- /dev/null +++ b/research/direct-mixed-flow/flow.py @@ -0,0 +1,198 @@ +#!/usr/bin/env python3 +"""Capped whole-integer lockstep flow, retaining unmatched jobs as paid exits. + +Generalizes Jacob Alan Sussman's separated multinomial construction. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +This is a finite flow, not a theorem that it attains the mixed-root saving. +""" +from collections import Counter +from functools import lru_cache +from math import comb, prod + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +class Flow: + def __init__(self, targets, paid, n, extra_height=0, height_base=None): + self.T, self.P, self.n = dict(targets), dict(paid), n + self.K = tuple(sorted(targets)) + self.m, self.kmin, self.rmax = max(targets), min(targets), max(paid) + need(2 <= self.kmin <= self.m and self.rmax < self.m <= n, + 'finite direct-flow rank contract') + need(all(isinstance(v, int) and v > 0 for x in (targets, paid) + for v in x.values()), 'positive integer inventories') + self.cap = n//self.m + self.height_base = self.kmin if height_base is None else height_base + need(isinstance(self.height_base, int) and self.height_base >= 2, 'integer height base') + self.G, least = 0, 1 + while least*self.height_base <= self.cap: + self.G += 1 + least *= self.height_base + need(isinstance(extra_height, int) and extra_height >= 0, 'nonnegative extra height') + self.G += extra_height + self.zero = (0,)*len(self.K) + + @lru_cache(None) + def column(self, a): + return prod(k**v for k, v in zip(self.K, a)) + + @lru_cache(None) + def points(self, height, cap): + """(a, u(a)) at fixed degree; exact multinomial integer weights.""" + result = {} + + def visit(i, remaining, c, weight, a): + if i == len(self.K): + if remaining == 0 and c <= cap: + result[a] = weight + return + k, w = self.K[i], self.T[self.K[i]] + for count in range(remaining+1): + new_c = c*k**count + if new_c > cap: + break + visit(i+1, remaining-count, new_c, + weight*comb(remaining, count)*w**count, a+(count,)) + + if cap >= 1: + visit(0, height, 1, 1, ()) + return result + + @lru_cache(None) + def units(self, depth, rho): + return self.points(self.G-depth, self.cap//rho) + + @lru_cache(None) + def demand(self, depth, rho): + result = Counter() + for a, count in self.units(depth, rho).items(): + for i, k in enumerate(self.K): + b = list(a) + b[i] += 1 + result[tuple(b)] += count*self.T[k] + return result + + def merged(self): + sources, exits, boundary = Counter(), Counter(), Counter() + units = columns = 0 + matched = 0 + path_counts = Counter({1:1}) + for b, count in self.demand(0, 1).items(): + sources[self.column(b)] += count + for depth in range(self.G+1): + following = Counter() + for rho, paths in path_counts.items(): + batch = self.units(depth, rho) + units += paths*sum(batch.values()) + columns += paths*sum(count*rho*self.column(a) for a, count in batch.items()) + for rank, repetitions in self.P.items(): + new_rho = rho*rank + copies = paths*repetitions + if depth == self.G: + need(set(batch) <= {self.zero}, 'leaf degree zero') + exits[new_rho] += copies*batch.get(self.zero, 0) + continue + child = self.demand(depth+1, new_rho) + if new_rho <= self.cap: + following[new_rho] += copies + for b in set(batch) | set(child): + supply, demand = batch.get(b, 0), child.get(b, 0) + e = new_rho*self.column(b) + consumed = min(supply, demand) + matched += copies*consumed + if supply > demand: + exits[e] += copies*(supply-demand) + boundary[e] += copies*(supply-demand) + elif demand > supply: + need(supply == 0, 'Pascal demand cannot exceed present supply') + sources[e] += copies*(demand-supply) + path_counts = following + sources, exits, boundary = +sources, +exits, +boundary + need(sources and all(1 <= s <= self.n for s in sources), + 'all sources are positive and fit parent') + if self.height_base <= self.kmin: + need(all(self.n < self.m*s for s in sources), 'default top source bound') + need(all(1 <= e < self.n and self.m*e <= self.rmax*self.n for e in exits), + 'all paid exits strictly smaller than parent') + need(all(self.m*e > self.kmin*self.n for e in boundary), + 'premature exits have a failed boundary term') + mass = lambda h: sum(k*v for k, v in h.items()) + surplus = mass(self.T)-mass(self.P) + need(mass(sources)-mass(exits) == surplus*columns, + 'exact rank-one telescoping identity') + W, P = sum(self.T.values()), sum(self.P.values()) + bound = sum(P**d*W**(self.G-d) for d in range(self.G+1)) + need(units <= bound and sum(sources.values()) <= W*units, + 'full integer unit/source count bounds') + return {'n': self.n, 'height': self.G, 'sources': sources, 'exits': exits, + 'boundary_exits': boundary, 'units': units, 'column_mass': columns, + 'source_count': sum(sources.values()), 'matched_jobs': matched, + 'minimum_source': min(sources), 'all_sources_above_n_over_m': + all(self.n < self.m*s for s in sources), + 'rank_one_surplus': surplus, 'unit_count_upper': bound} + + def literal(self, paid_word, class_limit=200000): + """Every round returns before the next; no merging of round paths.""" + need(Counter(paid_word) == Counter(self.P), 'literal paid word matches invoice') + sources, exits = Counter(), Counter() + classes = 0 + + def process(depth, rho, incoming): + nonlocal classes + classes += 1 + need(classes <= class_limit, 'literal replay class limit') + wanted = self.demand(depth, rho) + need(all(v <= wanted.get(b, 0) for b, v in incoming.items()), + 'all incoming whole jobs fit child slots') + for b, count in wanted.items(): + missing = count-incoming.get(b, 0) + if missing: + sources[rho*self.column(b)] += missing + batch = self.units(depth, rho) + for rank in paid_word: + new_rho = rho*rank + if depth == self.G: + for a, count in batch.items(): + exits[new_rho*self.column(a)] += count + continue + child = self.demand(depth+1, new_rho) + passed = Counter() + for b, count in batch.items(): + consumed = min(count, child.get(b, 0)) + if consumed: + passed[b] = consumed + if count > consumed: + exits[new_rho*self.column(b)] += count-consumed + # All unconsumed exits and this entire child return at this + # paid position, before any later parent round is issued. + process(depth+1, new_rho, passed) + + process(0, 1, Counter()) + return {'sources': +sources, 'exits': +exits, 'classes': classes} + + +def approximate_leaves(targets, paid, maximum, checkpoints, extra_height=0, height_base=None): + """Exploratory floating point recurrence; never an acceptance certificate.""" + m = max(targets) + leaves = list(map(float, range(maximum+1))) + saved = {} + previous_cap = None + for n in range(m, maximum+1): + cap = n//m + if cap != previous_cap: + recipe = Flow(targets, paid, n, extra_height, height_base).merged() + source, exit = recipe['sources'], recipe['exits'] + count = recipe['source_count'] + exit_charge = sum(v*leaves[e] for e, v in exit.items()) + previous_cap = cap + leaves[n] = (sum(v*leaves[n-s] for s, v in source.items())+exit_charge)/count + if n in checkpoints: + from math import log + saved[n] = {'leaves_approx': leaves[n], + 'effective_saving_approx': 1-log(leaves[n])/log(n), + 'source_types': len(source), 'exit_types': len(exit), + 'boundary_exit_types': len(recipe['boundary_exits'])} + return saved diff --git a/research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md b/research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md new file mode 100644 index 0000000000..4badb40f09 --- /dev/null +++ b/research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md @@ -0,0 +1,313 @@ +# Finite precompilation of a mixed-target rule + +Status: constructive bridge under the precise native hypotheses below, +independently audited in `../transfer-audit/AUDIT.md`. This is a written +argument, not a formal proof or a completed integer-multiplication admission. +The companion finite scheduler checks actual integer flow and ordering. +The original immediate-normalization BIT interface failed hypothesis 3. +`../bit/DELAYED-COVER-BRIDGE.md` supplies the distinct delayed-cover +implementation, with a finite local-ring check and the native binding in +`../bit/BIT-P3-NATIVE-BINDING.json`. Its fixed rational cover routes are a +costed program schema, not dense coordinate gates in a plain native word. + +Substantial OpenAI assistance. Apache-2.0. The mixed-target asymptotic flow is +Jacob Alan Sussman's Theorem 1G, PR4268, with the detailed proof at commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a` of +[`wht-power-saving-lean`](https://github.com/jacobalansussman/wht-power-saving-lean). +The source, exact scheduling code and notices are preserved under `sources/`. +The contribution proposed here is clearing the finite flow into a single +uniform native supplier before applying the inherited outer theorem. + +## 1. What needs to be assumed + +Let a job of rank `s` apply a specified tensor operator to `s` selected +coordinate blocks of one array, fixing all other coordinates. A block has +an arbitrary positive tensor multiplicity `f`. A completed rank `s` job +therefore acts on `s*f` axes. All productive inputs are arbitrary. + +Fix one mixed unit with productive targets `W_k` of ranks `k`, a chronological +list of paid child ranks `r_j`, and a finite number of scalar and routing +passes. These assumptions are required, separately from the moment inequality: + +1. **An all-column native word.** At every integer column count `c`, the unit + computes exactly its independent rank `k*c` output jobs. Its paid rounds + are rank `r_j*c` jobs in the stated order. All borrowed data return to the + declared endpoint, and owned storage is explicitly initialized and erased. + Its finite operation count is uniform in `c`. +2. **Disjoint splitting and spectators.** A rank `a+b` job is a rank `a` job + followed by a rank `b` job on disjoint coordinates. The resulting programs + preserve arbitrary complete spectator fields and accept arbitrary data. +3. **Whole-job adapters.** Any job passed between two units has an explicitly + priced, permitted embedding into its destination. For the intended complex + application these are fixed monomial binary address maps and unit quadratic + phases, together with role permutations. The adapters must work at every + tensor multiplicity. Rank equality by itself is insufficient. +4. **Finite-program closure.** A finite composition of these words and + adapters is again a permitted finite supplier. Constantly many owned fields + may be supplied with their full cost and no productive output credit. + The eventual ordinary recursion must have the same arbitrary-input, + restoration, scalar and precision interface as the retained supplier. + +Put `m=max{k:W_k>0}`, `k_min=min{k:W_k>0}`, and +`r_max=max{r_j}`. Require `r_max g*S`, keeps one +external weight throughout the entire finite circuit, and lowers only its +final rank-one leaves. All rational matchers, role routes and their inverses +are fixed before choosing the odd prime and its exclusions. Every route +uses complete equal-multiplicity cover fibers and the retained, costed row +permutation primitive. This gives the same finite DAG argument in the +rational-cover program category. The BIT binding supplies the actual native +projectors; a rank count alone would not provide this implementation. + +## 2. Proposed conclusion + +Suppose the preceding hypotheses hold and the mixed balance has root +`tau` in `(0,1)`: + +``` +sum_j r_j^tau = sum_k W_k k^tau. +``` + +For every `z` with `tau=2`, a fixed number `B_N` of productive arrays, +and only rank-one paid children, whose number `P_N` satisfies + +``` +P_N < B_N * N^z. +``` + +Every productive output is the full rank-`N` job. The construction may have +an enormous finite scalar word, role inventory and owned-storage requirement. +Those quantities affect constants and the eventual input threshold. They are +not omitted and are not credited as extra output jobs. + +If this uniform supplier is admitted under the retained native, precision and +fixed-tape premises, the existing uniform recursion applies directly. A new +dynamic RAM-to-Turing-machine simulation is not being assumed here. + +## 3. The integer lockstep flow at a fixed rank + +This is the part of Theorem 1G used by the compiler. At one fixed top rank +`N`, its units, source jobs and exit jobs have integer multiplicities. +For a multi-index `a` on the target types define + +``` +c(a) = product_k k^(a_k), +u(a) = multinomial(|a|;a) * product_k W_k^(a_k). +``` + +The exact Pascal identity is + +``` +u(b) = sum_{k:b_k>0} W_k*u(b-e_k). +``` + +Let `G` be the largest `|a|` with `m*c(a)<=N`. A class is indexed by a +sequence of paid rounds `s` of length `d<=G`; its dilation is +`rho_s=product r_j`. It contains `u(a)` units at column `rho_s*c(a)` for +each `a` with `|a|=G-d` and `m*rho_s*c(a)<=N`. + +For one parent paid round, the Pascal bijection matches its job copies to +target roles of the child class, at exactly equal integer ranks. Missing +demands are top sources. Separation ensures every parent job is consumed. +The source ranks lie in `(N/m,N]`; only the deepest classes produce exit +jobs, all strictly smaller than `N` once `N` is outside the finite base range. + +Process a class in word order. At round `j`, suspend every unit of that +class, complete the entire child class fed by that round, and only then +advance the parents to round `j+1`. This forbids a unit from requiring both +an earlier and a later round of the same suspended parent. The resulting +dependency graph is finite and acyclic. Its edges carry complete array jobs, +not individual scalar values copied for free. + +These integer quantities exist before normalizing the sources to total +weight one. Let `S_s` be the number of source jobs of rank `s`, let +`S=sum_s S_s`, and let the ordered exit batches be `(e,t)` with `t` jobs +of rank `e` each. This finite integer flow is the compiler input. + +## 4. Clear every batch denominator constructively + +Induct on the integer top rank `N`. For each smaller rank `e` the compiler +has already constructed a uniform program on `B_e` arbitrary arrays, +computing full rank `e` with `P_e` paid rank-one calls. For a sufficiently +small rank use the ordinary sequential program: `B_e=1`, `P_e=e`. + +For the current flow choose an integer `a` divisible by every `B_e` needed +for an exit and every `B_(N-s)` needed for a nonzero source remainder. +The product of those finitely many positive integers is a valid choice; +their least common multiple is a smaller optional choice. Set + +``` +B_N = a*S. +``` + +Assign `a*S_s` of the input arrays to each source rank `s`. On each of those +arrays, first complete its `N-s` complementary coordinates using the +already-compiled smaller uniform program. All such batches are integral +because `a` is divisible by their program widths. This preliminary action +commutes with the intended `s`-coordinate job and fixes its input coordinates. + +Make `a` copies of the integer lockstep flow. Route its source arrays to +their exact input slots using permitted whole-array adapters. At a deepest +exit batch, `a*t` is divisible by `B_e`; replace that batch by copies of +the smaller uniform rank-`e` program. Restore its role ordering and adapters +before resuming the suspended parent class. Execute the finite DAG in the +lockstep order, and finally restore the original source-array ordering. + +Every array has now received its disjoint complementary job and source job, +hence the full rank-`N` transform. No copied scalar input or blank helper is +treated as another independent output. Every original array occurs exactly +once as a source; interior target slots are jobs on those arrays, not new +productive inputs. + +Induction removes all recursive calls: the only remaining paid children +have rank one. Clearing denominators multiplies productive arrays and paid +operations equally, so it preserves the per-array leaf count. In formulas, + +``` +P_N/B_N = (1/S) * [ + sum_s S_s * (P_(N-s)/B_(N-s)) + + sum_(ordered exit batches e,t) t * (P_e/B_e) +]. +``` + +Zero-rank terms vanish. Any plain rank-one exits are the ordinary base +program. Scalar and routing passes have their own analogous nonnegative +count and must be included in the asymptotic cost used to choose `N`. + +This construction uses full integer batches; it does not assume that +fractional pieces of a physical array can be routed at zero cost. Its exact +replication factors can be impractically large, which is acceptable for a +fixed finite supplier existence statement but must be disclosed. + +## 5. Why some fixed N has the required saving + +The independent audit sharpened this step to a direct count of paid leaves. +It does not require a running-time comparison between a RAM flow and native +tapes. Let `L(n)=P_n/B_n`, let `w_s=S_s/S`, and let `x_e` be the exit counts +normalized by the number S of source arrays. The actual integer compiler +satisfies + +``` +L(n) = sum_s w_s L(n-s) + sum_e x_e L(e), +sum_s w_s = 1, +sum_e x_e e^tau = sum_s w_s s^tau. +``` + +The last equality follows by canceling every internal matched job in the +exact tau-potential balance. The source ranks satisfy `n/m0`, concavity gives + +``` +n^z0 - sum_s w_s (n-s)^z0 >= eta * sum_s w_s s^z0. +``` + +Indeed, for `t=s/n` in `[1/m,1]`, +`1-(1-t)^z0 >= z0*t >= eta*t^z0`. For every sufficiently large n the +exit coefficient is less than `eta/2`. Every complement and exit has +smaller rank than n, so strong induction on the exact recurrence proves +`L(n)<=A*n^z0`, with finite A chosen to cover the smaller ranks. Eventually +`L(N).lean, byte-identical to + third-party/openai-math/). + + b. Modified copies of OpenAI's proof files. In each package, the folder + Work/Fourier/ (for example Work/FourierC588MHH/) holds copies + of eleven files of lean/OAI/Computability/FourierTransform/ of + openai/math and of five definitions of its Goal.lean, made the way + section 7 describes, by Shea's script mkchain_c401g5.py or by the + agents' generators that copy its output under a new suffix (for + example community/c588mhh/generators/lean-gen/mk_fourier_h.py). Each + begins with a + comment that names the upstream file and states what was changed. In + c588-repack these are Shea's own copies with the exponent changed. + + c. Files that contain upstream text. The files Challenge.lean under + community/wht-c588/overlay/Work/ and community/wht-c588mhh/overlay/ + Work/ contain the RAM cost model of + lean/ComparatorChallenges/UniformFourier.lean of openai/math, + unchanged, as Work/GCert/Data/ChallengeB2Ge8x.lean does (section 2); + their headers say what differs from that file. + + d. Files adapted from Shea's repository in community/c588mhh/overlay/ + Work/XHost/: + - HDef.lean is a copy of lean/complex588/Work/Bridge401/GNetDef.lean, + HStage.lean of Work/Bridge401/GNetStage.lean, HCert.lean of + Work/Bridge401/GNetCert.lean, HGeom.lean of the instance part of + Work/Bridge401/GGeom.lean, and HEnd.lean is adapted from + Work/Bridge401/End.lean, each with same-run hosting added (the idea + of DaysSky's pull request #442 to CrocSwap/integer-mult-bounds) and + the names changed. In Shea's tree these files are those of Nil + Mamano's submission named above (his SOURCE_MANIFEST.json records + each as taken from submissions/dft/nmamano-dft-record/ at the + verifier commit above), written by his generator gen401.py on the + layouts credited above, with the engine of this repository. + - Frames.lean adapts lemmas of Work/Bank401/Adapt.lean and + Work/Bank401/Frames.lean of the same tree, which come from the same + submission: host_adapt is bank_adapt, host_pad is bank_pad and + slot_frames is bank_frames, each with the new coordinates chosen + inside the pending set of an idle climb. + - HSchedK.lean copies the lemmas about lists of + Work/Bridge401/SchedK.lean of the same tree, and its checker + hostSchedK is modelled on the checker schedK there; HostK.lean is + modelled on the same checker. + The header of each file names its source and says what was changed. + One header is wrong in part: that of HEnd.lean says that Shea's + End.lean was written after a file Work/Bridge377/End.lean of Jacob + Sussman's. No such file of his exists; Shea's End.lean says only that + it follows a file of that name. The header is left as it was compiled + (community/c588mhh/README.txt says so). + The generators that wrote them are under + community/c588mhh/generators/lean-gen/. The same twelve network files + of Work/XHost/, byte-identical, are also in community/u8xmhh/overlay/ + Work/XHost/. + The log community/c588mhh/supporting/L2/skeptic/logs/ + Work_Bank401_Adapt.log is of his file, compiled unchanged; the file + itself is not included. + + e. Programs from Shea's repository. + - Byte-for-byte copies of his files at the commit above, unchanged and + without a notice inside them (the same files are also in + third-party/shea256-fourier-transform-below-nlogn/ at their own + paths): + research/complex-transfer-588-596/experiments/generate_global_lean.py + is copied as tools/community/route/generate_global_lean.py and + tools/community/repack/tools/generate_global_lean.py; + research/complex-transfer-588-596/experiments/bank_reprice.py is + copied as tools/community/repack/tools/shea_bank_reprice.py; + research/complex-transfer-588-596/verification/exact_moment.py is + copied as tools/community/route/exact_moment.py, + tools/community/repack/tools/exact_moment.py, + community/c588mhh/generators/design-tools/exact_moment.py and + community/u8xmhh/generators/design-tools/exact_moment.py. + - route_price.py, in four identical copies (tools/community/route/, + tools/community/repack/tools/, + community/c588mhh/generators/design-tools/ and + community/u8xmhh/generators/design-tools/), contains functions + copied from his bank_reprice.py and generate_global_lean.py (its + header says so), changed to price a local word through his route. + - The generators of tools/community/c588m-gen/ drive or adapt his + scripts in third-party/shea256-fourier-transform-below-nlogn/ + research/; each adapted file says what it changes. + - community/c588-repack/overlay/comparator/fourier.json is his + comparator configuration, unchanged. + + f. Data. The certificate of Kothe's #588 circuit, its bank schedule and + its price, as published in Shea's repository, are in + third-party/shea256-fourier-transform-below-nlogn/lean/complex588/ + artifacts/, unchanged. The packages' certificate and data modules + are derived from them (VERIFY.md, section 11, says how). + + g. Data derived from CrocSwap/integer-mult-bounds at a later state (the + U8 circuit). The certificates of community/u8x and community/u8xm (the + files under their Work/GCert/Data/ whose paths contain U8X), + and the host table and data modules of community/u8xmhh, which are + computed from the certificate of u8xm, are derived from the U8 word of + the repository CrocSwap/integer-mult-bounds + (https://github.com/CrocSwap/integer-mult-bounds), a circuit of that + community: Jeremy Kothe's pull request #869, on his #799 (which + carries Chafik Boukhalfa's frame changes of #741), on icekylinx's + gauge44 construction (#645) and on the earlier work that their + notices name. Only the word's additions and their frames are used: + not the owner maps of #870 (Kothe, with Hao Yan's #858), #890 + (Boukhalfa) and #942 (Jonathan Capalbo), nor DreamingOfClouds' bit + supplier #589. The agents rebuilt the word with that repository's + own program + research/complex-t21-owners/vendor/pr870/construction/barch/ + reproduce_barch.py (recipe U8; #869's builder, in the copy of #870's + package that #890 keeps), in a clone at commit + 407d52ff15b2217b6e22bce44728b4c3907b6515 of its main branch + (13 October 2026). The word they obtained has the canonical sha256 + 24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c, the + value pinned for it in that repository (the file + LOCAL-PINS-barch-U8.json next to the program). The logs of that run are in + community/base-logs/u8-word/. No program of that repository is + included here, and the word itself is not included: the packages hold + certificates computed from it. + That repository is published under the Apache License, Version 2.0 + (its LICENSE at that commit is the same text as the file LICENSE). + Its NOTICE file at that commit differs from the copy of section 6 (the + state of pull request #193) in one passage, which + third-party/CrocSwap-integer-mult-bounds/at-407d52ff/SOURCE.txt + describes. Complete copies of that NOTICE file and of the notice files + of the folders the program comes from + (research/complex-t21-owners/NOTICE.md and, under its vendor/pr870/, + NOTICE.md, UPSTREAM-NOTICE.md and t16/NOTICE.md), unchanged and at + their paths, are in + third-party/CrocSwap-integer-mult-bounds/at-407d52ff/; they apply to + these data. + + The new files of community/ were made on 2026-10-13 the way section 4 + describes. The credits, with links, are in README.md. + +10. Files added in the fifth revision outside community/ (package/, + scripts/, tools/lever/, tools/lever-hub/, tools/reproduce-search.sh, + tools/compare_results.py, data/, results/, research/, + notes/how-the-lever-was-found.md, notes/open-directions-4.md and the + additions to third-party/). + The packages under package/ (the sixth result, package/u8x0hq, and the + recursion lever, package/leverF, package/leverB, package/leverA, package/lever2979, package/lever) are laid over the same + clone of Ryan Shea's repository as the packages of section 9 (commit + 52394849c7ecf3412d39b925d75fc7fdb98994d8, folder lean/complex588, + Apache License, Version 2.0). His licence and notice files in + third-party/shea256-fourier-transform-below-nlogn/ apply to the material + of his repository that files of these packages copy or adapt; each such + file says so in its first lines, and the packages' README.txt list them. + Shea's tree carries Lean files of Nil Mamano's published Big O Speedrun + submission (bigospeedrun/verifier, Apache License, Version 2.0): the + gauged interface, the nine-stage network, its bank lemmas and checker, + its end theorem and the templates of the Fourier chain. The hosted + networks of these packages (Work/XHost in package/u8x0hq; Work/XHostD, + Work/XHostR and Work/XHostT in the lever packages) are adapted from those + network files, as their first lines say. + + a. Modified copies of OpenAI's statement file. Each file named + UniformFourierChallenge.lean under package/*/overlay/Work/ is a + modified copy of lean/ComparatorChallenges/UniformFourier.lean of + openai/math at the commit above: in package/u8x0hq the folders + FourierU8XM, FourierU8XMHH, FourierU8X0, FourierU8X0HH and + FourierU8X0HQ and their twins ending in Neg (10 files); + in package/leverF the folders FourierL3945F and FourierL3945FNeg (2 files); in package/leverB the folders FourierL3945H and FourierL3945HNeg (2 files); in package/leverA the folders FourierL2979H and FourierL2979HNeg (2 files); in package/lever2979 the folders FourierL2979 and FourierL2979Neg (2 files); in package/lever the folders FourierL3945 and FourierL3945Neg (2 files). Changes: the exponent + 1 - 1/(10^(13:ℕ)) is replaced by the package's exponent (in a folder + whose name ends in Neg, one unit stronger), and the seven names of + section 2 receive the package's suffix. Everything else in these files + is the upstream text, unchanged. Unlike the copies of section 9, these + files carry no comment inside them: they are kept byte for byte as they + were compiled, because scripts/build-and-check.sh derives them again + from third-party/openai-math/ (scripts/derive_challenges.sh) and + compares the two. This section is their notice. + b. Modified copies of OpenAI's proof files. In each package, the folders + Work/Fourier/ hold copies of eleven files of + lean/OAI/Computability/FourierTransform/ of openai/math and of five + definitions of its Goal.lean, made by Shea's script mkchain_c401g5.py + or by the agents' generators that copy its output under a new suffix. + Each begins with a comment that names the upstream file and states + what was changed. + c. The community's files. third-party/CrocSwap-integer-mult-bounds/ + staged544-terminal-gap-fill/ holds unmodified copies of 32 files of the + folder research/staged544-terminal-gap-fill/ of pull request #3945 of + CrocSwap/integer-mult-bounds at its head + 91f81d131252db704f945891da1ea54e29d46b8b (Dugongue's branch): the owner + data (FILL, PROFILE, ORDER, DISPATCH, PLAN, TEMPLATE, the two words and + the files of #3815 that #3945 carries as old-*), README.md, PROOF.md, + RESULT.json, SOURCES.json, LICENSE, NOTICE.md and the native lineage + notices. BLOBS.txt gives the git blob hash of each, as GitHub stores + it. That repository and its contributors' branches are published under + the Apache License, Version 2.0; the NOTICE.md and native notices of + that folder apply to these files and are quoted in substance in (g). + The files of #2979 (research/rank7-joint-endframes/ of the main branch + of CrocSwap/integer-mult-bounds at 20ecf289; Marius-Paul Dumitrean, + with the files of Mason Hale's #2917 and of #2942 that its NOTICE + names) are copied unmodified, 12 of them, into package/lever2979/ + and package/leverA/ under generators/tree/wht45/lever/p-alt/dl/ + main2979/: CLAIM.json, CREDITS.md, PINS.json, ALLOCATION-PINS.json, + the allocation files DISPATCH, FILL, ORDER, PROFILE and PROVIDERS, + and the data files PARENT-base, WORD-base and WORD-extra. + package/leverA/generators/tree/wht45/allheads/aA-data/in/alloc2979H/ + holds unmodified copies of its DISPATCH, ORDER, PROFILE and PROVIDERS + (beside the table with every head kept, FILL.json.gz, see (d)). Both + packages also hold #3945's owner/inputs/PLAN.json.gz and + TEMPLATE.json.gz under generators/tree/wht45/lever/g-heads/dl/pr3945/. + The generators check every one of these copies against its sha256 + (generators/tree.sha256) before they run; the same licence and the + notices of #2979 (for PLAN and TEMPLATE, of #3945) apply to them. + Both packages also hold generators/tree/wht43/bound-check/k-word/ + tools/build_tri_869.py, an unmodified copy of the community's word + builder construction/barch/build_tri.py (the same bytes as + research/complex-t21-owners/vendor/pr870/construction/barch/ + build_tri.py of its main branch, whose notices section 9, item g, + names); the generators do not run it. + More unmodified copies of the same folder of #3945 are in package/leverF/ + and package/leverB/, under generators/tree/wht45/lever/g-heads/dl/pr3945/ + owner/: 21 of the files above, and #3945's build_fill.py, check_gain.py + and verify.py (git blob hashes equal to GitHub's at 91f81d13); the same + licence and notices apply to them. + d. Data derived from the community's files. data/native/ holds the + canonical native words of #3945's two words (and of #3815's), the + output of #3945's own program native/run_native.py, run unchanged by + the agents. data/gcert/, data/residuals-*.json and data/t74ctl/ are + the agents' conversion of those words, and of the earlier T74 words, + into this project's certificate format (tools/lever/lower_b.py and + t74_control.py); data/t74ctl/inputs/ holds the community's T74 + inputs repackaged in the layout of #3945's package (TEMPLATE.json.gz + unmodified, and ORDER.json with the same content as the community's + T74 order). The Lean data of the lever packages (the words, the + dispatch, the tables of hosts) is generated from such conversions and + from the community's files by the generators in each package. The + tables with every head kept (the folders fill/ of the packages on + every head kept, where shipped) were made by the community's own + allocation programs (on #2979, its fill17.py and double.py; on #3945, + the hall_lp.py and build_fill.py of #3815 and #3945's offset step), + run with one added condition; each package's fill/ README says how, + and which of those programs it copies, with their notices. + e. Programs that re-implement or adapt the community's code: + - tools/lever/pricer.py re-implements (does not import) the community's + moment engine and kappa assembly (research/native-complex-moment552/ + engines/moment.py and outer.py, research/gauge44-frames-x/code/ + assemble.py). The package "native complex moment" is by Rohan Arun + with OpenAI Codex assistance, on Dugongue's #552, eumemic's #543 and + #558, and icekylinx's complex-cover notes; its outer assembly is + eumemic's, after icekylinx's #144 and Zhihao Chen's #23, with the + balanced prefix of the RaD project (hipotures). + - tools/lever/heads_fill.py and g0_staged.py re-implement the window + and family semantics of #3945's owner/verify.py (they do not import + it). + - tools/lever/lower_b.py extends this project's own lowering program + to the community's borrowed-helper words; the meaning of a warp + follows the community's native code (bw_transport.py, bw_emit.py of + #3945's native/vendor), which was read, not copied. + f. Scripts. scripts/apply-overlay.sh, build-and-check.sh and + run-comparator.sh are adapted from this project's community/scripts/; + scripts/base/, cc-jail/, bos/ and lever-run/ are the agents' scripts + as run. Those in bos/ and lever-run/ package a proof in the layout of + the entries of bigospeedrun/verifier and run that verifier's three + phases; the verifier's own code is not included, except its function + strip_comments (scripts/verifier.py of bigospeedrun/verifier, Apache + License, Version 2.0), whose logic scripts/bos/fspb_submission.py and + scripts/lever-run/isk_submission.py copy, as the line that defines it + says; the same function is in community/scripts/bos/mb_submission.py, + community/u8xmhh/scripts-as-run/build/fsb_submission.py and + package/leverF/logs/fc-engine/C3/scripts/isk_submission.py. + g. Credit for the circuits of the lever. + #3945, as its NOTICE.md and native lineage notices ask that the credit + be kept: + - #3945 (Dugongue, with substantial OpenAI Codex assistance, including + three parallel Codex agents): the terminal-width construction (26 + protected helper terminals from width 4 to width 5, with scalar and + native frames refitted), the idle-gap absorption proof, the + source-guarded recipe, the independent finite checks and the + integration. + - dataisfire, #3734: the staged544 supplier and its full source closure. + - zxv, #3682: the staged pair; #3638: the earlier T360 allocation. + - Ross Richardson, #3605: the staged entrance, cleanup and residual + checks (helpers 644 and 660 from width 8 to 7). + - Erwan Secousses / ChaloupeMusic, #3815, with the #3638 lineage: the + attained T360 owner clock and fill, and the allocation programs that + made the table with every head kept on #3945. + - hexapode (Pierre-Loic Doulcet), #3802 and #3875: the earlier complete + endpoint combination and its refinement. + - Dugongue, #3857 (general proof and evaluator work) and #3929 (the + transported-frame compiler). + - Sagar Thakrar, #3687: audit_core.py, which reimplements Arham Tahir's + coupled-carrier audit; roger-sato, #3693: the whole-word audit adapter; + roger-sato, #3642: the T530 release retimings. + - Jeremy Diviney, #3148: the coupled-carrier T740 packing cap; dcharb78, + #3133: helpers 586 and 588 lowered by coupled carrier folds. + - Marius-Paul Dumitrean (mdumitrean), #2979: joint rank-7 end frames and + five paired extractions, on Jeremy Kothe's #2957 gate rewrites; #2802 + (hostee moves and retired-lender aliases) and #2733. + - Jeremy Kothe: the frame and preload machinery, #2833 (dirt-entry + rewrite of helpers 530 and 542), #2957 (gate rewrites on Mason Hale's + #2917 words), and the source pipeline, label swap and order and fill + of #2462, #2588 and #2673; Mason Hale, #2917 (nine paired helper + extractions); Lyy-iiis, #2857 (shared kernels) and #2848; Dugongue, + #2863; philippeVV (Philippe Van Velzen), #2853, #2559 and #2679 + (evacuation, six pre-life hosts, the refit alias). + - Cinna Davis (@1337isnot1337), #2226, with OpenAI Codex assistance: + anticipatory dirty borrowing (the borrowed helpers and their warps) + and the native exact Clifford and operator machinery. + - Tekalign (@tekuuu), #2436: the four lifted targets, the joint + twelve-source construction, and the sparse native accelerator, with + the authors its SPARSE-NOTICE names. + - zxv, #2530: the eight source-partner aliases; Mason Hale, #2696: + concentrated source-partner assignment and an independent local + interpreter; themilkman216, #2621: the priority order; Vlado + Vojdanovski, #2322: generator utilities; Jeremy Kothe, #2312: the + helper width exchange; Dugongue, #2309, with Sagar Thakrar's audit + #2315. + - icekylinx, #433 and #514, and the retained native ancestry; + DreamingOfClouds (with Claude): the inherited wrapper and outer + machinery; chafreaky (Chafik Boukhalfa), #458, and its lineage. + - Josie Elliston, #1956 (bootstrap carried-cutoff repair); Sagar + Thakrar, #1964 (label and adapter checks, mutants). + - The T74 words and owner construction underneath: Rohan Arun (#1218, + #1297, #1319 and the T74 exact-fill owner construction, with OpenAI + Codex assistance), Marius-Paul Dumitrean (#1625: the pivot-566 + kernel, words, edits and rebuild scripts), Jeremy Kothe and LeverRank + (#1672), on Jeremy Kothe's k8 leaver word and seven-slot line (#1018, + #1042, #1274) with Thomas DiFiore (#1148), Jeremy Diviney (#1193) and + Chafik Boukhalfa (#1196); the outer and the assembly by Vlado + Vojdanovski (#1673), Chafik Boukhalfa (#1699, #1786) and Jeremy + Kothe (#1377, #1839). + - Rohan Arun's draft #3939 and his #3934 stack, and Chris R / + Clear1nsight's #3883, #3936 and #3941, are acknowledged by #3945 as + neighbouring work; they are not used here. + Checks of #3945 by others, which this project read and re-ran: Chris R / + Clear1nsight's audits #3969, #3988, #3994 and #4016; the exact + eight-stream operator replay of ChaloupeMusic's gist, on the operator + model of Nick Petalas (#3187) and Matarener (#3296). + #2979, from its pull request body, CREDITS.md and NOTICE ("All original + notices of the exported predecessor packages remain in force"): + - Marius-Paul Dumitrean (mdumitrean), #2979, prepared with substantial + AI assistance (Anthropic Claude, via Claude Code): the codimension-2 + census, the joint end-frame lowering of 22 restored helpers in five + groups, the five further extractions, the composition with #2957's + rewrites, producer and checks, the overlay stage, the six-class + adapters, the literal T74 allocation, the cap certificates and the + complete fresh replay; also #2930 (cap allocation, relaxation + tools), #2942 (four normal-45 extractions; its words are #2979's + parent) and #2843 (the flow model's starting point). + - Jeremy Kothe, #2957, #2948 and #2966: the fourteen declared gate + rewrites and their applier; #2894 and #2833: the preload re-synthesis + supplier, frame accounting and cleanup, source materializer. + - Mason Hale, #2917: the nine paired extractions, the T74 chronology + (ORDER and DISPATCH), the allocation checker, moment auditor, + extension stage and adapter derivation. + - Jeremy Diviney, #2908: the paired input/output extraction, its + compensation rule, the two-sided certificate and the closed-adapter + admission chain. + - Dugongue, #2969 (comparator composition and baseline), #2863 and + #2839 (packing lineage, owner engine). + - Yiyang Lu (Lyy-iiis), #2857 and #2848: shared-kernel words, staged + native and overlay tooling, the flow model and realization of the + allocation. + - Ross Richardson, #2918: the rank-seven obstruction for helper 408. + - Tekalign: the independent owner and chronology checker; icekylinx: the + exact free-operator auditor (#2833); themilkman216: the integrality + observation behind the allocation's face step. + - Gareth Davidson (bitplane), #1995 and #2013: the fixed-word + terminal-subspace bounds that frame stage 1. + - Underneath: Cinna Davis (#2226, dirty borrowing and warps), Jeremy + Kothe (#2312, width exchange), and the T74 line above. + The table with every head kept on #2979 was made by #2979's own + allocation programs, credited as above. + h. Credit for the Lean route. + - Ryan Shea: the conversion pipeline, the generators and the Lean + instantiation of Jeremy Kothe's #588 circuit (lean/complex588), which + these packages are laid over. + - Nil Mamano: the files named at the start of this section. + - Dugongue (#401): the entrance gauges and the banks of the nine-stage + network; Zhihao Chen / jacklightChen (#377, #425): its compressed + layout with banks and padding, and the written argument for mutable + sources; lydakis (#275): the bank patterns; DaysSky (#363): the + bridged layout, and the proposal, with a written proof in the + community's terms, to host helpers in idle arrays. + - Jeremy Kothe and DreamingOfClouds: the community's lemmas about where + a helper may end, on which the charge for exit frames rests. + - For package/u8x0hq: the community's U8 circuit, Jeremy Kothe's #869 on + his #799, with Chafik Boukhalfa's frame changes (#741) and + icekylinx's gauge44 construction (#645), as the community's notices + record it. + - The idea that Theorem 1G extends is Schönhage's τ-theorem for matrix + multiplication. + - OpenAI: the cost model, the statement and the step from the lengths + 2^k to every length. + i. research/. Written for this repository by the agents under my + direction. The sections cite papers by title or arXiv identifier and + the community's pull requests by number, commit and file hash; they + copy no paper text and no file of the community's repository, with + these exceptions: research/record-track/programs/a-fc/r2/tools/ + fallback_patch.py carries a modified copy (made tolerant, as its first + lines say) of the placement loop of construction/build_fill.py of + #3815 (Erwan Secousses / ChaloupeMusic; CrocSwap/integer-mult-bounds, + Apache License, Version 2.0); and research/record-track/programs/ + a-fc/r2/tools/fillmodel.py copies the window, family and width logic + of owner/verify.py of #3945 (Dugongue and the lineage its NOTICE.md + names, see (g); CrocSwap/integer-mult-bounds, Apache License, Version + 2.0), as its first lines say; research/why-the-savers-save/programs/ + helpers-narrower-ends-skeptic-rules/asm1042.json is an unmodified + copy of research/community-frontier1042-audit/ASSEMBLY.json of the + community's main branch (the community's #1042 audit, integrated by + its maintainer Douglas R. Colkitt on 13 October 2026); + research/record-track/data/a-fc/design/ + ORDER.json and DISPATCH.json hold #2979's allocation/ORDER.json and + DISPATCH.json (Mason Hale's #2917, as #2979's NOTICE says), with the + same content, re-serialised; and research/why-the-savers-save/ + programs/helpers-half-reads/bit/xcheck_base.json, the report of the + community's checker xcheck_p.py (DreamingOfClouds' line, on eumemic's + #555) on #589's word, has the same bytes as + research/community-frontier741-audit/bit/xcheck.json of the + community's main branch, integrated by Douglas R. Colkitt on 13 + October 2026 (these three: CrocSwap/integer-mult-bounds, + Apache License, Version 2.0). fallback_patch.py, and tools/ + place_patch.py, tools/hall_fc.py and tools/mkpatch_fill17.py of + programs/a-fc/, apply their changes to copies of community files that + they read by path (#3815's build_fill.py and hall_lp.py, #2979's + fill17.py); those files are not changed. The other programs of + programs/a-fc/ are mine. + j. What is mine: the mixed-target recursion (Theorem 1G and its Lean + proof in OpenAI's model); the lever (the head test, the half cut, the + full cut and its 24 + 24 split, the head lemma, the heads-first + certificate, and the tables with every head kept); the A-fc table on + #2979's words (its class solution and its tolerant placement); the Lean ports of + #3945 and #2979 (the conversion of their + words, the warp checker and its soundness, the networks of many copies + with hosting across copies, the dispatch, the generators); the Lean + engine of this project and its extensions for exit frames, mutable + sources, centre reading and hosting; the checks; the search and pricing + programs in tools/lever/ and tools/lever-hub/; and the research in + research/. tools/lever-hub/network/Gates.lean is an unmodified copy of + lean/complex588/Work/Bridge401/Gates.lean of Ryan Shea's repository + (commit 52394849c7ecf3412d39b925d75fc7fdb98994d8, Apache License, + Version 2.0; its header credits Dugongue, lydakis, jacklightChen and + DaysSky); the other files of tools/lever-hub/ are mine. + + The new files of package/, scripts/, tools/lever/, data/, results/ and + research/ were made between 2026-10-13 and 2026-10-20 the way section 4 + describes: by AI agents (Claude) under my direction. The credits, with + links, are in README.md. + +Not included in this repository and fetched by the build: Mathlib +(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its +dependencies. The comparator (https://github.com/leanprover/comparator) is a +separate tool and is not included. diff --git a/research/direct-mixed-flow/vendor/higher-moment-README.md b/research/direct-mixed-flow/vendor/higher-moment-README.md new file mode 100644 index 0000000000..0a736ca89e --- /dev/null +++ b/research/direct-mixed-flow/vendor/higher-moment-README.md @@ -0,0 +1,416 @@ +# Higher-moment strictification: tensor power 150 and a smaller uniform rank + +**Submission authorized by the user on 2026-10-21.** + +The complete p7 mixed supplier in [PR4416](https://github.com/CrocSwap/integer-mult-bounds/pull/4416) +has productive ranks down to 5 and paid ranks up to 48. Its chronological +product, paid target completion and disjoint splitting overcome that overlap. +This package improves the charged tail estimate in that construction, then +generalizes the logarithmic compiler bound of +[PR4411](https://github.com/CrocSwap/integer-mult-bounds/pull/4411). +At the same proposed conditional **κ = 0.00268647**, the results are: + +| Quantity | PR4416 | This package | +| --- | ---: | ---: | +| Chronological tensor power | 6,240 | **150** | +| Product ambient rank | `121^6240` | **`121^150`** | +| Independent productive fields before uniform compilation | `7688^6240` | **`7688^150`** | +| Maximum paid rank after splitting | `10^6240` | **`10^150`** | +| Minimum productive rank after paid completion | `11^6240` | **`15^150`** | +| Sufficient uniform ambient rank | `2^16201843136005340321` | **`2^349300000000`** | + +The tensor exponent decreases by **41.6×**; the exponent of the sufficient +uniform rank decreases by about **46.38 million×**. These are comparisons of +specified finite constructions and sufficient bounds. They are not runtime +speedups, practical template sizes or corresponding estimates for every +precision/storage constant. The winning uniform word is not materialized. +The selected frontier is unchanged. + +There are three connected deliverables: a general higher-moment splitting +bound, an exact smaller paid native construction, and a uniform-rank proof +compatible with the complete consumer. This is the larger scope chosen after +the H completion obstruction; no numerical measure of scientific significance +is asserted. + +## 1. Boundary contract and expansion decision + +Retain PR4359/PR4416's all-column native contract: a finite chronological word +computes specified transforms on distinct arbitrary productive fields; paid +positions act on the actual current physical owners. Whole-job normalizers +are restored, complete spectators are preserved, and owned centers are +initialized, retained until safe erasure and never credited as new inputs. +At every positive column multiplicity, ranks multiply by that multiplicity. +Matching only rank numbers is insufficient without these native hypotheses. + +The source product algorithm runs one U copy for every productive role of V, +then substitutes V into each common chronological paid position of those U +copies. Fields may contain correlated data but have distinct physical slots. +Never combine two different paid positions of the same suspended U copy. +The targets and paid ranks are products; their moments multiply. This is a +finite chronological substitution of algorithms. Read +[the pinned product proof](vendor/p7-TENSOR.md), especially §§1–3 and 6. + +After the product finishes, normalize each complete rank-K output job by its +permitted whole-job conjugation. When K= 1, +u >= C, sigma = t+u >= 1, +J = c^v, L = b^v. +``` + +The bases c,b and the power v are integers, so L and J are exact integer +ranks. All moments here are finite sums over the actual rank inventory. + +For any original paid rank R>J, write R=qJ+r with 0<=r= 1`; this is why sigma must be at +least one. Keeping the original P_t^v as an overcount for all unsplit calls +gives total original-paid charge at most + +``` +P_t^v + 2 P_(t+u)^v / J^u. +``` + +For a completion D=L−K with 0=1 and logarithm power p=1/q. +Its proof only needs the logarithmic factor to be increasing. The same +argument works for **any real p>0**, including p>1, which is useful when +the separated unit's ambient rank m is itself large. + +Assume the finite source/exit compiler in +[FINITE-PRECOMPILATION.md](vendor/FINITE-PRECOMPILATION.md). Write +`L(n)=P_n/B_n`, with ordinary base `L(n)=n` for `0<=n=m its exact +integer-batch construction gives + +``` +L(n) = sum_s w_s L(n−s) + sum_e x_e L(e), +sum_s w_s = 1, n/m < s <= n, +sum_e x_e e^t <= sum_s w_s s^t, +e <= r_max (n/m)^theta < n, +theta = log(r_max)/log(k_min) < 1. +``` + +Choose `theta < theta_bar=a/b < 1` and p>0 with + +``` +2^(b−a) r_max^b <= m^a, +theta_bar^p < eta = t m^(t−1), +m^(1−t) < 2^p. +``` + +Then **`L(n) <= n^t (1+log2(n))^p` for every integer n>=1**; define the +right side to be zero at n=0. + +For 2<=n=m put `A(n)=(1+log2(n))^p`. The shifted logarithm +condition gives `A(e) <= theta_bar^p A(n)` for every exit, hence + +``` +sum_e x_e e^t A(e) <= theta_bar^p A(n) sum_s w_s s^t. +``` + +For y=s/n>1/m, concavity of x^t gives +`1−(1−y)^t >= t y >= eta y^t`. Since A is increasing, the source complement +capacity obeys + +``` +n^t A(n) − sum_s w_s (n−s)^t A(n−s) + >= eta A(n) sum_s w_s s^t, +``` + +with zero-rank complements treated separately. The strict inequality +`theta_bar^p < eta` closes strong induction. This uses no concavity of A +and introduces no unknown multiplicative constant. + +This is available for every separated unit with the stated t-superpotential. +Choose rational theta_bar sufficiently close to one: since r_max max((1−t)*log2(m), log(eta)/log(theta_bar)) +``` + +satisfies the other two conditions. Thus the leaf-count estimate has the +general form `L(n) <= n^t (1+log2(n))^p` with an effective fixed p. At fixed +p, a target gap z−t requires a sufficient H of order +`(p/(z−t))*log(p/(z−t))`. This concerns normalized rank-one leaf counts in +the finite compiler; it does not bound full word size or physical runtime. + +The compiler's integral batch replication, arbitrary original arrays, +whole-job routing and finite owned-bank allocation are unchanged. With +N=2^H and desired uniform exponent z>t, the final sufficient condition is + +``` +(1+H)^p < 2^((z−t)H). +``` + +For the new p7 unit, take `theta_bar=6/7`, `p=13`. Exact tests give + +``` +10^7 < 15^6, +2*(10^150)^7 <= (121^150)^6, +eta > 0.144386809622024146828684313913 > (6/7)^13, +(121^150)^C < 6.907234273066686405887998346943 < 2^13. +``` + +The smaller logarithmic power 12 fails the stated eta condition. Let +`z−t = 1/700000000`, exactly the uniform-saving slack already used by +PR4416's outer point. The rank **N=2^349300000000** satisfies + +``` +349300000001^13 < 2^499. +``` + +The preceding grid point H=348600000000 fails its corresponding comparison +with 2^498. This is the first successful multiple of 700,000,000 for this +majorant: the function `(z−t)H ln(2) − p ln(1+H)` is strictly convex, starts +at zero with negative derivative, and has just one positive zero. This +does not certify a minimum native program. + +To separate the two contributions, retaining the older power majorant on +the new v=150 unit already gives `H0=37443877100` and +`H1=140829080288374101`. That is about a 115× reduction in the exponent +from the changed tail/rank separation alone. The logarithmic majorant then +reduces that exponent by a further factor of about 403,175. + +## 5. Complete consumer and finite constants + +The complex uniform saving is **376107/140000000**, approximately +0.00268647857142857. This is exactly PR4416's uniform endpoint; neither +its tested saving nor its outer parameters change. Put + +``` +kappa = 0.00268647, d=(0.00268648−kappa)/7 = 1/700000000, +uniform = kappa+6d, b_outer = kappa+5d, +a_outer = kappa+4d, q_outer = kappa+3d, +epsilon=1−d, beta=1−3d, r0=d/10, stop=layout=d, +ordinary_BIT_saving=0.0027. +``` + +The checker replays the byte-pinned PR4405/PR4416 parameter ledger and +requires exact equality with all saved p7 parameters, nine rows, 54 checks +and three extra guards. It separately executes only the historical +`check_ledger.py` ledger function and its comparison constants as another +oracle: all nine rows agree and all 63 predicates remain strict. Its derived +grid/backoff is recorded explicitly; the old m=73 admission code is not run. +The minimum nine-row saving minus κ is exactly +`524529867/122500000000000000`. + +Mutations close epsilon, remove layout funding, raise unfunded κ, close +the uniform gap, underfund BIT, add an old per-axis scan or make group width +equal to global dimension. Each must fail its relevant ledger. + +The newly compiled word supplies its **own** finite constants. If U counts +actual raw p7 instances, allocate U distinct owned centers. Let W be the +final productive width, P the paid rank-one count, and R the full native +record/normalizer count including completion, splits and compiler routes. +As in the pinned closure argument, use + +``` +G = 2490856*U + 8*R, Z = W+U, +E = 64*(Z+N+P+G+1)^3, +B_constant = P+E, C0 = 32*N*B_constant^2. +``` + +Pay actual coordinate movement separately. Retain every owned center until +its creating unit erases it; centers are excluded from productive W. +The fixed-word recurrence and eventual constant absorption have the source +form, with these newly expanded counts substituted. Numerical full-word +counts, denominator heights and practical precision thresholds are not +computed here. Neither a smaller N nor a favorable moment supplies an +independent proof of the inherited physical/analytic premises. + +## 6. Reproduction, provenance and coverage + +Python 3.12, standard library only, from the repository root: + +```sh +python3.12 -B research/higher-moment-strictification/verify.py +python3.12 -B scripts/research_package.py --package research/higher-moment-strictification --check-only +python3.12 -B scripts/research_package.py --package research/higher-moment-strictification +``` + +To generate a fresh receipt, use `verify.py --out /absolute/new/path.json`. +The saved [RESULT.json](RESULT.json) records all intervals, finite parameters, +integer comparisons, ledgers, controls and source/verifier hashes. + +Logarithms use 80 exact terms of the binary-reduced atanh series with the +geometric tail. Exponentials use 64 terms after binary scaling into [0,1/2], +outward rounding at precision 2^−192, twice the next term for the remaining +tail, and outward repeated squaring. Negative arguments use reciprocal +intervals. Every decision uses fractions or integers, with no floating-point +acceptance test. A separate exact small product/pad/split example checks +the inventory and preserved surplus, and a sublinear-tail counterexample +guards the theorem's exponent restriction. + +Canonical base is `12fa8c5c844be21bfefb38a19503fbd867a11244`, priority revision +7. [SOURCES.json](SOURCES.json) pins the orientation metadata. The 15 unchanged +exports in [VENDOR.json](VENDOR.json) include complete source paths, commit +IDs, Git blob names and SHA256 hashes; the verifier authenticates both hashes +without requiring Git. Pending commits are represented by self-contained +exports, not implied publication ancestry. Source exports remain unchanged. + +The PR4426 invoice oracle is compiled from its authenticated source bytes, +with only ROOT and PHASES rebound to the exported file locations. Its literal +controller, supplier-receipt and port-recipe checks remain intact. The two +ledger oracles retain predecessor code and attribution; they are arithmetic +cross-checks, not fresh native supplier admission. + +Local validation used Python 3.12.8 on macOS arm64. The registered replay, +metadata/pin check and committed-byte preflight passed. A separate Git-free +copy passed `python3.12 -I -O -B verify.py` in 0.333 seconds; changed-source +and changed-receipt controls rejected. The optional full source-history +preflight could not run because this checkout is shallow. All pending-source +inputs are self-contained exports; standalone replay does not need those +foreign Git objects. No Lean, Docker, native all-size or historical suite was +run. These checks authenticate the stated result, not independent scientific +acceptance. + +Overlap at 18:19 UTC covered 536 open PR bodies and 3,279 discussion/comment +records with complete reported pagination, plus local notes. The newer +#4420/#4428/#4429 checks cover earlier strictification proof/arithmetic and +slightly smaller sufficient powers; #4426 supplies the invoice replay reused +here. No remote closed-PR-body or arbitrary code-diff search was performed. +The task metadata records the changed scope and remaining direct-compiler +question. Submission was authorized after local review; no Discussion claim was posted. + +## Open next questions + +1. **A direct compiler for overlapping ranks.** A finite acyclic integer + schedule would remove strictification altogether. Start by replacing the + Pascal matching step when a paid rank exceeds a target rank, retaining + arbitrary inputs, complements and chronological suspension. No such + termination/matching proof is supplied by the mixed moment alone. +2. **Full finite-word size and precision.** Derive compressed upper bounds + for the compiler's batch denominators, widths, scalar passes and owned + instances at the specified rank. Ambient rank is only one size parameter; + this remains the main barrier to assessing practical constants. +3. **Independent scientific review.** Check the higher-moment inequality, + the p>1 induction and the native product/adapters at their actual callers. + The unchanged raw supplier's internal paid bill and all-column/physical + premises remain separate inherited obligations. Another search of nearby + c,b,u,v values would not resolve those obligations. + +Prepared by zxv with substantial OpenAI Codex assistance in discovery, +implementation and writing. No subagents or independent human review were +used for this new work. New material is Apache-2.0. Native/controller lineage: +zxv's PR4359 and its retained contributors. Product/padding and p7 controller: +@1337isnot1337's PR4412/PR4414/PR4416. Integer mixed flow: Jacob Alan +Sussman, Theorem 1G. Logarithmic-majorant predecessor: zxv's PR4411. +Invoice replay: Ryanson Jonathan / @pinterbanget, PR4426, with Claude Code +assistance and Apache-2.0. The retained supplier and outer sources preserve +their original contributor credit and notices. diff --git a/research/direct-mixed-flow/vendor/higher-moment-RESULT.json b/research/direct-mixed-flow/vendor/higher-moment-RESULT.json new file mode 100644 index 0000000000..e66b39c674 --- /dev/null +++ b/research/direct-mixed-flow/vendor/higher-moment-RESULT.json @@ -0,0 +1,384 @@ +{ + "finite_controls": { + "rank_one_surplus": 13, + "sublinear_tail_counterexample": { + "J": 1, + "R": 100, + "actual_charge": 100, + "invalid_upper": { + "lower": "73.245553203367586639977870888654", + "upper": "73.245553203367586639977870888655" + }, + "sigma": "3/4", + "t": "1/2" + }, + "toy_paid": { + "1": 5, + "4": 9 + }, + "toy_targets": { + "10": 2, + "25": 1, + "9": 1 + } + }, + "invoice_oracle": { + "laurent_monomials": 14, + "main_targets": { + "121": 224, + "25": 448, + "41": 448, + "57": 448 + }, + "new_kappa_claimed": false, + "paid": { + "1": 37305, + "16": 448, + "2": 10695, + "3": 3360, + "32": 448, + "4": 1530, + "48": 448, + "5": 300, + "8": 1464 + }, + "paid_idles": { + "16": 448, + "32": 448, + "48": 448, + "8": 1344 + }, + "rank_one": [ + 131723, + 131115 + ], + "status": "PASS_PR4416_INVOICE_REBUILD", + "targets": { + "121": 224, + "25": 448, + "41": 448, + "5": 420, + "57": 448, + "6": 270, + "7": 840, + "8": 1395, + "9": 3195 + } + }, + "kappa": "268647/100000000", + "outer": { + "ledger": { + "functional_checks": { + "fixed_halo_explicit_metadata_branch": "13475000001/175000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000", + "new_semantic_group_guard": "3/700000000" + }, + "margins": { + "boundary_algebraic_matrix": "329093274529867/122500000000000000", + "fused_gaussian": "329093273589601/122500000000000000", + "global_coordinate_router": "1880533/700000000", + "group_bit_router": "1316373794358401/490000000000000000", + "group_scans": "349999999/350000000", + "main_transform": "329093099529867/122500000000000000", + "microbox_face_corrections": "13475000001/175000000", + "polynomial_products": "699999999/700000000", + "sparse_union_movement": "50094718274529867/122500000000000000" + }, + "parameters": { + "a": "1880533/700000000", + "b": "940267/350000000", + "beta": "699999997/700000000", + "bit_saving": "27/10000", + "cap_xi": "111344718099529867/122500000000000000", + "complex_uniform_saving": "376107/140000000", + "d": "1/700000000", + "epsilon": "699999999/700000000", + "kappa": "268647/100000000", + "lambda_": "39892541/40000000", + "lambda_prime": "174529867/175000000", + "layout": "1/700000000", + "q": "470133/175000000", + "r0": "1/7000000000", + "stop": "1/700000000", + "tested_saving": "33581/12500000" + }, + "strict_checks": { + "actual_bit_above_effective": "9467/700000000", + "actual_logarithmic_gamma_guard": "1/700000000", + "actual_logarithmic_group_guard": "11155282162970133/61250000000000000", + "alpha_logarithm_absorption": "1/7000000000", + "boundary_algebraic_matrix_above_kappa": "699529867/122500000000000000", + "cap_above_band": "50094718099529867/122500000000000000", + "cap_below_cell": "11155281725470133/122500000000000000", + "cap_below_phase_cell_power": "133655281900470133/122500000000000000", + "complex_above_effective": "1/700000000", + "complex_below_one_over_32": "9997233/350000000", + "complex_endpoint": "1/350000000", + "epsilon_below_one": "1/700000000", + "epsilon_positive": "699999999/700000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "698589601/122500000000000000", + "gaussian_above_main": "87029867/61250000000000000", + "global_coordinate_router_above_kappa": "1/175000000", + "global_gamma_power_slack": "9/7000000000", + "group_below_dimension": "1/350000000", + "group_bit_router_above_kappa": "3494358401/490000000000000000", + "group_gauge_power_slack": "11155282154220133/61250000000000000", + "group_key_fits_record": "1/350000000", + "group_positive": "699999997/700000000", + "group_scans_above_kappa": "698119469/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "477749790400418148631/500000000000000000000000", + "lambda_above_internal": "1/1400000000", + "lambda_above_sigma": "3/1400000000", + "lambda_above_tau": "1/1400000000", + "lambda_prime_above_lambda": "1/1400000000", + "lambda_prime_above_leaf": "699059733/245000000000000000", + "leaf_saving_above_effective": "349059733/245000000000000000", + "main_transform_above_kappa": "524529867/122500000000000000", + "membership_arithmetic_fits_record": "1/700000000", + "microbox_face_corrections_above_kappa": "2155924779/28000000", + "microbox_halo_volume": "55300000003/700000000", + "new_complex_uniform_saving_above_b": "1/700000000", + "new_semantic_guard_with_C1_one": "1/700000000", + "polynomial_products_above_kappa": "69811947/70000000", + "positive_layout_slack": "1/700000000", + "q_below_effective": "1/700000000", + "q_below_internal": "1/700000000", + "q_below_leaf": "699059733/245000000000000000", + "q_positive": "470133/175000000", + "short_record_fallback": "349059733/350000000", + "source_axis_superpolynomial": "1/700000000", + "sparse_union_movement_above_kappa": "49765625699529867/122500000000000000", + "stop_below_one": "699999999/700000000", + "stop_positive": "1/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000", + "union_tag_work_per_visit_fits_record": "3/700000000" + } + }, + "legacy_63_checks": { + "actual_bit_above_effective": "9467/700000000", + "actual_logarithmic_gamma_guard": "1/700000000", + "actual_logarithmic_group_guard": "11155282162970133/61250000000000000", + "alpha_logarithm_absorption": "1/7000000000", + "boundary_algebraic_matrix_above_kappa": "699529867/122500000000000000", + "cap_above_band": "50094718099529867/122500000000000000", + "cap_below_cell": "11155281725470133/122500000000000000", + "cap_below_phase_cell_power": "133655281900470133/122500000000000000", + "complex_above_effective": "1/700000000", + "complex_below_one_over_32": "9997233/350000000", + "complex_endpoint": "1/350000000", + "epsilon_below_one": "1/700000000", + "epsilon_positive": "699999999/700000000", + "fused_gaussian_above_kappa": "698589601/122500000000000000", + "gaussian_above_main": "87029867/61250000000000000", + "global_coordinate_router_above_kappa": "1/175000000", + "global_gamma_power_slack": "9/7000000000", + "group_below_dimension": "1/350000000", + "group_bit_router_above_kappa": "3494358401/490000000000000000", + "group_gauge_power_slack": "11155282154220133/61250000000000000", + "group_key_fits_record": "1/350000000", + "group_positive": "699999997/700000000", + "group_scans_above_kappa": "698119469/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_online_final": "477749790400418148631/500000000000000000000000", + "improvement_over_pkg_k2": "1008477392794717479267911225169191627777122102965890395790280701170194526587548469132116575062403/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1699": "1008828268656645435748941712936355250934431507/1000000000000000000000000000000000000000000000000", + "improvement_over_pr1712": "5044141343283227178741362020680007884145727138632283638941299969772687285461029288600736779707649/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1758": "1006724491197700948453466314800026327686526580209199320247542619067215757027414399369818327775017/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1786": "10067152118499510912194521335000000000000000000000000000000001999999800001/10000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1828": "2013430087748910957328658012158594846003377122994839409079344959674400000000000000000000000004006719019826502178085342683975683/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1839": "5033575219372277393321645030396487115008442807487098522698362399185677258698371805868475000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1875": "5033575219372277393321645030396487115008442807487098522698362399185677258698371805868471719335776838627743415457068895139647759399172939286143496816535216421325187363046885361425772909502231218314437622205930116079297234806627210590217190600996553729143901162562581526621534715086055386213403722175000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1876": "503357521937227739332164503039648711500844280748709852269836239918567725869837180586847171933577683862774341545706889513964775939917293928614349681653521642132518736304688536142577290950223121831443762220593011607929723480662721059021719060099655372914390116256258152662153471508605538621340372217196657216794137380775174500330086462142358142864921147118845386980694114022172311249292673931726844600000000000000000001001679754956625544521335670993920702577/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1897": "1006715043874455478664329006079297423001688561497419704539672479837135451739674361173694343867155367725548683091413779027929551879834587857228699363307043284265037472609377072285154581900446243662887524441186023215859446961325442118043438120199310745828780232512516305324306943017211077242680744434393314433588274761550349000660172924284716285729842294237690773961388228044344622498585347863453689118814253082419197486359454032147189198319033143866021423837056207677317517847011467076188001061138620310116832610271556685687769184940440093096226243113127523863162928128796969576356494654526264864467/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_previous_local_final": "477749790400418148631/500000000000000000000000", + "improvement_over_previous_package": "10086500976855635663689448641223998986170598784229341400200650717283025923262102542077285802551153/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_internal": "1/1400000000", + "lambda_above_sigma": "3/1400000000", + "lambda_above_tau": "1/1400000000", + "lambda_prime_above_lambda": "1/1400000000", + "lambda_prime_above_leaf": "699059733/245000000000000000", + "leaf_saving_above_effective": "349059733/245000000000000000", + "main_transform_above_kappa": "524529867/122500000000000000", + "membership_arithmetic_fits_record": "1/700000000", + "microbox_face_corrections_above_kappa": "2155924779/28000000", + "microbox_halo_volume": "55300000003/700000000", + "polynomial_products_above_kappa": "69811947/70000000", + "positive_layout_slack": "1/700000000", + "q_below_effective": "1/700000000", + "q_below_internal": "1/700000000", + "q_below_leaf": "699059733/245000000000000000", + "q_positive": "470133/175000000", + "short_record_fallback": "349059733/350000000", + "source_axis_superpolynomial": "1/700000000", + "sparse_union_movement_above_kappa": "49765625699529867/122500000000000000", + "stop_below_one": "699999999/700000000", + "stop_positive": "1/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000", + "union_tag_work_per_visit_fits_record": "3/700000000" + }, + "legacy_backoff": "21/5000000000", + "legacy_grid": 10000000000, + "minimum_margin_minus_kappa": "524529867/122500000000000000", + "rejected_controls": { + "closed_epsilon": [ + "actual_logarithmic_gamma_guard", + "epsilon_below_one", + "gaussian_above_main", + "global_gamma_power_slack", + "new_semantic_guard_with_C1_one", + "source_axis_superpolynomial" + ], + "closed_uniform_gap": [ + "new_complex_uniform_saving_above_b" + ], + "group_equals_dimension": [ + "group_below_dimension", + "group_key_fits_record", + "membership_arithmetic_fits_record" + ], + "insufficient_BIT": [ + "actual_bit_above_effective" + ], + "missing_layout": [ + "positive_layout_slack" + ], + "old_per_axis_scan": [ + "old_per_axis_scan_above_kappa" + ], + "unfunded_kappa": [ + "boundary_algebraic_matrix_above_kappa", + "fused_gaussian_above_kappa", + "global_coordinate_router_above_kappa", + "group_bit_router_above_kappa", + "main_transform_above_kappa" + ] + } + }, + "predecessor_H": 16201843136005340321, + "rank_exponent_reduction_factor": "16201843136005340321/349300000000", + "rejected_mutations": [ + { + "failed_at": "complete charged normalized moment", + "mutation": "too_short_product" + }, + { + "failed_at": "tail moment exponent at least one", + "mutation": "sublinear_tail" + }, + { + "failed_at": "strict finite ranks", + "mutation": "lost_separation" + } + ], + "schema": "higher-moment-native-strictification/1", + "scope": "Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.", + "source_sha256": { + "research/higher-moment-strictification/vendor/FINITE-PRECOMPILATION.md": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "research/higher-moment-strictification/vendor/FINITE-TEMPLATE-CLOSURE.md": "3f8508c63862dd83968bd30df91b08ba5afcee1e10db15ca546cdff0caef95d9", + "research/higher-moment-strictification/vendor/LOG-MAJORANT.md": "3b74b9b22258bd265a025a7e6f06f199e1625f3f0b735b972e6e91047eeb8e45", + "research/higher-moment-strictification/vendor/check_ledger.py": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98", + "research/higher-moment-strictification/vendor/invoice-review/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "research/higher-moment-strictification/vendor/invoice-review/vendor/NOTICE.md": "da983933f88516f311b2bb8750802e4bd03a537eacc0bde351cfb36b77a93f15", + "research/higher-moment-strictification/vendor/invoice-review/vendor/P7-FACTOR.json": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "research/higher-moment-strictification/vendor/invoice-review/vendor/RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab", + "research/higher-moment-strictification/vendor/invoice-review/vendor/SUPPLIER-RESULT.json": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6", + "research/higher-moment-strictification/vendor/invoice-review/verify.py": "a72b0c0da8beedbdd1a65e83009295c31fcd30664e85aeb1b620235042cbf0b5", + "research/higher-moment-strictification/vendor/outer_endpoint.py": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "research/higher-moment-strictification/vendor/p7-ENDPOINT.md": "e7056020bb9757d45fdf1a8eea9e811040ce72d53bc16e7f90f72a5e712fa3e9", + "research/higher-moment-strictification/vendor/p7-NATIVE.md": "26bf9312cdb496b1113c9ddd8aa0fa922ed9e480005703212942af358394183d", + "research/higher-moment-strictification/vendor/p7-RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab", + "research/higher-moment-strictification/vendor/p7-TENSOR.md": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + "status": "PASS_HIGHER_MOMENT_STRICTIFICATION", + "strictification": { + "alpha": { + "lower": "0.999999984403907977028692329024", + "upper": "0.999999984403907977028692329025" + }, + "ambient": "121^150", + "cutoff_base": 10, + "delta": { + "lower": "0.877942785206780917722562601792", + "upper": "0.877942785206780917722562601793" + }, + "floor_base": 15, + "gamma": { + "lower": "0.903981539721477814868265523050", + "upper": "0.903981539721477814868265523051" + }, + "materialized_product_or_uniform_word": false, + "maximum_paid": "10^150", + "minimum_target": "15^150", + "normalized_paid_upper": "1000000635204363556136250491144161837938214611877310981113991233610194892493163042995932145748443566398677069212449817849347590568236176459579539001979969712918643865874634198553766207360874447748594152802372160823515706917812863624324588309448164247279181670682524587922166460943924036141865870233593287572765694512062966529681268238027148629402289227769948550454004579273122673115283917084645472692704053780372399331749927451738974321744119172945600769747/1000001500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "old_rank_one_bound_lower": { + "lower": "2.524485503105612497245887828271", + "upper": "2.524485503105612497245887828272" + }, + "old_rank_one_gamma": { + "lower": "0.998191712473006243732169576257", + "upper": "0.998191712473006243732169576258" + }, + "paid_moment_exponent": "16216419/12500000", + "productive_fields_before_uniform_compiler": "7688^150", + "rank_one_surplus": "131723^150-131115^150", + "rational_upper_limits": [ + "99999999/100000000", + "181/200", + "439/500" + ], + "strict_moment_gap": { + "lower": "0.000000864794339252354870976549", + "upper": "0.000000864794339252354870976550" + }, + "tail_offset_u": "3/10", + "tensor_power": 150, + "tested_saving": "33581/12500000" + }, + "tail_only_power_majorant": { + "H0": 37443877100, + "H1": 140829080288374101, + "N": "2^140829080288374101", + "scope": "Tail transformation alone, retaining the older power majorant.", + "theta_upper": "6/7" + }, + "tensor_power_reduction_factor": "208/5", + "uniform_rank": { + "H": 349300000000, + "N": "2^349300000000", + "eta": { + "lower": "0.144386809622024146828684313913", + "upper": "0.144386809622024146828684313914" + }, + "eta_minus_theta_to_p": { + "lower": "0.009586237698168518342122636732", + "upper": "0.009586237698168518342122636733" + }, + "gap": "1/700000000", + "grid_step": 700000000, + "integer_test": { + "left_base": 349300000001, + "left_exponent": 13, + "right_base": 2, + "right_exponent": 499 + }, + "logarithm_power": 13, + "m_to_saving": { + "lower": "6.907234273066686405887998346942", + "upper": "6.907234273066686405887998346943" + }, + "previous_grid_point_rejected": true, + "smaller_logarithmic_power_rejected": true, + "t": "12466419/12500000", + "theta_upper": "6/7", + "uniform_saving": "376107/140000000" + }, + "verifier_sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" +} diff --git a/research/direct-mixed-flow/vendor/p7-RESULT.json b/research/direct-mixed-flow/vendor/p7-RESULT.json new file mode 100644 index 0000000000..ebb30a9b3b --- /dev/null +++ b/research/direct-mixed-flow/vendor/p7-RESULT.json @@ -0,0 +1,296 @@ +{ + "endpoint": { + "compiler": { + "H0": 4307773805920, + "H1": 16201843136005340321, + "N_encoding": "2^16201843136005340321", + "delta": "1/1400000000", + "exit_coefficient_log2_upper": "26640", + "final_strict_power_gap": "1/1400000000", + "h": "1/26", + "materialized_tensor_rule_or_uniform_word": false, + "negative_log2_eta_upper": "147931769/1250000", + "paid_max_bound_encoding": "10^6240", + "rank_one_induction": "131723^n > 131115^n; target padding adds equal paid and target rank, and splitting preserves rank", + "t": "12466419/12500000", + "target_max_encoding": "121^6240", + "target_min_encoding": "11^6240", + "tensor_power": 6240, + "theta_upper": "25/26", + "z": "139623893/140000000", + "z0": "1396238929/1400000000" + }, + "gain_over_PR4359": "38647/100000000", + "gain_over_PR4405": "19069/50000000", + "gain_over_PR4414": "33/5000000", + "gain_over_allfresh_p3": "5223/25000000", + "kappa": "268647/100000000", + "ledger_source_sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "minimum_outer_margin": "524529867/122500000000000000", + "negative_controls": { + "closed_epsilon": { + "actual_logarithmic_gamma_guard": "0", + "epsilon_below_one": "0", + "gaussian_above_main": "-1410399/122500000000000000", + "global_gamma_power_slack": "-1/7000000000", + "new_semantic_guard_with_C1_one": "0", + "source_axis_superpolynomial": "0" + }, + "closed_uniform_gap": { + "new_complex_uniform_saving_above_b": "0" + }, + "insufficient_BIT": { + "actual_bit_above_effective": "-270533/700000000" + }, + "unfunded_outer_point": { + "boundary_algebraic_matrix_above_kappa": "-525470133/122500000000000000", + "fused_gaussian_above_kappa": "-526410399/122500000000000000", + "global_coordinate_router_above_kappa": "-3/700000000", + "group_bit_router_above_kappa": "-1405641599/490000000000000000", + "main_transform_above_kappa": "-700470133/122500000000000000" + } + }, + "outer": { + "functional_checks": { + "fixed_halo_explicit_metadata_branch": "13475000001/175000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000", + "new_semantic_group_guard": "3/700000000" + }, + "margins": { + "boundary_algebraic_matrix": "329093274529867/122500000000000000", + "fused_gaussian": "329093273589601/122500000000000000", + "global_coordinate_router": "1880533/700000000", + "group_bit_router": "1316373794358401/490000000000000000", + "group_scans": "349999999/350000000", + "main_transform": "329093099529867/122500000000000000", + "microbox_face_corrections": "13475000001/175000000", + "polynomial_products": "699999999/700000000", + "sparse_union_movement": "50094718274529867/122500000000000000" + }, + "parameters": { + "a": "1880533/700000000", + "b": "940267/350000000", + "beta": "699999997/700000000", + "bit_saving": "27/10000", + "cap_xi": "111344718099529867/122500000000000000", + "complex_uniform_saving": "376107/140000000", + "d": "1/700000000", + "epsilon": "699999999/700000000", + "kappa": "268647/100000000", + "lambda_": "39892541/40000000", + "lambda_prime": "174529867/175000000", + "layout": "1/700000000", + "q": "470133/175000000", + "r0": "1/7000000000", + "stop": "1/700000000", + "tested_saving": "33581/12500000" + }, + "strict_checks": { + "actual_bit_above_effective": "9467/700000000", + "actual_logarithmic_gamma_guard": "1/700000000", + "actual_logarithmic_group_guard": "11155282162970133/61250000000000000", + "alpha_logarithm_absorption": "1/7000000000", + "boundary_algebraic_matrix_above_kappa": "699529867/122500000000000000", + "cap_above_band": "50094718099529867/122500000000000000", + "cap_below_cell": "11155281725470133/122500000000000000", + "cap_below_phase_cell_power": "133655281900470133/122500000000000000", + "complex_above_effective": "1/700000000", + "complex_below_one_over_32": "9997233/350000000", + "complex_endpoint": "1/350000000", + "epsilon_below_one": "1/700000000", + "epsilon_positive": "699999999/700000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "698589601/122500000000000000", + "gaussian_above_main": "87029867/61250000000000000", + "global_coordinate_router_above_kappa": "1/175000000", + "global_gamma_power_slack": "9/7000000000", + "group_below_dimension": "1/350000000", + "group_bit_router_above_kappa": "3494358401/490000000000000000", + "group_gauge_power_slack": "11155282154220133/61250000000000000", + "group_key_fits_record": "1/350000000", + "group_positive": "699999997/700000000", + "group_scans_above_kappa": "698119469/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "477749790400418148631/500000000000000000000000", + "lambda_above_internal": "1/1400000000", + "lambda_above_sigma": "3/1400000000", + "lambda_above_tau": "1/1400000000", + "lambda_prime_above_lambda": "1/1400000000", + "lambda_prime_above_leaf": "699059733/245000000000000000", + "leaf_saving_above_effective": "349059733/245000000000000000", + "main_transform_above_kappa": "524529867/122500000000000000", + "membership_arithmetic_fits_record": "1/700000000", + "microbox_face_corrections_above_kappa": "2155924779/28000000", + "microbox_halo_volume": "55300000003/700000000", + "new_complex_uniform_saving_above_b": "1/700000000", + "new_semantic_guard_with_C1_one": "1/700000000", + "polynomial_products_above_kappa": "69811947/70000000", + "positive_layout_slack": "1/700000000", + "q_below_effective": "1/700000000", + "q_below_internal": "1/700000000", + "q_below_leaf": "699059733/245000000000000000", + "q_positive": "470133/175000000", + "short_record_fallback": "349059733/350000000", + "source_axis_superpolynomial": "1/700000000", + "sparse_union_movement_above_kappa": "49765625699529867/122500000000000000", + "stop_below_one": "699999999/700000000", + "stop_positive": "1/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000", + "union_tag_work_per_visit_fits_record": "3/700000000" + } + }, + "schema": "native-p7-padding-strictification-outer-endpoint/1", + "scope": "Source-bound native p7 geometry, a finite tensor recipe with target padding, exact moment and outer inequalities, and a specified finite uniform rank. Native tensor closure and the PR4359 inherited precision, storage, analytic, fixed-tape and recovery hypotheses are written premises, not a full formal theorem certificate.", + "status": "PASS_CONDITIONAL_P7_OUTER_POINT", + "strictification_source_sha256": "1f3c2a38b34d9dad7266be212ca5d0225827d8e05bda4831e6c25c5713f624f0", + "tested_saving": "33581/12500000" + }, + "independent_interval_crosscheck": true, + "scope": "Conditional native construction and exact finite arithmetic. The finite word and inherited physical, precision, analytic and fixed-tape proofs are not formally verified or materialized by this checker.", + "source_files": 23, + "status": "PASS_SOURCE_BOUND_CONDITIONAL_P7_PAID_PADDING_IMPROVEMENT", + "strictification": { + "alpha_interval": { + "lower": "0.99999998440390797702869232902431332", + "upper": "0.99999998440390797702869232902431333" + }, + "alpha_upper": "99999999/100000000", + "completion_decay_block_length": 2, + "controls": { + "one_decay_block_rejected": true, + "undamped_completion_rejected": true, + "unpadded_rank_one_tail_rejected": true + }, + "cutoff_base": 10, + "cutoff_encoding": "10^6240", + "decay_block_count": 16, + "decay_block_length": 390, + "delta_interval": { + "lower": "0.64382470915163933966321257464784307", + "upper": "0.64382470915163933966321257464784308" + }, + "delta_upper": "2/3", + "exponent": 6240, + "gamma_interval": { + "lower": "0.99819171247300624373216957625759087", + "upper": "0.99819171247300624373216957625759088" + }, + "gamma_upper": "4991/5000", + "materialized_tensor_or_completed_word": false, + "native_inventory": { + "artifact_hash_encoding": "Uncompressed UTF-8 JSON, sort_keys=True, separators=(comma,colon)", + "artifact_sha256": "12784fff6a13e3752ea6e80018e0484c5766a8adf2e88a7e71c80cf2bb68f398", + "contacts": 6720, + "dimension": 121, + "factor_receipt_sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "fresh_helper_fields": 6120, + "keep": 232127, + "limits": "Finite exact physical controller admission; inherited all-column local word, tensor strictification, new full-word precision/stock and outer transfer remain written proof obligations.", + "main_fields": 1568, + "native_scalar_allowance": 2490856, + "native_source_gate": "PASS_ACTUAL_ARBITRARY_HELPERS_AND_COMPLETE_PHASE_CORRECT_IDLE_JOBS", + "negative_controls": { + "omitted_endpoint_translation_rejected": 784, + "wrong_native_orientation_rejected": true + }, + "p": 7, + "paid": { + "1": 37305, + "16": 448, + "2": 10695, + "3": 3360, + "32": 448, + "4": 1530, + "48": 448, + "5": 300, + "8": 1464 + }, + "paid_calls": 55998, + "productive_fields": 7688, + "rank_margin": 608, + "scalar_allowance": 2490856, + "schema": "source-bound-p7-all-fresh-complete-native-controller/1", + "source_sha256": { + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "research/kappa-rebuild/bit/complex_controller_factor.py": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497", + "research/kappa-rebuild/bit/mixed_productive_bit.py": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e", + "research/kappa-rebuild/complex/fresh-certificates/THREE-base-HELPER-BOUNDARIES.json.gz": "f90517e395bde58c72cacd5d3481c4ea31d459fe4535384ac16547ac40460555", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39", + "research/kappa-rebuild/complex/full_identity_rebuild.py": "9af2ffbb0038c92e2a7d281081b0daaeadce75b11b566e5427845dc1af91e33d", + "research/kappa-rebuild/controller/P3-NATIVE-COVER.json.gz": "facfc6d6ecde151afb7e6a167776f3fdaac1c816e785a21a39f7f0bfd9140f3f", + "research/kappa-rebuild/controller/p3_native_cover.py": "fae71fcbbd20b9ee73b049cf6f43ea1d048217fb15feb6055a007e47da3363fe", + "research/kappa-rebuild/transfer-audit/p3_cover_audit.py": "a0fe9a26f77556e83b31b0c91fea909d6f3d8209d0f9f7ad4e5bc1375d33615e", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902" + }, + "status": "PASS_EXACT_LAURENT_ALL_MAIN_CONTACTS_ENDPOINTS_AND_FULL_IDLE_PHASES", + "targets": { + "121": 224, + "25": 448, + "41": 448, + "5": 420, + "57": 448, + "6": 270, + "7": 840, + "8": 1395, + "9": 3195 + }, + "whole_idle_profile": { + "16": 448, + "32": 448, + "48": 448, + "8": 1344 + } + }, + "new_max_target_encoding": "121^6240", + "new_min_target_encoding": "11^6240", + "normalized_moment_upper_rational": "10240625039/10240638976", + "paid": { + "1": 37305, + "16": 448, + "2": 10695, + "3": 3360, + "32": 448, + "4": 1530, + "48": 448, + "5": 300, + "8": 1464 + }, + "paid_rank_one_moment": 131115, + "productive_fields": 7688, + "rank_one_surplus_encoding": "131723^6240-131115^6240", + "schema": "p7-paid-target-completion-tensor-certificate/1", + "scope": "Exact moment bounds for the documented chronological native product, paid target completion and disjoint splitting. Native all-column, precision, storage, analytic and fixed-tape premises remain separate; no full multiplication theorem is formally verified.", + "source_sha256": { + "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + "status": "PASS_EXACT_P7_TARGET_COMPLETION_STRICTIFICATION", + "strict_moment_verified": true, + "strictification_gap": { + "lower": "0.00000136095023295546357907266586564", + "upper": "0.00000136095023295546357907266586565" + }, + "strictification_gap_rational": "13937/10240638976", + "target_floor_base": 11, + "target_floor_encoding": "11^6240", + "target_rank_one_moment": 131723, + "targets": { + "121": 224, + "25": 448, + "41": 448, + "5": 420, + "57": 448, + "6": 270, + "7": 840, + "8": 1395, + "9": 3195 + }, + "tested_saving": "33581/12500000", + "theta_upper": "25/26" + } +} diff --git a/research/direct-mixed-flow/vendor/theorem-1g.md b/research/direct-mixed-flow/vendor/theorem-1g.md new file mode 100644 index 0000000000..36d2399f35 --- /dev/null +++ b/research/direct-mixed-flow/vendor/theorem-1g.md @@ -0,0 +1,264 @@ +# Theorem 1G: mixed jobs with grouped paid blocks + +This note holds the proof behind the recursion lever of the record track: an extension of the τ-theorem (in the +form argued in [../../existence-routes/](../../existence-routes/), "Theorem 1") from paid moves of rank 1 to paid +blocks of any rank. It was written on 14 October 2026 by an AI agent working for me, in a simple model of jobs, and +it is reproduced here with its notation, cleaned of internal file names. + +**Status.** *Argued by hand, not checked.* Two independent AI skeptics tried to refute it on 14 October: one +re-derived the logic and simulated the construction with its own code, the other built the construction explicitly +(units, random matching inside the prescribed classes, a generic deadlock test) and checked the hypotheses of the +induction on the actual flows. Neither found an error. No person and no proof checker has read this text. A Lean +form of the theorem inside OpenAI's model was built on 19 October as part of the lever record (section 6); its +status is the record's: *proved in Lean*, as part of each of the five lever packages (in `package/leverF` and `package/leverB`, the modules under `Work/Mixed/` and `Work/MixedCost/`), with the official comparator accepting each result and three skeptics upholding each. + +Labels used inside the proof: [argued] (an argument given here in full, by hand; no proof checker has read it), +[computed] (a program, named in section 4), [what-if] (a price that rests on an unchecked step), [open]. + +## 0. The job model + +This is the model of the τ-theorem's proof, recalled so that this note can be read alone. + +- A **job of size s** is: apply the Walsh-Hadamard transform H on s chosen address bits of a register holding + 2^ν entries (ν ≥ s), that is, a batch of 2^(ν-s) independent transforms of size 2^s. Its cost is counted per entry: + T(s) is the number of full passes over the register (one per single-bit Hadamard leaf, one per free pass). A pass + over a fraction w of the entries costs w. +- A **rule** (a mixed unit) at block m: a word, correct for every number f of digit columns, with W_k registers + carrying a **rank-k target** (k of the m rows transformed, the other m - k untouched), paid blocks, and F free + register-passes. Applied at column c it turns jobs of the target sizes kc into jobs of the paid sizes r_j c. +- **Split**: a job of size a + b is the job of size a followed by the job of size b (Hadamards on disjoint bits + commute), at cost T(a) + T(b). A **plain leaf** of size s costs s passes. +- **Φ_τ** of a set of jobs (weighted by fractions of entries) is the sum of weight times size^τ. +- **τ** of a rule is the root in (0, 1) of Σ_j r_j^τ = Σ_k W_k k^τ (the *balance*). With every r_j = 1 this is the + τ-theorem's M = Σ_k W_k k^τ. + +The community's recursion is this model with one target size: a paid block is a recursive call on a whole register, +and the W arrays of the next level are W slices of that one call's batch. A rule with targets of two sizes needs jobs +of two sizes at once, which no single call's batch provides; that is what the construction below supplies. + +## 1. Re-check of the rank-1 case (the τ-theorem) + +- **Step 1 (multinomial flow).** With p_k = W_k/M and u(a) = multinomial(|a|; a) Π p_k^(a_k), Pascal's rule gives + u(b) = Σ over k with b_k ≥ 1 of p_k u(b - e_k) for b ≠ 0, so M u(b) = Σ_k W_k u(b - e_k). The region + R = {a : m c(a) ≤ L} is down-closed. A frontier point b (not in R, with some b - e_k in R) has size + c(b) = k c(b - e_k) ≤ kL/m ≤ L and c(b) > L/m. Confirmed [argued]. An exact re-run found 0 unbalanced sizes, + Φ(sources) = M to 10 digits, and sources in (L/3, L] [computed]. +- **Step 2 (Φ conservation).** Each unit is Φ-neutral at τ, so Φ(sources) = Φ(leaves) = M. Confirmed. +- **Step 3 (free passes).** The sum of u over generation j is (W/M)^j, so the sum of u is at most M/(M - W), and the + free passes come to F/(M - W) per unit of leaf Φ. The passes spent re-grouping portions (one per class level) cost + O(1) per register used by a unit, so they fold into F. +- **Lemma 2 (lockstep).** Process(g, λ) issues move k of all units in the class. The outputs plus (λ/M) Source at + generation g equal (λ/M) J at generation g, which is exactly what the child consumes. At level g there are + M^(g_max - g) calls with λ = M^-(g_max - g), so the sources used add up to Source exactly [argued]. The literal + simulation was re-run on 1+4 in 10 at L = 12, 30, 54, on 1+1 in 4 at L = 30, and on 7+38 in 88 at L = 12 + (7,833 classes): every class was fed exactly, the sources used equal Source, and the leaves equal M u(0) + [computed]. +- **Step 5 (top split and constant).** Every rest has size s - c(a) < (1 - 1/m)s. The induction closes with + C' = (A + c0)/(1 - (1 - 1/m)^τ). A sharper constant is C' = (A + c0)/η_m with + η_m = min over t in [1/m, 1] of (1 - (1-t)^τ)/t^τ, which is at least 1 - (1-1/m)^τ (Lemma A below). +- **Rounding.** The number of fluid portions is the number of lockstep classes, at most M^(g_max+1) = n^O(ln M/ln k_min). + That is polynomial in n, not the number of lattice points, and still far below 2^(n/2) batch entries, so dyadic + rounding costs a relative 2^-Ω(n). The claim stands; only the count in the earlier text was wrong. +- **A hypothesis that both theorems need and the earlier text did not state.** Each unit must be a correct word at + every column count f that occurs: products of target ranks in the rank-1 case, and products of target and paid ranks + in Theorem 1G. The community's engine also asserts m^2 > 2 max(r)^2; what that halving constraint asks of a new + recursion was not examined here. + +## 2. Lemma A: the top-split induction with leftovers (the exact condition) + +**Setting.** T(n) is the per-entry cost of the best schedule for a job of size n (with at least n/2 batch bits). A +*flow for n* consists of: +- source weights w(s) ≥ 0 on sizes 1 ≤ s ≤ n, with Σ w = 1; +- exit weights x(e) ≥ 0 on sizes e < n: jobs the flow leaves over, each completed by a separate call of the whole + procedure; +- an internal cost I ≤ A Φ̂ (free passes, re-grouping, plain size-1 leaves), where Φ̂ = Σ_s w(s) s^τ; +- a deadlock-free order, given that each exit call returns a completed job. + +The schedule splits the top job into portions w(s), each portion being s + (n - s). The s-parts feed the flow, and +the (n - s)-parts and the exits are done recursively. So + + T(n) ≤ c0 + I + Σ_e x(e) T(e) + Σ_s w(s) T(n - s). + +**Lemma A** [argued]. Let ψ ≥ 1 be nondecreasing, and let β > 0 and n0 be such that for every n ≥ n0 there is a flow +with + + (E) Σ_e x(e) e^τ ψ(e) + ψ(n) Σ_s w(s) (n - s)^τ ≤ ψ(n) (n^τ - β Φ̂). + +Then T(n) ≤ C n^τ ψ(n) for all n, with C = max{ max_{n L gives ρ_s c(b) > r_j L/m. Some b - e_k lies in R(ρ_s), so ρ_s c(b) ≤ kL/m ≤ L. ∎ + +**Lemma D (exits)** [argued]. Outputs leave the tree only at generation 0 (d = G). There each class has at most one +unit (at column ρ_s, present when m ρ_s ≤ L), and its P outputs have sizes ρ_s r_j. Φ(exits) = Φ(sources) exactly. +Every exit has size e ≤ r_max · r_max^G ≤ r_max (L/m)^θ with θ = ln r_max / ln k_min < 1, so ln e ≤ θ ln L. Exits of +size 1 are plain leaves. +*Proof.* By Lemma B, outputs at generation ≥ 1 are all consumed. Every unit is Φ-neutral at τ, and every consumed job +was produced or sourced, so Φ(exits) = Φ(sources). G ≤ log_(k_min)(L/m) because c(a) ≥ k_min^|a|, which gives +ρ_s ≤ r_max^G ≤ (L/m)^θ. Finally r_max ≤ m^θ (since r_max = k_min^θ ≤ m^θ), which gives ln e ≤ θ ln L. ∎ + +**Lemma E (number of units)** [argued]. units ≤ Φ(sources) / (W k_min^τ (1 - k_min^-τ)), with no log factor. +*Proof.* A unit at depth d sits at column ≥ c(a) ≥ k_min^(G-d), and its input Φ is +Σ_k W_k (k · col)^τ ≥ W k_min^τ k_min^(τ(G-d)). The total input Φ at each depth is at most Φ(sources), since Φ only +moves down through the tree or leaves it. Summing the geometric series over G - d gives the bound. ∎ + +**Lemma F (order: no deadlock)** [argued]. Procedure Process(s), called with the parent's round-j outputs pending: +1. the class's inputs are exactly those outputs plus top sources (Lemmas B and C); +2. for j = 1..P: issue round j of every unit of s, running the word's free steps between moves as the word says; if + d(s) = G, complete each exit job by a top call Do(e); otherwise call Process(s.j); +3. return. +A round j+1 is issued only after Process(s.j) has returned, which means every unit that consumed a round-j job has +finished. A unit starts only after all its inputs exist. So this is a straight-line program. Its recursion depth is +G + 1, and every exit call is a smaller instance (e < n). ∎ + +A careless order does deadlock: if a unit took one input from round 1 of unit A and another from round 2 of A, while +A's round 2 waits for that very unit, nothing can start. Lockstep classes, in which each child class takes only the +outputs of one round, rule this out. + +**Theorem 1G** [argued, job model]. Under (S): T(n) ≤ C n^τ (ln n)^κ for all n ≥ 3, where +κ = ⌈ln(2/η_m) / ln(1/θ)⌉ (κ = 0 when r_max = 1) and C depends only on the rule. So T(n) = O(n^(τ+δ)) for every +δ > 0. +*Proof.* Take L = n. The flow is the tree normalised to source weight 1. The sources lie in (n/m, n] (Lemma C), so +K = m. The internal cost I ≤ A Φ̂ with A = (F + O(W))/(W k_min^τ (1 - k_min^-τ)) (Lemma E, plus one size-1 leaf per +unit of leaf Φ). The exits satisfy Φ(exits) = Φ̂ and ln e ≤ θ ln n (Lemma D). The order is valid (Lemma F). Lemma A3 +applies with ψ = max(1, ln)^κ and β = η_m/2. The batch-bit and dyadic-portion arrangements are as in section 1: the +number of classes is at most Σ_d P^d = n^O(ln P / ln k_min). ∎ + +*Remarks.* +- With every r_j = 1 the tree is the rank-1 construction (ρ = 1, exits = leaves), and κ = 0 recovers O(n^τ). +- Exact O(n^τ) for grouped rules, with no log factor, would need a flow with Φ(exits) ≤ (η - β) Φ̂ (Lemma A2). This + tree has Φ(exits) = Φ̂, so by A4 it cannot give that [open]. +- The log factor costs nothing in the exponent: every saving below 1 - τ is reached with a fixed constant. OpenAI's + goal is a big-O statement, so an existential constant is allowed. +- Without (S): Lemma B needs r_j ≤ k for the pairs that meet, and Lemma D needs r_max < k_min. The case r_max ≥ k_min + is open. An example (targets {3:1, 2:4}, paid {1:6, 2:2}) has a fluid linear programme whose optimum was still rising + at n = 480. + +## 4. Numerical checks [computed] + +Every program named here is in [../programs/theorem-1g/](../programs/theorem-1g/) and its output in +[../data/theorem-1g/](../data/theorem-1g/). All were re-run on 19 October 2026 for this revision, on an Apple +M4 Mac mini with Python 3.9, in under a minute each and under 300 MB; every output was identical to the one made on +14 October. + +Three test rules, plus a control: +- A: targets {4:1, 3:2}, rounds 1,1,1,1,2,2 (τ 0.746375; θ 0.631, κ 3); +- B: targets {7:1, 4:1}, rounds 1,1,1,1,2,2,2 (τ 0.928234). This is the truncation of the pure rule {7:2} with paid + {1:4, 2:3} plus a rank-3 idle block; +- C: targets {5:1, 4:3}, rounds 1×6, 2×2, 3×2 (τ 0.930659; θ 0.792, κ 4); +- D: the rank-1 control 1+4 in 10. + +1. **Literal lockstep** (`tree_flow.py`): explicit round sequences, each round in word order. A, B and C were run at + L = 40 and 150 (up to 259 classes). Every class was exactly fed (no surplus, no deficit), the sources used equal the + merged count, and the exits match the merged count by size. +2. **Merged exact checks** at L = 10^3, 10^5, 10^7 (up to 1.6e10 classes, counted with multiplicity): 0 unbalanced + points; all sources in (L/m, L]; Φ(exits)/Φ(sources) = 1.000000000000; the largest exit at or below the bound + r_max (L/m)^θ (16,384 ≤ 21,761 for A at L = 10^7, 2,048 ≤ 2,391 for B, 177,147 ≤ 295,508 for C); the unit count + within the bound of Lemma E. +3. **Cost of the whole schedule** (`recur.py`; F = 0, L = n, exits by recursive calls), T(n)/n^τ: + + | rule | n = 50 | n = 400 | n = 3,200 | n = 6,400 | + |---|---|---|---|---| + | A | 1.612 | 1.896 | 2.034 | 2.052 | + | B | 1.144 | 1.197 | 1.218 | 1.229 | + | C | 1.177 | 1.192 | 1.249 | 1.246 | + | D (rank-1 control) | 1.162 | 1.180 | 1.183 | 1.183 | + + The grouped rules grow slowly, far below (ln n)^κ; A's local slope over the last doubling is 0.759 against + τ = 0.746 and falling. The control is flat, as the rank-1 theorem says. +4. **Re-check of the rank-1 theorem** (`recheck_t1.py`, which imports the τ-theorem's own programs from + [../../existence-routes/programs/tau-theorem-and-laser/](../../existence-routes/programs/tau-theorem-and-laser/)). +5. **The community's circuit T74, as a what-if** (`hub_whatif.py`). Control: the balance with one job size reproduces + the community's figure for T74, 1.6797550e-3 (1.6797549561e-3). The mixed price, assuming every idle block of T74 + is a head or a tail on its own array, is 1.8169468e-3 (+8.17 %), separated (8 < 25). **This assumption turned out + to be false**: only 11,010 of the 22,748 idle blocks are heads and none is a tail (the README of this section, + section 4.5), so this figure is **refuted** as a price of T74. It stays here as the test it was. + +The skeptics' own programs, written from this text without reusing its code: +- `indep_tree.py` rebuilds the merged tree independently (toy rule A and the T74 mixed rule up to L = 10^8): + 0 unbalanced points, Φ ratio 1, exits within the bound. `partial.py` prices partial truncation, which showed that + the result depends on how many idle blocks really are heads. +- `explicit_sim.py` builds explicit unit objects, matches outputs to inputs at random inside the prescribed classes, + and runs a generic topological sort of start, issue and finish events as a deadlock test independent of Lemma F; + Φ is tracked to 50 digits. Every lockstep run is deadlock-free with Φ(exits) = Φ(sources); a deliberately careless + matching across classes deadlocks, as it should. +- `cost_fit.py` and `check_E.py` compute the actual flows up to n = 12,800 and check hypothesis (E) of Lemma A3 at + every n there, the unit bound of Lemma E and the exit bound; for the T74 rule `check_E.py` checks every n up to + 20,000 and every 997th n up to 3,000,000. No violation anywhere. They also + confirm Lemma A4: (E) with ψ = 1 fails at every n, as predicted. + +## 5. What the new recursion needs that the community's uniform recursion does not have + +The community's recursion is one call per job: a call of size s slices its own batch into W rank-m arrays at column +s/m, and each paid block is an independent recursive call; no call ever needs a job of another size. Theorem 1G needs: +1. **Several sizes at once.** A unit at column c takes rank-73 arrays of size 73c and smaller ones (rank 49 for the + half cut, rank 25 for the full cut) in a fixed ratio. These come from different producers' outputs, never from one + call's batch. +2. **Fluid portions.** Classes are fractional portions of batches, which needs a portion and relabel step in the cost + model and dyadic rounding with at least n/2 batch bits (the class count is polynomial in n). +3. **A class tree in lockstep**, ordered as in Lemma F. +4. **A top split** of the top job into frontier portions of sizes in (n/m, n] plus rests, done recursively. +5. **Exit calls.** Jobs of size ρ_s r_j are completed by fresh top calls. +6. **Mixed-target words.** The word with the head blocks removed or shortened must be proved correct for the reduced + targets at every column count f that occurs. +7. **Hypothesis (S).** On the circuits of the record track it holds with room: for the half cut every paid rank is at + most 48 and the smaller job is 49; for the full cut every paid rank is at most 24 and the smaller job is 25. +8. **The structure of the circuit.** Each block that is cut must be the first operation on its array, acting on that + array alone (the truncation lemma of [../../existence-routes/](../../existence-routes/)). This is the head test + of the README, section 4.5. + +## 6. The Lean form + +On 19 October the recursion was written in Lean inside OpenAI's RAM model as part of the lever record. Two things +changed against the plan in section 5: + +- **No log factor.** The Lean cost bound does not use Lemma A3. It applies Lemma D at a rate point z1 and argues that + for every exponent z above z1 the exits' share of the sources' Φ shrinks by a factor at most 2 (E m/n)^(z - z1), + where E = r_max^(G+1) bounds the exits; since E m/n tends to 0, Lemma A closes with ψ = 1 for all large n, and a + finite maximum covers the small ones. The statement is: if the balance holds at z1, then for every z in (z1, 1] there + is a constant C with cost ≤ C · 2^n · (n + 1)^z. The constants exist but are astronomically large; only their + existence is used, which OpenAI's big-O goal allows. Lemma A4 is not contradicted: it concerns the exponent τ itself. +- **The program.** Units are coded as sequences of roles (the Pascal bijection of Lemma B as arithmetic on codes); + each paid block of a class becomes one child call whose answers are read back ("Hadamards on disjoint bits + commute"); the leaf class hands its exits to one fresh top call; the order is the lockstep order of Lemma F, by + induction over the word. + +Status of this Lean form: *proved in Lean*, as part of each of the five lever packages (in `package/leverF` and `package/leverB`, the modules under `Work/Mixed/` and `Work/MixedCost/`), with the official comparator accepting each result and three skeptics upholding each. Its module and theorem names are listed in the lever package +(package/leverB/). diff --git a/research/direct-mixed-flow/vendor/tree_flow.py b/research/direct-mixed-flow/vendor/tree_flow.py new file mode 100644 index 0000000000..31a9c1ae4d --- /dev/null +++ b/research/direct-mixed-flow/vendor/tree_flow.py @@ -0,0 +1,167 @@ +# tree_flow.py (bound-check/rl-prove, 14 Oct 2026). The DILATED LOCKSTEP TREE of PROOF.md section 3 (Theorem 1G), +# for a mixed rule with GROUPED paid blocks: targets {k: W_k} (k in K), rounds r_1..r_P (P_r rounds of rank r), and +# the separation hypothesis r_max < k_min. Exact integers / fractions. +# u(a) = multinomial(|a|; a) prod_k W_k^a_k (a in N^K), c(a) = prod_k k^a_k, m = max K, +# R(rho) = {a : m rho c(a) <= L}, G = max{|a| : a in R(1)}. +# Class s (a round sequence of length d <= G, rho_s = product of its ranks): u(a) units at column rho_s c(a) for +# every a in R(rho_s) with |a| = G - d. Round j of class s feeds class s+(j) only. +# Checks (merged by (d, rho) with path multiplicities N(d, rho)): +# (1) exact balance: at every point b in R(rho') the child's demand equals the parent's round output; +# (2) every other demand is a SOURCE of size in (r_j L/m, L] (root: (L/m, L]); +# (3) exits only at generation 0: P jobs of sizes rho*r_j per class, all <= r_max * (L/m)^theta, theta = ln r_max/ln k_min; +# (4) Phi conservation at tau_c: Phi(sources) = Phi(exits); (5) unit count <= Phi(sources)/(W k_min^tau (1-k_min^-tau)). +# Literal lockstep simulation (lockstep_literal): explicit recursion over round sequences, a pool of issued jobs per +# class, every class must find all its inputs issued (parent round j + sources) and consume every job it is given. +import sys +from fractions import Fraction as Fr +from math import factorial, log, prod +from itertools import product as iprod + +def tau_c(Wt, P): + lo, hi = 0.0, 1.0 + for _ in range(200): + mid = (lo + hi) / 2 + if sum(w * k ** mid for k, w in Wt.items()) > sum(p * r ** mid for r, p in P.items()): hi = mid + else: lo = mid + return (lo + hi) / 2 + +def lattice(Wt, L, rho): + """points a in R(rho), as tuples over sorted K, grouped by |a|""" + K = sorted(Wt); m = max(K) + pts = {} + def rec(i, a, c): + if i == len(K): + pts.setdefault(sum(a), []).append(tuple(a)); return + k = K[i]; e = 0; cc = c + while m * rho * cc <= L: + rec(i + 1, a + [e], cc); e += 1; cc *= k + rec(0, [], 1) + return pts + +def mult(a): + return factorial(sum(a)) // prod(factorial(x) for x in a) + +class Tree: + def __init__(self, Wt, P, L): + self.Wt, self.P, self.L = dict(Wt), dict(P), L + self.K = sorted(Wt); self.m = max(self.K) + assert max(P) < min(self.K), "separation r_max < k_min fails" + self.Wv = [Wt[k] for k in self.K] + self.lat = {} + self.G = max(lattice(Wt, L, 1)) + def R(self, rho): + if rho not in self.lat: self.lat[rho] = lattice(self.Wt, self.L, rho) + return self.lat[rho] + def u(self, a): return mult(a) * prod(w ** x for w, x in zip(self.Wv, a)) + def c(self, a): return prod(k ** x for k, x in zip(self.K, a)) + def inR(self, a, rho): return self.m * rho * self.c(a) <= self.L + def units(self, d, rho): + return {a: self.u(a) for a in self.R(rho).get(self.G - d, [])} + def demand(self, d, rho): + need = {} + for a, ua in self.units(d, rho).items(): + for i, k in enumerate(self.K): + b = list(a); b[i] += 1; b = tuple(b) + need[b] = need.get(b, 0) + self.Wt[k] * ua + return need + +def check(Wt, P, L, tau=None): + T = Tree(Wt, P, L); tau = tau_c(Wt, P) if tau is None else tau + G, m, kmin, rmax = T.G, T.m, min(T.K), max(P) + theta = log(rmax) / log(kmin) if rmax > 1 else 0.0 + N = {(0, 1): 1} + src_w, src_phi, ex_w, ex_phi, units, bad = 0, 0.0, 0, 0.0, 0, [] + src_sizes, ex_sizes = set(), {} + # root + for b, x in T.demand(0, 1).items(): + s = T.c(b) + if T.inR(b, 1): bad.append(('root demand inside R(1)', b)) + if not (L / m < s <= L): bad.append(('root source size', s)) + src_w += x; src_phi += x * s ** tau; src_sizes.add(s) + for d in range(0, G + 1): + layer = {k: v for k, v in N.items() if k[0] == d} + for (_, rho), n in layer.items(): + us = T.units(d, rho) + units += n * sum(us.values()) + if d == G: # generation 0: exits + for a, ua in us.items(): + assert a == tuple(0 for _ in T.K) + for r, pr in P.items(): + e = rho * r + ex_w += n * pr * ua; ex_phi += n * pr * ua * e ** tau + ex_sizes[e] = ex_sizes.get(e, 0) + n * pr * ua + continue + for r, pr in P.items(): # children via a round of rank r + rc = rho * r + N[(d + 1, rc)] = N.get((d + 1, rc), 0) + n * pr + need = T.demand(d + 1, rc) + supply = {a: ua for a, ua in us.items()} # parent round output at point a, size rc*c(a) + for b in set(need) | set(supply): + sup = supply.get(b, 0); dem = need.get(b, 0) + if T.inR(b, rho): + if sup != dem: bad.append(('unbalanced', d, rho, r, b, sup, dem)) + else: + if sup: bad.append(('supply outside R', b)) + s = rc * T.c(b) + if dem and not (r * L / m < s <= L): bad.append(('source size', s, r)) + src_w += n * pr * dem; src_phi += n * pr * dem * s ** tau + if dem: src_sizes.add(s) + emax = max(ex_sizes) + bound = rmax * (L / m) ** theta if rmax > 1 else 1 + ubound = src_phi / (sum(Wt.values()) * kmin ** tau * (1 - kmin ** -tau)) + return dict(L=L, G=G, tau=tau, unbalanced_or_bad=len(bad), bad=bad[:3], sources=src_w, Phi_src=src_phi, + exits=ex_w, Phi_exit=ex_phi, Phi_ratio=ex_phi / src_phi, src_size_range=(min(src_sizes), max(src_sizes)), + exit_max=emax, exit_bound=bound, units=units, unit_bound=ubound, classes=sum(N.values()), + ex_sizes=ex_sizes, src_sizes=sorted(src_sizes)) + +def lockstep_literal(Wt, P_list, L): + """Explicit recursion over round sequences (P_list = ranks of rounds 1..P in word order).""" + Pd = {} + for r in P_list: Pd[r] = Pd.get(r, 0) + 1 + T = Tree(Wt, Pd, L); G = T.G + st = dict(classes=0, src=0, exits={}, issued_before_start=True) + def process(path, rho, fluid): + d = len(path); st['classes'] += 1 + us = T.units(d, rho) + need = T.demand(d, rho) + # fluid = parent's round output (points in R(parent rho)); top it up with sources, then it must equal need + for b, x in need.items(): + have = fluid.get(b, 0) + if have > x: raise AssertionError(('surplus', path, b, have, x)) + if have < x: st['src'] += x - have # source from the top split (always available) + for b in fluid: + if b not in need and fluid[b]: raise AssertionError(('unconsumed', path, b)) + for j, r in enumerate(P_list): # rounds in word order; round j+1 only after round j completes + out = dict(us) # one job of rank r per unit, at point a, size rho*r*c(a) + if d == G: + for a, ua in out.items(): + e = rho * r; st['exits'][e] = st['exits'].get(e, 0) + ua # handled by a new top call Do(e) + else: + process(path + (j,), rho * r, out) + process((), 1, {}) + return st, T + +if __name__ == "__main__": + rules = [("A: targets {4:1,3:2}, rounds [1,1,1,1,2,2]", {4: 1, 3: 2}, [1, 1, 1, 1, 2, 2]), + ("B: pure {7:2}+idle 3 -> targets {7:1,4:1}, rounds [1,1,1,1,2,2,2]", {7: 1, 4: 1}, [1, 1, 1, 1, 2, 2, 2]), + ("C: targets {5:1,4:3}, rounds [1]*6+[2]*2+[3]*2", {5: 1, 4: 3}, [1] * 6 + [2] * 2 + [3] * 2)] + print("(A) literal lockstep (explicit round sequences):", flush=True) + for name, Wt, rl in rules: + for L in (40, 150): + Pd = {} + for r in rl: Pd[r] = Pd.get(r, 0) + 1 + ref = check(Wt, Pd, L) + st, T = lockstep_literal(Wt, rl, L) + ok = (st['src'] == ref['sources'] and st['exits'] == ref['ex_sizes']) + print(f" {name}, L={L}: G={T.G}, classes {st['classes']}, every class exactly fed, sources {st['src']} " + f"(= merged count: {ok}), exits by size {dict(sorted(st['exits'].items()))}", flush=True) + print("(B) merged checks at larger L:", flush=True) + for name, Wt, rl in rules: + Pd = {} + for r in rl: Pd[r] = Pd.get(r, 0) + 1 + for L in (1000, 10 ** 5, 10 ** 7): + ch = check(Wt, Pd, L) + print(f" {name}, L={L}: tau_c={ch['tau']:.6f} G={ch['G']} classes={ch['classes']} bad={ch['unbalanced_or_bad']} " + f"sources in {ch['src_size_range']} (L/m={L/max(Wt):.1f}); Phi_exit/Phi_src={ch['Phi_ratio']:.12f}; " + f"max exit {ch['exit_max']} <= bound {ch['exit_bound']:.1f}; units {float(ch['units']):.4g} <= " + f"bound {ch['unit_bound']:.4g}", flush=True) diff --git a/research/direct-mixed-flow/verify.py b/research/direct-mixed-flow/verify.py new file mode 100644 index 0000000000..c0dd794858 --- /dev/null +++ b/research/direct-mixed-flow/verify.py @@ -0,0 +1,232 @@ +#!/usr/bin/env python3 +"""Partial direct compiler, nested integer batches and exact size controls. + +The near-root direct exponent theorem remains open. No floating-point result +is used by this verifier. zxv with OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha1, sha256 +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def source(path): + env = {'__file__': str(path), '__name__': 'pinned_or_local_library'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + return env + + +FLOW = source(HERE/'flow.py') +Flow = FLOW['Flow'] + + +def authenticate(): + result = {} + prefix = Path('research/direct-mixed-flow/vendor') + for row in json.loads((HERE/'VENDOR.json').read_text())['files']: + raw = (HERE/'vendor'/Path(row['path']).relative_to(prefix)).read_bytes() + digest = sha256(raw).hexdigest() + need(digest == row['sha256'], 'changed source: '+row['path']) + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'changed Git source blob') + result[row['path']] = digest + return result + + +def bigint_record(n): + return {'bits': n.bit_length(), + 'unsigned_big_endian_sha256': sha256(n.to_bytes((n.bit_length()+7)//8, 'big')).hexdigest()} + + +def ratio_interval(n, d): + scale = 10**18 + low = n*scale//d + return {'lower': str(Q(low, scale)), 'upper': str(Q(low+1, scale))} + + +def compile_counts(targets, paid, maximum, force_unit_replication=False): + m, W, calls = max(targets), sum(targets.values()), sum(paid.values()) + surplus = sum(k*v for k, v in targets.items())-sum(k*v for k, v in paid.items()) + need(surplus > 0, 'positive raw rank-one surplus') + widths = [1]*(maximum+1) + leaves = list(range(maximum+1)) + units = [0]*(maximum+1) + columns = [0]*(maximum+1) + slots = [0]*(maximum+1) + largest_sources = 1 + for n in range(m, maximum+1): + f = Flow(targets, paid, n).merged() + a = 1 if force_unit_replication else widths[n-1] + widths[n] = a*f['source_count'] + leaves[n] = 0 + units[n] = a*f['units'] + columns[n] = a*f['column_mass'] + slots[n] = a*(f['source_count']+sum(f['exits'].values())+(W+calls)*f['units']) + for histogram, complement in [(f['sources'], True), (f['exits'], False)]: + for rank, count in histogram.items(): + e = n-rank if complement else rank + need(0 <= e < n, 'all recursive ranks strictly decrease') + need(a % widths[e] == 0, 'whole integer subprogram batches') + copies = count*(a//widths[e]) + for records in (leaves, units, columns, slots): + records[n] += copies*records[e] + need(widths[n] % widths[n-1] == 0, 'nested divisibility') + need(widths[n]*n-leaves[n] == surplus*columns[n], 'whole-word rank-one identity') + need(units[n] <= columns[n] <= widths[n]*n//surplus, 'owned-unit upper bound') + need(slots[n] <= 2*(W+calls)*units[n], 'all compiler routing slots counted') + largest_sources = max(largest_sources, f['source_count']) + f = Flow(targets, paid, maximum).merged() + Cmax = W*(W+calls+1)**(f['height']+1) + need(largest_sources <= Cmax and widths[maximum] <= Cmax**maximum, + 'single-exponential width envelope') + n = maximum + return {'n': n, 'productive_width': bigint_record(widths[n]), + 'paid_rank_one_leaves': bigint_record(leaves[n]), + 'raw_instances': bigint_record(units[n]), + 'column_mass': bigint_record(columns[n]), + 'routing_slots': bigint_record(slots[n]), + 'leaves_per_array': ratio_interval(leaves[n], widths[n]), + 'width_exponent_envelope': Cmax.bit_length()*n, + 'source_count_upper': Cmax, 'rank_one_surplus': surplus, + 'paid_above_99_percent_linear': leaves[n] > 99*widths[n]*n//100, + 'nested_batch_checks': maximum-m+1}, (widths, leaves, units, columns, slots) + + +def finite_flows(): + rules = [ + ('separated-control', {3:2, 4:1}, {1:4, 2:2}, [1,1,1,1,2,2]), + ('strict-overlap', {2:1, 5:1}, {1:2, 4:1}, [1,1,4]), + ('source-open-equality', {2:4, 3:1}, {1:6, 2:2}, [1]*6+[2]*2), + ] + old = source(HERE/'vendor/tree_flow.py') + rows = [] + for label, targets, paid, word in rules: + for n in (20, 40, 80): + f = Flow(targets, paid, n) + merged, literal = f.merged(), f.literal(word) + need(merged['sources'] == literal['sources'] and merged['exits'] == literal['exits'], + 'literal and merged whole-job flow agree') + if label == 'separated-control': + predecessor, _ = old['lockstep_literal'](targets, word, n) + need(merged['source_count'] == predecessor['src'] and + merged['exits'] == predecessor['exits'], 'unchanged separated predecessor') + need(not merged['boundary_exits'], 'separated case has no premature exits') + rows.append({'rule': label, 'targets': targets, 'paid': paid, + 'flow': merged, 'literal_classes': literal['classes']}) + strict = Flow({2:1, 5:1}, {1:2, 4:1}, 20).merged() + mass = lambda h: sum(k*v for k, v in h.items()) + without_boundary = strict['exits']-strict['boundary_exits'] + need(strict['boundary_exits'] and + mass(strict['sources'])-mass(without_boundary) > + strict['rank_one_surplus']*strict['column_mass'], 'omitted boundary exits undercharge') + return rows + + +def inherited_rank_size_bound(): + old = json.loads((HERE/'vendor/higher-moment-RESULT.json').read_text()) + p7 = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['strictification'] + T = {int(k): v for k, v in p7['targets'].items()} + P = {int(k): v for k, v in p7['paid'].items()} + v = old['strictification']['tensor_power'] + H = old['uniform_rank']['H'] + need((v, H) == (150, 349300000000), 'unchanged sufficient ambient rank') + W = sum(T.values())**v + paid_mass_upper = sum(k*n for k, n in P.items())**v+W*15**v + need(W < 2**1950, 'productive field exponent envelope') + need(paid_mass_upper < 2**2701 and W+paid_mass_upper+1 < 2**2702, + 'every padded/split paid call counted by its positive rank mass') + D = 1950+2702*(H+1) + need(sum(k*n for k, n in T.items())-sum(k*n for k, n in P.items()) == 608, + 'underlying raw p7 rank-one surplus') + return {'kappa': old['kappa'], 'H': H, 'N': '2^'+str(H), 'D': D, + 'width_bound': 'B_N < 2^(D * 2^H)', + 'paid_leaf_bound': 'P_N < B_N * 2^H', + 'raw_p7_instance_bound': 'U_raw <= (B_N * 2^H - P_N)/608', + 'owned_p7_center_bound': 'one per raw instance; <= B_N * 2^H / 608', + 'routing_macro_record_bound': + 'R <= (A + 16*(W+P) + 1) * B_N * N; A is the complete fixed-unit record allowance', + 'routing_slot_bound': 'slots <= 2*(W+P)*V, V completed-unit instances', + 'physical_scope': 'Encoded whole-job adapter/move records. Their permitted physical implementation and tariffs remain inherited, separately priced premises.', + 'winning_uniform_word_materialized': False} + + +def verify(): + inputs = authenticate() + flows = finite_flows() + toy = [] + for T, P in [({2:1, 5:1}, {1:2, 4:1}), ({2:4, 3:1}, {1:6, 2:2})]: + row, _ = compile_counts(T, P, 100) + toy.append(row) + p7 = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['strictification'] + T, P = ({int(k): v for k, v in p7[key].items()} for key in ('targets', 'paid')) + direct, counts = compile_counts(T, P, 1000) + B, paid = counts[0][1000], counts[1][1000] + need(paid > 990*B, 'exact direct rank-1000 saving is below target') + kappa = Q('0.00268647') + # ln(2)>2/3 by its first atanh term. 1000>2^9 implies ln(1000)>6. + # exp(x)>1+x then gives 1000^kappa > 1+6*kappa > 100/99. + need(1000 > 2**9 and 1+6*kappa > Q(100,99), 'exact target comparison') + direct['target_failure'] = {'kappa': str(kappa), + 'proved': 'L(1000) > 990 > 1000^(1-kappa)', + 'scope': 'This particular finite rank fails; no asymptotic impossibility claim.'} + rejected = [] + try: + compile_counts({2:1, 5:1}, {1:2, 4:1}, 10, force_unit_replication=True) + except ValueError as e: + need(str(e) == 'whole integer subprogram batches', 'correct missing-batch rejection') + rejected.append(str(e)) + else: + raise ValueError('unit-replication mutant accepted') + try: + Flow({2:1, 5:1}, {1:1, 5:1}, 20) + except ValueError as e: + need(str(e) == 'finite direct-flow rank contract', 'nondecreasing exit rejected') + rejected.append(str(e)) + else: + raise ValueError('nondecreasing-exit mutant accepted') + return {'schema': 'partial-direct-mixed-flow-and-finite-size/1', + 'status': 'PASS_PARTIAL_DIRECT_FLOW_AND_SIZE_BOUNDS', + 'direct_exponent_theorem_established': False, + 'finite_flows': flows, 'exact_toy_compilations': toy, + 'exact_p7_direct_compilation': direct, + 'existing_supplier_size_bounds': inherited_rank_size_bound(), + 'rejected_mutations': rejected, 'source_sha256': inputs, + 'new_code_sha256': {f: sha256((HERE/f).read_bytes()).hexdigest() + for f in ('flow.py', 'verify.py')}, + 'scope': 'New finite matching/scheduling and batching/size bounds. The direct near-root exponent is open. Existing conditional endpoint and native/physical hypotheses remain inherited; no new kappa.'} + + +def normalize(x): + if isinstance(x, dict): + return {str(k): normalize(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [normalize(v) for v in x] + return x + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = normalize(verify()) + if args.out: + need(not args.out.exists(), 'new output path required') + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt') + print(json.dumps({'status': result['status'], 'direct_exponent_theorem': False, + 'p7_width_bits_at_1000': result['exact_p7_direct_compilation']['productive_width']['bits'], + 'target_failure': result['exact_p7_direct_compilation']['target_failure']['proved']})) + + +if __name__ == '__main__': + main() From 3e50dabb65bef74bd6be865eb0e2b41e1705add3 Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 15:13:48 -0400 Subject: [PATCH 02/26] Bound the completed word and inherited precision constants without materialization --- research/direct-mixed-flow/README.md | 113 +- research/direct-mixed-flow/RESULT.json | 17 +- research/direct-mixed-flow/TASK.json | 16 +- research/direct-mixed-flow/VENDOR.json | 21 + research/direct-mixed-flow/VERIFY.json | 5 +- .../direct-mixed-flow/vendor/P7-FACTOR.json | 5114 +++++++++++++++++ .../THREE-base-FULL-IDENTITY-NATIVE.json.gz | Bin 0 -> 198063 bytes .../direct-mixed-flow/vendor/p7-NATIVE.md | 180 + research/direct-mixed-flow/verify.py | 40 +- 9 files changed, 5480 insertions(+), 26 deletions(-) create mode 100644 research/direct-mixed-flow/vendor/P7-FACTOR.json create mode 100644 research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz create mode 100644 research/direct-mixed-flow/vendor/p7-NATIVE.md diff --git a/research/direct-mixed-flow/README.md b/research/direct-mixed-flow/README.md index 65da945a22..68af46c23d 100644 --- a/research/direct-mixed-flow/README.md +++ b/research/direct-mixed-flow/README.md @@ -52,7 +52,7 @@ the predecessor leaves productive width and owned-instance counts implicit. | Source complements and full uniform output | Source integer-batch induction, with nested divisible widths | | Direct near-root saving | **Open**; rank 1,000 fails; no global conclusion | | Productive width, rank-one leaves, raw instances, owned centers | Explicit bounds below, with exact finite controls | -| Routing slots and encoded adapter/move records | Counted in the stated macro grammar; physical implementations retain their own tariffs | +| Routing slots, encoded records and source finite-constant envelopes | Counted below in the stated grammar; physical implementations retain their own tariffs | | Native all-column, physical, analytic, precision and recovery premises | Inherited; no full replay or new admission | ## 2. Partially matched integer lockstep flow @@ -230,19 +230,24 @@ each call contributes its own local unit instances. Exact compilation checks this identity alongside widths and leaves. In the macro grammar that records a whole-job adapter, inverse adapter or -whole-field move as one record, a slot can be handled with at most eight -records: up to two whole-job conjugations and their inverses, and park/load/ -return/reorder moves. Allocate separate owned scratch for those moves when -needed; no zero-cost routing or free copying is assumed. If A is the complete -fixed unit's nonrecursive record allowance, including its owned operations, -the final macro word satisfies the conservative bound +whole-field move as one record, a slot can be handled with at most sixteen +records: up to two whole-job conjugations and their inverses, park/load/ +return/reorder moves, and explicit scratch initialization and erasure. +Allocate separate owned scratch for those moves when needed; no zero-cost +routing or free copying is assumed. Let A bound the fixed unit's complete +nonrecursive record count, owned operations and scalar coefficient heights. +The final weighted record allowance satisfies the conservative bound ``` -R_macro <= A*U_N + 16*(W+P)*U_N + P_N - <= (A+16*(W+P)+1)*B_N*N, for Delta>=1. +R_bar <= A*U_N + 32*(W+P)*U_N + P_N + <= (A+32*(W+P)+1)*B_N*N, for Delta>=1. ``` -This is a **description/record bound**, not a new tariff for executing a +R_bar bounds both the macro count and the sum of scalar-height and native +record allowances. Every owned bank has an explicit initialization record, +so total allocated owned banks can also be bounded by R_bar; the sharper +raw-center bound remains separate. This is a **description/record bound**, +not a new tariff for executing a general matrix or permutation. A dense binary address matrix and quadratic phase have O(N^2) descriptor bits. Explicit role indices add O(log B_N) bits. Thus an encoding of this finite word still has @@ -296,7 +301,81 @@ one-center-per-instance allocation. These are large upper bounds, not emitted words, smallest widths or practical precision estimates. They replace one implicit part of the source finite-constant prescription. The native adapter bodies, analytic transfer and physical costs retain their original -conditions; full numerical precision and tape thresholds are not closed here. +conditions; a closed bound for the source's finite-constant prescription is +given next, without a new physical runtime or exact-recovery threshold. + +### A closed envelope for the source finite constants + +The exported THREE-base native word has exactly 22,633 records in each +orientation. Source-bound counting retains all 15 copies, the literal p7 +controller, scalar allowance 2,490,856, every productive/paid/contact/helper/ +idle slot, and all routing and owned operations. A raw macro allowance is + +``` +A_raw = 15*8*(decompressed native JSON bytes) + + 8*(literal controller JSON bytes) + + 32*(2490856 + all declared slots + 15*22633) < 2^40. +``` + +The payload-bit terms overcount the coefficient literals and full local +descriptors, including both orientations. The 32-per-slot term overcounts +whole-job normalizers and inverses, field movements, initialization and +erasure. It is a bound on the declared source word in this grammar, not +independent verification of its functional correctness or physical tariffs. + +For the chronological v-fold product, its number of raw p7 invocations is + +``` +U_v = sum_(i=0..v−1) 7688^(v−1−i)*55998^i < 2^2392. +``` + +At every product level retain the whole-job matching wrappers. A conservative +product allowance is + +``` +A_product <= (2^40 + 32*v*(7688+55998+1))*U_v + 32*v*55998^v. +``` + +Add 32 records for every final paid call, completion role and original paid +position. Counting paid calls by their rank mass gives + +``` +A_completed <= A_product + + 32*(131115^v + 7688^v*15^v + 7688^v + 55998^v). +``` + +A dense local binary map/quadratic phase and role index fit in +`64*(121^v)^2` bits per such record. The verifier checks the integer bound +`A_completed * 64*(121^v)^2 < 2^5000`. Thus **A=2^5000** is a valid weighted +record/description allowance for this fixed completed unit. It includes all +source coefficients and owned operations, with a large deliberate overcount. +No instruction list of the completed product is emitted. + +Since `A+32*(W+P)+1 < 2^5001`, use the envelope + +``` +R_bar < 2^(D*2^H + H + 5001). +``` + +Apply the existing source finite-constant prescription to the **newly expanded +word**. With Z=B_N+owned banks, G its scalar coefficient envelope, and P_N +its rank-one leaves, we have `Z<=2*R_bar`, `G<=8*R_bar`, `P_N<=R_bar` and +`N<=R_bar`. Therefore + +``` +E = 64*(Z+N+P_N+G+1)^3 + < 2^(3*D*2^H + 3*H + 15021), +B_constant = P_N+E, +C0 = 32*N*B_constant^2 + < 2^(6*D*2^H + 7*H + 30049) + < 2^(8*D*2^H). +``` + +The last comparison uses `2^H>=H+1` and an exact polynomial integer check +on D and H. These are explicit, very loose upper bounds for the inherited +semantic precision/stock constants, conditional on that source prescription +and its admitted native record implementations. The exact numerical outer +input threshold, prime exclusions and physical tape costs remain separate. ## 5. Exact finite checks and the open exponent gate @@ -365,7 +444,7 @@ the verifier independently compares its merged and literal traversal outputs. Those are two internal implementations, not an independent mathematical review. Canonical base is `12fa8c5c844be21bfefb38a19503fbd867a11244`, priority revision -7. SOURCES.json pins orientation metadata. VENDOR.json separately binds eight +7. SOURCES.json pins orientation metadata. VENDOR.json separately binds eleven unchanged exports by commit, full path, Git blob and SHA256. Their bytes and notices are preserved; direct replay needs no foreign Git objects. The source theorem and earlier finite compiler remain attributed hypotheses, not new work. @@ -384,11 +463,11 @@ claim or PR has been posted for this partial checkpoint. with a proved bound on premature-exit potential relative to the actual complement capacity. This decides whether the flow can replace the tensor/padding layer. A larger rank scan is not a uniform proof. -2. **Finish physical word and precision bounds.** Bind the macro-record - allowance A and each adapter's actual implementation to the fixed native - caller; insert their coefficient heights, routing scratch and movement - counts into the source precision/stock formulas. Macro description size - is not a physical execution tariff. +2. **Independently admit the physical expansions and precision prescription.** + Audit the conservative A allowance against the actual native caller and + bind every adapter's physical implementation, row movements and recovery + exclusions. The encoded constants above use the inherited semantics; + description size is not a physical execution tariff. 3. **Tighten the constructive width.** The nested product is an explicit upper bound, not an optimized LCM. A useful next step would control prime valuations of the actual source counts; another arbitrary batching choice diff --git a/research/direct-mixed-flow/RESULT.json b/research/direct-mixed-flow/RESULT.json index e2f0b121eb..4f305a54c0 100644 --- a/research/direct-mixed-flow/RESULT.json +++ b/research/direct-mixed-flow/RESULT.json @@ -107,13 +107,23 @@ "D": 943808600004652, "H": 349300000000, "N": "2^349300000000", + "compiled_record_upper": "R < 2^(D*2^H + H + 5001)", + "completed_unit_description_upper": "2^5000", "kappa": "268647/100000000", "owned_p7_center_bound": "one per raw instance; <= B_N * 2^H / 608", "paid_leaf_bound": "P_N < B_N * 2^H", "physical_scope": "Encoded whole-job adapter/move records. Their permitted physical implementation and tariffs remain inherited, separately priced premises.", + "raw_macro_allowance_upper": "2^40", + "raw_macro_and_payload_allowance": 319592968, + "raw_native_record_counts": { + "backward": 22633, + "forward": 22633 + }, "raw_p7_instance_bound": "U_raw <= (B_N * 2^H - P_N)/608", - "routing_macro_record_bound": "R <= (A + 16*(W+P) + 1) * B_N * N; A is the complete fixed-unit record allowance", + "routing_macro_record_bound": "R <= (A + 32*(W+P) + 1) * B_N * N; A < 2^5000", "routing_slot_bound": "slots <= 2*(W+P)*V, V completed-unit instances", + "source_C0_upper": "C0 < 2^(8*D*2^H)", + "source_precision_E_upper": "E < 2^(3*D*2^H + 3*H + 15021)", "width_bound": "B_N < 2^(D * 2^H)", "winning_uniform_word_materialized": false }, @@ -470,7 +480,7 @@ ], "new_code_sha256": { "flow.py": "460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a", - "verify.py": "8104bbaac3afb1910290f97965503564f4299f3d6008af0b043742e9baffcead" + "verify.py": "80ba21844b4f77b865091969edf9b8826362754df5efe714d366ee245ebf182f" }, "rejected_mutations": [ "whole integer subprogram batches", @@ -480,10 +490,13 @@ "scope": "New finite matching/scheduling and batching/size bounds. The direct near-root exponent is open. Existing conditional endpoint and native/physical hypotheses remain inherited; no new kappa.", "source_sha256": { "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "research/direct-mixed-flow/vendor/P7-FACTOR.json": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e", + "research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39", "research/direct-mixed-flow/vendor/higher-moment-README.md": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", "research/direct-mixed-flow/vendor/higher-moment-RESULT.json": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156", + "research/direct-mixed-flow/vendor/p7-NATIVE.md": "26bf9312cdb496b1113c9ddd8aa0fa922ed9e480005703212942af358394183d", "research/direct-mixed-flow/vendor/p7-RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab", "research/direct-mixed-flow/vendor/theorem-1g.md": "c4a96c55c2509ff36e8bc6bddaaf6a8b1a34a5d794e4e09ac5214c82b51510e6", "research/direct-mixed-flow/vendor/tree_flow.py": "750782f6d1cc0a9fff8a768899f3f4c62a7efdf0696d8b5a5d640b1836f5ab72" diff --git a/research/direct-mixed-flow/TASK.json b/research/direct-mixed-flow/TASK.json index 5522334d94..2164fdf04b 100644 --- a/research/direct-mixed-flow/TASK.json +++ b/research/direct-mixed-flow/TASK.json @@ -76,7 +76,7 @@ "budget_minutes": 60, "stop_rule": "First prove exact whole-integer matching, chronological return, top sources and smaller exits. Then test whether the complete recurrence supports the desired exponent. Do not infer exponent admission from moment balance. If it fails, preserve the first counterexample or missing lemma and the explicit-size result; no broader census or new kappa claim.", "outcome": "partial", - "evidence": "README.md proves the finite partially matched direct compiler and exp(O(N log N)) productive-width bound. RESULT.json checks nine literal/merged flows, two full overlap compilations through rank 100, 880 exact p7 nonbase compilations through rank 1000, global surplus and routing-slot bounds. The direct exponent target remains open; rank 1000 fails.", + "evidence": "README.md proves the finite partial-matching compiler, nested exp(O(N log N)) widths, raw/owned/routing bounds and closed encoded precision envelopes for the existing PR4433 supplier. RESULT.json checks source record counts and all integer inequalities, nine literal/merged flows, two overlap compilations through rank 100, and 880 p7 nonbase compilations through rank 1000. Direct near-root exponent remains open.", "author": "zxv, with substantial OpenAI Codex assistance", "ai_assistance": "Substantial OpenAI Codex assistance; no subagents.", "open_questions": [ @@ -87,10 +87,10 @@ "blocked_by": "No uniform boundary-exit bound or direct exponent proof yet." }, { - "question": "Can nested divisible widths and rank-one potential bound the whole expanded program?", - "why_it_matters": "It would control widths, owned centers and precision constants beyond ambient rank.", - "first_step": "Choose B_n=S_n B_(n-1), prove every smaller width divides it, and telescope the exact rank-one surplus over all raw instances.", - "blocked_by": "Full route/record counting and endpoint binding remain to be written." + "question": "Do the complete encoded resource and precision envelopes survive independent native/physical admission?", + "why_it_matters": "The closed numerical envelopes depend on the source finite-record semantics and do not independently establish their physical tariffs or recovery threshold.", + "first_step": "Audit the raw/whole-job record allowance against the caller, then separately bind physical adapters, movement and recovery exclusions.", + "blocked_by": "Inherited native/physical/analytic premises remain outside this mathematical count proof." } ], "publication_policy": "LOCAL ONLY until user review. Do not push, submit another PR or post Discussions.", @@ -120,5 +120,11 @@ ], "specific_matches": "No matching public scope found; the later search matches this local task itself. This is not proof of novelty.", "limits": "Open bodies, discussions and local notes; no arbitrary remote code-diff or remote closed-body search." + }, + "scope_deliverables": { + "finite_direct_compiler": "proved under inherited native/adapter hypotheses; max paid < ambient, no near-root saving yet", + "full_finite_size_bounds": "proved in declared encoded native-record grammar; explicit bounds for the existing PR4433 supplier", + "direct_near_root_exponent": "open; requires a uniform boundary-exit/complement estimate", + "scientific_significance_target": "in progress; not claimed achieved" } } diff --git a/research/direct-mixed-flow/VENDOR.json b/research/direct-mixed-flow/VENDOR.json index b05d41179f..d95b1124e8 100644 --- a/research/direct-mixed-flow/VENDOR.json +++ b/research/direct-mixed-flow/VENDOR.json @@ -56,6 +56,27 @@ "path": "research/direct-mixed-flow/vendor/p7-RESULT.json", "git_blob": "ebb30a9b3b94fb159a316350f7da57bde4a30c25", "sha256": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "path": "research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "commit": "e9058860b5c850760fdf970e796a96aefcdb1d98", + "original_path": "research/pr4359-p7-padding/P7-FACTOR.json", + "path": "research/direct-mixed-flow/vendor/P7-FACTOR.json", + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598" + }, + { + "commit": "e9058860b5c850760fdf970e796a96aefcdb1d98", + "original_path": "research/pr4359-p7-padding/NATIVE.md", + "path": "research/direct-mixed-flow/vendor/p7-NATIVE.md", + "git_blob": "394d9a03c165336d1cfbcd41921c93741042393b", + "sha256": "26bf9312cdb496b1113c9ddd8aa0fa922ed9e480005703212942af358394183d" } ] } diff --git a/research/direct-mixed-flow/VERIFY.json b/research/direct-mixed-flow/VERIFY.json index 690caa1ac7..de075b7c20 100644 --- a/research/direct-mixed-flow/VERIFY.json +++ b/research/direct-mixed-flow/VERIFY.json @@ -12,6 +12,9 @@ "research/direct-mixed-flow/vendor/higher-moment-README.md", "research/direct-mixed-flow/vendor/higher-moment-RESULT.json", "research/direct-mixed-flow/vendor/p7-RESULT.json", + "research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/direct-mixed-flow/vendor/P7-FACTOR.json", + "research/direct-mixed-flow/vendor/p7-NATIVE.md", "research/direct-mixed-flow/VENDOR.json" ], "commands": [ @@ -22,7 +25,7 @@ "{package}/verify.py" ], "timeout_seconds": 120, - "checks": "Exact partially matched whole-job flows, chronological literal/merged controls, nested batching through p7 rank 1000, telescoped size bounds and rejected omissions. No direct exponent theorem." + "checks": "Exact partially matched flows, nested widths and global resource counts; source-bound finite-word/precision envelopes; rank-1000 direct-target rejection. No direct exponent theorem." } ] } diff --git a/research/direct-mixed-flow/vendor/P7-FACTOR.json b/research/direct-mixed-flow/vendor/P7-FACTOR.json new file mode 100644 index 0000000000..04c7ef620e --- /dev/null +++ b/research/direct-mixed-flow/vendor/P7-FACTOR.json @@ -0,0 +1,5114 @@ +{ + "all_boundary_entries_integral": true, + "coefficient_matrices": [ + { + "exponents": [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + -1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix": [ + [ + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + -1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix": [ + [ + "0", + "0", + "-1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + -1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "-1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + -1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + { + "exponents": [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + 1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + }, + { + "exponents": [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + "matrix": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ] + } + ], + "coefficient_variables": [ + "Q", + "D0", + "D1", + "D2", + "D3", + "D4", + "D5", + "D6", + "D7", + "D8", + "D9", + "D10", + "D11", + "D12", + "D13", + "D14" + ], + "endpoint_after_stated_free_Pauli_normalization": { + "121": 224, + "25": 448, + "41": 448, + "57": 448 + }, + "exact_diagonal_monomials": [ + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + [ + -1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ], + [ + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1 + ] + ], + "full_Laurent_identity": true, + "keep_idle_mask": 232127, + "left": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "left_program": [ + [ + "SWAP", + 11, + 12 + ], + [ + "SWAP", + 8, + 12 + ], + [ + "SCALE", + 7, + "-1" + ], + [ + "SWAP", + 7, + 13 + ], + [ + "ADD", + 4, + 6, + "1" + ], + [ + "ADD", + 2, + 6, + "-1" + ], + [ + "ADD", + 0, + 6, + "1" + ], + [ + "ADD", + 13, + 5, + "1" + ], + [ + "SWAP", + 5, + 12 + ], + [ + "ADD", + 2, + 4, + "1" + ], + [ + "ADD", + 0, + 4, + "-1" + ], + [ + "SWAP", + 4, + 5 + ], + [ + "ADD", + 13, + 3, + "-1" + ], + [ + "ADD", + 12, + 3, + "-1" + ], + [ + "SCALE", + 3, + "-1" + ], + [ + "SWAP", + 3, + 11 + ], + [ + "ADD", + 0, + 2, + "1" + ], + [ + "SWAP", + 2, + 4 + ], + [ + "ADD", + 13, + 1, + "1" + ], + [ + "ADD", + 12, + 1, + "1" + ], + [ + "ADD", + 11, + 1, + "1" + ], + [ + "SWAP", + 1, + 10 + ], + [ + "SWAP", + 0, + 3 + ] + ], + "maximum_boundary_absolute_coefficient": "1", + "native_operator_contract_independently_replayed": false, + "omitted_idle_windows": [ + { + "index": 6, + "kind": "initial", + "pair": 4, + "rank": 64, + "retained": false, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7 + ] + }, + { + "index": 8, + "kind": "initial", + "pair": 5, + "rank": 80, + "retained": false, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9 + ] + }, + { + "index": 10, + "kind": "initial", + "pair": 6, + "rank": 96, + "retained": false, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11 + ] + }, + { + "index": 12, + "kind": "terminal", + "pair": 0, + "rank": 96, + "retained": false, + "stages": [ + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14 + ] + }, + { + "index": 13, + "kind": "terminal", + "pair": 1, + "rank": 80, + "retained": false, + "stages": [ + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14 + ] + }, + { + "index": 14, + "kind": "terminal", + "pair": 2, + "rank": 64, + "retained": false, + "stages": [ + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14 + ] + } + ], + "pairs": 7, + "physical_events": [ + [ + "LOCAL", + 0, + 0, + false + ], + [ + "LOCAL", + 1, + 0, + true + ], + [ + "IDLE", + 1, + [ + 0, + 1 + ] + ], + [ + "ADD", + 0, + 2, + 1 + ], + [ + "ADD", + 3, + 1, + -1 + ], + [ + "LOCAL", + 2, + 0, + false + ], + [ + "IDLE", + 1, + [ + 2 + ] + ], + [ + "ADD", + 0, + 2, + -1 + ], + [ + "ADD", + 3, + 1, + 1 + ], + [ + "LOCAL", + 3, + 1, + true + ], + [ + "IDLE", + 2, + [ + 0, + 1, + 2, + 3 + ] + ], + [ + "ADD", + 2, + 4, + 1 + ], + [ + "ADD", + 5, + 3, + -1 + ], + [ + "LOCAL", + 4, + 1, + false + ], + [ + "IDLE", + 2, + [ + 4 + ] + ], + [ + "ADD", + 2, + 4, + -1 + ], + [ + "ADD", + 5, + 3, + 1 + ], + [ + "LOCAL", + 5, + 2, + true + ], + [ + "IDLE", + 3, + [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + ], + [ + "ADD", + 4, + 6, + 1 + ], + [ + "ADD", + 7, + 5, + -1 + ], + [ + "LOCAL", + 6, + 2, + false + ], + [ + "IDLE", + 3, + [ + 6 + ] + ], + [ + "ADD", + 4, + 6, + -1 + ], + [ + "ADD", + 7, + 5, + 1 + ], + [ + "LOCAL", + 7, + 3, + true + ], + [ + "ADD", + 6, + 8, + 1 + ], + [ + "ADD", + 9, + 7, + -1 + ], + [ + "LOCAL", + 8, + 3, + false + ], + [ + "IDLE", + 4, + [ + 8 + ] + ], + [ + "ADD", + 6, + 8, + -1 + ], + [ + "ADD", + 9, + 7, + 1 + ], + [ + "LOCAL", + 9, + 4, + true + ], + [ + "ADD", + 8, + 10, + 1 + ], + [ + "ADD", + 11, + 9, + -1 + ], + [ + "LOCAL", + 10, + 4, + false + ], + [ + "IDLE", + 5, + [ + 10 + ] + ], + [ + "ADD", + 8, + 10, + -1 + ], + [ + "ADD", + 11, + 9, + 1 + ], + [ + "LOCAL", + 11, + 5, + true + ], + [ + "ADD", + 10, + 12, + 1 + ], + [ + "ADD", + 13, + 11, + -1 + ], + [ + "LOCAL", + 12, + 5, + false + ], + [ + "IDLE", + 6, + [ + 12 + ] + ], + [ + "ADD", + 10, + 12, + -1 + ], + [ + "ADD", + 13, + 11, + 1 + ], + [ + "LOCAL", + 13, + 6, + true + ], + [ + "LOCAL", + 14, + 6, + false + ], + [ + "IDLE", + 3, + [ + 9, + 10, + 11, + 12, + 13, + 14 + ] + ], + [ + "IDLE", + 4, + [ + 11, + 12, + 13, + 14 + ] + ], + [ + "IDLE", + 5, + [ + 13, + 14 + ] + ], + [ + "ADD", + 12, + 10, + 1 + ], + [ + "ADD", + 11, + 13, + -1 + ], + [ + "ADD", + 10, + 8, + 1 + ], + [ + "ADD", + 9, + 11, + -1 + ], + [ + "ADD", + 8, + 6, + 1 + ], + [ + "ADD", + 7, + 9, + -1 + ], + [ + "ADD", + 6, + 4, + 1 + ], + [ + "ADD", + 5, + 7, + -1 + ], + [ + "ADD", + 4, + 2, + 1 + ], + [ + "ADD", + 3, + 5, + -1 + ], + [ + "ADD", + 2, + 0, + 1 + ], + [ + "ADD", + 1, + 3, + -1 + ], + [ + "SIGNED_SWAP", + 0, + 1 + ], + [ + "SIGNED_SWAP", + 2, + 3 + ], + [ + "SIGNED_SWAP", + 4, + 5 + ], + [ + "SIGNED_SWAP", + 6, + 7 + ], + [ + "SIGNED_SWAP", + 8, + 9 + ], + [ + "SIGNED_SWAP", + 10, + 11 + ], + [ + "SIGNED_SWAP", + 12, + 13 + ] + ], + "retained_idle_windows": [ + { + "index": 0, + "kind": "initial", + "pair": 1, + "rank": 16, + "retained": true, + "stages": [ + 0, + 1 + ] + }, + { + "index": 1, + "kind": "middle", + "pair": 1, + "rank": 8, + "retained": true, + "stages": [ + 2 + ] + }, + { + "index": 2, + "kind": "initial", + "pair": 2, + "rank": 32, + "retained": true, + "stages": [ + 0, + 1, + 2, + 3 + ] + }, + { + "index": 3, + "kind": "middle", + "pair": 2, + "rank": 8, + "retained": true, + "stages": [ + 4 + ] + }, + { + "index": 4, + "kind": "initial", + "pair": 3, + "rank": 48, + "retained": true, + "stages": [ + 0, + 1, + 2, + 3, + 4, + 5 + ] + }, + { + "index": 5, + "kind": "middle", + "pair": 3, + "rank": 8, + "retained": true, + "stages": [ + 6 + ] + }, + { + "index": 7, + "kind": "middle", + "pair": 4, + "rank": 8, + "retained": true, + "stages": [ + 8 + ] + }, + { + "index": 9, + "kind": "middle", + "pair": 5, + "rank": 8, + "retained": true, + "stages": [ + 10 + ] + }, + { + "index": 11, + "kind": "middle", + "pair": 6, + "rank": 8, + "retained": true, + "stages": [ + 12 + ] + }, + { + "index": 15, + "kind": "terminal", + "pair": 3, + "rank": 48, + "retained": true, + "stages": [ + 9, + 10, + 11, + 12, + 13, + 14 + ] + }, + { + "index": 16, + "kind": "terminal", + "pair": 4, + "rank": 32, + "retained": true, + "stages": [ + 11, + 12, + 13, + 14 + ] + }, + { + "index": 17, + "kind": "terminal", + "pair": 5, + "rank": 16, + "retained": true, + "stages": [ + 13, + 14 + ] + } + ], + "right": [ + [ + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "right_program": [ + [ + "SCALE", + 13, + "-1" + ], + [ + "ADD", + 13, + 12, + "1" + ], + [ + "ADD", + 11, + 12, + "-1" + ], + [ + "SCALE", + 12, + "-1" + ], + [ + "ADD", + 12, + 11, + "-1" + ], + [ + "SCALE", + 11, + "-1" + ], + [ + "ADD", + 12, + 10, + "1" + ], + [ + "SWAP", + 8, + 11 + ], + [ + "SWAP", + 7, + 13 + ], + [ + "ADD", + 5, + 6, + "-1" + ], + [ + "ADD", + 4, + 5, + "-1" + ], + [ + "SWAP", + 5, + 8 + ], + [ + "ADD", + 3, + 4, + "-1" + ], + [ + "SWAP", + 4, + 8 + ], + [ + "SWAP", + 3, + 12 + ], + [ + "SWAP", + 2, + 8 + ], + [ + "SWAP", + 1, + 10 + ], + [ + "SWAP", + 0, + 12 + ] + ], + "stages": 15 +} diff --git a/research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz b/research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..b46d44c6ee624968dd57be928b0c15d9d45f3b2c GIT binary patch literal 198063 zcmZs?2{=^Y|NkvJV_(M37{k~}veV2M%!nDr5+a16WSL|uF&G)4SrD=fLsZr%OADgV zHpY^*ETa%Ak<#`|-|zqV{eRDOJ+9Z>=l-1goO2m-=02a#`+ifqD#-Qkhnr{P;dE2z zQGDH=;Rh=zAG;}r_54TCY~I+?3z=F2S^x*(Ovd$NTT@TAvtNDQO?4`i6Wx^+KbyK1 z{QOdT-^;(1@BTdh^mixq*N0E3Kc7eceSYNEljzjn&5!^7RC_#s`RC)m-)A5HUjF;% z{=2`kYJb1KdHnke_V2gm)E^)Ie*cjA^Ub?Q@BS>_SNj~8`twWb-}~>PY@hDknAq%8 ziBA2om%9Hu@bcf;*>{)!J`eO}{|RiI-kZH2fA-zGwGZ)+%0+*#Rkr-P{B!WJ+v9z? zrDJ~)pMGEe+yDL053CQI7yoT> z!bqt(6`Xph>;5M8fx4QW$AkTB^Y^pUuPXl#-(;+P+66=h{N8-?XJB@H|7t3Dw)qd~ zraw3=ZvSfD?9D~o$(9%VEyCcS)&($e*wFU~C@6=puR(&rW32@zCWpP#nDC$t{55_w{t;5m02m{%6jmEd?I~8}6qjG!nGJgDwZI9u+M+ z`p`tQ2h_XPzn0GbDi2g(D6f7eGjQy4-XnjZ<)7Q14Eb7?{n9R%<~-}*ioX>2XTFxp zqd4pLQ65hFb;HfsBwj|CL-slL0OnqUjy70qpqJ(teEVN zF~^>!0Rm$7ANtGl-0U2&avPE7ycwydu=0=vHy}7z=U(&R1!3+NMl%RWm;z6rVzGzB zf-=tt$TR-Qmkt#`PjH}!XP8cfR`^0Y%9YvsrvLZ1Pfe%$I=CLDUg(qHl@ApA)FgtC zdzJb1BkFyB>)d1DR>K`04-4@DOF`n--e1-BqcG`LJO-6z;TM&!T2q{bpEGr+B7%$T&F~9Dprn&)(2?+{|iZfYm^3@Z@jjsmrRWsbR(1Hu5!Z$pb&}V;wT4pAVmOIfw~p0qiGf$!u^RQRx{m zH4Rq$_Vq?)M0ns*d>F8ENy7@e-(SMSs!^71c>%#ct=0el_aky(8n478!RnFGPA%8z z0cT$!*J8e!BgE}*A)wTXo!t=&*{8iP4lA))7Ai-soqHq&vy^?~L5?zl{Y@hOr=}NG@_;%8#-B#8LK=rngtml9##d%H5i^UcHX5yRNs1z24IOt5?%b@r^+x zp}n)^4JJFsk&!RvsS=7O(p0oY^|7V`EVtQEDTp8LBPiX|{v0i( zo%~05tvUOTumQL*Xz~&Rde-$_3g4NrO5f%)V^ycOTE9nkgD?y+WA#r?r^=&(28)&s z0`m4-X&r5}^NsIq@^0(Du6)w}R+8ETxqWQRo^A$MX=)B1ItCO!WFp<_d=M(A@411gCuIY4~1>G1w2u1cEa84!-MXZ-wyfU z(;=-$fN!;UhozDDM~7GMi236j960T(He#7MQ90fr{}J)QMGg+%Y7nm~IDjt(G~Q0P z^Z5!hU5_88HeU!MYmWN+ImGXP-;UqKq_u2Te0Jdil-NVdkRri@f6|X^%Y2LB(G>HZ zkw__ro6L?;8(C;xcd;$NyrgZP(>LzVF#IK%m+rHU`!`Uj2=7(y1n@WI?22qh9;O&l zz>P#c+|`R_OPCGS7VxfL&R2-1BXS1$H^14UmWTI2`m^LalffqIcchCiRY{kW4{ab% z4gNG%r8Q0zW%M$7%I}~EMWY}O&7qxqFdpK&Nfj(-9H)kNTm9%S&DQd`4SPI?eP$(6 zH2<2`KGROC%P^hq#f=U7Hqh?kqG`R31A^Qc2Y*vC)JNusUdhyu_mF2VNcknwDu*h^ zRK2>@lfg3*y-q_6S>%56=Imm(#mtf_3_Z1H&_Z{Kz6f{tw;Iys%T!z&;=cFc-24u9_wH_rK! zxgXJT53Ht?hX%OCGj2NBdLCr53#r@{Z;!bLLr|2cf(nsx>@lD5I+7zpu#@&*isQ)x zy)Y6%d?lGHAX60?sR=N21Nz%!iFhSSS#U)P5ZsOS39G#6sH8LS?Q!nf3O=+gpg~jhTLHje)n+X$l63_&tq%(;r8uqpEdE9{}KBia$+F=10JWz zAtx5{|4Xd5Cf-}~U#p`T`yV)+|LOnFMMyDIa6{Lb1DF+nGE!p2^UwFT9*mxYC~$xO z(H1v$yq!`Eo4L&yjuHNXr8Jk4} zUWQTwGuKVZ29&|V2Tg4k9kXbmrG`6P8f*>7&HgN2bpb#F?+*mv1{@0SA_Dn6otzr; z^Zm+|{j5kMz5?!De5$+^yjr)s#Q-Xss~pNB6I3!^0z0KG({r!EgwfR>k@i@@C2&mxO8L)LQtg9z*ltr?mNI6j%XCq4Y%n`E^af<^ zG%fQdaE1heFYxY5aFYOcBJ-p}M`w9`cK|Qg#f%7z7^>^j!u7W4;F{m475 zq1X3?w!fZB|8?mG=zoRe58SjZG1fdBSPBBTRxPT9mb~H_q97B{aZq;F%-HQ^U6*7B zA-`E(_}Lqv@N?Ma%Bu*uAN^o^wD6T#-o=<3Amu2w>^D9`EnUrD_@`%g*1%dB@|uRQ*8C?L_@?;u|pa^=%=c{R0XuwVf$eQ zd-99WPp%khk?icw1Lrqfb9^NkWiOV$gf`vVV1$K<@mdwvd}z`~g_>~4);PqRwnQoX zq7~Vc5HPR*QC&fJH3RprWQ#3uTmNvhPpL_C&Pa3~-b82^RhP$9eUS;b(Rqa1HoZYV zp6?iCX&57AnX{@vX{zO|hFzKXhaD3ZyYSTyqUcWa)?R}suR@du1{K*LWk&BG1nq*C z)oitsuxNm92TbQUynp^5Wp_BR!v>|zpfTJQB>9mpvo|Fd`Q%0&>EV~v-<>0z+y(e^ zd7s=O{(7*RxbL}Q%xz88=!5DCB@m^ygvW0OE|5yKW~3{C0SjFF#$nRhQooEiv>D3| zL-pHoWYKo|pPB323Dx0H9xOUqoBGxbyHGD4_kICGB|QJpF|J4vA=1%zYQOEid<_pK|?(oJFskb3_H-tq(?@K?YbzyQHP? z(5N^QA00I9;ooqXtnmS@=Y%_x zDgjp#;#A&>ODXJSAfKuP80=+itOClj4H3{%D*6b`Di1Gih)z9)>ihHnTr$1W z?J=sJCl(;C)(Y74@~&RwDyUSfIzoMZNC_2qWD%m59yFW8lhFQVPq~1NTofb$z&5xrCUf0WRD|C`?(Xi0TD?U-K?@0vXMx&buE83O%e3AZz2-f zeB3%|KAA8qbF6<48W5_bYo7O@S=BnpSjRlC%v0`*SXAsq0m_+AAY4lSZ%~Xzi^}#sxpx6Fb>9{Vg$_7Fww187WWypL|`_1os6LB+x04{Nw=P zm@4y2DN;rgkQ2JwZ<}dgfE~#w0vssS0AHXbUeWp@<|;D{3*#&E6t-B*DlPIiVDJCs z*87=DJGu`rQ2t$3HlkAge>sjzv~@LxJbH#DA$+BU9Xwz_+0 zJzIc0@1#N9xKP>s5I1yz-$C_Z+c`cnQ2VLq>idW1EAx%2=NfD737okIR*Yzojp(8I z)=dwy`R~;@tpR5w4enU8`Ff;_@&icu0jus-SiGsTROwOtBpRO#7iX2X$ARG37naE< zqv$jyyr6MlR%&pTI`AKmgVc>g_F*fh=26R}z$gN(cLC6GPHWUVO||Cyj(oY?LE6>g zVd4um;uM~O%mI^R9HexFHE}W~u7EI{%m_o9igt(4s@)z1(PetUzKRZQra9~Y^79a= za{X)K#~{E){Tf$gF=`zNz*L99M;>YynEDKf=$-VHH7Ocexy6SWHyy1kxa|%(R)cDC zB>3l9z-AV>#krLvpP-*}o?0zcA1q+`mz5z-N5rT#Y62vWiXEAazZNLZLt+vWxf!85 z0!gZe#mJ*-0z<2TLC~2)kT_~xd9Iy$%@NMt)c)ACHCe{-^thwsU5%lA^~}g+F7;Up zSimm}lGMRYJILTdRe>c}`0iQiSUh4nmhvO? z4(~04CXOz1C0H!|dx8GDt)@u)Mu;N;r`L(`- z&oXA|{9B_=8hfiX1k=0WkeB+3=tEZ>Sud&yRKzF><7evTp{&Er79nS#E;=mUG*Psp>qkqF8`)YXwe%bua2Kq5+ z(fZY7#FJ(+LRg2vj5IQxy}I$pnUKvFRUct*>cg&emIb^t<@P?R<7KLdmd)eGIn+=* zM`_-MF@s|-mv#C_*19qjzXJSWVuR@9{tQ6_PhQ(ac!4=TA)^j9_U_8g$zp=IK`!md_y?p3f>g* z4FZ&L88X%pI5`RS*Rp07&Ga0v7Ol#hc@X!?hx`mD=TpqH%9=#$T~jh>kLmn&L3DBv zj2D6IYJ;-XchMMd+(j^RlN7U!bF?rCs{FdT7iVYZYVD9H;WPaiV7jcTm@8&Zb;p_0*6H zkKHc3IrbYC$D^jBT=q55M{E;z&S?5PF@isVw;q2H#(Y)JF)E-Zd#r0k_mfaM4lpfQ;``R zVxK8QU;|>g8TAg;+C)@^QGdQ~x<5a(y49$mINUg%W)aaAoX|H`xH&wst~lR(z6g_8 zRY$yTBWJ;7gML0nVtQwO%UZ>(%4cH650}6Qd|BDJx>E!w0evK1)1s9rI_i8xEat;O zf#J5-aQv)Xx1d2os7?93n<#OlQZ>(TdHv?kuGLY;i2Gj0C8iZ7!X|e((=!8&)E7INM(Jo3lA~@Xd&ni8|x2y zqrA}dUisP|XIZVY={1B8NR|HDSw1c4gUlvLY18u1e5kLR^f@PVR$TRN`;f6gd%4_9 z6`)a&xN|JrUbo#5Xk~{6ZiDVi1G_mhakZ=3+{oY+>8K#C%buVJu!~kY{^MbR#5T)k zHR30T#KDwwm+PE5!i*c5R%mk_a!n1A{0ao^3NK~bW|V=(!U$J~f*Bz%+{fVInqy&f z_hy0hA<$hI`hw*eG6aHt2U%ANyHOFotod3ElJo}zMaB6BnTQr}F3PW0S+GW3wavI6 ztS(pM$C)6>ACvq0SAI+16ACit(%WmpS`EtqCA-tAYxSz21_i&J1+Ghtp;_YyJ)AYF z)Ng^i1qhj1O=UU>c-w=_{u69p{3BZ!!oL>irkB$b2^L=U^}sMqRSbV}Y>Rk%isLXu%$ z^_Wgt3JqxQj}Y4$wq->-{?4~&5_Q5gwGXqmbF`bw;yChB^HBeudIrgEe#bol}IRzKh`QMA6Gd zbe+ztD@s@one!{oktQ2L&()A<;hmQs2!g)3($&3CTX?3W!>Q@hDYIHE(GFV)S1YHZ z<#{*9eZT0+_w8Oi(N%$IIF8?h9C%;z&a>dhljvKl(0Altb!ZMa z{>q9#8KO6i-~B=^Q8ioZb||&hcDUk3=sD-{W!!s&on@$3>+ptdyQGYQx`WmWr}b)Q zjW9V}JiUCu_H$!SfR+CI!0Rh*n)Xr2Tw!|Ge|=pGcJBy-8f09+j%2$mRbiH@UOhYc zQa6%UY@5KhAa*YoYu@Dy=z*yWeAD$T2;$7@{iEGtZfRX&F#&Z$ht6I|%ebJz-nq!i zvU=(>>kzIKd~$f0xPUMR3r`3)3$eJ)QeQkO1^sSv`|_!D;cbK~?&n=*VK$<+|7rne-0&1o zNA|>Ojy+vZ>@Ygn%N193S4*4eTkoAn@mo9$AAVWNW(81g2s#K~mAmyPfU%#T&=w{# zZNhKTiuE}dmRoG%n9lo8QsflbrDm-5*1D@qszJy=-z64dU(4+s>V2;I`KP_-TKM9} znQnzWP`j9!|viIyP<>Xk-*RfGT zAG)z}NJ)JF zY!c3U??d@r#T3*rjW{C(&%SlFzI!Ojjr54T!9U{KmfVf5yJyqOg32m1eK>yR%xwOQ z*4fHaEDN0kf6R!A(GId*-HLe(NdNTK>_X!utSQ;4Q0lrM?&c2$(exYQ`Y_N+(3UcF zC~Yc>SJK%E*gYG^a$Z|Oyg3K7B210s73VzjI+0O`cnPo(a&fGT1Jp8IDKubHZT>RX z1z+!d7Ug~~BJq5!K*Wro3uop~L&Th~C5^w~to|CGnI*O%U z7e1bJ)Vs5x8&$tu9I=1##UdVD3Czwj~72)3iij{D7Y|0xvQAt6?ehT<=42}9V@bP((UL+@v z#=Sm!G@+KVuO;{FM86HH)b`j7iP z1oSr9(!=X)D1<%IdY+xN!VMl&9WW9i(86ORe5vF2o;uZc*iMuSZd zb5q9LlAn+%`SId|vF0$>{zAuqZsEN9n1X35Xvy+5x?@;3p7? z1C{x&&W!P~iv`Fb7;c(T89G!;tv=Ks?WTiwarPqe^;yb}g;YD(jehrdRoIwuKI|jgf7;68nBixnYlZ>bS^JF2oZ0aR)+UwqfTCRL zh!3Ah+(w&H9*M1%#T*g5~H`IMsdzVsd#bg1!dw##R->$;EI9Yc01S zP zRr&te3f;I4>9|!he(Novxr^ps`Id0?euBxjeF!0+2y8d6v^l41iyA|U(WRU#*&^Lc z)SD6CrXvrv_4-HLIWmi>D?29GJs?~ICve7^*()|qNk4L$FlwqTp!OrlsP$?bxLeTG zJL~nwwI!!-m{MR7<>vD>*UZAc^#MXG3voF(VS&2(+I-q8nVT5LAit8KvXua+#!kro z*try0tr;b_pVoS@*g$dp3b^}FwOC&d6a5~MKyIC=tZetV;kf^qM{rve;U3(UZ>hk- z)OkxBOwVP(=B4V7%QQPAkVPiTJJo@TjV=z|t=Vl?>#^v7Rk2^f^KkB2Zcb(ef4&Kd zfwoA>zd&lfY5cjoEUoLp-|+r+;*i~sNh1iFJTk5(<;*TB6m(C;XuHoodX?qBfR>-x+3I$CsWkx=S5qDq)?6n^lG7K%P4g+6tFPnS~}E9$rndu?hYh)b{xe(e+OhD~xONFWxqJKen0!MtsH+g>lj^cKI*VyJAxvobL;j?3l@dDl#hK6-DIjbp#IYiO)Q^S zSdTS|Ig&_F8KMu$2@lG-wLhu}Pcf3{kyjZIafG_3jS@mqR4l$ZL7VnR341AV zODSq9iSL{Q-tPS;TyW!zjyplcc1H>JDRB$mRLeUbIzgj8jS^-r{tHz&p+LpPC;`d| zhgHiHZ*b0iKT4n_#4V6iR1!}*3A~yZC7izyx8Sd$VsY$$hvl3Q`fB1J3_QgxkY-IN ztXTwwox=E7e#|={)rax1ST~3n3toHC&g3igmg;*7Srg@{%@d`X#rNmzrBp%g!l^HS zQ-Zm62T4rCpBdPXvpg%!265bQt$j!J>2p<~_lb@?$596IkZVz7n{LAPDzH@Ktkb?A z1XUHL&RhkUR;7m@_kHVb_YN%=(LLm1WI9&(pr6P;<6*+ZKjP!R3j5C;f6rLwaV+`Q zQ~0*h6-wHE%d@m@VQb3rANF-Yz@s;O6>NYtwFWijEPwIeO1oyRZEj|(+>F~SdUaYN z58{qs175NXnU>Dkm+0>Td1RcbEYDbHI~Oo_5ayg3%R=#Ojzc&k-!^xk6>G(G(v98t z;^u`_)5_62dkr4#o^R8e+)(_`G5zfm6!Rjd=9Z(^rl)Y`0oTd)y(jrImel25R7(=w zx_UVBdiu*J=RsU>Q29rJ0)youMPEkm_DWaq^u|lbuh};gB(S1j5?C&Q zQKzatx%%f{InvNc=z0lc{iul>KyY5%M4@9vUoGU5ZdrXq6}jmF#C-eUep7#tyPNaM zOP;bja#KReypQaNMlpmUqF>s-9NMl0pvOk*4Mxf(gZ#2#2BxDOxXO4sWy<;RED$ zd$)Q`!A5sZ$VN~Zrcz0P6asU%EVC=4#g;zY$oT#PdRsKif{(DfxBg^cYoYU5B{J&w^&1izV6OinO-+c-9PdU$Z?49z! zgtZg~s-sp@L3EmPs5M4(!Cukols25~D}H4|uP`3fyO>_YWQ?LR1#%XSlPD~|(* zac;XalG2)bMx69|Nv`!K56L<3rlre{@fS28p#b|&M*~RF9^kC={ErqxDx<2eoQ5VR z#?Oq2HL!#R48cQJ0?|b1nHlsLiR0`#dh}8nbm+9rri%wdMM#RXD(srjrz?UNkEUCX zW>afgnbPR=eaEEjAi8u%KowMAO=&n42%<+3hCeHz)ObWElTvC<5(Lh4ry({#u6l<3 zAVb8?sV#(3#0=V8aorJ`f$bXZWTGMmk11fEKGYRtp_GGyoHRZ|ge6b-`UbUQ`2FP4 zU7QwAec(3drcD>q+H;>eQOc`^32xb)+xQInr5WUZteBS7eKg zPPC|ju|?L7qu9&RXLjUgcB;~^JmEvzjJen4Xz)W4_#vldFK++vwDcoN_wuAHhBMX( zrCPY7v2XpwW7D>>wQNJgf}GaRkH?Yg3SrSySakJ2jFOZuYUO;bzS(}dy3rKPxNh^{ z;lBm5%(*>L6=0T!?bD+@f&zp>dw<)vaT3ASf-aBTI{hE^3N7fXY~`Ha>>9u69JoiP zY{Y6zFFUq9%L~1xG^}b)wT*&YyhIQknj@K6jb>3hVp#T{=k??4NNZ|lE}7(M z!uh7W>YtUt&-!waP^0eFVH)r!eyVpl{aovBRcdb6;~+|U}TJcxNuI*Z~ehqyIXn~9eU=tMV?W+hLr?oJ#)Lzd3y?B z&Mb6R>_>=0%+|~DWh|QVSbR~uju{upNg4$iz6&tC@g{xIoYX{IKL}6`jUeZrrYztz}gzpk6svAqeQ^>Is{p9UJ<4#z&O;ko4G zw1~;?SDBkS9#kz(2h-_FlUZBv<4%~D7(*%M)gRr{fx)I8)iU`s}eXY(8FFnZ3m^pK*jIf}II7 zTiB$Uy3>79lg`=%%%>?k6cNFCl_znO>d$};#xuYUojUxWH?KF8Z?p}pJU45(XeMYw zQqCKq&uyAPO91G$Q|`n|NAb_*hEf#lS9T1BWzQeQN6ewVq}ZFE%JqDAAEK089rqmB zW7x$LA{3=`ygCz(zdh*Ic=;&RINNzwNoOK@wLh1#{`mfhZ#{j&Y9<_J35`bRuY-MS&W+;iadv7sWJlh0+^!g4J3 zIS5<+<9|B;4gY6PPT3HkeCR5t{r=+@$oJl5vi>X$xb^fWd>y=hfb;sAqDBFly!-_! zIdz%ra_9)ktXPeaJcmetrDke-ab{lWQD>|fPHxmazPm<0I=afZ+T6|T`E1RYccy3q zw!V5*+koZn$Eb-!Mpuo~X%LtbI_<4$ikt47pbbSCQ!2)4$E)>0V?OA&wCwIfwv;P- z%kTDb{BjGB7>bc+nI+U#ApjP+xH!nCHRB=tvb?zm?YqZQ3+_ma>b7Q@@I z1uM(>`5Taz&(NjUYE0FfBJ41%OBf&RgbxttkUNHnP+E1=Jh7;qF@)x)2sEU$aWsT} zeb}e?#46*XA&_&4AJyd_G;U7ZckFE6Jb*u9i?Wq=YR*qg11zd)&w^1+1p*{x zfgEK4=bwTF-w1D2Vz;fCWz?QXvYXcq6Jrw^kyN_mY$3}YlMWkSG|6f(Q2 z{2!}j1Jh+yxEz|2Tm}0V`mM6>0_5Sz@I>vKkC3V_Aeki(>XEJ%V-lDMh(KQ zTg8Fn3~EB%54Y<=9uKJQutI;KSqyDoWR1)dEl@`sj6zWMoTmt3ia34@wE@1{+PgqAbkpBKnv%QCOikK9IG-2-Uq&3g`P%c*;aE#6l(+8!R}0R^*b4p1C)_FSK#s>nr z{U7e=+IttOAAd?tIyo?QdcfvjXodXtj>4D!!0G%KPWV3^E3y)PSAj$9u7YKVlGT6s zvioD~{FML(jXARUJqGs|qC9@YGI*u@ePVYqq@PdfQ z{mU)SiE$3*9@i#u9d-t*+P3P>k(ka7G+I8##6og2&~!tbtjZk7c8V?*hNfNJ2~npP z9!E%4`8o486iGoo7^IIMAtmSPHMA^k)IS4^>H5R+6RtLpVl?*M@P?cc9*MV~@Bk8Z z&E4;jZSVb?<$|Dr7Gyg|$z)Z=X)Q%}+KU!T_c7!wRjs+g#n+3>oi4a*0F-~JFzDcO zt>F;I_m#4pp^e3R0Xf8a*~yuC4LTmu7XzV8t2RJi^|VG$SWKO6%P?{=5y(8d2*?Fa zh*Vz#m-~blaXLp70K>57c7wv2G1Zf{SahPcE^Kv1y%hXd6QlG3z4aVrrhOy`0GIN&p4O#8#@B-Z&=%#4)X6TM3#{|y2At1Q(9?ty`z$rk$%MBc#g)5Ibv!}QAiF28` zxWtEmAd@>6k4PAZeB{3cuJ|0o^%@-n&JwEILI}`*bEOMv%3wQtp_el&J>@&}0frK&M?%EkxJ1{S|e?<g+H;(~N>lgpI{hDFmL=3H$x8g`s`RTx&S$2CoY!=gCj2gs}Z zFsc$4i4$}mh+&mSD&ZmqAol@yGAkQkz-Zvi0OtTViEw8PLr#&O_D7~Bmh9O=R7IvZ z|L7-Tsx}Buhd@uFUBCkSNIL&>?hhA!G!YG}B{V-p(Uq!4v-h?0v@fq9*DLZ@k&2K* zxcZR0y^em4mGuSg{^6z!Wl<^m>JoR2=G$SbC595u%Tk!IP&FC!(U-idpS@jBeHB`c zx=8Yt)I1wYAJwIX=V)5-3GQ(LJBM%${%<+f1|Pr$3}w`>9tzlHNK6I>#liI2yf06N zM}l4V9dkZ%%CK|T@q6@p@DGKTG>jwE5tp(_TdvS9^M}1iF^#}g)GFwA_4l7zU-oQmP3rrR39Lufq~rN> zEtoh_tKq||d=>Q(Ow!2h80g$^4ye%41$tkZ;}PNbg+dc+X>C`b28>;!7D)@PJM2T2 zLkS!+)4FlB*sx7J^<6o}q(Ip-z{N?(8RLBx`sVf+I-N?BEq>r%n7>Uc3;k3_Q(^*a zIg)04fTkb04}R~A)$nP2On?=7`U^*71?Eo*HT7uTvZ_Fv1XCgR*<%^SOHhvWQ0Km; z`>V+6GG83)S7zbuAV40kyGf+9Wi2{(SK5pbIXDHIn85lC&%5HkM$p|~Ta;ew537T$ zOwbCB1qPWW71~^Z?4?T;Msciht74pTpU&|gfp1@=j6!NPs*=C{bDKE1%E?~}XxMLI z1_8!cw`l&Q!@R?Q3*_6&4o&yQ;ZgZ-4s4~%b>UEjSsm)LaeFnz z`6Lt9!!127rA+kwoSQ)J_ODkZ2VbDd`IfUCCchS{QN$o<5IXZ$t2Ac3oto`c4ms%s zZGcap3-2d)i&gcHa4BDFiuk8XL)yuQJu(VbbPH1ad1L}~3#xs2JRS85LVUEvTllr( zeYB4?yCDMdoW!s5>kW#XC7--P#6Qbn=TCrYC7)A{JR==>25+G9VZc||uVX)dUlP*W zQg+%>7HHP_R~rCK8~yPC;nlYGIKZB_ocwMV=cuLs!0G(AAG3=mP?`Yf0Mr@N3gH*r zFDsV^Dwh{tEpzKlCZvJ2p?Ah{KH)sBSYGQiQ6Yo5Q-KSZpwC2HS3AwSsoJppGYNua zpej%l8wxlHOx#B1uu1wY2k5euA=DflBF-&`Q6=LH*C|NHY4e5sTXG^?^OW)ia*7$P zebk`%jVfda%b17{)*by}JS_W?D2CK16y$5o30;vH8S!0(vtc9g?ViFqHV(MN z9L8rE=S3ZAzlS#QCbf*<&X1*tR5-^y(9*F1xOkU=d*TRuPUtViAqGl25w`C-g02TM0CcZ!L&7eizO!I=sI1CIr)!l;mHfVLaTtQmYzb7#p( zRwo0;H^ND?V+eSHHS-zB-b-7{&%yAxH>F$4>)H>#Y7p*wliT+u*x)$gb)GP+q5J$j4y(5HY#V?X}E|jj+o7 zoJdt%IaN1i`GN3?n~Za_uFM%jsWXN#yAPQ^H2}7p|K-caY>3rzkJyOK&p+rtu;9*B zArvHFlA77~E#{(b+goHeYz#qt;tUN>R_2XD<`WpIm~m)N1Nbheh_EZh-r=bQ-_d(zUZRRr$|}y%r5M zc?Rz`9(HqP5go?e7XX@va@nOuaXcE`=9BGJYv>m(Bo4Wi=-f(@NC8@;fE1a}0sWtr zbSL}&g4vfY-w{nR%8kr*G;=)uq1f#Jdk#GRbNpy%f(I-iCL5<*9; zO;%JCKIG?~cY5aMG})!`ac;P8k`lW$WRVcpegWTpA+BBYWVrzTDIdO>FSeMk^!|Zc%LvY!FPQX&EFgsRwDOPt$PIoCpXNjP_PBswm>7+l2l(zaVIU z_LMciB~A{R0RPvJv>JoZ2F9ZSRG|~$0lFMFm|ZLET8&r0^jWOWG)ImAalXU64N9%{ z$9dwzHFT^S2}7gY9B=3aL12^y$)2+&Jeu>Vk#18n3G+NdKtnN*T_jGgshjBd#IN-S zc7}OOao^cKFd|e{`_+}nH2XHXOdZjYQ&n!l{xuK)N$OU3US|kU(LmFIA5DqY=M z!$E{knnSL#hNvYrH&a#Q2PXGBX5&kWZ|o(GutvQ(NWM9U@_$0E8RQhWvR>e>Fp>X| zi$vu59Q?Lp(o`?$B#p~ylgBUpAB5WFw-=|9!PJiO@UN(GbJD(+`#XrAbB@RxgqrWF z##IrWm+;Ubc<9H2&YKCtH$t^HLWasiISiDCUVE+lNfv<@Ml~jaxgQ*D;}{zlry15C^VrfA#(pm#&|VLfuMe5% zrmD(zwga@b=a`?5m-O`i!`NE@#T7jLqBz0b-4lYlYjA=SB)Ge~yCk?vaCdiiclRKH z#hnEfdCUL%zFT$gef8>9{q|JP^wH^=K0R}~dktmIYQMQ@VjkHgAORRfNm`Q?$RmvK zs2!7N`8vP?rQ?gH<1?Uh&||y-h`f=LrEG7N6f9x`35Oq-tx;#UQ#c0lMPCqP~&tJoZa}LTNfloT`MHi@Q;^V zz_TLo$(USx=4?w`JlGb&RiGOi&N6v&OZc~;Om8Pu)|zFq;+CYlK_oo}_2Ln`6d zQq8I?Q&?70<1){SoRti5qij6*;b4@Rt0KG=iPk@cyKnK^v2loJ%}B{N|H4Gv>A>8v z(U*6<`%ju1wRjQ#HIQdrg2XeNSSwn=%_1RmK^a#8ZO@a^lT$E4mw1o~)d(-~E}L{T z0`-82YE1-5o}-GV0Gi-7FzQKUSl~xp&G?fawI52+^%wYWoUnb0r>SUm0A=T*M>719?cn+VY-yd%pC+o3Kt`O=N zM>Rp-bTus6iHLMwXr2JjcGN^xF}EikG-Q>|>%ubQ4|E_VETsoKLAe{p)%)y|(}7p$ zSiW5-{yt$LsK~PENMJUJqxVD72@+G9>Ip?%bjxoJ^%N<8iwie#Qk)r~iQ8_&Z{BAPc&m#_*O<1;JvE(1N|*^ML^B;4dUD zMu92Gz4w4z0T2{kK=M#=BBgObu=E{%EDq^6&Clnq{R!p?o!>ip#h!v$v(F%tC2hab zy#(q6LGwP1W;W0f!ze7q9)I(dSnpP3$x3-4I%r#AjURzpS|uqhJ`?*|UGikoRqlc= z(+LgBr(zIS+%U>be{_l^i5Rc2pQtvb36Na3`*smKjz?eVQW#%LUPi?$O)&^w&c*VM z5-M|mU`=W$iC-uLqY6voQjAWw^pBwOzfQwg3Z%N9Nzjz#m@Ts(%l8w$5=uQvd`pD9 zO9}lpbelx8SuRQv%!}ELjqbb|P@lhg<`Qp)N;=8?j4GI>hz-fEt-pZP0xC__23mzh zlS`$LTNB9qA}Uo|AqPiR$Uhf}^hjGv$5BaO{^p1bryuL3;w*zJXKR{0K+5_=0;7=2 ze?FLQ;zE6$2}bU?LO~o|Q=B)nI=Gj4&B(y#CyrL7Z%W8tM3#^LX{;~EX{>Ejyx}>d zwijh$!PH)x?y)dc&MKTA1ADD1ASVnnce;p{L(0RtB$02kzb4|y1!1Id?aCGYM7&S%-)(?hs-nneKY=J*mwz^p7 z%wQx&b;-2Hcj9tIGb~USv(Bk1C4Lhrj^~_-K(Zrr?E6k7ml$6(HhVn~fo4a@N0n=? zN_*X+sPf4?Fm!4yvgpvH$Co~b@)t$4pp@}UWNhzP7)Z@V;$@KB2*y&2a8ZGnNFho` zMbm_DEi3C$L}@NM^oPv^Ig)o=5ntTS*Eo`Aom$Zs$$w{Z<@A#x*`#X0hHz{VIloyV z2ob2=bDMu7+m4CjjDC%zN03*OF@R&63bu(3)X@fX_dFG(^K(9KIjQeLT#XbN#=o^H zQO(1`Jjw5B9Ag5!yf}4>qGuE56acZQ9O~`R&$k4I$+*TEJ>yI8Rh|YG8sv4~u$pYRsNz}Ek7(D_KM-h-}O9C^OLy-i9*r5%PqAzssn=d)6{buYp53bP|<& z!xV0QDJQT|)7cc7_FX4YqX9xr$!q^oX<8V%mtAE^l_s-k4C8={l3mv4r?d*Lsf-h}t>tBH%4doJVgcc2X91zn-JHs*izT&zN4QQv(yV&RZTSSO4SaR=olCZ{t9mw@Wad)n#LASGyb`-CN&Q02d?y0YSh`{nsZK3BVF>EPuuCDqin^EH)dCxQIl*fEQko! z!@`?d^7HuTJb05 z_I@4lyj}5c{Mq?duyb=yw*RB%J*~z4H|WT}YNI3cQ4D3I>b!B$&bFXr+1|FGj0;Rv zaDk~RvzF#LjoY6a7L`L)wl2#z%iOZouBSv*_hjPM1x;@Q9GlVAejjDWkBujI-a^ z1>+I8O0MIdr1jH&Y4e=+Fr#}(Q|FSTwN}fzMODmC+r}T~KZvT-d%#tkc1?5IQy*1s z717J%_TbVh&z@c55Bu=VtuMe4R^V#3vp=y*?3N7h(Q#4G&3tQr#1Oce&~HQL zYQSdo&GX{j1|$r6o2h$uzIfN!5PoMNYWBAS312oX1GP`RtM0p&pY^PLYnr-Ow0Ep+ z&ziU%w28c{qPv!d^{kC+n(9{8SO2>@)4OV_Yxz*m+PS8wZDoDa+V-M}3#k2H)iyPp z8`e_~+6`UH{}&0=zU^A}so~tQp87vYqnf5wYsLrd-(Ac97YWp!=vsEFY1*`A{69&n znx=K@st4_guI2xOw5lQ-d7H6)Kk9zJU48%GAHQ=&d&9cwys5bb<$0S6;JuN1X&c=A z|5+%py#f#0*PQno|F<{hcMm83*9|iJfS#dsH`0YSONvfAs+x_`-(1@ap})Bvmc@2{ zBKg`g-gPz20{?#(-WzfCP|LWzcSqvZhxUbR!%}TKwNNx{&p2CKh@ZEe0NxXMmyF@v z|L+BVZB%B^`IK8LphXe1>q_LfHLMrx{WbrxDx$lE@_G9g;C~gobdH&}U0aacE^Q;b zTWFrQQvf;5gL05Nm60t7^LyTDH}H+^jib7vS%qw)G@xR*zwX=OY&RK#a<0H>1!s(Q z4nq&riCottJ61!bIxhRWzl*F{H|Sb6bXhy64%WAb3~xgbcq5sdF~-d?P0tkU%*=G) zzpZXi6aYVtKh-7e1>BZLgStEAaPeQQ)EDFnHubT`|Z&c*J+pgj;Z|}E#|}9 z*#w|ZW2F^|##7)HkJGJ2^sX>FE1)qZVGkdyhw?bxYK-R=HCb#6Ziw;@4ja6$0GTwCW4%3VCl(v?ihue1PpwY2SDTTvr zqYvr~kKO&ja}5aEEN`2s%Fu{Ud?MvtD_WoS4O`kY*PQa5G`ToWY->?G+!jjr2ANzK z(>jx}r-RbQHb>+S|LbaPEs}@Zgz4Va|HHkt8l37hH}vCa)-$FtblXhi5{~-2qPbA} z7SnZ<(lZUhu;lU*(e>+7$#ty_2M zH`S7Lcu$yKFs8P(=p1f4rGqplHb=A%g_ha&Wu32!+uEdtIoWnDO)k+pBwrYHJ!1zs z6D~u;^iL101P&eN`qi<`%u-X*i3z!OFzbL3x>Rp(akHqA;A@3nj+_Vyu>&6_E5BC# z@Mq@f5(l43u>@p2iak0bJ!Jj4x}U(=et)tn+Sr?DBnGK!-LXuaKdgRcZ9^9mwqarB zmCyu{+d!6 z(!$%PUFUIb(RVH0GsTDsBdRJHMza|8IAs)L51}K>Yb-90X^nn?*{lf zF!|Rx=WF5}qc>-|+Vl?xumQRYprSWH)eFS=A5pVEqF%1n7yTGa6Cc9eXlz9-poJ#2syCE!-D~tiQc!3|;u1KG1pU`sy1t?y9M%cD&r)%AEGj407t`R{t z!Z}|Z?-w0qZK6lz7Oj)L{SskKT@&B_?ZOqB>7!AtO*&I4HYsk~aXKWcn>PLzYMMZ1 z`?`Q4{n#x(K{wF->iLQ>aH>1g_M^Y72)lH#MV%%a`cxt3gd)DL?2uX$cfYQX_4uZ! z`CnVDLUV*cOkt9%YJ1)1Pg51X{85DTx~H8%ykEv1#rX_dD%`mZ%;|YQuOajIWcT#b z0!`-RC1!!mLe!wjZ#t;~y;J9o;s?j#TPbd{}34*^Y`GFJV#@g@f5-5CdXcV;?A zuL1YlWA{GYUL7v?#*9(tc>K>sQu=3+#r1MIXF$bfpmXoU^HZ0+Tl}%!`am@nhEDZ7sLTY1~E-7c0}EXr3(_xXchze zv^$eG$J=%K0qlIb8rff-=Nhi{Bt?s|=B__KQ17&6bqKv}Zg$x{E24E@3rn3q3q*+V zVYc(NP8HF;VAxQw{0?A7R zDLDnnGB19vW@l_KM8bTziawJ2BfD_KpMVJtC616S&TGz^b%THQJ49iC0A zr_9>7NaG=-y~uSYW<(7<6r%+v7>s3DSxInoAs^)#HeT3(*7he2@O~Dh0@>O}fzyTR zFf+R?I=o_m9#8Jjr>R!H3l9?Q-`t-z46(umgmQOitYZiUlCLnY)YM|MV&!d!0;pU? zy$A{LdC`3Z#T0pd^&%9z$e$wt7g0BZ(QBwRzQBR7J75zZHE%cD$G zbCCeAe2MUk`G>YIGL00^qQN(~#T>pDhKO6|%5lCuEy68~S|C$?lns8`ZOip{3;wBh zomap66Zc^+0qIJqeE$3qEXHB4La-bkaudI{V$|7^i_+$G2>$94P8!J(ND6l<3S%q{ zX6o6Q&AY_QdXgUXrwo-Zj0+SyA1o%6M{P7mUW|tRXXjEs&-s$H1P!#cgy-yXk{F@P5`s5Db(b;KE+0F}MRu?7wejdN-i?@&)Y+a!2z`3(CNFhBUyUbT+2QHI zJd*0rDbwIV@bOL3wWPa)gn1&Sq!$GDPjZr8c5u9qBPKX`sjyii*fxB-te%I?sJWBy z5@`r8t^xRc8EqH#r;Rz=5O8r^fqZqh^CDKwY4~~ugIf*5;39P=3V@FAjkO&6zO!=< z#es3ar`^&Y+)L7%V!@i#FI@%yY!!ASTfwel?NxaP>!UM%T}#-hHb~`4Lf6S&4@C<9 zy3=6Ezw5}$rs09<@yWa|@gn3R#)7=riC*(K1_1rZ$@Xgv_(>2L7!LK@yo#e1YveF; zTv8L@&aX~=1}TGl{y}yx=*mYW!HDjx=5*KDYhGgn>^$7#o_ zr;1+`wA}Doc%vI!R-?=^#eF7k)F&gx;{k`6LU?rMDXZJNKEC?-=N z4T5;>wDot{tsYCgZK$R)KmvzvBVJJ zpE)>cf9TAyTvGo$(<#E`@x{*T-$J+5jnBoMYW_%C$i>RslvV z&#l&q@d)97b`!eQr{(pDBH)%musTs;TD%N~jPJ##ltB2JP54X`sJNk6>G^zCZ68r} zbzf$c7c1sM4n9S%6sc}_2SMEaLcaPjxXDQJb-@cSSej4$%s{7(82M=~jb}vC*eku5 z2kMb*A&~_s^wmgWsSYbIU6exF9-DjK^`b^PhRr5zOYyspJPkkoQvE!+Dk1qYpA8iiTSkuVbr+vZ@%?(e%l2hr1kVePMZqr27LH4I16Jg| z>nlNDlejejeqCh@wOAeytvDF%6rmhfkvSut$!_1kc@e;AG_D~3k{%!>Pnl}*6^oF4 z^`(i3FZQPTPF8r#KFK_X0Hd{xO7p3N!!wR(_bW*VZrBz$G6f9^%NMy2&Gh^+{|HjZ zk(7i}5S>IM&J8`y$H<#gl{DD&(y%; zJ`5yg(*Q2-h>*BvHJ;m7Vm;*9jwuDIcXftZu?cy;;H@SR(LZTQm?Dj&JGp(@A0u<_ zP}j74&O2yUh&@$XWL^!C{{56*uMt4nMa5Tbu6a!JqOgi>n$vWjNj|djf|)>b_VvN! zsVFX%`;Og^gM*$ zsy(oH06_p@6ZZ0Cq<6EzBMz|*>=U-=(0LayZ;nM3t%gunZx+*DkmK4 z`z_2YxpZ|(VLAtKlI*xvQ0_TGRMghme-l74NCqDnVb@=G?3?5d;;*EMok-lahu5Zs z7RZnP6i>Ws(G7Oah3;I!dVL=V=8IKAtWboay1G_Qwtv>9;jlF+ zB_Oa03(LsMGqWfqU}XvR;KbF$w;mqO_(J3y!m=7P$w`$m>AE1CF1+&=lj!@_cGQqm zJhG6zBf*EkX!ERyN`>>o2el^boQfk<59D9wovQoOO-JrbzrKqO-AnGfzW<125;Kzl zv}u8oX>ZSE9A)w6Q2fQeeBM;-MDRSTiPkVQLK4aeWQ>qG+SFRxV(%n&z@``z|IwjzDKu=)!PB0BsD@_KUW?-Bhz3MH%iOB4 zMtsI zqQbyvH?`E@{jvf+uQ~Y@&R_I7+h?*+y?&}7CK@Ht5@k;zo+fo=Xa(}AIRvWiBSM;o zM;{#wm=d^geCQ@+WirAO9S)zPsHAhbAlvV5L= zyfSLv^%pyX2;8T=myr$PxpiJYNmE-;W2#{y&_}`~e+!bO6y+XMa?OQU3QXWAM=vIZ zI-`vjF0Cmg7fOg{@jtQ!tBAbhn1Lf2~yp)Y#@OYDr|pMNLxh zL&atOx<$s1n<%~M%?M9N!>L>9bokTA%;>MC$hd!LMWxlV#86vl7HKeIg5VYGT@xoF zV|AteO|vP9 zI6k}Ew^k#9*y>$8z$Kb@)S$9BF~^{SxQ#j$M>#w!;+=}r8kzC;*bx(CX%u-P3~!u9 zRS_~RabnKF*#S5ZQD|5TA+p2hB22PKkX1~u*?+^e#zJ1PRWpspI)daXV)*4VlDw}) zs}O{+)Szha88EOW-o8eg1(ZJ`&g_T)Uo}p2_YX@I!lLAt!Uc0EmV>j4SY$A`7fp`j zWyBim-{O}g{^Bby4gO_+K$|CtwmvMitL*SP*Cqf542V3#CVc%r=OMv?K zoTbfP!~aMZ$s%k{deDN}NDY&fJ`z9qTa+xNB=?x~m)+)QG%I&W_6`Lc%m9^sP?`rE z1kmpVFpmNA{MmoE;#a{WViYE{BU+Wd6Byn82+HX%J-6l?ot(%p@-zjIc zb{F9GDk~X2bt5v2?$KU+?yLZT^LT}jV-#K1fb5%l?1zJ+=i9<)r*JtWyNr3w?z88*zzvAN~;o7$9q+;sspu%<7 zI*rwzXD^#^t8FFdyec!XN-!juBJ|K%Zwyvnt~R!n0`EIANi(-(F7cN>(Ke5&`rL|F z@-&56BRztQlRm}xKp^yPbU=CKeg6RyJ6h&~98jF9tUKFT@avl;sI_n|Xz+))4ff!V z>yV~~@+XMwZTzyVU+d+i(GP-~uMeS&wYEOkq_8Vw)QU=?<`Mvsh_0~JFWVyF^_79^ zrKM;noK7=-KX@(!@x2uZGzo#f>nWaSqF)kZ{bXo*3KR5I#+c8)1$CL#uD<@j{zr$# z;j@$Wo;kaYM<@vwU~ttiu|Wa2!t2Iuh$YHWHliL635P0Jl$7wbD76*M-v2ae27e$| zZ?t5nUg1H~xbnzRb8V?->Z-^2O?WLLv@9#kwt`~Y{1y5-kOvpwi=VsB#e#We(;go;kfJNQ{1cLvxfLtmU^%j_ZZkoM#xA~L2o^?2HctYsuf)E6OT>XGa7 zpq?;mv|LMnT=N0M_ZLv375UYExR-``$a5JfTT#agbDY+SC*G48ORw|e7Oo!!T5bGQ zQd5C0x23nxz%J)Pw~oV5Co1jwMQDk|nDMW4VKE49udBK(f1Xn#w-@>DEWQHD#x{-7 zWUC?6?Cj_k6t(qlr2UjztVC+Eg&h1+yA1C3UThIDGN}X1S0;48DT|El8(VfPIOWa- zhMYaPMg>A1v@ZB}0T1OFxE zlp5%!P-GlUTPgnXIR!5_HL5@OJTmf&6cweMI`F+a8_JYCY*!+#R6Ai#(iVw0eN?~b zNyKxfN(IRNfHgE^0lRaOWMozlkI9e^%#sgG?jxHLJWi8_GC$7FDD+Y^X=8M3f5G49 z-~$ADfH;;H+IN6pF<8Xl`%zW?iQ@YCmnh{lNXbm0SBwig^ab2mDc}ycKW_IwY>4cl zw$RRsfN!}_;4sJhbln0cRcTmi?C3p+K5~;ON_qIKxBe9)im4CntxQ|^A!Y>$TlK|W z=jE0Zf4^Yn^eh6V7V&>-kbu%_OJ(r9Yxo2X+&xJGm|6q*KCi+p8$w?TosvZ`?rFwB z=|Pm+28+*0GeRtJk+{s3YJ;Iv_TQLgkP0rw&$=a zZ?|_%_g6^^V8jz{;WWJ!IY9X2=jS?&>%c{JbefjfqH_hRfRsSdQ4rs7FGNCwb*^(x z74pF@bkm#&8RDKA$Dj=OMN1_wDuE&>lm&#%vKiLeU^C!YkQ~&4&ElB-A@1`zg6i(k zW&84Xad*lX==Dz^SnCI7+=zg+SmqrupQMNvbe)-40vM7^0ea|;Fkk_@N+NSYR-7mO zXBfwVhcVsX%}Wum1x8rCu)Txj$bfk8NuYmgv?Y%ibKOMZDk4F41RcOZKLcL^e$Dj) z=820$KWM(xEp<_O$zQL(mtD#IfUl_$hZON0D%usiqNHu<+YFP|{OHD*&_A@Fba;F(aaj={Ju65mk8LVVv{O5gAL}Znc{QPP9lMrgH(T?>r=Ew~7 za4Vde;AX-cGfttY^2+J*Fbg`OI+munTHntR@s&F<6qc7C;)VJUud)nEY4dSzwB%A0 z7_$EZE8g-lSPa&DYsnJpSz}EEfFF@g^4utj7SJY-0QB?%c046Lt=@qrnfTD!U;`mA zrd`SxiAIRS=UZVmgL;5~Pp$$Xpp*iY(5Qr>xg3KK z#WjqynF$o6AhTa-OCX&Aj-9IsaznKE%X%NkV-=AXUNzyT-+0#~zjk?q47PQU7n9&m zO7kB;Rgr<~Usk6x5XQhDY$Nv)9qhev&3%Z=gQ_^+`w;I;tW^jWG@S)Jxbd?%bSXY zm@-k>`zWF+fM@?L+}K#x75fm>*fe|5kG2cUeJ{1o8&n>GSD6t>+7wP{=8uNZhJ&NH zJjI8Gmfn9yy7PYnzMsCo3BO&RlD%&T`@#CZ@c9uO`KPbIb3H2;%reihPYVYIX+X@S zqrr_4p~#t;Mbcby+b|sLyBBQvr3O5!ll*m$9SP8S?(V>U?xTw$-U}NQwcD&{<+_Vg znm+~SYplhS&Amhv5rzJSN9Mr5iz0_Qmw3e$gu<&U3)9ap`U-@T7r~gH5$9x})W~O^ z-#d<$rTrG;XpFvfy+WP&C^XhhhWv16h((YKXZ#Cd$$MC`v|c21SoO(tCr||*ksV!* z^i}$8Z63`>=vYcp^|v}L0@X$8_~Ukt;~OOOqCsWh8EveRM!n$~<=kTaQl!aFysQ)( zl*%;9aU9IL=g9<_ajg5z{&&Sa+n8iCq==+~A*z%Y5fNi=OVdg`S zV=s{fyZ9m=<8185wT?VEB(pg7{H&g+FHnsk*+xhK);4t4U*lpu?U8+Lx;R5w!>|Bs zVGLIXw52tON3f>}=C}uI`pv*Pfw)J}1NbhCV<`o>mEF)eCmUNv_gp!m9I?*u6 z{F$qNnoR!J#bhAq{6Q$HiCOLxIshU_MEK^ZFvsQ5Xc7F3moa|^vy@vP)&$WBf_-6c zST6?XLu)^WEP3>4ezla;$*XpMr7c}ln?y9^#8R|`+xt!tbCAR6>sR7Gm^G1uClktu z<(cv+iy6e6fY^bmW=8IZ>`DE829OfUxl4TIzC5lh^xVSt5}j=|y^&pmb}e9(fM_R) zj8;)=ic-{0YSsB7laz0jDz@X?9;o>x$@qVcRaNT>%H!C}M#&lUz4<}j08dXc+6ndK zz?;DEuV0rLiZ_9#H^k-WNK5vp-R$nP*se4hso!djuCQnArpR{ z$(0Csl;V%dVK)om4ars%_Lg+d*g_`k$<3YQFS|lNQ@Hg??}5K<6yV2%E?8d1Y5AMo zgJpY+W7S~*gH6?GtTvMXV?T@6my-QU(KAqnM;_C_>SaQ#_p&UqNMp-c%K#Bob=y!U z8d~MqkU#3QNUozFpLqBa3+GoxG0WUb_n#})fN=e+=G|1Xj%N6 z(`}}1BerEAXV;%6e!F4s2Fwq|T4WFF4HSOieimnCHPd7_nqGJ}ulXqNeazkslD18X zv|9tyl@EgUkk^^Sb5Jk3TW0?@PYy}F%v$WbncY-_^KRWSS;raFfgAo9x(>j7V26y6 z&MViCoyOQlz4SUHc5}GxyAevE*r4}UGyI8;`{3y4 ze$dNcpYb*^ENzYz@sMknd^GYa-WtT0mG+#?f4s862;0OGw4BxnG8LX}-U%V08Ln>M zH!oIdJhN}oCO742Xy>fuO~cB3rc_hX#;plgx0ij4%cJH%X7ucq#?IWKhU5Cf%rwDW z>%7#-=bp3N&&KkNcEzpKjchomVP%ijkD>39I_!%N{eOwN2(YSumpHIkD&WLpnHN;9 zm8Oxl@;Jc|wyk>9=_9VKa#n+w4Enwm;GX0aDrFV$)H|jhqYDkxJ zVd9*aJ+X_EHH%ZgHb-^)d~fayA)eQ`oo+m#@?>}RY4FosT9=BHfS4Ko+JcYb!cf>I z_n2OP)5ur! z##!l~u?b(&)=M%Ua4k{=VL*e%*C2H~) zx1r|daP^=JiQa0^J=zF??%z1bg|eC@!XjhumqdW<&xWNOoGn1c{a{m%>{Y0=R+S zM=kt$qLe0ttk?}oAY&Z?R_=EKyhIQqwUE4@ZJj#hu%l8@8pSb>-m=bBF;w{!%gEP9 zV-kNRc^lna8!1&_uQ)_Xk)=KEE#(7r%}HI^$-(bT4{Z9!y5CDM9Z4}Z{Di3?>$>(e zEiSqAjL98tf4&FRWjjO#sBT~;H2N-9ExEfY$OYD9=_MFcUaDLx^p^P|NZ|j-Q+C}= zaaDs1M}U$)l|z?Qw{R+D2kVG_!vqM`4y=5ot}}S(s>^?^t@H+chU5J5rC!9L8Mc?T z4SA=II`qwbe_130ECqLhdcWg6IwV+OcsTGxVHs45+e69YJ$ig{3Pj+MPc!tudZ|V& z{l^L?kHqz%PNsf0nSBAqduYdhnj+ohck#mE^^y<&535VCX<4EzmRhNfxqIZquX=&F zLE)U!K|D%i1{p|8ig1_dO4zW{t|jG8k0>(p^02;XBvdveg||}GZdA^F(Gx+M&UD(f zlZPwrc8oM>k=DEOsMT^e?Qhj?g24=c4?7cj9OP!dwi*$aWH+H9(Gj#P@-f8hs%N=Vby{sA;xu6j>PN$Sa z2QZ~o~_)qG`l$gxo!GsX)xNewW5(pOL@8F- zP0$oK9Uv=nBJ#TE%J?xlT9=g1FtJwAyg8{U=&|rg?yTV$-?MzwmV=Q&irHD2Pzf+dkeV(kjOP{9h_%#40@PW^*$}O8kaH2kE|;0^e5oU%w6^l7q-FyQ#W85TwB zrI_@RY`RTRQt8YFfdWEO6NLQSs@&T zmt{f37Q2bf&F3Fv!0_{Z|1Sk{ErRMGz$hv#tm&NBfmF*iKwR_pmam&ho@K zpnmauit=PneDPoRTvuCUo6%g~ z13u}Rh$?*3;5mDbIv3-KAj}P2@_ET`iguJ^u3s#h_&r7Nsd^hbL_&=0dZ@M&S|?Q8 zY*r`(Srh`ww!mIo`e#C%53-x}?&cezHRST>2HG>xN_%Ja>TA-1+;Wi(TZ!=f)R4tn zpD5)W^S=}mi7tO(;*s|ZZ>uTCfm^EK$~}L>8S4FPCTYmot-m8r_}+~oaM~O8Nb;QL zUN!&KJ^35oVB$7+q>=sBU4z0Ir^SEN#6lM-6hK4mIFHktWCOiNT==dXoD#qZPrfiF z`=$H4B>#4uT4lT3hx9L zM8c=rQrAmQ_xdLHMQVRvf_+CXFFm#wV<+<*2RBunDt?Lo`8ylLyeYV_k%Bcfw@2!y z?v~cor?l_!E)nx@FlwiSEenTfp!a_ z+(zseMg&HZ%NBF+)fskuUuNd$fyH-fdAhOm{6>TXwi>_+@`YbUc!}_E<)PWHiAO?J zc{-Vn%PhY=-5Yn}Hrp_?m3Yy4p*4a%iE0^}0Qc9zOB3F-zk5S%{VyCozOYifm(y48Z~` zgy*pSFjpnwj5j3OL<*iNf^VssC5!r6MU$?I5RQge!Vus6hi-~-^R~4~dEZE+ck}>d zg3o%py;jTPDW_=YF?HF>^&h)&nXUT+A4y+*(5d3Ps$kStoknR!mp01b--8~x_k3OJ z$4lK;jGeN${m^t3B}Gx=_Mz4y=llp<-Io-6m<62i6Gf=;@ItTW5*CQ9|% zDC+3~4?=}&78S3|*keDO_h~OnD@MQS8Na*}hEziJk|4-6KOENJ#l;buxU}-Q4#~J+ zChvRE+>$Y0ix40x=aJHXM^t)yKD@}8VI_l~0V;n(@pE+^|<^X7%q zD;}Lu(dfKMfy!^BG{wCGh2KbgaoR)A#jAoM#E1VLA$~ecB+A+vulLsHo+_7ojG zDudGTj{V#b$YC$c2k!E&88hwgwFMIn;E28$np8 z*Q9XmLpgRzJSppji2T%t0jMjlLK==SIZBx$W%|k(|%XT#9z1wbiX#|e=m9pL3*s>cay6Kx5%zaITWARd% z>2+^7Al5Uwo&^UsL`Yc5oK4az^Bo)Q-rICI%ibwZnQ4gMJTAY;*v94h=1{ zjSj0Xt$Cvz7R`OS39Yrj`(9Srm);$DM=i5k5&0aMbB3>XSTjkw&Px8B-kV7yQDilvWw4Jvl732iqc;uGL+;+ct9Fjk_@PZRP$jAn$LKU*3dSa>z7GP}?&! zpHS~K>usbusan{lNhV@vRNTzF`W*O6hU#D5^9w4uvTn0P(~dQH9R5>pG}f7IkD4BN z&FWnT&ukzFSQyu*d;aD-n5N%fuYkYr_>B^LKalS@);8MTC?Z4n$%V=nhi~qEYYzq-{S*U6 zXxc#*jnnJ-E7rj-vY*gT6M?nvvW1!5qXrn<`Y7hCEuWpL<63F52m0#JoHajgAJi2C zS@5*kxKA0?l*HjjWlXp1RzFw%N?*vQFJ-PQfqZEew|I|2*mA?jGbf|aBH2ebkg{27 zi)q)BMrx6QpO5n#B;-E(bSFcKh}!vOTD||)oUZWi-NG4l)jZXpzYMEikfTkjc@4Ba z96KUFi$il7Z~RBFdc}hzv)Er`XovPz~2B*V!~O5YbHhsG4P&z~mWVYoG64AVEr`I(gS* z{0g8*C0|4+4*hAz|GfA8M(t>_k+s8(Ac-VlN==jrN~P=-aUN^R1=8aI98{{ zNZm^AODgot2;nkN@*T^PpLrJ4HAAg3iHke?TMKk;sgl;F+~Ei2{0elNRnUS5 z@F9y&>QkF55yF}yH1NX*S_#6q2T7f87*@J)Z6YuLU(7#a6T-}1UI9|R*s}_*edq|6 zg_U2Kn+3|xhOF<~_IvH#+@{N!T`9KU-Q#zOZW|!a86iw-v>He+BJ}gf+WoD%TZ|MV z3-UYk1(M1Hsc?p?`JE}${Lg6QN~AnS=euC{-2JusehwT!;>n%TX4~7qWw)eK>{)77o)ZfKfzxzB#Ua;gPTd_iZkbGnH?n74EykwNxXSH z?qmPTHDT%R-f)m^Qg%Jak#ayN4`L?L;Pc3=RZNq&@2LwM>mZam^(*+Adi;&t0r|@s z_tU8i0lO5>F0>@N>7Yh|-; z+NAMYZa3lNCu-g!cS+bQ*v;>>Uw5ey2RxciT04!sWS#8#O5dBc{vWR1GAOQS-PR^( zAV`4V?(Xgu++BjZySux)OK^9$;O_43(!m|RCVQWI&v*aO#jI|MTGi{VF~&3In&$A? z6Y3&s<-DJ7OB_>nEB%u5I#mL&_~u>|B!~4&HrYfePz7l(i`!F`fO#= zJx{RHi|Ip`?1r}mv@zF-XxX=sMmlZ4-Tcm_qM-U~HC3D+zBdih7EC#hYR}^1o`ZMs zW3aPfyQ!?ZoQV$TGN(kWZtBP_22-;r1xEVd?q!(=n-6fYD>C=Y+jFk91ZPvr9op`UHYL^CJC(w62eSJpqOyX9zg_^PvDt zo`7g<#{zY;kx^aYa#G+JxzrJe9y!_?w$9LGcua2`^mySZ2U7f%TxScGLqq9XOFnz9|mhY%y9tA@X~cg>+78-}h`Fh}wqjO3n$yR2iiSWJaC zx3I_rE|kYzn4;YgC*)AMFNK!p=(M2fROxz9`|w+F{(4ov;Nbm{ZsYPSGKe^J6ci`?I zini&Ef_LcDkH=!@C0(k&VFAAgFdf0pZxC{;-LeQPU~P3oDcg7w8p`urwITcOhFEdP zT`O4hZxy^AMr+@RrkVQYyNP`74S9j0qxAoZjt6^$u)O!IgY;zgLiY{)t8oLiyk}#& zMiZwGZstEvUa)}TiOwShzX*au<9K&Hp#>Hjf)uede;=E~-=4W|2NTIgND&b<#sO2R zImADu=JOVf3WZmt&DO9~%TfK}$lscK& z9#&?xXXW+3Z^Uq(ThH9O5g*RFJ6T@#~06x@GcUs}8yDQsSxCa~Z#>O!iHA(F{N!J7bUqse4fJ-II9oTYbE9+J_4j5pu z5NpUipA8v)43)G%#v;o2t#>vhkb<<=K=(Ff3F&lVIf$ARV8|Gvj2EJBZP_lmTcF6D zt*+DZK(!W1h3Aej`9|}%6jt=%JE&n(0uPQLi=OHH1XH9Z4;;BG`iYa^p@(|>9}m;# zi+wOnGwt|}aY1u<$RN&mdbmP2J4Ey0Ihb6LfIX=Bub?@L8nP_zZRPG^_3YR%=t@}e z?8FcEN+rMvLiU~85JQKv{fRe0CF0hs`at6`?ZTz+$QEw+UeS)4U5fI%U;VDrt@0^q zGh!n=>Q6D@$^eM@9zm|&KM!7Vb`cnAZa0?K^B6cB`<;=h7*o_DNy`cGxZ!FIKl;ct zF+hIor~1BUNgXW+Y+u6cb5Rh zV{KEK!>7pTc=vCnv&|Z8P2T2c>bYw=%OFQ*(FeUrR~M)P)$!_WD4e}Sii20b9kx87 zjdL;?{ERe9aS(P#N-iO&JA*ps^D92@{5e`g#IoExw53w+CKXz%e-y<7r=Z@fYN^SJ zE}w>ME>rrG(X4i|&nh1TJDX8&MAWbITw2cHqkI`@EdN=c=`nG&rcyI~d znY~j34w^1Vg(F-=Bv2>$T${%Yk4PM+(EOY-l!?N-e9QEFYDBO3F4-O?Z@c1rTgs;D zC*BWK4~KhCl03P%L`Xk}M?F0ON+-9;^BH3&>5i!~C@)!LrOE?`EC*abOR^awK0TqV zuh2h;GFN6#sgXfms%#`?V)l)vtGR5MUgRmGbeuSI;)A}D^0GzKZytXqngxgF)61}v zngF9yaUEcEdZJYNprvFITM&$R3RZl6|EX7IQ-5m#5A+ZZEsOPM$J3M6FNEz)<{(^= zc^6a3Ans>qXVF0cD^4?L2QnD(`O^EaFwN${`z=-t_Hcct;>w`?pY|REL3wZtcI9KI z;9mOa+NaViGqX1KEtpw`yDH`j%%1uh%BPk1#dBxfBiWYBS^MZZDp^Ugn&tZ_C@(hl z1z1_?*O3Mt!2CnjHi|{J$`_MPLHGC5023B%m6_1)K&-*@4-7WD6Dxh8gF*smm?Z0I z|9IGF61m}xHc5>*8O*lQnp2)5@XiHm`WnAyJ1~#T~f=z<;a@ zYjxkAErAJ39U^WrVT^qVvR}RZ@p1V)jU|yg4s2+wzXlXoNq`?~xF0~M)^HpZ0f%E- z&-AiFS-!l6Vb3mPG70`xMjRoCN+WvbrVc9TxKgIpq>)@1eIWFI&5LvBgBP_r-=iRI zM!en*z;RzTg`Q^J94t_dA@A9aE}e$ODn%~xHd_7{UR{m*xKi7RdD_y>r_1PjT)o9# zD1WAMj;<9(9)DqCIx`+#AomZH7b(vWj%PbDoqLt_Wgjbr~dU`#A7A8k@VYsoy+rwEUN! zA{4`JwtIHtQVew(Pq?=z_Ng9+TrN@d)vq%nyN6vAc=Gq_+yTx46Nuv**zJa%?+XBh-zz%4HXhxUnWC&2V0U3{b;Xf9w2 z1=wtYv;8hIeVL5@x@}yF=LOr)k^JBZocq?x`(pJxgXeN9g_J<&y_nUrYrcKnJ#3wD zO`H={RnE;mnUVjeKshSk3E}Fs*q9U%8maG_>Qm=I!4`Mg3lAy>BZfu-?3}%Q5rtKJ zK{PU8>2>1hAsV?&XY1iGdi=lxs66(Fv6r~Tama+AkQ;x9?aW6CyaIK{ioqS5RNqLN z0Lx1XCbg$#f@Dq*y}?ky*`?@ULmJiaQq?vM*v14~-6P;AjxaY{hlcHyvIsnE(C;Q-w(#P(% zIbsC>|7f&#LLZRhhX04-YJ76sG&&Y;Y72@Cn`HG5?+MJ^?GTYfB#f~xM;bf53xybP z8kmr3;=w6xjf_^uBZY>@eJ;INN#j_Fu1hzAUjk$DL6BnsPVN+qX+G}Qu^1}2}2mYmqWmHU=zD+y42_=P6P3&I{q}|WanhH@W<fe0nU$w@^DMjGv4(qIF z%8rkL3}FD3vPeM$tX$I1)7Q_(=YL8VVC#c(6A!w`;>ul{4-%UcC_%cgPLd4L^{=VU zevo}8q~}tDUHjzqnhzQ^|9TzT6;5oeGla9oK5koXVH;W4^(yC1rlPPw8ms7}3i5U- z4_9QyK=Ti?Fu%;7*$zjc);^pC?s;|7+;6_#R4v+ow<1Z~<1=3qqXEnSfF2Qeu2oIJ5cfLR<8$dzA{;}=#Z2_Ls6Bv`ie#WGG z1ADWmA+EjjQgOC9xmXRihsUjZDVov*pbmuWFPM`7j(=-IZkhk?HJ^x)#<`KQnZH(G z$(e}pX{mo_BOFaV4Aw#7Ic8=KoP-y{LY-z1^*sw~VWy*4x zvTdVsDJ?53#sC?DRsmMMER{Z$1O8KVh~i+8wz_f|7U;J)Ixsh9y%GSCOAoy?ApuJe z+$@iK!2b|iDs)o#AS#%yabB6=m=$dq@BI(f@^P zG5!~_t=nQ>7r|T{2BH@CM~lVpXnfv8jLBXn8oQutg}Bff`0$vq=&~MWR)>t)k~54A zf3f!Cfe9(`Y7fEy@v}JYs4Y9Wl{!oVSPF1tC}CkeH$Hs26S!qH$Kf6zW=W5}qL25; zhSnB6M+v6`dG}1o8XGx(VgyT>aWF{}5D2^{B_Q(Oo-HFu$CpRjZy&@Rai5|r@ zxsbd}_`=M;fa8`j^*aVhBMhk=M2IS>?`P*@{InvP8)V;(7CHAb+!)w(+!v>~%Pko4 zSJq(x%8dWF^MSL-nKTNV70bW%-{rWBv)!}*g1F%qkE>_P!y(kg@^AdofEo}?|6zW1`M4 zKl^^)##gPx_c)7_9wP() zY`}(CwtM*{^C*C*vSOJfhj*}b@k$p8bi>|W5x&(awNF`J4578ID? z8|4%H57+v=wEoiC`b(ZwwE+I_I?NFk3MheSzvD3~{vMLkbEqYav`MPp#Ig#_Vg*w$ zQlxtUeu_JfYguO#Cd?^kr^+NM&a6?3bKyCfY{Xux6UenNNNsVGkcwJv2CsneBor7w z&f=QtGY;bm+wmPLf1+A;EFi{};H6zl(V#P(hz%CS+aki==uYvNil&h|RKFW!$RanX zQXC-LSQe=@5R(c3n~moR|Llf6ojRi1agL`4N_^=yL3inB1P+OO%AoC3@7S{AVp^zD zHrMGX0SSu)yS5H>TPZ%VIdGxwksjk)7mE<*Yw3jmgY}n_%`zyUAF(!LhB#s$a(vGI z{Pdv^%^PV**$f-UR7)$c*wJ_nEOszio!Y2rQ&md;h&mWx@E(JuV_&=s^ZqSe&5kGC8_4jK$pP`0pTYHuiXpVB4!8L!Y)B* z0+y|7R)~caP9h>Wiexay5YPH3j|;y)#gtB-Vt=7#^$P$QMeu=uXg^g7e>9WAcM zlXCM!xR;L6!o#s0^VQ9UM&*PfK8ecYf1^-q?M|@Evj0S(PppYJSS;fyxlUu;SKM2W zSA3F|)4|N_y&^xevph#ma`{8!yT2tw45CWu(=$b@qjlWS^3%H^j53%)$`Yh+fy5X) z2|msG?~4te%&RA;|FSd+W#Int@FjT2=;#P4g2vI~i;7XI9(1N2#xMCTis*q*g2t(` z5jhS&RWy1OiPa!%!P10t>bW3nivz}gK0*s(79$pZmQ0uCjra#qr$IwGd!RcRN4b=$ zT}9Hqe_x_Y>MSSBro1~!mmFV@zn&cIO|-lRbU}u*_%0zO6vzFZ_W?d!0?u|We zFwK)>Ulf4&)DX%Jg+v8~0FcD0_Or0*c-vIsKT2;={)p41vw}8B)W&kao~kkWV$uUv zL@>p0Dv+RT<>95PnhQu+7v#Pq1bA$zp2U&zCR$VreU1j>mLYoR1|6M;>3{g-^SxeW zihr+@@CzUIz(2Y&RG#0xmn}9b@_(Uh2mwoB8ms!e3`?QtuWf~gva+9!WKak!cq?Sl zdvF7bbev5)_5RzIvsZ^OH+~^VPj|D)cUT2NW+$+;J#kcZK*LuO48K zT3X8)IG(!kWuwz=G-@`_7~XMkv5ZyQTRh4#z#1v6FsYD*g5E0KBy-_J+`PB^d3ra* z$0ceBMbqv5x13bZYKDOZolNXTxA=Pj3GMox?I6e|M#!sANfEQqm3A3npV2jMEtk5_ z=t_W!Z7}O}qm*iS`)aG3PFLoS_8bQ6ktQsB546=AoIl&8z?Q00B-!s@A-6E5B!#w) z<^h@xg=tbKyK%D#!GZ4>hhMFM$Q9nHOh|W?*WT=O)n~1A8<>7R)}Pi30+%MImGWhQ zK!hS+@muoDUD+f7y%pY*z2Y0&%0uKSF7}>RnGdv|*-J@^W>#%EumDyt^8r59QujG0 zHb3Wtj=AAiy{Hyo0nF#K0QNWWBj`_MEUlKLrc(Pnkw8SR02tDq30>ucW|0GhMlh;J zfF@(W5A!`yy%3~N2NHDc@!;L4U{X4btMc%Lcf!{7 zczRAU2sk4CUP9D{_LTE9o*eykDDMs#|2HK}kaXjCFa9ADoc}>4`TrVVVWZ+#oX?bw z-!ekAA-)mj|5oV%E!+O90QMKy0E1oEzgOPG&fs>MDK7~K#$?J;52q|816DUGOlJb8 znrGiEhJn?Mb05S$Hz$OadeBzmQ$@<7;5y`h;HTsNRKU3ZcLgl?Uj>ZZEv$O~za6l; zC5XRof&t>*a>??NU-_gifX$6YWQk-{k|pA0!QH<7CDdOe{@CTa`wif4uev}IGXY z>-lqn&wFl4_P-waHM~I?rsRv$n}CPSvGB1`cvO#GB*roD2PdwY z&A7`GG=}Yje7G5#ge3li{j~AYt9om!#bV$io$BmL8%)sqUSL;xNRI z8DAj~M`wCH+B5jpP3zcHHD#6x>aE2W6N{u1QwNPn_dIN9Z$j|ubAj~4Ff^)k{Oi<~ zViL)f8>wHUUNzt*RVx5j-hQ6ad%j@AMmLj9Th#BV!VLFog#P zSSiH@)|g@QiR%$%RM_gk!t8+d+;S1;Zc1PJ$mWi2N^2|@XKG@j1Yu~rt;HhcpbArn z&)P^%e94<<*okumj27T4urdTi^V$2FQpr*kllsXSpd2Oo*1R#B(DAD-vu)|@YrH|% zUV8m$_XxbH(&Iimg3?-ayh)dV1~pJ{T$$Ypj4)lEKg;M|JYZV&Sf;4!@89CI`lJ|O;cB2kaby0*hZ3^BWAyu~NEV%0YcwboneHqTkR zhXMDsiLPl7OY7et7d$7K)DJhmp=>JHjrBcQCcdO?YgU!Z6KS?ini3pMS21te>4p9X6_^Qbt7<7afy zgwzQG`BOxo(*KK+fcx^7m#*+%<6XTO4r@|b3vxo27KsrvaZrWJS@F0L>Ru2*vMsFO z#Ewnjp}kQfJhZI~q8XQ%KO; z?m#SG)kM(NLcngfj_0?I5BrX>do5J>Xx3H}2n3_dN~C64*Xj~d?KjY5jMRy0WrRxWnn!?Qt0~$#Th}bya)pj<)Fs9h~5J`J9 zV5x%rOOZ3R*ibf)5mD!2Q>MW^>!(mLE2C!NaYQL7cOTbyl>7`kG#;XqU{AONliO@i zUmE@;o|m(Rwd?bK>$#&;@iX{oP)LAQk6nQA$)%ItXEMQ%S4~bl4G2zfE1A*$^{-V9 z$I|#t!)B(|)=1Q8Lwt7x=*Vd_skY$K2XQw}eRkgzz=04zI9?P&Yc3=I!xx#0l3c&8 zwCnyvL)}x@v>JG`l~#l__bgHOWu1v7F{lG!C+`8&u#XrtD#z(t^?UpYn)-;ijZo8z z;h$Sx--ChHbVcUq)Cpc4E&UH+6=exFLDc7g+1v^?(J9vy`w0p`Z5N2M134!XA`krD zxyDk07b|~3mmh{xhLTYP#xK(gzNk+297rJJ8+dQG07jRt{ z8-(2)dGGFklE!_BgiufCc1UkkRNy6kwnR<0|B#I25otCB#3b>(5md%_b2tx%;#g^y zY7T?3LEHL+Uw!J6(tgyp;uRJ5Z)WqK8rH;#^Vfg(Jx@*CkU}BVtCT`1D&CiBC}WD% zmc3sJ$^D? z)(jjIxTfAsNQRgK=#nn^cpU-Oy&2JG}Vn2Le$cuviXLbCq>hv`I3GSMYkDn_mhGNZISj zO)qxK2s(9-Siz5*PzNJNY(3>_T|LGI=UZxh6H3V5EDMa%ZHN%QiaO1RsFtHkMQB= zA+(Yg4=sWVl#j*PU=jkE(?|pj|CthV|Cth455OHNpM9=e8d+fth$oNS|1y!;|1yyR z#-gB;1j;$*vY%`I5h9Uh${m>vdp7~VF>&!ZCKy_1gOv=_!cqA@vSi+}ta&ph2|5;` zi!?+o_}6DIEE; zHnEzg8|g@!5slHN&Cg_vqxuh=F7ZNKHQB5d=VzB1nf~J@rEQi$luTB)atTRV=Hr{6 z^2BU|bv9UzElh97ivb$XHWmL*gEbbB6^!CXbFnpKeKeI>>?~N=)@$Jqfyw8T_@t%K zeYUSMAQu2X-1^st)qhaL)O6!3g}o>=inkEr;H*o{ZUv8r)*2$%X9;5hSi;!PjK=xe zb~ioHN!is0oD%8$-22f;TW2;`YPj&BEV_dR8);mfHV#wrr~Jfd(zRr`FOL@EF8PdA zZ{c?k&!cl~5hfXuK#mbElP1W$S-iR;uwWBSouCFB7H?f@8=u2MRf2Q(YEyZ4J+}rp zEmBRSC#ZLOEMbc<4}eajpxDWd`;}KxJPT*4Kq?CF&?!L4!2Cn_zA#Z{K*;p)CV;Jz z14il|m~Gx;PS|Bg2mXd4F_AY1{gywnsVPjFW-+VRMEYhYo!G!~62r0((F-S&2yoY@ zWGK}$2sfiBl`gOQQX@BF zpyBMGoLbRnXOvnLzp9sfLY7U{UDPns(d^v9SY(2xdZ??gRK&HLl6HO<4P`&M3)RP$ z+F!#vEB{kGkVO$C;S1Z43$R=sU!sTuH>YH8?x?)-z9s@EDvv(cs0=^>uI*Oo{wU;5 zBpg59T-4nJmBK+rHk2_@=~PZsk=*wa31VA!uj5QJOW_<7=q{#bz=7NTP*!!Yr?4D;8kIL2B4h<2lb>+d#3R()7qtz zD>hJ7h_KG~Y3$4Un`5U^vi{Twveu&l?rIY>Oq{1oN<}xf9eVe((kQ2^PdyLgqvSxn1U(AM7M8` znpplJeN*7-I|*7Z0a_AG>UeIGrIY-+H5f#~7vQOAgWKMzTR<4%O_sz!BL!eiYhs*f zTKZ^$RGUr%M!y99U~ zgk}A$rU(QNE#~8Fk&6l0nIpkHq&#%DKWy=KKPc(G8!Y7^AqvrDJj)*S~2T~e`Cf*;4RWURoH^E}rcTzG(G zXGUo;%L{tl(MBnD*pjhet#>MC)22>roGqK5 zLmQR$%fVNWmE|9z;B{Z+I=%DKS^}9hBkA~CEwDs>+7DB&%vtE{HkC)U8}Gf5Id6N7 zuv_-gZ0Ozr|G7gagY_gT%S^sbgu)7)+A$o+d-yh__@LO`yZFw~`J9Izai=^F6a6IQ zZOL-DTQh;QF$jX3Au45NEeri;qUqCFx_fU_4J=&^q$$CO7wJYThBjDeb%+_~&v4!B z#2&&r&?6Aw6o+f0Bn7DtVt33g5#1`|{ye^h(ZD5Qhx0hg(B}R=%BxYEn^S>U*Q1BP z-vIDKE|eig7dZ|Wj{WDg7ubjFf*mgBR*lgEF7ODo6(Y5FEKU+?&LaW?4v&nIK;bbD z=&?f&KQg_QOr6^Ip^vAn_oddu58z=LOCL8Mz#p$VAE^xQH{BmgcYGf&eBL-dZ+8(k zcV>K>;m%sz`(G41I@1H=AQR^`Q-=8qFplopFwlg8LX6_|>#!p+?X;_3Qt@Yf5x${S zghAwd$y_QySLwz0!$O6bI^Q>2hl-b+!F)t$d??4BG>30bT5j2YN%MqBQ(1hbCgm_nSYTcqCsdYx!1vLb;ats7yB68{NuCG)Tl_ z4j=M0pAY^a)q3D$zUOhD^TqF;oBmpB`G}9T z>`46i%U`$TQA&t(hYN>LL@Q<@woHh@c2vMEHw!{SRipG9wDjwo;cKlh=Xu{t7rq-@ zyiZP1<_~@j@%Z*CGL))nXkNa$?cn_!u^l=5AR&H60Y5{*oFa&0cVT7l@Tu6VUIhjG zH0FBZgphNV{o2K2nyI3VsZ0RV!vA2Wvo_LIhvCUX1CH%&V2G#878qqq3;+Y5?KHJ=OgfJ*ZH-!B| z_|TNcZ4`dtzXQ%^51xM=`e1E3M0@=%oiR7nlRC2k=>bO9{H5f+3W(TO-qG$hFU{X} z2cTMb;<4J9Nr{tr*HmMM=eUM{t#po}y)0jO)SA?b+V4g02lkslT`sg=-Qoh>e~vun z$1&bcoWwFwP;IvnU$8g+$y#4SzHC08+W|A+Cfi%3_`=$Tg*wng_D}R?WNRGb!g(o<%K*REj@IJQ)vYB#5e9$VO)wMd zlW0jKIX>((kCBm<26AV4{3L*OAB-VF4A@Ga*3S{~Z`Vb(jIBH!;TdE%2|*W0HI8gq8||EHeY;}!HU4@9x!V*FUq;MD zObBpj?wwc-pPk0BUX2W~+#`<3jYjcbtPOR(6~dx{Vw(iAKp0rx4>f z!4&KhpeC|u7be~m*hA)=yBY7~g zss*_UfagQ=<;4vN_xU~ahzI-?FYW!s3Z0YKK;YWxsVP8If+R1+U`@ySoU{}7u?N+U z>0MHJy}xB_kmw@0|7+L)Esx*#C)<9gd_cw=VXLA&VDZ8Q7SC`i>KyD=d!$?S8j$qr zv2h#nRFNXwY#&WeRT=q?QvvfHuvZ&;U1K8P2I1LS!!STGP7DG}Z!}-wq>AQaN{>w5bX#@qV;%EIpghx zuKC+@SjTv59ykDPjw^v7PdQ2@Ij1n#Tl^O{Yf~?? z3wn>Bi5Og;@)M`G4wiOYjE`%t7i7M`#2-Rp(CO{htS(sBmdyKOHLS{(7f1sACx9X2Op`%V|Ri?{(J{UFCco ziQYS!S!W-Fwi2a-BgO|KD4`d+dM7Vq$2sYQ$K56Eoal>Q7aA{Sv&OZ$a6;Ls{~lQK zGUdrrJe7T7(H$Guth#hpF%`^VFz*}xSD`gO0n2f8cnUz)u(M$NB_~Gb{!PT5Dch+t z?(o;@M}8bjrs8mSHg-r+dET4xgRsQX%cXUc8@4A1WKMDt7t_7tIw%Km2|b>7&HDD4 zctd4!K@G0(-aIj2p`SbXG#L0~l!YfD-BIiq58Sgy_)Fg@2oeUP6r9VoINs<+WnxwE zrg+BlppRS;KIN zIw+)aZU&O~F@ih2u50dfWtJ_U>gHkh+EUb4U>aj;8G#Qcn)Q@#J8)z4_>!K-(mVaw z5`9|vwa=k=#g?!_RI=>sTYM84+g6r4BL=$B2O+eS{FnzRabKoNS1hq|s2)!>wu;51 zQ^3R$+TCW{tgHMOk77iGxM~T9B0A~fGuI+1#iDm5QxL9s&V>&dUDS$0Sf}?u;R}`e zBMgtj#uVuK+1=0#v2O5&f}SDi^4c4C#?z_I*n|zwMb|?A`O@BHB&B=3>cBo8gnZwL zK2PYX0vH`|v+~VErIY6-6O=q1v0rI?3XN;`;n4e}dDg!3L_NoE^G2$1#GD8!apd4S z&Q>iSdZ@53UA?dG{s+rtWMN;L)?ax8j9TsO=mgvqQZGZ*gpVzS!kQ`u-ImwbA%t?1 zgWpR4TG8&X7}?>ql`aYxT5@e-`u?>Q!T{Y|ecv{feOsH(5Uw}7y(&Fj00$HbvXyrIMi@YcXk zX*SWXhohiXgtR0N((ts?%2v)iKBrtZweHansNs2US7S@MWEAbO>3h4Q!0{4iX3=#@mS zXQF;l4&be7hRwaG=Rz>vmGY)>8*YStiBd}}-kbfwRJY8J0e75XD;R~CPl_(-88^_A ze0%{CM90{BWTeir)xDvV@vf@5!Rx^NB6J5jR)>9YtwQBXaDLv;Bh?8jmau8>`ai8_ z`4&|sGLklp{jH+qnR*Ka8xecN3DS1n+9klkvdeM{Zl8TT1I`}w6xJ}k2_;snlBU!g zL+`gR3c=<)BRx}RZ?3W)*Fz931F`gT$H(>FBfJ6d= zkqQB&unu%DGd_+#$0tM)GwtcpTog3TjvTRPCk+N=D%N4|JA25M(eCco7W=6vFfeooR*v!-SE>Z_&HHEL^aSk(Nf zP{bgH94mQZ0Uie1HK^(X`g6C-r~w^2-*QRp^%~J5qU=3bEnS)!eX3-dB&o*pD07_i z*B#l{o7bQRT> zBBRrx0duAvD@#N#)6qVBdqDI|4Ph1VQg7)fgrQz1mHPBE*4Z$IMc*V%&`#xWe{U4K zo~c!l59%d0lcw@~fn)sO-%?)-x2TR!NE{BP=Vf*rT2YRwSgYntS#yDHK5sbGNEfZG z{EbI^`lc6m5?T6%5qI`y+S8Y;;Cjr)wGhiT{)M|928Oj}ea|2FnA~RV#h?%RicM|j ziuMdu>dp*H8ibJi=+eD9aBk1mTf4@}rz{gyZm)XBWb!gy%@6%8)Rof63cxeD+uJp* zr2dSr*{s<`hRxhsG+iSdpQ4}PpW65;L2`vMFj2Zh6;}AQbDlqY1fEx#?LTk@&E%7& zXn5)t-DFljBj-MJt;uqt=Uclcj$kLb>jp9X;F#0jq1|Y`8$cfx0bsU zbzkXw^QzB+FKGsd>7O@W%{kvcru<2^QXNmK<>FU7>#giMPYb+A99K)d{Q4Ikvj?~D zaXs%)J7h9(r>d#9+t(oKlL(OA+#00ChAEniM=2R#V!iI!{`)2RX)N88sVr56SguzwcbG1}xQS4|?;&!`a_sW@c3WCbrzZ$B} zLD>{4S4Su*Z?(^$K zLU&!;R3FHrep5Dd$|nnow=KRIX_05mtsZuMkWRhDG9?Z#FR&O{oVO3j`+)8%Ku)Ej zSGGeYq!EfFh`)`TOMA$T#AC3uf!8NXoLXkrqZB$o1?K5 zAd&7boFY4{PB1G=Kq*p{-nhxAA)z4=RN)d-ehaguP~=S25ZBVl-mM1SI3cL1hWjTq zuqp%ML#H$ujuJ1>u`(DUd*~h9X38(jl z*#VBJy>ApJ&smNYD}wb?^WK85#s%tonQlpNs`@S1#Wvj>`0;V@^uoch8IH3(iK)Gn zvtOXE4D(LZa`?YILzVz;+LI1aoj2QWq|a&W^}N;cobGVO%fVGubHIg7s1*3x+i(qK zynhMg^;wtR^kV}zW7djs&&*uU|AJfU3?Q<8@H%$t*=s*)vVO_*H;b1PHDoOlL>B(A zB7&!MDKwx!T)a#yx(l0ml$3d6Q&+Ll-2zZsbfKr0%=W0M&|6);*j&Hiy4@Le(l0hz+jE>eIk zh|%Ip38k2_FY(5_;cyfgBkrNh<2N#l!6?XFxYM^*&k11_QLI_4^5GI@ zb`v8%ML3=A6T~aRv`3Qzr@-r5E)0>Vj-N3GksqsV8F%?b=SCvol~(5cLyfRa8|7-% z1mP30c@?S54)rLEJUIQ!W=wdBGNxHI#2dB@ranszh8$G1U$yrX#!^|pL&W9GGD)dX^OVmMyBFiNbt2_RQ_ z-0d?(tLt{0iOOCoP${iNVP`B&hczCE(!Ic&dgX8gfQJc%ce8#&fwXWD?S|Q~H!4k= zVnTq>4tk(o0K`0Pw5oJZQO|R@AA+~RxlmpdD2v#}EIpkrF9{vb5Z!r{iQUrcEPBw+ zdN1WP<+-m>IKW8?Ttl436<@!l)3dj8vGN0-9%PQEX84O1PJF9x2fcj%aPldPVqW#4;v$_7nREL@_T-lP%4L8Hf4E_ri)X9n}ieJsU z0akk@d|&Kq13;lf&Z>GUu&xeF8O3Mq#Og$Z!q)9^>&j+GQg0(NCONh4*!XXvh(>Jb zqO{W+E`?KBn~uBF+JHJ%bIr+?AB^=Z`SN`WYskT$4%0`3gveDz(et!qoHC$ zFD`z`y?T-~w*dX4NW6@p`;_7fd{7s1+k9KBODIKb7DT1_0MH_T5~uY1a#IG#Q%EG;FWW4#IC&V*-#VI zQP!ag*#QyNjD6*~5#KGF;-(?mu;(8Qc{!ZIUl_ukP{FV0&>e6#u)UT#7|qEeOS{jI zqbRCfz0f+?2K}?h#)`*KTu> z)^6l9z`WI$EpOzmy%(2Y_WEP#ji|DSXaL9Y375%u)qw`x#rQ1~D6ax$OJ=;aOGpEt zqPReMLnq>bZ0B;~9c48}`##Le3cgxW^DwsoPWfBaR$yk6#g`4agk)R}orku%_+li9qgx(4hvE4KdmGJ$Pp<4G39jRS<;NvSD|kP73wwYviO7x-pW_Qvf< zV~S9VFSDR!z7@Qk*(_yg(z+cz6kMuYJpRjl!q)^gHP0{ZnhI=W|mC9A2xL)jYN?xAGg4*x#@%0M;0X^B0y z-u+S61k3?kn@zipI)#E$&IJRI|>3j97T`LZ!gQ_rgm1h0F|N6%S@u?W= zIqGv*^?K~Y9SOGWy6Y4V;MQ_OcQPjCOmIUH$4vL1C-*w!daAr}%any`%X<}|ba0cd zMj!Hn$U#*Yi`}wrvwfFQwzrIuD5DGFlF_m(&goJ=<}{Ntw~Q=sEx8>wYnHQ2?m`jA zOi2CW<8{bBU00PRvE`&+=IQDB-_=?wR>et?+sia<9nyc>tVM?J#I*a|p4iydJ4rmyO>3UukK$PmYD1-Xza9&& z{ZZ{ZOm>;-)$F$YCVZ#It)WFCt`Q|(c|~L*N+=NSN;v|&g+ykw;}()68Bi~RR@IM-giu9J2Q=?xA`_QPP6(w<33 zi8=FdW@Gi`gCw4K?$^=UVW)LD@m#Sgj*~i^N33r+zn_nIiGUZ`hv=qDhudQdi8*9# zY7cf@`zDXPfidieFQ=?4RD}@-Mo>1Fd0-Qiy*Xa1aTWfOQ$U{DFheDKIkW8=%Ry#& zc(&tu7I-g<{4NW3xLcK&mx{tIiwHbs;plFKw44*KJFN9C$pd*7!xr;4ELI2lE0h8` z9hpANtC)ShQ=KHGAidGsXZvne6|3T;w1&T0c5SIn68Bg#_njsDl@)}F;$_8_S+LqJT)s2)adRLMUWjgB_>U>u=G80S7>7nYjopgrU zmR>;_mJaI~>UuKPo*peTS$a8RcHK(JV&tKiO_@$!O{Co4Su^X?q58VVAw3~xNZTmB zEhp7{JzX{*z(izU(l0(_y&+m9Ag%`8UM)$Pxo#w1 zTfNdD^+ExHhMZTR3L=iU1Gyu-5BOXWR2fAJy=_C=j*$_!zvs>|;!f97Em9d^_>B2p zvvZfbU&L^ceTZ)QWVtnLtrg~Q%b@^IzBn`Zp|T=X6j2a_bfj4jqS*3~0l6*qkTfnH zxm^33M(SdS)Gt%x$@SXq(!|i9_GTMKs5i5%SQRI+o%ToDChos&wu*=El$GaeOST$} z-99Ph=|aoZ>?%}+NrlM?YM*CqZ7c@bksiLY^c4DXJxm}xd+Vqhy3l)5>poCv@393Z zA<;C_V@&G~Oi2yN3rGizj-E+c_gLyt<@&ahwBPOw#Z7tublpd3=Mrq&l@?BZbSQfA zajCMm$Jx&8#7i6Q&cyz_0=-1JRD;_~Xbme%Sp7k4y1v6-n;zn$S>brP;UT^^Z(ny3 z>*IYg-+ zl3r?|wwm=}kg67yAsg4^rGBP8JtE!8NS|@;=rKGCVz|gYL^pjh+*;%rc5XR%;0Y5) zPne{#4!WVp>eZ2~d($pXY>r~M-(vgnD&uh6L9AG5@_Y4UDBCRdRIw^fD(l**_Gn#! zSMbfgKV>t0CoJFbH_uYi=R1^OD;283q!JmH%^i59tE__IzO%-F7A}*}>gO!EVG5UN zo#YlSlN5L@#ggIu@^$RFAxVMP(kxQ2Osf)=_VkaJuAy|6q7p^RrKlO|DdmP0rOmjn zAp}Fwa;+n_3wm7J^bwT1&pTcC;Fro-sOOCvmguGWd>MMSD&_6dO@W?=zn$k8d2PGu zqB#=h4CBk1n{ftt1Iy7(TMU*@ZAU2;W@YWK=id8o@{{k5ZnsIxy)zZ7;c8!l$+=qNd( zjC3*?O(se%KV?&8vtG;ttJV3@((V_Q0T&o!Keka497*9iycOmPr#!Q~j3J1;M@f9M zhk#p?LAHRrTW7$!tE4DkB+uo_zLs^7`{Q{stMw@4Zt|JZ_%+ zdX$G@^$|LK_z`4`(3T$|xp?p-mW;fK3=NAXF_Vhh^HxSutMf**h)!vS4gG%Q5JI`M zc7jsYDVG_b+HXz`~^JDY={r!qrX+AiV`^mandIZHmFk~r$h-1e7swNu^!Jxh6+uY zQ9n)9aVEWiV#9fyXpD2Qk)cAJH|n+5beu`6px|(y?iRxoAMb}$>uq2hxsCm$<4hU{ z1&8xE2E?VZrK7^kHu81!YOPaZn?%`sJ&`KLYATyS>IILwj^lNl>8MkE1|Da2%LOU| z$%hJDXF-(`P5fA|r4CaBROjQ5E5#-+!f(jsH_PfA*l<#>X5=GxY@ewpZ;lqL4|!Nd zGiX&d&X*%vNiD4fTxY4M4dCY&DuJIJ)fp+R16z11%G4v+IR&27DN)Z&h={;d389d} z=b}FNllVJigs=#bHbxz+a~}JUdp7(Ht3~O{{)pAt16D`oXGZQV!KVeqZ|BKVRw7e@ zb5}|!t)^~$$Ea`lvZY;U zyj?Xgzq&a}xIN<-w=CrdxtCH=&Zv;|_S0K-${EFV=kGODXWX)sxYGr01LMfO6!eyz zl13$Zp7J<`!~6a;q@q@b9Nq%COKQ}uQ`V?Nf#{w#u5r)iixtc2pahcpPrZ_LN*k3Z z6rIPJ?^zxubJO|}prZ_Od{TqS^crYWH)A!Cb<67DH7L74ZN_y<)|03(FOB037-`O| zTUL~;CuIFPa;?{%tjCmoI<5TU%CO0cMjwEbrWAOjo>n6l5Jhw)ULsQIi@1sv4_m!O zi|7QXNDZ`9XwOp)OvcZEz>jOL1bra?JX^W2+E=}iQT$>(TAIvnAvNh$yiR$EY9|6$ zEQCUC>jmF$dHO~f+N&f6X0VGngA!4}UqLCA3cf;pzCy-dq3T!oDS2vTR%he^tAd>v zN(4_1Fv>#D4wHI9skqN&!7uY5tUT^5P=RYtI*W54>wV^?dxk$ZS1gC6)!vbr>XRR4 zGMM=%4&BWap?MhE6G%7tG3CC(SvR3%6E~@iz>wQK)V07MT12OME0iU3Fn0CfBp{o| z>B`BJ)+>b`RbNpavO$!#^?4^!M5Y=U!aSwuNLAZ#*f)>!%y?2i$WV4)a-<%tbyj_2 zMo}?Rn1SN%p@n=|5)qi9=Hs7}(NLNTriFY=qLrtp>2s!>Gl`q`{k9um_8^O6feqq|d@_hfl!fz2WZJZXZLG~@ax@xXm` zCWz~6%6cu3GvoTWYENdGfR?grNc*?e%tbZL*AJOzlh^)kEof4Hc5gw}ze`xC*-_Hu z*-iP`y#?mYl`pH7{4@h&^0RwUI98Oz@JX|rq!}8MpWTbXq~aygNi&(G861-d`jbim z*;)nPnlx8QnxQedFeQ*#-CdgEK)3D;jLDozx`5>A(J9w;TUcs*4mk|BmP0dJc)7uo9_Mm><@q|+-l?%4Lu5^qP(J_2f3^# zXA%U2OC+nWkybSM$f)Xy(uyWg*Bk+XFBZnZl&0+Y9tkn zJ@UPxoT4hEqlket7j*L+HCK&{qU32I2wX)OMU&`)PHiW3vWmI;UCKB@BcmvNGg1<3 zg5{1ys+D1!NesmFd>caygh%s3*0iMcPSk}|=VX-S;`ox9EZ|P)XtV@@J6gg}xAY_i zD8)*pJur)b(ovHYWfT=KnrphzCNWTZ98FDz7@&HtzPGLSfY`iT9nQ^9F;G&MDA|?* zBmrtZk^)j7ug>{9DWwK|m^=#s3a8+QPlhR|v>1_U15+(K3=i zlCPDWNhk@VI;Q+3#)>>wd~6*QW#oWN-2sF$Kx!FAQ8uOkV|rOL5G~IS0#Ar99t0(= zQaPhxGBq11ahX)H-vjg(s3@jsFnr04R_2gu4<$$^bajd0`x~hEl>i)IoDvFd=JjO-)0s8zPWBOK$-u%R-+$+r6$h= zJ^Sd%SB+Y6o?qBS+ptw&$i!XeVsTf0^Hrm=dg>+tX@X_}H}2?a=&q!<)?!4lkkE`p z+wjw7$W&F0+;yzD)_NIXyZo%FD05wiQ);MMFXIZP>$g?|TTA*GdGk@;I@QmH*x*`? zU|hO?Yn{QYq@R%s9%Zc)xv9p_T1{zEXe~xcsn#!u@WDgag8ERNei$^y+jt0$%wBcmf_bF9^{2HZD5bO19z4z_(!J7N@-8wHe_&K5`lkYCA~9;ni_kC$BJN5T)#)wOR6@XY8sion-Cu zZQxrnGKf<4(Aq3{P#NDb5s4q}^O;g_3w!)khy&l65r|De*zL0N!dJ#+ zQCrw!vw~u-+Z04kmAR-YS2Kd>DG;3QA8K2BizJ(^SFNB;LG)Cai>h)pBZ!^?!Rh{? zHZYF7L6mRpvT7w2o^$xaO1(q!fZEnxHbFjlMJu%_h@NUC6`r$UAfWS8BDaBYc6$i zvJocMbf^vN0Nv49cR(|0z)}6T<}PEL%$g3hfpO%9QUynfqvS+ z36*iw?%gI34prr%id@Z#^Cf@9(+0-T6RMKUS;3+dDB6rb-+1$luw2v@_E^Ip9-}s) zU3ipwHyD_Pt0NGpE$mTM@eGrU{1TK~q8Ty1 zWtn)4I(>4 zcONQ6Hdl>Wcm3ov!!4CrpOZG*FO}z7cg;1U)*YW5BgmJs#gjfKZT2{2u65V^^hRJi z-u(@{Aqnp7L3l%H!+6-Bx^A0->L@Nb+@HXE!>ykfjo45ioPuQsuK8Ij>k#i|gziOO z8SdCT#D>ah+Az)>dr}$x-Hd>{7&;iTc?gMui(H~K3 z`3#zex9XDez2gmG!0D|oZL`Nob6wKrvr+kyH8v~CgkN1n+w4=C=gODO7o+keYiw3< z2vrNsRom=w%3S%f%`xn^dO?v6%^T9dd4|SH8%AyieOa{$8A?%8w;*j6Fw{lH%{Ej4 zTVdVm*>7`*90j0BRMX}meUZ>F=<72xkV?OBcWaUa?9FUL=S_ar7vE8dz-+7R85&GDYxj14dB^g*dl^pOC}+obQot8Q>H@7 z&A<}UR;Hn-4Gbg2N0K}aqgAVy>h!i~NdV9GC~5;|Q&yvI&O54Lrx_K>DVmC3I1xzzNiM@Re4b&_T%3mr^E9JAImKD=3nwB0kQGBF zgJh!$Aypu328fU%i`X_0(fJqqH`gkBhABo7LMlMm3=koS7`6>WBmjz5kW-dbqt-g# zGZu`Htdy72HXA;Y$6D*pFwH2n&KHe=BIL|Mw}g;3dzdm7TkpddwaI(k>t@s@XIz0B z+H3^bHP*g+bZZfLWIabxl8XPDWF-YZNr14Kx%e*C&Y5wt05tcU6v z6ONFa0=ybS1W>}CGPK#lh?zsR+BD~=_pH4(14T$Dll3zccbn9{9){ISrU62Dl1gdR zB`1!tf(B89>IVzMdgj-_bK4jw!o=yvg0|U+Rjp4ix6NFboXy1dZDXJa6K4gB+GY=< zh1P=%Q;j<7tfN^tLW;wfE8(r*knA^XG0x|@+K2!5_i*yftj_0e!F zJR$if$-aw<$S5UjEhBoBi1nxd4DX=t-m_B@xA2%#D!B}g8GU_A}G86+U%z>}}xv)n|OQ?S%t zA-fqhzuA9GzN?I+bug-Ax4GswRU{xK)IfdG9$@DcLVc!?<|^53uKL}ccc@YIo6=dc zN1?#z4?ow!Y;)D`=K4d_zjZz^bOM_*Lh=uJ`0VT>xLsoyU;}oN?7~Ma?@KBK@IgM@hzOHl8u`mZ@Q_bp| zUT~JBsPR|79BQ&Rqb!c^5gW`tq6n>qFu)q6 zHPmHmMroeFK?}hf-zQ{_YLYe_*)-I<3Em1Rpm2g_6&WY|ZyMTg#L-agrWsh{#u)5o zV2u;Ugbr<+fX(6FF2%q{6E?b8SYrxDi$fa@r1YbFn=0_e{*oZbTnC_yMTEErSnLH* z=2lYD$TLgO3Zs>j`ZBhD1fNrSCT;<6A~`atzSUwZQsp~R1(2%Wk*a#Y!n)vN7+3LC ze>By$pXx}eeUid?^v`BG_OIWOKbnnO@nP4!9!=h@X7gj85{q&8KsCPb96mrBwbQC6 zVdH5C;+qp65d@iOwUYqXfhBVwK;SDSV7Px&WM5n3{b^TrQtqh!P;F~Wzb9*X3mCaC zfpvZaI(wsvL?;za0)awKYj{2t|LC;hLAX!QtY{Aoe-M$ZN>LsiLIk;=t&y%(%Kt(l zcFqz)wM$CgE$nJAiJ5uhukyWvEGcz0g znUzXNt&QvWwI98$Ci}7OaI$VC6+TIg>!9~G#Y~0(=cUPH&ek#XKl$84_pn@cBoL_U z%U(+kO)q!yxySDQU}0nb06x&gv!t*V5OQejjXA7^HhHIoLf16Sb93v^6*|V977R}_ zSTcvF^e0v15EMY`nsZCeAt;0_=d_gI{j8>9dY1K-v5i*`>>&JJ> zkKn0uq6Ml(9Qaq@ncZ}sN<~Ij*8m>9HR5OYkCD^K$m!3HoWARxRg8fCWn9=-{S#nB z`TRUPQsrc2?aP_A@A%xlnvK?_Jo+p{_oL4;^e=$Tky%_(x=ml|%(pq{ij!lyA?V7c zmB&@D0;@PZCes3jF8_G~SHV+};Py-_BU)lSRipD9AjR1>nHI`IJm_6z9RwBKOABQo z7NdI{s!>jXPO-~44Rpd4C*x2Fatdam>5wDt|5wj`9V>zq&?4BI~LzB13>A9toL z>sOO>`$=l#hWlJCssVj8$NaJU^WJXBb&9B=5)>Xh4>V=;#2VP0XZb~M2R2#dDK=EM z*Q?QD0LssGd-*){kV8Q0bIpseLfW&P7O+})0f!E|b`BkM4<(d5MC83&hX&FX?Uasc z=;mvnm1fDslupXzDtc#%@XHUGa#GN4h$rVF@K`MMlDgaXPJ5s9Du1f*N5XM#b zFS-YnGV@f^!BhuY>2uX~_w?ON(+4BI>3=kvvSh@re>|CeSk-RkA1p| zRLz`u_|iyKn^yc-^&%RTc50^u@CiQqd8f`1r;*AOF)fd1srs4MQKhskJ1taWMQG*0 zA3OQwV|e)mo;NzJFtBUVJi|LJRANOO2QduOn(hJ;mrN_8SA@=M2#w5>1vOD!P=*_Y zDYhhEz2Gq=29J9%QoiKPY>+D7kt%>x{f^WC#Y)rq?-JurpW=m%oE?nNYr zv5-aZDe(V-@a9N1)THh*tSn^&+I1&OoPy>XGF>VYmU~!oLoV8(>Y{$J*+m8rJjE^6q<;w+>+WX{GSQlfVhWj7D-3#8qQv zJiypGeh$}5mw1$Y$;)+>-6aTvnUwpElmn#vcccbG{wK2$Jj%?tU4MV_UEFFmKlU|!5**7fhJvg{ z<~f$1izhKH6t6!p$*tq{xp)%OLNWRJ${$|mQ%t^3?;26uy`T)K#9!P=jG zWc@0(-c$4f(L%Mrhcq;K9YF6HKpHtn-t8;v`XN<9m{aFGpAl6X)yleF0WVJ|{HP_7 z?X56=)wjuNLRK+~>1Er-^izU?QYbEE&1my?h>zr}K~Fs}D-rbGYy9r?0cSmYhW97WlV{fbAs z?)hM0WB&p^LF8FBRIu2`I`ec+6_KA$N%np|g&%vm1@-ri|J zT#fkkhY;0}jUC%*LEPpwa{i@NjBuY$3t5KiT>f>=(!f>InH0J&6apFsb~R(~GA&fQ zDM*gIIAk!4KkdpK&y_g6hi^aaDGWZ$oaJzC^z?F~TbY4OvvPj_ldn)J5p^;%3oiR@|Pa+yoTbIaTQGqqa%9h8 zLY_wk9;NRVJ@oh2ex_r0Fw>Y0W~!F8pX}arKl=J(e+Tw3pFU1(0(k0Yp3a#~=sa{< z$Pby~xayadHx5Ln1^tk5X33nRghNeRPg1f@$1XtZ!TdaBBB9OSNujGpj1_qRcueU= z0$&%IbBe5QM48rbTSV(*bW-r+1ZR$-ur3cBkn&aXo1xQpU zf*-Dn$>~A?TSN=x`H1@B^!gd6L?4;J0Za=e^imCCOiVE&I^9DHW$ltc{Wy51)4c1` zLkq3r9^659NjP#i8|@#iugIUxrhK(l?S97kp}zwgsPY$w`Cy{@ zh=-gbQ$iTpjGY#=M1^tHFRg0q#!d@~cX>PwESXcgc(TF}EtI|`YEr7GVsy&ilEX_2 znW6;elY?95Xz?LFv^;vZN}TnO^JmJ#;$PlpDBk629e6+GTDf=5Ln|U$5@$Zh(LDJb zDBPrWT;+95jr5yEV<0Fq+0HKWr*uDg-(~F7N;f=}>m&fgb*(iGP0=C9)}N#(VD7$t zDeU)%R1Hf~WCXcyUoI|vLTboQ0=oNg5npr%6Lq9WP#`;@<4$Nfg(IScxvyp_-4#%K z()(yGp@jt-aPOl}qTQ#td}RFKB$qImP!x=RZ0lS?H9VA%V?rJwS`lo{7DUKVri3m7 zDT>iRJ|Iu^mY5W}3#!&BOY59Ju5UwrY^|-D;$C$_evL58w)D_KA%0pvP1WEzch9}& z9$F}Gfy(dd*7+mB7&qtaAGV7*ZnDm;=Uo;Jh-ywLy+)9Xg!g<=Q zOgN1i)Ztc?zMhH{Aem-H2TSdP4AH9 zrv%H2Dle~feyRG*38j#V65~2#U@J2Sr97mNu|O-24H?VJoYjv>1?0I%&V7dZn0cT= zDGw=>Lq?;9N?GT63iX+mL-}>Y+YknMJK;t{Ob;!T6X=p9swwKpLNOj(zU8k+U7CCb z9O&m3tvoY=>a$WfwerI-Jc{hpdjFKrPugg^Ok@$N>P+tFdrg$GSLcXHrL-hPf#R&& zlrvIV2@!SoZCJz?-N8gjATxemi1I)R>_(t)Z|I6=dH2d*JnYiWN%}`OeuU;wPM~<&? zUZmUJT2i|oJ`;$a%GXm4U6dLpD!j+N_3PV|8OQlvYPnUT7!4J{D7_5;E#yh!C6{)c zg9;;8xoR~Ts|oiomD|8-Of4Xj2=T{!tTQ}zT$br7k{no+XW`}_=pykHUt=(G;vT(OqYwos-;qhf8kMGV1z zsBL{})B!snrKY3{j_a+byJZ#v_p2yV;SK~7(VXCeUAxUPp!9r>Mm^zlOR`EZ`i8DL zF@d_F#@hUGlH;@p){dt8p^pQh|FWJmtY_ZRx4a^m*2fscwv;^jkmn(!@#%{LBML2kT&0*w;bTT){ND}dzj2^U^TkeR1QpHjgyB~N&sjS z*SfzPjl+##Jt7IDfCv3zlG8nn?A>J4*P@!>_f)uXJ(9rPoD_JaUrfg*GwbdqKkYb5 zsM`ku?{CpjokHR07gM>I!WnDtChG{@hd4Zq;0y`#TG1s=z2#&2r4PJ;=-^a zW>M$3_}<-Aj5U#LaJ><%NrZ#ckD*^oABvI-2WqOuRaD=R5VFSWF3&pBr1xacX^ihC zqxv4z)Xu3l0$owKr)6yEC)2!N_PJU4x$nI`5(Lf~4~Gkvx*-qCS>u_*9eZqe>r@_e3xjb@Pu#xu6YDpbySf zUDPD|8i@(IqO8KhRD`~dgr0a(FwJQaF8ax&wOviDlYV73fps zIpJq(BJuVX8UC;ibi@#~tsh77o#ObNCeg>4(D|zyMMo(WdhopwT)Uziiw;h|n7&ix zdJlI~olg{LO?@N;XBV)eQ?DicWZLJBOA6dg?TmwQMC^lqMndtve)v*@l$`>8-K{v1W_LF^V^OzcITaIAHDX8FJt0so zqaJa2#{oh@&TSp!o}bmD%t`p~CQCi?J?M!V!D$lSwLue`>}jshWysXxoRRWAw;}en z_0vp_Z5cn(EFm%{{MYaBQEKbnUAQUqynH*dhMEM*vdJ7w>aB??U&%%34gsV4# zCFz#X%@^ipVddIjchmeV^mOxwrxAeORpT2MHC+r;IzBSB+3rO(b!ulVDtIGrU4N-^ zG}m7)^eyOqGAdwsy59Rp$o8ezdl@8Bm_^^kiIDH6WGsp-txqFZlx)5_e5pw}qJo}< z=WRU<>pK#B7|J8c4Ps()d^>uj7p7*YM`W^~YBU#ei$_WGuZn`VU`n_%ed&*_*fNPQ%@sUl`4JXu9zlHRsGm9VQh7B+CD=eysO&X z%J{8jD{uRw+!C-LQR-BM%)+ALmvOL8jiq9ZD~8~0ec0Gg!qbPuFWS~q_=>xqDf#~X zIRWwP2JtLA}@AUHot){HlJZ#3(4?6t`OykMuc<-y6FBGgK=6X$2mh&19 zDn?4z-ls**vt}H4SU)>nKc?SF(DePRA=Y|xpEeKTzFL|U!&Cg4`vS6bO*hZP{nmI` z?=kmV)9KImF>$~CQBahg^ZIrd?w7dkFVzD0mwozEP~Y9whfN+%zmwq2Glexd()MHd zBcs}0Ugbd5ypdv6>^(?@}NUd33_>E|`~Md|Z8 z{po`8p%0tz-uFSdKkxmU#x3;=49k?e#VPi~9(CP3vnJ$uSRXv*zE|$AhZNv} z*X&^BT8BYha)-6|jbCQlI@NR}1OEJK`#hdbk0;=wycwzrzz8IW>aOn;bDU+bqrb9e z7IIOi7{ET2DQfA#+^+RLRp5e5arRr^+{&gY+f<BDgKtP0xA4rvV`XHHnJONOUf1ZXdSdc{(WOF%8ml!exffi1oPD2in_5Sv1G^^^5 zy$t*Z4eK4g#H(K7lc9ycJp|rqsO*lDpkqJelj;vod;0zaiIZy|cJ@qvOuv(0?zd`S zMhFwqP)-B)i3|AvAJ}Kbk6?v|``JK5@UR(6m!Q%m0}huFQ}TgZusIw?oWl}>QaW6s zVd;`py0o(9iW@;ZACL!|>(>a8Sb}~!3d2>*#iU%E5-bwbhM+Wrb6MYlDvyVRVQsC+ zNeVsh1RK|q0l#7B&78&I;}+~B_z1>mpf?zuaiLWCF60rS@d*I17u-g~!0WU11~Q?K zoHO3XS@&@^kRgoxfWQK$IosUe9|FpfL@i+?0&Q=`J9xa$TTykX7*L(o387q2k^|SJ z39(?GnleHh-X%l>OwmWi}2XF;9LNGpk`}X1b00X?9x61$>bWj1-D7|Ww9%z&? zjqr_6Sb)uGH{uA^c#re|66TlfC#REgdMyXVW8?kx6H#C@{~93(YotwjunZZ`GUzOG zGN3ITxpKuhRj^|xDWOd+lo`xrKZ0A{6~^^$Q9EQ-CrrG|;c4WCtrS_U6cbw2u~Va? z36P4Tu$eNs-t8CEHTvq`9iI(MKp(ka4L_=eKSin$E~CRPpikeaPUA*T`}#b%dISQH zkt0^~ovQg$x+Vh5bUX}13%FKCP|PP)@j*b-!hOd~?%-SOTWo(z#5 ze}|^uVZsy;e4(Qgpy%6_YC#kN@Pd@lSN>{sm*JD=k^P0`Qc<}y!$zBbU=Prz?yqaa zKFAuthw~>+cz-?Kd><}s%DmK+c^QC}jz@vsdZ#|%QJVtxa^Pv@@`z3Nba>m6=NdiaYcRv>YL8g*IDPX+ph}hz7V_yUx0zo@ z=lU8)QXW9cg*Aer8o~S+a^-<#K){64n1>H+2GBjrh_HCqPz)?b$8k7(i&cFwg2Ze( zXi{hDT8KLZrn#5VWrjQ5EGi_zW5G5oWpe~?RP`Vh^|k}~CQHgmyzP^CyWfbJo>L7= zhOCldZQ1ksY)I;CD!}lm@qSgDqH_#ZrN2_g7lHpwU!+mEIKPJ@ z{k6XX5Es<~(|}=13qUF^0T{wGgd}Bgd`=p4%JkQ+qatZ}XiOj(^q>iy1OifWKi zs#uAEecFq)d%fn20)FZZ}IhBjxiKzu!gV((XY+CZ1OI7ybbW5g6e`S~s+>5GG zt^KK9kr=V6&{<#oQIjMp5@U{nA|yup!($|dS0si{>%FK@9nBe++gfyMSieAZ@*Hk` zzrHd>bYrNFSE$aD*xUZl>eCoR_gany4WAV#TA7`QjsD91RQRD4iZ;2DJw<}C!V>4e zfnH=01wI%-O? z*9>kiBinrHBg3t!#NgIs7aGw*EYp=hp501Zt^B2Dw0HG)n;+WD=u)XRGCYaam#j$p zIye;aJSiR&ZavK$19sj!eRzsB&IujjMA1iG@XcuTaBG{-DK4mBuOtT>!arMw?n#~#bn<%oQ3%+XbEWMXSMLd(7 zRdsl-JNKNV*sFNWVEg$y1`9ei&c@ZpnvM$J5-_ED+@_s$oB2MwDcGZVXiOA_?Lx#KB0I)~Sz0n@m-enW;!d;B*}{GAuM0+rgQp zm2_HYpXo~AKJ%>O(Z)?iIoVsAsGMaXp`oe>;q=%LPy|-54w0g=6!S^NJJR>2UjMBIid&!;wJd&8W%HWPnAlYC1J^b|LnHe2G z5Pdh#%yV!SRaQY+3v?hSm%5*G7Ellcc|EUaa-ffclc>Zw!otrvR2p3?B*5Rd;>W2X zIoO6q`&5Y`Y;;J17iCi|Q03qh3qVujk@5a)>12Ph93)zhXDSCV&+Z2b3+ZHh9SZv6 zY%r*nP0*OhHat<%x;(9zPr~5vN!HYOWV{F4b+89H3puX>p0vSr19aY#inRryJsXUU5Eu!w08iJu&9@p_ktPK>U^Y2~Lm7$!CM z%E3HqT@>-z?+%nxSzvpq4Q}|9*UJ>8dw}hwY{cnsu#B6fMtW!EVM>+e#vq<&4_e_& z6jS7{WOAU7gHqop2ZmTDf6be~zjCn5Bk?_b4UKjXzNjjrBRZ|$E8>Vw<2_xBsqx4g ze)r>MIA0S3#4z18K2Ma|#bSbOQBwrH*JD?v83qjYr03I@Nx5#(jHlLdHucsKp9?Va!*sj=c4P^5CDoJZr|(cw`UZ76W9& z3D2yRbXq9Eh_1w`bn<>ytn$qkI_&u}cy|5K*!qT|eS-iY{pi>S;lAS74+9W#j`yWp zn*3CYe^}GzS$UN3NeAKpyXV|a_xhE4RZ5V_GgPH`;+AZ)5=FH!91g5%OBf%uh8bLL!&*C z;7G>1BZJJ=QsE#eq+_n)#dk;cn>{$(9qT<9(z8T-rc*vS(~0*P$-z8p5S)XxpJ}8; z37kKD?6Y->CfOQsfb-{IOs$Wc(QV)6K+ZV`GjeDE(LyhLU5Oi#4yKuB>6L@Cw4qGQ z{q8_T)}m7#Wq7Nto!?2GSJA1CGJC&W>;bDW{$WkK&kEJF)q$J@R=L>+Qv%2C`YV_m z;Bh>PHc}1@F~$CxH$i^opz&UztS|jcqxXuya?+R)EQ9w-{yqHk<#jTq)5HbtV*)cVNiOe-;T zrqjC$xX*MYaGw#ns&VvHE{4TB-i>8wv@PCp4xXs;|=!!$%u4NsJ4 z)E`Vi>x~e0vpN{xDdQr?eyY9TQZ!@xD?=144m{(u6Ao}lf9JsbB%s{-7vIv>YlU`a z8X9fAQ+6lav@fgIj}<{@@h^qd*3|mQaCa)!3++y}BoM81v=Yd&TeEDO8?(%h6;Ew> zXtN;~Qu@3K!^--lqDpF2eofI>YtG7$s74J-zA`^F@^e)b z@XW}{bDlK{*03LYv&{y zoxv0EBvXM=mUqR_FW<9^w9A)a*QE?zK1j0Qfd)x8NvF&&A*y+Wn5eW66XQb(ZN+%7 z6WuH0=6fzv=^4HjN<`C@Cyz2}4bb{M{7M)#-HOkc=*YT*1Dmgh65da;0<@zDYuh;b zqa@=7y`>*xolvr|pqNj>{=Cdu1KFdRuEra|npz(jl^XFwRI}*BbL}z)ArUQT8B!Ed zkk3Bbc}TBdeZ3gQE=n!LaViBGZsah~rTwyO4Q7sNfw~5kWur(C7omya4{O>yD<7e{ z9H%NlJ_a*?O=fqq#eu&1>Q6YpzPRW5on&gh$KmMZV!b|y)nRC~6-i-rR#kc(HsQ0X z(j%*jF||H2+?^Vvk9H?#z#v+XW%-O{#1)=fHDur27Kb)la0tVOOJe=@kp3V1s>Zx{ zT)h2saIpPeQt&VD>RH3hnzxe?XsTN*8%Pr7`NLszj89B7Bp8YA?9O&cZBMxxBsb_ay)12cY{;D$u3eRE2 z-!urT^`@zS0b+xGLKUL^;K$VZ$e5k+fSr-+!&JB1o#9}2MxP(?XIxGBO3#f^p{6P( zWv}{7UDq>`D7Ji!yVDy}Uja zH4s*0GhlQss+Ah#Z61?aMQdCyQmmqF(3)#Ba+>w5Vn%AA$Q6yKylaGI=*m>@&d1Bh z|JG~2#b)y08K|A`fM0OW6J-i&AgRuSRpW_Lr~v%fXh-(Q{>;PvOzX-bvOmkXKa(*v z9vSb?e6&ByOAE&+qC*)r?9R2DLt=VH`}0&RH*$Os7378c zFQ4qc&iagxb3QrE`4RzWVXN|cnjyAI?|@;0m9=CRQ&$=pR*b3jk+HEN&$;YMG*B7AQhY!m@Sp;}rE#)0Ab#GSf3MI?_rF z9qD|%t3bOfT|E3!|cf*+KHS#KASxfTAJ5zdG0snlq->r-kg0 zN^Qt9S(34mz6u!AA}e8NP`_qpKtZ}U5^MF%u!G%~M&mkt%_EkHH6W?aV;#L71^OE5 z;2@e4Fy^NWt24f4WRxw<85N7xp@urGb0*~QR5Nu3=qJ=?{SJYCln0#9^tp7s1yCKq zvo{JMI2_#F9fCUqcXxMpcXxLQF2UX19fAjUcX$6z?*HC*-&gfs)vvl{r{>Jg+3ud{ z*`4k#qQHR&fah3KZOEZwZ)lq#p$-5ZPe*Uy3th6HFL-_v!uf>?h zVvU3ot5_4_Ft;nedSp5nEa>MKe*SLn*SRGGTZ%)4wzVEW+o<$-;OqlNw(a{gs)eNk z#WS1ShLd$Fww}=enYx1W%Pj%M?elkH2xwd>yKv5)r{HdC0^}4@>A4+>;b}F;@AT_9 z1uk(mfJ=p%n$|X{_W!cZg=d?d==x^wYv!I9`!NNAbfo)R+V#{@%dBlWaVf-)igv;@ zR>#v6Q#a#0$AWXeXf{9ecD7-9s7Iu8-sCo~hM$NsP*na^>hb7)n@G$R!+&Tw_l0)~ z{6bCvEPJ(lY3#0{_2c8YIujT37o9B&-5)u>emUP|B)U%iyS`7-YW{CC_M!0&m0MVZ zhP+aqdbyz_U9Mr_Ml>CL{#=|69zxfRGYLQ)6@StkZ-i-_2u<<8Xj~7r08m1km@?!ZD@-O`*%dktF|4>~-gJVKl&$ZGed>}Fp|!H@sIq7uoovNv zgboMYlN=M{EK@#~5^xfQys^0OAt`((>gUpQJz)f{p}ZSMaEr-;?buWXIh-Qufoa_u%f`XC7V2w3vQPO`AK%3dM3w3m($?lF8qSlBkpX}WDL`mFIRk$N4;OH=;@ z`i(t~je;&DLLlcvk#HKOjtqtOEWxp5A%AjlnvBh2J&RCP$JIP8StPeQXVu$SKHW0om0GPjNK#Q_jP13!NX);C4(*Z^}F@aMT@3>gaU{M(Vqx4{}{%!Za|M)WDkNSzGM@XZ(H`G}Sw;2g9$r`>Gkjr-KW#XQ23nKRKDi1KTk zb=+>pi}$pA#r@l)s9-1<%Az>Gl&M3}6`^#zk14jo^*gP|rfCv4U+_>(`;R1`~Hwc^uNyl21 zA@3V?dw5s93Dyp`FmDu+3R&~mXAA#Av~3Akn*{EIquoj~zV85RUNj)~HMn;)EZEh| zZKq0kg#Xz*C4%f0M7J*;Pu3&EVi++_ru~+jOU)R!S}brX0JkZt1_W zZk7olQF2Yf@NrI2up8Bm{EbyRY@Q~QggayD4y zDtT|GC4Y*vLvLaIc$v=2jOK<@Hy`w5J0^D;r=GeT-~^^ri|Mur73G*vXrS+xX^7FDjLuS2a;E2U&O*8x0mfCYYa`eeYcGWw568^Pn;I0h z$Fz?J0?X)VW|waBfRnq9Grg1z*yqVaovCz{94y3l%lzQJLAH_f*IPs(EEs1h?aZ^A zo=G0qIK+DhxTw5WZ--~t8)>*8q3V{B?(`3^F6)PYLxv7Z^|Pj$Xpbk0{FcI47G>1C zd8OJV^}-6W73t&kfNE~KWRhxbcJA<(nM7bmhhhD$&%$2*+mUHZcJ2VLAIu4$iJSKq zUq+Tb#(!qq`{gwy^+;Cp+ff^ZNJPLI5Lqt!z4^u7hIV*Y^N|@G;g=dArO}ham&9_O zhX1}c693^kosxC&4Bzod1w3l}E|vBjc0XHj$UVjNBx$uq)8i8tM95P|PCW@#`mc3t zDEbn>znJOeks4EUZ}MIJaHnu^(`jWY+?&hyH#DYi_|H@bHq4iBcXA{WkK|yG7_u_S zEUw+d+nVTbxU#TV%)85ZM|m%3ry>3;`i^mf1LpvAAS*{eRA3R?J*2dB`bJ5rH54cwIyZI*kdG5@3I>?B6ioMx- zzqM2^Poulna)4rwFiG}51c^kQT6#zxRROJ>9dczudlcOZqEOi;dhqO1X{|CTpihDz zmjV9*R3htf@Ib>r4WmYepVlk^>iv2XjS0u!SrH=Is#D>H;_k>w?dMiQ`yf%%%uG1O$X!C6lhb9H8(;0BXF9&-$?b*oxZ=TuxMGt-# z{YWv-eEZV;sBSML%#+0Y-|bflmP46sWd1ep^K68)01o|Fdc@Vac#Q@kCQJ)NE8U8NqOBQSh^oZ!DO0iC{_hu95Rtn*+1Br z8E@ttJUPf8!t3xY^|;I4$|21QKWj`U-{TuUODBw0D?HNaQDv+c{BV$=52vq$F+GS! zLa9y6C+YkSMe%r|ulAau+h?|OxZ$Ote2r(J!etwW zRxmR*4mneqM~Mh-H5`#+3Y;!g{b`-S3HU}iE{%teonLj(LAulpVN#3*6e3HgrYiH- zzD~9w&pDv&kjy8Pw#z~^l?B-2+l{#p5UoxXev1YjM?#}bjzc-So(W&_{H2(pzig)D z3eQCC(B@u&i!Mc;!32zXkSH;++)>t!*5w3CG*E@jn+6w**xSzEh51?%$z2EBl3a+- zy616l&9||CGtqMAMSXTeS}&>R-{`e6`wvT9oB207L`Rw3hM8A$f7hzFIc4{FsCtrY z|8iegYvm6ZrhId{E}xDt%=9V-f70h(4I1mR3O3Um!07u$PWUaV&wPPK8pzacByf0u z+C_U#dp{z?=yn!!9p8YcG2pMav?Y7^A``x5ZC;#ilc7rv?Xt6#Gqkx0g8g(=Kx7%D z3do31o40{7ye#(AJ}$fC#x2AB@utU=k0ic&;RBn3#*P`oeU}%rjR{SY3Pyth&dsfd z9)HK}5ujwr4#QU!rs@{o_@0)k#=*_|y;`bl!YRe?xqbz>UZB_4=hP;q&RX>8XpHw& z!zJV9!}3iiJZz#tb&!cyszSIPJUB^6EzooTO?!t~Dpk#A%nmajd#~(sdc8|C?VTV? zkx2RGY$ldf>bR}8+`U|v3CFaw_7vDZLn?YKAoI|kNbZSz?)P7&*L&MXPZi8=oKJttYqFwWHC`w#^wWV{3iOrAJZWo!ph`ceknPJ77wWAI;{A^QvF~TV=`pIG8cqqgo zA)j^6dM+m~t#g|a3QEC?q13Z!k3Sf|fO+l_3%w{DXYQ&{EAxfu2f`9Uw}VKEtWV!iJz52Wul&|3P|@IDvKq+`ztMfKKBQxq>|hk ze6Xn$yE{h|g@Q=g+Udc1gnnN9qm<&p+LJ%WVsRBEZd>aJ!6Ad{I>ivyTik6FX>_yog zZV|l7@iGss0v`lb3rnkI16J^17?CzJ1_#-_OHi0&vL^Cr^2 zytWaR9~5i;SRnmX5#)LN(avU$7{0?2#V_ak-ixrJ*RdcXnI!sh;iuaAelA+ni*w*7 z5`xo(sbQE*5omS$Ts-d-+RC}(N^XGLU zstj^$sp2R9cvKp@UW5{d>4lje`J}D)*rrfoq@XP&9!UXq((8`_=!JBShN~tW)Fa-` zQ&R;PC%H>&;Atc)n-)qJrr`z=1#xPTp)cCC+dC--%LJ*n6+Ou$>WbLF?_@_mio9XM zt&_c(A`+l{rP$~04hsmaJ81*)yyC>tq&umy=pw=uLHKkN)0@E z^x`u}<)AqC@})MlsZUjd_z|3I!bt6~qMG;Kf8@2d!Au1|cJ)y&LUwL^VH4dg& zh!AKU(>~$JpTG!PY9SU8H{X|qu4w9FH#O_Mecsd%_iTgnvQUz~O0<uu9^}WVGE) zT=G+EPVWL(PX4gYl=>3BI<{nJQL(yp$1BO&UKg+Kg+MT9%UH8N`%I`x-oiolpu%g* zLLjtUs!R1)2*g6QC=%2HoECL*z0IDU>8`B0*pyPJ-y zW#2KB7K)~%?aO$S-{H=%9cq)R8vhQ^Ei>fBr#&_-|NERkMK6Nf1d&YVcn z&*lv0FGeu5CL2jCTr-RrS`qGoDD$r_nd z`!Vn4oeUF7Q$7SkC%_7Ww~$oi#JJWXj87MywQL1ip{{pqn~AjM&YLv+n)iKlJ{VPA zX@>72UB=yIb5m4?R@yjH348dZCUCP>k#J#_KTr`*mrhq8^S1J+?jci3mPb_oA|U|x zD~|_?f(L4^$-4kgm>#*C8=mn|8^nFBT&Q}uaK4uo%0f)lBOV|dL=0G+wUNwmb=4l| zfBX!S%3@n;ukPYHBzvo6fbTF}S&BH!vk1gzI5h=i{G`sE%y;GA)pma$P~Cxqx0$Rl zs2~3^qbGC4wRT#&l-qUu5ZG|x`@*;8f*TK^#aYwP^=SU>^MHBHg%3<(2^C_=bZzy! zpuJZ^Fg9=J))P9>LD-w4P0e5H(<(f5_61DOY)s;y9*&Nzu!WD#Z>81KBkXLb-zRrq z3C^CrQ<@R3@cF}g-8X)&c4&fYVerwB>3JsAxr~I7Y~7)8?qOl=uWu4!KnVS9V#jxU z(u0KP9JGk%{k9j%g6;K$=+AHE1vvTsL;iA7ViugTSdvM}g!MD1qPR8FcqQI>E8(7f ztdZyhGO_28rR>;~sE~vB)aWhI(vf{(^3=ysPq8b`#vyZhzlrz_p?I|gA`WlTmIk6# z#%`?s$mp%Ew#VOHo$;bV=54|C-L~+e=b`y&g#Gy2+wJZMml68rf;ab9PWA?)~t3&O*VV;Hi3*Yzth_jYc z@KV3U&ld74%?8rJz5F)%@ntD@udW|&j^`6UgZr3)q>43nukT5Ix@(b;w-2E0rK64J zBZGQd5?&Kv2PY|h^ZmIPT<=}(`0Kf>O^c z-mwDGZkQp$O0mDD7`ZyB>|JGWNuJNOtT6ki+OihGhWD~%%M;nh=i|5=Lg|u1OAP(| zG0PPBdBw|Q^OQr;_{L0!|8oa$NV(f*LpCjca3WPNMfKCpJ#Fh-BG;Z{DK6gI?T z2kl1os(XrPNn;F;;p5)Z{61QG{Dwsyd)@_1n_usIJy$8=l|R}>a@hFChX`!qGFRU5 zimvRUn%7}LGHguNC-_&(UC?uy7h!$VZ7!)e?bzFOTmRVJ>toTsCycFH-LX7cH@h00 zmf>Fvk4TutX?X7Z?5KOdPJRsQY{wX}?ffOLn)_?=(Pja&U1p0M$7|K0gYiKcmu&^E z8^#Okij;t=li8`G5ogyeVKW@>u_VY1blQ-xzCO0Bvq}0valk+zk8x99%b1u zIWz6E0mtsKk!)o(NqHp(UR(9xn-mp*m6#lHK5Z*{@WQ3aHvCQhs1+F&9PiT6Z>I6x zX2a# z{Ic@U6M)e%3r4m0ZO)o_+3>eF1E+96p2ZN++;eK~0iTi8Bj>nS2WocKPD`js#nnT) z>TfXpBqM^icGd^QE1EGEQ63m}zrn;{6b zPJ*i#D3AlPi0p6H){$JIwo-MIJZCj$*$tm2ZqJmSH!{?Ia~~W;iZ|%_ktpIWZiU}h zu;yxnX~x0!Tvbt4*)i(PD6OL0ntsGU2{$AMC$lD@Ak%AFbWP}pwJU2(N0zr%ja1QI zsaD01trn!P6kD~iQ@2BDU>_7&mzYOAD0P!x^XzcfR{Ck>%+*FMIf+0<m${d2F1{iWM-Ce~yvUQ^eHv-@{0hE?WwR&5rl@H069 z>g~B&u_8&Rwpz;=b6EMlya_sZL(q*o?RGO>i@CjiM@{1{O|3uTN*$?{zk6dEo3DAH z`!T9Uey;JU-Q&-7Y1g=Fw_V9X8TwG4GXNR1|Q`K139rd4Filoy@H|0yaPz-4?&K z5c_FtKd(NtI-8DSXak*rH~MN?RVEIXl7|dlQmnjuyW}0QFA@&Y+84UVuN*tj9HY+- zCzeE8Q}}ooj3tWOA*`$%^5AUGc<167Idw;M5hYHd&bD6Pr1rsEh^c(q=>2fM%qs=g zdStZUY#y{EJy246icm=`R#yF$ND>{~%0NWw{pft~6L>3aSFqo#OlLFv!PvNdiwV!6 z&$p+@PDqxExc1Y(oY!PdPh3g0Y6ol!d{X+J7?6lC(s!A6ulLwY zY_V-e$7HR!y{x^BH8*#NG&9q;_319SSP4@kC;vIXA%i$pB3(d>*78DqG8B=wjrVPD z)F0MTO=-1#;CO0EUwLXu57kwGqi~=opm+! zG;dBT_mPN?E8P(i1Cwv+Vi2@JV|qx+m8upzA@hh_!e@JD#$W8k1upp`%KA zZ0RPWDht!w#7?=qY_=|X(4A0i-Go_M+xEoKW;pR#noGi7OOmx%(Dtf30l!$}#f7~d zUa-2P)6As~jZ#Ih{;OPq7kx(m!;C(^6@STt#cXaZwS=fG9FBUdD2Kpk!TYMJbyaIj zK_Jj-#q&(U;zMhEw&$JhM1qq}OQ&Y1)BK_9cD;c0p35pq^_H2ohv=YE&g5myOT>aq z1KFflZbCz0?y@m!p$gi8@j%4txF`sts!lCTyRldo&S5rVg`#6ybXp20)x3CdK9)A) z>a9FvA&O)pLl)Ly#q*A&+Ry7Bk!mhG$XKpu=P7bVNj`SW6QhfxwBRa zgtOx4SL!P-uaE5ET`g^W-`kJ>zzEb zE>UKUpmERjeitLPDzs)c!kT&^jyUO8Nsa38d$bvBkOE?EXE3u!K|Rd|W(}90R-i2! zoxDrP*W=HxE;JhNsoup+fs5a0V}5Ce*>(}v z*D&-Db_okq0P|VfDNpc!UiEw)ZGC8_CD*88F-bgeCoK^MjG9k*3D8e{gUcHq+j2o&mC*_q4;7*s>V1`v&hmIQG%GbA zxh)saWgV@6@K_+M!QNL1>a>hkgTE~|P;oAdGBmmGUp)?4n1wwn#84Gys7%mRC+n(} z^)x8D@7G={yH2Epv2rW$}TC@2ed=t{bw+TM7f`6 z7U>25KpIIvFCvAIJ56m3S3D!KLn0DEcv3*0VJVn~Fe1f?L_8A3i3*UAh{5Ioj9r3i zteHBAWJP1C1@WMM`*V!pBM(ZrCKAdz-ec{O@?yg5l6GMMiBK-^cL(zMB7xe~;Ys(t zr9cw=k3{|>@jw#6D_aW2ISyh(lsJI+SB9 z0vwToxdTrgvLBa779D^tgtsgk%_aXAe3x`+MkhQeB;ch~h&UJFG@i=xyUTW~(cgew zSwsq|!%M*|((q=XtV-OZD6aTDSck;gRe(bx2se-IAU@QN<3l_%euA@o&MB? z9UL2`B9Mm^91wt|21P)kz!~8v1fV`faY*cV;X5QI+Ib90+){cDN(6d&0ox|9jjDQg zQQfHGt!v@BE%fz-JgMS+3t=n(plYBgKt?i2lnVJu#a3~}BUI%99_TKcPJ367<8`vL z8pD&6Ggt*Dc-kzHD8|4dHaSouPG@n#I(_iF94LVaA=v>h9K4=;h=jesA{qJJaf}eB zERW}&d~%B1Oq75>`=G?M!dfYqtEqJ-7ET!WqlEjp>$SmNVV^AaxySYL!*<*dVtI_|!b7&(L*94}NJ zSE}bm4fajC<%;b(tv;ikz>!$+I9^zMZUml31ov~o>t&(sx~N_wf`Ad(Z*g7U@jIZs zSDyVDwQ3o9jm-QERdD&jPtnZ#&_TGoB`%L}fETsR5l~dqw{Lq*N$ZUv7c(UL965$n%!O&LpMcC{SD;>Zq6+>DDdbdLiQmFN_sRk$e zuQ3LwReG;u{8_8x*=7jdhiVm3{}-Alw-8Oi7@>?Ppfn<&R=l7Ute|IfK;&CrtGgSh z+d=;an8S#*nkfIUiF^uS8Hy3g8s`s$03>JyxH-$QXxRidRUKIHs zEKi}<0s9M~J%ne$c7mrdMgl^sjCgU0xLHx8a!SM+*m5lj2$LYn5$yrd%J7uF|HeXF zc$G4el~5q1G z5OqJy6fcx1oh4s{IcQEvLr+|zqYriKfAhRygfi&4pna&J!Zc+M zOGAQ$127o0@bk^3@#9@q=y@zLH?jd^-}J#wQ(EgcP;F35%P!+^V<377!RKb*V5J5w zdp&;Q`!=8ytXsS}@Uvfz;l~+F`|tB{?{Ri=6TKwe(PtyLp9u@5+^SqT&1SB5H*_S* z$Liht8Xx2%R=-6ApMCsbwdpZTfw^CDbwW+3oMsPR8|VouJ70Q|?Qf|kJJ0k^X+)#0 zf7s{?b)EB~p$zoy-bOGE!N791Im)7M6G0%)HlBO$h*_o`H+Snjc3XV!z&mln@4jRY ztGRf(?%0@=->1R%9^4wJVe6Nr->lzq&F^d|)q1ENZ&H(^N9L?vQk_V_8u^$7+MzQgPWG%FGhBUcBX(~P-Cyyn`ih;M@FC*17Y_Kkje79L&&VVfHh=jS{Aud?8Cl?S zd*%9DM8@*Lzwv%kDpoxMH#NxS=)S2X*QKn!aIG&EJv8~Evg>&H<)^S&!t8s;M#rZP zF{IX|YYwI4dk4J5to(Zb-(C^>m#vs4!ft@*-o(|8TgUXVuxBIKNq(*a!(HUMRyRH+ zYkkdxuAEae(K2`yw%a|zV`7BY z;vx&dG}{jW`1c>@+Hm6+eY%cZQs>?6r$RhD7@m|Zxa4gD%h@0`mC$YOesX~O3>|!E z{BcAd=&KBxdR^s@boRp)xAN%-4*DQ!aD}99n*XRvTaKu66s zzTh3q++)Xi%}I0#c+IJZ&rdi1Hc@l)f*_}>k$+tYb)GxBTfK~^V2fc3ynZzZ(;7PHyOq8V5DFF-xI4kWaqv%R2Z5 zzd;*<5Y2-+-&Yypk$+)ECyDZ9efF|=mH619i66;FaE{P6Ht>iYUcRPxfgC5?Z-m3j(%?plY-Oo%NZ_bPJ^~_M z|E}2awh1t_m^G#s0UkrOG1szhyq?D{O_6Xeb(cTzee20+)PpYQXe`mb%%64=%R97e zMBDMT>vUsm7%$y|c^Vu!maRR7ABmN1p$X(-!=XMqbDQ}5_X4&th8XcU(vzs&y*~I) zSRJmfqhGJBJ>)d2Bf!oCQ13wh3ATcc7m7S83gVaToh1?;+ix(ZO6{@ki;X3jkmJ4y zrMRWOO0+x_gdB%&ICo@M5*720+ZR-jf3800B~sG?on{i9WJ?B1?-DLug`gdg;d%=zV60-Jcfk(F&AgTFchrNPT z%{`9x#``ZGwL*f5gCqE`l)5|4AmkFeC-7b^_T}XuAz)fHxWBrt*i^cD0W(;J4%=H7 z;!*D7km1OTKG#>SQ|C)+Js7f@&Mw^WG z5H$taNja1=G-6BP5h#}tXpW!?Tn!GFter0@FT+X7dQX~$?nRmYCf;KG(pEEWB_lg~ zZZN)1TlniRK52Q{`p1&hMP4ZIRv7O$-T8q8&TL*s(z>YhX|)qxeq9OFG?;OvA=?@T z;UBPf%d(Mp<&c{0-mQkssvM>2H+9^Qqa0}=ua;MlBVKk?-*+eMfz1mUs)DYHU|IAU z!Y)_9Ut5~|ejW)>*&6y{b{I5EiO*HNPQ#lUi{uLv^h@@DEyfLNbLUQx7WaX zfxnyn@q8KLI24YXZ~i1;Fz@=rt8c~$LRU5RH%l1Va)*rfy3|bSU zCF(4h>g)lx^l-SVxo_KImAAH&B*vZ;^6yX^d_(vIge_=t-u^?X!PlVenv6Y=?kAug zZGND!>f;yeNMgu)PHt=wJcbbneYKF{h9a%_`ax(7p8k(2sHdR5ZXj>?!NhT0H4Ne% zL3h=yb4d}u5sV)^?A-L1KTL@u@ux4hMNY>tXtBJO?0#Nt5$^xj2%~mm0Ty-J|&kc55%CZrwH9*VM)=hk%@g=36veaFC+ zb~wgMQ?(d=6FcKwym_7VjAJ~}TMkzFpb%ZfBXaxT8%V@#!XItr{>EhHmiPD@sr?dg z^LORKXq<27;1cmJ3qk)2to^#gs`S;zWIBf{2A{u?iwEOkH1`@KULqq)+1JW{>C{qo&DyoCDx(Yv_; z9r!M=)j=Zti~?>CVI+66P4^UV<`$;!BzoE*^vq#&<%Y2^^35;%i4Q6t(=+Xc$6GtF zQ4GeF7~lW{>4fXKv_XZ-?YA2}!pX!$%FZ)V^Nfj+wc-Nd^t)L526z4?6^EO^TukVy zQOt`KMR!&+O`tV+e#agYZPu@t6+Q~}?7S)dLGgT)3U=b%-4a>7=k895Jg+#J2351Ae|tBL-cAZvGo)- zKYy3{`#{*F55wII7G};itAbf8<{`e^9ad#Uskm-M5k#>^NKFb{ z!@lin+%pUV522$Zszry$9@)KHU*7@+)a$n&>U>D}7i#{CmDm|O? zm}_I+VviG^+a;urSZ{Gpz1$gZoxaLJ zT43$hr9Xa>vDS~c&Tz(#<+^!Ikv z>q%4P<2i%6?F?LL`~xO_`leQT*D?zUU=4c@X6d-yt&AT5DJyX)Fm4rhMw1~IS~T7X zD*R(M_K8&d7J&I6wU$k2$Plo^)J&c_jbjN;k1sLyWB|vd_x2yW_~p0hR*LrqI)Md{N^eIaAz3$}NR6IV9sKGc*gtabv_@*gf93!CBBU@5O z`hF8?{pQxouC#!B`Bo;m6+~IVo{Vx2l3W9U^AjOj6t4ngqyhM0^s~74O-z*#REvn9I;LO7uJ|M?< z`nT=5N0AGrs-3GBf7{(hG%~=y+;p#b7=>0}{@5fV80ny8_!Wm373AJP)OYOG_4HQk zi-Rs5kT-;@cM!)H$XCp#&UJ;A7|IU zOxl!S0=0`vUkq9{dQ$dUw;MVgnF>?LfwVVg@3v~LgulS?eo*UrLfm}^Kj*dkgGo?P z{t}h^EY?L<(Tl*pAXWzMDSjAELy}e4$*OV!TCdRnAlQy$J-Y_|d>*KK2`PDjtvO`R z*~6PYXZh>O^%NIK_!)dIajgKwojG=-`#~PIm)7+Zx5s9CW)wPvlJDcAkaRGy37IdO zLGj2ex?7kGZC2bjoBhe-Dd-eQ@SW4VeS2|g9y~Yi745zo;d_kUJzie>WUg2+p7Wx& z)w+k9L-AemSE6j?lK!>*#4yT+_AWyASr&S%a5!2lZ6+XWla3^l2kwK15bM!YtRL%cwxi%fjQo03Iga zG`+9}^;bH+zD-E9Hs^A^2fphEN{siu5YB6BJBozkECM3OJ#u4y`Qeod^gbs7V~z;N z0T=e}$nm+U9UjT2Jg4VyoOhR14?AeL&#$_t=8mSJ_O{KgeK$Bb1wCcEq91`VrUWcM zGx12NVD3*l78`j789(}-ZZi0IS9p6qUbAsgMHG-lL|MzwqWQYaI^BmPGG@h(9XxD{ zQ{(MCz{+&cx(_IBmU!}rkCNlFL=r>AnP3|#vYZkuJxHFKw`Ga6ppgPH5S9)MUc55#g@1Pzs)`eVi`@ z<9Dz!on2Ynb!L2ow0uc9K|Cb)-POM;E$D16LQz{Cd03xqYt$VSxiV~}Z20LU(k`rF z6U{nVRW5ZVuF+4=R^-9;oIM)7>O`zR*wY`BP79!@LHiUtK&d)3jqf|VyX`@QplG+I ztck4NDreteFWtiKI<;hq85E6+deh^j>NRv#6};f>+BU2sJkpYP5yhyD$yvTY<)Ozt5OGkgaHRN&nHy_4-|G5 zF@H0@a~a^7WI!NYRrpy`RY-^=g?iJFsN6$m$MSGH|M*sX5}b2|rCF z$zP?iNM%>ZFY|Wn?QyzS#<>^f4zJxp_oxWJ3$!*uSH+-PD6`qRGkKd_-=&s{O-Z}$ zFABN7LL^roHU0A@FCnj=xN|nC+|T`cjsqT{V?nl>lWj+I6tvfd@v^!Ho*AUmuMC)` zGNC6Dx_mxzkgHpZHpK_66_LV{q%f98y4Q`E|WEm@3g}Wn*r{4XN{I!W^Hm_MNWm%X`02g9IK1+p01Gfwq6F=Oa93&!S%J`UYo|>-a`PhA z;3{B>7YNgWykmh!O*f<}-t)#&n?zKLL@2M+AE5;NS&@+1MR4NoK8dq>^?(@ao7c9H_>w8`w!GtuN6O!&n4s3zO& zCsnqmndYdvsFl!~9CJyZqZ%BUme*}K+K+x(e^LLFl|i)GOZ2eQ@n%$NHjARpG8Pte z_^7Q-Et#cQslI^o!EjK}s=SC_lS|_cM$c!cozil5u!L{Fz+Z^rmR`KwDIH(%T~=`( zDulQal9Cn0JVLks=Rwn*KtHe5#B0TEqtS3(7&Cb>^yl!(6;Jq+j3jm1jj18HFJuV^AdbqPUIf( zy>pn8#0&y|nqQRnLBu#Hh1E@0Mx8R$v;ZCT3D>1LFK{Am)Bx6h)||5Gr2nUz(7Iw_ z*ozxGL$%YUa3iY0Dbg7Cmh2+E$-!Sg-;=Ee!qcalB#BaDNc!G>eBlpz_mrSNWnSx$ zD0)JUZ89myXaxO#1*h2Xs(`s$%VZMJxdffxvZr`du3Sl!nK+`r_CpNmLlkodCCfZW z!apK=QzE@QJQU}-xw0Mv?jUfE29n>a?_S;!+K|N1Vk2BFe&z>n+V0Zt_YcGTlA=eY zy1zORQ*^mbij0*rlo%NT4cbi(FNEaC64V$UJT z!kSO4bQf_^Oc%(Cf<@21!{6gds`Zgpw!J4emOH-H>HS4#Re+830vxOS7pD}UF=IlN zPn)>Z8Q5Nxu09inzCQj$y>Z$RYeuZm1H-8v=)osd>Wq(5L1Mj-w%_&o$$s$pGC>y& zV~qZXUuZ$n$|=`onl*u^|WAfAP`AFNwumh#w%dk9VU(xi=*cKb)qF9UqDvi1VWWOST) zqEib3<@G09+kN8|pPFP|yPQdg+HW(aqA^8fj8(dGrF|;c*{UBZ#y%g-z(ZA|u2%f{ zk+(B8&z9DXYOF;$OVx~N7*5ss3)S+2jfAJw2(IvoM}->@(LKLO7 zuH<=8WFj&nIe19l&ri9UvwWh#Ye56tjOz1+5DehIoUvN{V~a6zQSq;@KBt*B#9yRBmtvZ&~z#^mn!PaQ2&MH4yHWDtS<$nabds~Ud}wt-4{SR zziP#N%vA!aukx^<@22zor?ab`h{`y9S`=D(C@bC@b$LFh(rk)6jfomyXJJdBW`HIT zJbR&(Is1jf+0x?kZz*#d!0YY)^V^(r?~|VNq+O{;quJ^0 z>hAgK@0w~{s5Zbfrgi&U1ik|YqjS==XVyH;i;xC+kM((g2kS1+sr&;~L?+#RPOahC zNyVq{H~V`M;N=ghBqe8|LAoRyNK=YtKSn z^FVQi!w-d5xWc=U=V2wn!)B=GOTDzf&mo%UhEp%OBH&$Sh-b0W!EkIOl&LsXv196L zyq-ezZjQds{6h}7W-H<)$G)K|-qH?+iOjdj6tx2dcY2S80{#=BiokY(+)Ao_^O02J z$L#TQhVojfnq?X%<4xy|P>fAx6?xcfNt)x4Q{G{d5`g26Um)oP4;9CUi6C0b7=DdD z$>rA0$BS!FqNG#df_*)~*K4(X9@E2%_UeXCFegoK$>GcK z#`MV$+JgQOf7omfjvAkzDc_8b^lMI@8x_Dc`@3bEu!3{IvMd6U!9%D-6%$4xH}zX1 zy@;NxI<8ie;4%dem;A<|NH{bSNb^(Vx(o5!kc`+4$D3i5`;s)=W@YC8Mw5&!iB@KC zhC+WgsO~4X#Q_6R!#_(SDrGsBQM6~cQxLZx^hZr<05ce13Q`ZIqIi5}XGA;AG%wO+ z_a^#xpNGq%du5>N>%VW9B$uo`9vTdf$e_(2{;!n_M?Kj{YM2Vq+SHtYW1FiJ?OFGw zg@^^UMip%$i;Umzfn+hzy{F9oV`jb(x-(E2FuSLv>LkDa99~|R(1u$YfQvWqKIA5Q zFZN(95>8$59{17I0V{NU+h&R4wY!XD8=EO$m~Cqs0uwtxl+_z&DFPo_Pq+86bi#=c zC_9uYkwL`h3nNfZ^A`=dA`&Jb{<==R}({bhbJ{U9#3fwrwMV3gj(=}Tcs-+Uo;Z*EaCusU7dx?n!(yTJQ~ z;oFc)trq$C@kZe4PifX0&9dkB^8wSrerWMIBZVU3c7ttq)S-BBwx~ale=kf@q!_DS zLF9wFO%mOtSP52KipG26lN>oKK5kyPQyWR!p+olew9RVkKtvC92sQY(%fj+V9z|Z# zudw4h%W>EBWow>WdGF%b3GBR!`Ox8-GD95EN6Zcn#0n2gqnJHWEUz2*QPVCe-?;+) zFb&w|=WJxHeHE)c<5|njVqWDP63}CcJ%&lqfxCb+MPSs3WZ7r0rA%TG`dn;U0jfsi zCq4{YTaVMkVYtdadicXWG6iV5ka>TncCF381~9?%;`X}}=!Wj>1U(az(!yhlj`$NE z3Rt1l7d9TXeBaS5`^G|>WFeNqe{8uQ+WTjj)B>g!L=W;<2}Pqe_Q@tx8rrOJfEMER z!$3l%fqjd;BdCc#USQ3Q2DW!9wVQv+4qrdr4u88%W<_A_v{t#OYd$-%b-Gj2mVMm* zDE~L<>{2Evc~e2roe2XkgEhHFZ2NZw(!V}uqz;KW<~2kp>vMWntm??{M4@g3>z{%t z-+EYvrorn<8%Z`(q|=O#T>N$$R#_~V3eHU1t0`D}L4DCg5%DV)-W?tj%{vMP)+*lP zW+KALE2a8bV5Cg zRt}K+568b z@v4fMJO&hA=auAxYimvIj+WX6W~cKq7lyYgspQJ#oeaQu`e|@&7H<}CpXLp%jI0it z%Nr;O>{Q}RLz^Tfzu1B-qJMvH`or#MNS`_=05ESxPt~aN@R~>S?{Od^{D>q`G!qH~ zfmcI^g-6d0r*nU4ucKGi9cf8o($%iv78JlP+vrGLRr+xoWBJc0qW_G70rlmdQ3f@* zd#gM9{FtuYih(2RA=MBhjxI*3xv}bRPQUZ@KK}CUMW7w+N~dh#d7sA2@rC%-@{1pU z(esC>Hhbs(hRdOIUybGo`7^f57mFkAB&Y(rH&bFT8$Og$MtAXzNBzy zGM?tGDpcT-EF@C+M~@V<`t;eW9b-o_zJ=5s<`ud(M||<(K7agRKF#ZzZHmc_>f%Es{VreDdRB+8z6X31{PS}W`B zjji3TTS#OciEDP0UDF>PY2PfzkgPR3e|P(-h9xQx>tM?;Ay!oSi~z|;n6 zc@7ixmmE*X%YdQ1fc6IT5_jv6U6d`dQwLw@%wX zFq4i1kG{H{cZ61kB$p4`tV-Bv0+0TVwr|ey8I79;ylGo$B@32~g>>JbN}8MaGlk;M zdod>(J(L~xVI{*Az2J60n>)2^8NSh8($OUJC-;5V$S6j<&Uje*qG-gXc(sWcbw}~b z8`+RYP&IL{Ve@{vL)hH_A6_0j2 ziTXt`x3@QI6S{_7Z(PcAGLO> zgh#Y2OzBKv@!7f6&`9@@7wT#y;k(?edp*5inIV=gH0uq9mPDy$tGe8rX}a|udfc(l zP-zq{ynF9aFUBW7`eej6-$h=OVkM_+AK%XJYt5IVo%fblL-ih~#}tYP#mA6RYo}A4 z=Wa{$s6B5~)8^pX(d(zdyiZKlhz|q4k4Z%``lxI#*l=!)yD=5@x=M$x-%fnX5t@}I z&yiA5Ju%1=rO{eIx{>-f0IdTgq5BxC4=CLg#DQ-Dey1n%aB`4}1iau6cKvFuixpWM zo%&Dj{+!*UI@6*kJV}v;{AmbS2a0k3pl9|zt$*2E$3igp90Wa8y@|~gj8*3wVWAQb z6xIXe^jiNrnYlnP;l{La*Ayb{eg%=lLhtv4yA24#@~b(6(@y_lV{D^G=Gd%Z_JMN8htt^n<$0G7Of zFs}5ft7+~f_c>n33`d2Y)hDVNFA*Xl5;{I2vb7J!xplM^`0o}(T{b5qT;!UGiGRC7 zD$!{Iu>3fbly^=KZv$?I_P>>I%F_M=bp>PmQ$ z%(<%s!5{gRR{HKAVD;WKKl{TOa!--{?Y6N4Lxi4r<%7EyF8BBbEgjD)Yn!enpf8m~ zusNne@ebc&x&;0r-H1;?etrndY`<)5_b0!9a$mm=agKAlNTbC~SP8{H8rMhoY6iOu zy%YHK1HgINnDUveGd}u8Wu-S2Uf=;BN^>W{gc9TlU zu;%XvmB+g&GyDs?n@Gt86d#-?dOexn-f;}G={4AejMR%#xmDj`JVdc;xck-trZqh# z0%ya+X%c19jKrV(UuWtBeDF&%^)-Sw-|}85Rc8{FGX+RVhFe@A2%$h{2C!+y<>Uk; zwEgy$!@1s5D^$5<!Dv>Aip?bHg=PG6W@th zhEG8O*;c0LFHC7K;_`cOT{J1f5-2s!z{?Y0^A*pi3+SYKe|O(f@+>9b%W65@(R{_D zJr9B3s=6EB?E?zwX`08@s)CkhF(2JJm=(-xQas&qf~x$J2?quV zh9fUv^X)}$r~C~VvK-@Wd2VZg8!oadj|hX$b3aF6X|%jq znqLgwPw}`MId8C%NEGk~n$te9z5a=C^MSf1idh2Su#ld7UKMo-)+~zVaSf*Ds2o|R zACtDlP+ZFSa%@8O0ww%6%}tMc4@&13`@7(zlf;Q)T&&R0&3OqCr!bvrLu5E!Ru3&= zx>8-q%8C)z)tI4UqW;?^r(&C>uyNHxQvBWY=&@P_enC zE0=WU%k*8m0r%-{;}JV)Mc{%#I9#snpVR}ZR?oi*+C}w$ly;4~f9fXfp?zu@xr6%t zp!mO<*{d7vZ-US(tTUZg-w$P-s@hAP(|8XtGx(bR8n*(* z;aJAd1q7cmW7r5~Yr<(D`hDu}TDK$MJD=JcU;i7El+s;8;rC)7@|wss*A8`ypT$V1 z-Qc^#+bL_U=;qSdb6L8|ChNCtalDkSz-dA^Pqlj`f7*5gWh~-eb$j62_=AH;dDWcG z`Q~+l%u*d-GfE)}+}LqrP@k8$7rF7L8=E7IYkfm}LrjI{AB6d~0TIa5u3Pq!t=9)1 zWdIL*Pmsk&?(3cMVAVX*h0K)NY6(ROX)136X@$ap-B8PJp9YkMe#}G-nY$fn?YmT;hlYfY5M==$IoEwPvtY;#CqVl#+hc+*8Sxuqz)RXUq&t3-UOGEOX!)#kp>gH^Z(`9ctsszN9B3IDLO?s1U3o-YtPfbN=o zNMqMY)!-~+x_Tr?SfBH|NF8aKHzxO!F-hNiZa{kbL7A{{-5}c31{ZxJ3&f(vt;_n6 z?%iK|Od0xYR#;5^%E5V|b-w{hZb-D;LP>FycR-aRlIkP-1kasmuC+)2%I)RP_Il;^ z&5-Dn!jK;MJK@qSSMF4yo;!l^cksy{lc6U9y45cY5za&K5jM~Q6qfQ_yy8H=zP0Ih zJ8Z&p)E(~)TZC=nW`%+bh=ShO)}MBcZ>~)E=$NO7G}^F-vPRILv>Jq;U~e_`;AbsJrx>D6-9X!jU6+*#x+B$XMl6pHtMe}i;~uoMjK3FQ90)kFgZtPY$OKhHUJu6$SZgF*P;J8ISY26-LIOKxB~D%b#rP z8tPI9E7~qf^w00ToBwt99awv+ZxBlV$YBaLg+GIM(gt#Sqm4$jy8l{W@`HI>e!Byy zW7X|h*QJHL`B-x28x2WrvfAwTPbT0g{9!MCM`q|UvBB}7pt68DW|8b~>XbvG{2qyI z>ycWhv**d3&JJ(VuGVfk8RfA;jCYIM^oK@eZ+yEeYXy9Bvfe}Dk69s0;^gp^??Pc$ zV@6yBt!&k=T3)4#9&IFiU0>xj?-dkB`lbiU@n7bGL<7E{db@r37P{D*B5Uyy`ooo3 zI|Uf$ExBBrWwl@Ueh+s6tFl}fPoPovoOe5p($yvGE3%fd2V_1WmF0I;?;}LZ^2D>~ z-$+R^40^E^Ki__q-RFHq%~Q3>kS6-BaFQXUNN4)TteND()u(HKlXY(2(b)+lv3A40 zQk~7qrC`at+2e|(Q0CIb!P5?5S&>h9#MW?6i7wdsjVIoZ2z8XEn@O{WbPVg4o+Zx#Y(DaH zVr@V{JR>$kmHy>H#^yqtEbUZT9%(9LG4v~br+)Kosv5YV-LrI>sFueVl+RX-M($wF z7DIQ+vNN27<`jf)+vj+$lGwonS&ro8yqhC-l+Ia?TQ6>&zHA7$+f6H9)86ZliBBQK ziWNLPG~%(v{Jp(LRvRMwNw0i0M?6}uJyuVU9H;Af=*Hi$*ImBoi|pb-@W|8du60)f zjmtaD+P;en5xX(gJj>v(LR9pfw9%7mJAN>c;^J!`$Hz`X2l^VUikpW2M&Ie)op<8Sr#!5uB`GD z8P@bRehTlTGf;b(^iGy{`^xw32*$twMN_5=$aXsK8tjO_+$42lxtwAMYTH!GaynRA zy4H|t=Kr3W8MEO=!%-7-RL~X*^_Q)Sx~K*aUf#t_l1PoPBF8CsF5iC2Rb=V#g5;Zk z`x`6%aGU;uCb4@nqE=hOS}A-V=*NkKdgfBJippaL5a0c8|_C%OIP*XrZ0J z&3tUiTU^i!m$!wMeDx=a(R{By`&uZ>yO8 z5lL%0pxtD`v-brLNVxQyvvZ4tVSY{(W#+!@67S9Zpr#;{Y!7VmRUXKEXL9NuHjHqa zv6bGngKEA%wlw4=3fiSthb`z{v2$SoOe}}{un1wYxYI{Oo8@Q@BOjXt*<54 zD^F)CFW8I5)(~f!Iq z#19)eTW)-)hoGTG+ER>! zV&qIZZ5MSiS$EA$@Obr6Lajz^p?y23U8JAy^l_*rfcye8Jb- zpy5`hlD7aqmSt2OTT*PK8E%teFZ^$9UMe+kQ9r@_rR<36V5tnTN$(rq$jvz z?;kNok}ct0rBUbXk7_&%HczFu^B(^ z#5NoI!z4t)-;HM4jPq0t>D&2Eirhu7y^ckl9g zVc^HewumA@-R7ufB8P~}WgiwN0)z%`T zcx4n%mjm_O_*@94xYX6_8}pWoz6`dP5ZFAyJ^3i9(>i-y~%)o@K~Lv44yfc*~?7+*17Xp!i`YJ`hY34!J|E zZGPZY8EJhqd$OW#XENMRt?z3|#Sz3GAx|+M51NV}h~RkB!-pR#E~u(AP^ys7 zn(f(dku3rT7!6b<58*|9(v?$ClU`tOmIfs5pe%p;an3C^!D--D6ImUo{f%=GghHf= zwG=&qpAL?KY)2CoAc(Juy|tGu2n;zjG8RMw&4`rklQYR0ml{-<`lvcoyx+IbdB_D_ zPU zz!gK>Pb0do?~RmC8KWVPg^J8PzkAKMG$i>|n3I;=oi!Y0<&0%b&|TDo0Z(GR%G&+&WsoceOy{)8+#pLa_>x~{IAf#NSh zxW-Qrhwj0KT1JK}GAoq=Ey|j4w=k_?>`V&qmBGjkB>F`c#SI>R!LjwDRN$Suf?IGsy?C3O#xvQsGg!3}AUscu zzU6tc%F3>{xE4g5v$PTj?YOH!5DG=X*UJv4LK=0|Q_wH7#mIfS97Wk)*C+%Mbhe9p zyNUTr%eC@Q9Zj`Vs-&W7IfzH)V!V1w7Fkz_kb4PK?**(6Jb{E89@GXetSfZ`oUAB3 ztPAi$Sh50%Zw;G?-!8;Qp3YJwal78DwkG~Em_D$#qVEXz1EdAfDr3IEm!z1Z*IRI2!{+ZYIR3)|bg?Y#F=o*x%3VhYwF36I}~({>04$O{jBzSzOu# zr5{dyh34W#f=RZmY4JzLr}@ha*K>-3$f`gJL{<&!;@W;G4j6-(AHq$3ITC4 z5jla8Be&DyxyOh4ZI;p~3uva+gRkVsuIyzH(cOp$dgAhGC1uwhoS(Q3E9Fi9zGH11$$d*%Q+sy~>^+hp9!bEY<&@DN1 z-@1SmNs2quhuy5cl9ogf(vJzG1t%*I%-L*6L`d%l!lfIeuiHQy@S42xVo%hZfY&mX zn3u!12Jb$?w3+k>K>F$~@|}81s5^vSNL8 z&OI{JJ=j z3VdxU8Ca_32Iq_~f^-g<-`C@fSg~&mb8yHTfd2Jp3t<-m)w%vY9aP1@S(rpfNi;g9 z>D}O$qxO9Gn%R|SJ%ZoR2=@lZStx!b*!}Bo2n)GYeegBn&{5Mh07qyMPO^#6Koqdv z7l}RG1Pe2t(z3i2HfHJR+Q@Ry?rgtdW=DvteiJKr2hv;A!5SN&Y{c5ZLU@SEOfB!8 zeDq}-nxb8`C+(h^Qjv$FIf8HbKZY81SyN6V1%@NnKC%S(eRW^(AD5K`I=U`|h<22! z!g7b)-QeDgQ(6inDqO>hZOE57i-?CJ`~3)#KS#9sBXhsfQ7 zktD?jqMJ~_+lj?P^z$|<_b0)v!{+z4o!0FVFH#B{T3F8A-p>E+4x#+}y3y3d5Ux~e z(kEr;b;e;%jP<&({vYS?dv*Le_OK}O_3TW#y5`kd&r!%lNEc78QjD3Wm<4bjfkQdg z)dwK^vX5wSPXBNqJ5y?-SkPN+a}NWB8s^PuQ!PRt5uuP}D1HS7)IZ`t@5q5mTu~lb zh<8PD7e%;ts}H5A?NWF}cV=9e<@83lzgMnRTPKRFkZX@2lnJ`*UymoZ`o0He0LC|x z$dF8|e|qsIERIOKhr>Yi2M38zj1)x97U5McBWBb{zDXu_z^pG!8Dx(TM58PV2;gK% z@eqywA#M`EPDsHzrT>!o%eS9Wep|C`Y~X9io)L9Fc)?NFYy%Et1tuXmPA23^4Mt#5 zh@~JIv~UDwJ^6!SmG6}_GOn}b%i}02^7%twI#<59ZCIo!?OWU8YFXM4Wn@jhb-Jj3 zCk*jI&&c`ds5<+K*y%wxa|G@k7&n1Z@6DUbn)EvI6Phw#$*_ut00io8jc(spxuz*x z^7Ws=HeN5jEJR4ofIyvDAV~+WJ?>|LdqM4d!E3?DS|Gl|t_A6%&{~qEn3mlIg{t~* zLV3-HzkuVdAOYp*Tov#W?IL{u=`lz}~&@y>T?L$K5`;D2bOo(Gcihl0_?9Y zC9wKmUAJ@0+I|#sp`9pYs)%H5AX8xg*-FOg3O3w?TpW?aUqUU~4wr>C=nF1Nl#YJ2 z?3a6G6Ks5A@94?t?~<>OFECC!-6DMPqcfUqBl1dwRwg826s<`@Vkd30m__G5uX`a` zida%F=fden?pHrWa(G_Ng>YZ1Q>nx`u46tV zk$EUXj={1qp}xceeQDW=&%j2(J)h8aQ)OWl-<@M&NkbEowMmiMATkByB0Tv4bY)s| zeeXO*@qbjaQ$7029TzcKzKCgCi0?ICmD9mM9)2-A+k&7w!qe|!74*_LRfP=d_MNXi zU?2sYkQ$E;zuDf^gIsFkfg#w2kdAOlY_T@n0O9_7eF~txYSUMRzi}E)yPy~UYo{yW z&mlDmy*H|(fON>y@%Am;&4Q`EX2Hj~O6_9&MVJrF+|;f1>;j-8JW$DTEYTtV|ja}@+hjVXB^0gs*2Uot@J z$~w1d7GV`C8YDgkVzOBifw@A4QIEa6!R$NAW>8nF}nidHh*GQXcM2s0S5vE zIngveUGl(~K;A@C^k()DLLu7%JuOQJ%}|9i&hE%xWo8Zc(_!XEsRc^mi2fxhGrikW zrxRg_{-G-{`2sZ0e|8nDnUShA6T{}`{CP=`WaCY-tI*Ot8gQZcgvef%sw4^+z}B#p zBs~WC;5|_t$+l$rVR2F2%%#hJMPgNAPJM5+wM5K>}L=&Y5=Etl_C8m^qfRq=b@o^j4KDU#TYt636%4kH31`Yy#_Mb;|p~b*e{arV!tXvZ5X?Bmyb*(Q_1QwQc zZ%t>CduE!&^-^$yFM}rdbaG(k7CJcsOUTcf6pP=XgQxPavaj{x57&rRo+KqTUB7k2 z6+_&YuutIG!$kZFlys?pm?!Wpq24SwF)LqCZejq<*@;orPc9 zn5~Jgh;h3k%BIvWh7wP_-3@4DZ68Lpf(xYeW`iX8Bks`t(jS`vJ83?d%fjr-J!Kis zKZf-W$Dp|<4IUue;(y8KZ}d3akT0QSB>DZ0AWFxua(cgo;6SOpQ(QGo+uT%y)MywO z)qX!%R77oUnC zfn?V85#JtUf-NJTGVXnnJ@d)BF}QQ;Ut^mD)%-TMKYn#UI3~X=b#1&=rOA(2*!z=E2eqpR z&fg&U{f^9k-{oXHAx@>s{>;CjgQC{p+d1TX-DYVpl9C6>HmNfwsgwcscC)4QqR-n+ zpjJUIa_g*i!ynLqkVm=4Jh2f)IktxT2R={A`bUv7{ZA6E{)=e+If0?IqVk4L5KA$> z1&ESOU3m>g*)v@Cy<>kwK&Q9lTE?Yip#Q5cU5a1OHKQ zc9XtsZac-ugKL2kb8s%-SUC5#LnoeMG#Hv8K*CK>++8IR z<->Q&uxd$A{F7G&>n}CxaHS19oE0#~gb0;2c$EP$C*r~}3|^I) znTACgJq3Ki9UPlR zmCA7Ga_kQDtgnnOGPWjI@ao@yb_H@%k$%s~N{pN7THDs>m54fa!{eO(b~80= ze`fkx=gsA}y|sT@I;@QlUjyXOG>+)sbTOIq5ghB#=;QX$oM==TXeB~7Yv5}bg)2fnzks3iKGIi5q<%yH zZb@2;m>@407LqBVw_vCd{YCx8>8u1kox#X|)k2;Lbc5XCWse$s)4oG*(k4vs+wojm z@^l&_D1O}l{h~$(yjh(EyQua}9>ud+jo6Alw+r}ExOC9rfnE*7LE5Cv4x=?T6B$t# zPfJ5ppR2xXu=erG>guI~?4K4l@Y~Z>YZl5?45m7#LP~G%XaMUPy~4z9m47q*p>RAt(RrFEb!S5Hgf8ScKE00+#waI!t@;K9h-esj>W7Z{C%UUbobPFFPrFJ zvb6Wb4ff&mKr~lw2d898LMM0l`@-8H+TQHW5-KMFMJIvR(_V*fy$jI?lJ9PtZRmz4 z>U%aj9Lz|1S z#eFAyh*G$(|IV_3&q2!(LdKXPe8py>9ZnYQ#{f44{rlY21f$IUIq0AHhonaxaNZ2T zx$@JumwsxcM1ZqpC?Af2T>1LLO`mcN^a%_mhPTu$&dM#$lVi@0^MKFsfVcZaqK{{X z&zHpjPydhMfG3B5*T>IS#?Ozb&#S(-y4SeRDZ|fqhtIpsk9Wq;L&MKwP@(Q~b@Sss z?{i=9b02gqN*}y`(C7Kt#SN|NMc%4Tq4}kf@t)TMf6{WxSI9IQl+PdM4;AiA!z>3%%}yA@y{Zwcn!RIovEb-YY^;k*aAbbP(NWVAaapjGCE-8k5yXO^Ej@$gG z^S4v5NL{+l`0RS$x4NA+ym~@Z6ubtU_x)0=Ci;y0xHX*lyrT8rgpMn%5$C+36m)u> zqX-sk2!9>+FEsSuq4YO?`~s@Pk~+M(O3>gZ2hD1MH>FveCt`u`jgQeJ{JYUb-yxQkm5Zur;E64_=x)>|olgzZ z+XW3P0N@kO;0n>Stn)(LM2Ee~0rY_c&!|h^C_CN6`Bsr zftc`xoAj3bO%8s7!MDxFZ(JMXtniBm6Z|Cs(UAk9cVEZsgr`SC5Cc4u32Ak~x)z+5 zeVSZwE134dC0tcS(CCoa%4rnyQb*pfy8e)X!4S!=F02b?EKP!HBG`K}IJax3H_g-v z>x(f~HuQWoP!F9yUe%J?)GM&Xi2rZz}*WuZiy7|!v*kaIj{dXl6(5lj?reE3*j_X2hWClQI7 z!d8UOaY2)jm2Zp1<&_E^;I3ucpfxn>H5h_%feZ$Z3%yfo$^A?8&WtbAl6SJ zxh|}g6Kz(xW-G#$w=fscae-oQ%ze#%UK+D0E(kO z-XiA4;m;o0fBdqErE$zlI=nso6Srn}OfPvU%Xy366ZaZUJlac~DL*Y8&B=JIS$lV~ zFRD2Mec=Z_^h=F;8)~fvQkCDw!QKA7!2_k6nm54vrAhb3rmKBFHPu~Cpm0R z;6)JR4PM`KsZ2xfLr{F)t-@(V;8SE@c&R!Kh&&fM(}8af3aZF~>!}mN3DD|%VQ7ZBw^-9Io-{ac8P<(>=lHOuw|S=Y6FF6 zGR$KCLKNppB=gVUXF*o8DI9brS#9Mo6=`n`)zm_cG$0sD$R3l9>56$FQahkwH)cy%Q^DAa$jzya0@#VP(K<3~Jn1HYVy4L7#!?@qjbxySY2e znm|?a!N5DaVywA3&**jK&Qk>uj0W{K6gqrSRhBX+NAxw5gj~iGQ6zm3Ldcd%+`{5n z#+0%omDU@WR!$G0fWhOB3^p*LJ733O*a;!BEJSMDL1Mv{O6?_f#UBZRan29I-+Jj$ zK;M_!VW3=2QrM%XjAEd0wo+x>CRLsan-;|;?@WlSc1UzI1APinb)}Lw4ln1WS#;e@ zsuYmH@d+Tf8U-jNVPZMrVq1U2A|qkkkwPBBiWCi8OH7Xkk~@)|S~{Fq?$Eto&(dn; za3DgjMnkRct>LBgsFdR=8>IIlnpx3^gdcZ-UI-=~N9R$(E~iW|CH0$tJ_DjaP>@|9 z1*RRFh{e^9M8(!3VuU*)(9hF525)4DA*>{j`5non}!n4 zs}0MuQY~pm8h&^{+d{34U|%R13Tu)|5eRvuP}QOBpNlE)BW8gY=ziOh=pVXz0jUAy zrucB@Lh()xUOSCTLL~^|u~vHk3sIFMYNnYHITqss2qVgaJxg~lO5lk4D|udfAbvDg z&pcduxhaVo-Hs4eeaSSq@W03oBl}R(B#A^+XSXwN;;2&5dddQ%0$ve73`X-6Y=iWS zKD<8K3Qi}ut6F}7T|gC8aZPY9uZWMB1=^-?{}G<(k@l#1P;f2mj1)awOm8E{P>cl2 z&;(|(ePTP_tWlL%VwglPNltUnG(dU>Y8@p+f@2A(U`7*}{87jmh5YeI3Z3o7l#~tk zImmaOoWZ@Yf^{Z24-sx>1d#`Qb!Lfc_JQRpp$d&D^Lz9c`7cG7Y}bF7PinoIc~S47 zfT2$WqSwgs8>}W21JoK^JD?u0-U3+= zNlcPFHjqQb7{bWyiFy!}J_;KaNCK;9;sHSN)GBeY&I|EI+oxv%$9f)WUtz!TWydD3 zmEwLnxxEuF3eqe>NS6z&XK;6&jPDCYR_IB3r7v+D3z~Mv6yrxYI-<%iDhfnSy!v($ zJB=JxN&xk94^B2rWdf4A3r`qji2p0+%UHc5)om-#Nx2iSggic4!4f#eZufJel_+~OEL|vn5wg<8BQ6%9#+4?7GeOUAGt)r zDGY{}K$g9UoS4NVWgiUoK&!=XNI;%ooG%s@6iXe-p^jXf8#=-qql6+RFENwwkge51 zR<;E)GJ4j8o*`IwJbv^@LqF3W)gj^9iSYV0aK9m!fuPz6Se`D`>5;bZZ&rnS0~vWi z><|WEdI{6U;+a&s_KCLKp`hSL@}v4mIoHM1fITj_rAYiHuoJ5YZ&d4I8%hKxGrxfz z#YB0I8KmSukn0)>n#GrAEEE$D*pxF>74&}w@`3{vvE9`bCI_>#L%Den0n_(j!69?> zl$`hq_FUO(j$GU|&dxgfd;Y&h-@}q#ktiSW6fQWk*BrPyHXWV&wvUp>MyXSZ#0)4Y zrDGKm@pH(zxuu<*6ZekDM`xrHlkkxL`&0O9j(3pVTV8gP3^3b_Koiv3Kx{CFJO10R|fW|D`!_gd?> z%GM1C%1@LkJ)=njVN$`e^H;R5MasoX{-*dLCbC$n zn;v~{-xyDOp9v}KU`e}$guIiYS#tJBWKfT-j;UzD=G@55po*x;$yjF`(_vV*@KQsg z+!1Z{Dd}!=1v6FdHTk{FDE9w8Wp>7Vmdrh&#yVkxmFgN|oLMDnXx5|!#~Qr+)^Io+ zKmk&Wu=hZFbezgp6jx6ey!^Vi=Y1Ay(kT8%TMGwo-|hv5rEvfk!yVbyrcTH&}fi->_}dNqZ%(!+!^{U zY6dV?u|h`69RkL6lDB&yQ)k_&a-twRp^d}cfu>`?4uK7}`D;?868Cidzu{A(QRO%J zo+cYCnW??~+Cjry$-)CEkkvW$*oNo42UL%WC&2D{aD~lBU68d^;IIn64pmky!B0SO zI-)-m+Y96B>n=4UVnJ#2C*o$6O)wxD$&YwTQ!0FzX&dvb^kj^>_y@NVfTb?7DqbW^ z7Eg?Ngl(ZC`+3SHG2Z6%4|)mgyp&5rm6bSwkvBUXy#bmF%vHGr`-ELVeh!rNb@b9v zydYKP%`fZE`{O_Dtw^)MW~h8+fIcx&2>hmgmk~o5Q4OQ`3Yq&16Fo51W2QInSiAh~ zF3lYK{PD{CaZo?poNlAmed{mehRDUK@oOdc1(ia68NYbqi`PUPJhirPfgSA+V_-QYEsG$E^*=Z{!c;U zl7|Cx*Nk7kWG%S~nJBiR#S^*b7J~uH>&9TJY#5cbmSm=g+3&;$8KkFe&+?*9trBNS^=T9JUOi&|^q<7YR{>xsF8(Ln7G$ zZ%RwIQm+>tW0!}Km<5O4f-tJ(bkg5*lYAI#*~E#I5$#n5E;Mg9&l7*c0iVmi5QGyT zPcr}8c6}4|{%RP7PL=u?@WKmMmM&tiW>Nl}t|3IcLIyr|jPE*k+ig~+QD;xrZV@f6 zpQmV~T}h5%z&&KT10N|r@1mpn*~{pdUyQ(SA<2U7C;NE3Cv9Gk4Fj|^l(I$nq8syg zJjZEvbzmwv!JhZLqUYI!=j3VFl6SSbDB{^!aJ8IIN57`hFmDk&Yk%`pYRaD_;qQl& zzs^_wd)kVv-VCWnQ>Bh*%-*(lSfnbn+u1K-hZZH4jW6eD=I91~)sS+|MV5(wrtvAX z?`YvOs9K3{7?7nLV?S^=g<8D0aIMm+NxfOMetuuyfnbX3E&gA}S-;FOuW@)VjZOS_ zxXj`%qY6{p>vg$xhuxx00Usps1uIUmRe&OWv~Mw@}t%JCB9`R`sY z^=sb54|5Iw1Q9OusJP5qB)xFeRwa1ZKQbU=SrammW6KG8<_yK@@bA=P0gtak6j}Z2C^X!@yY0 zIe~noF2-g}eL-3tY3!<@9MM_FAilGfNfjRaGAkjtnt{>%D92`1X3S5Xq#X+*pkzV> zcDRk8(1cqeX~TNj<+hsojI1IVon82d|YT*ALKIogx7BEZfh3Z3um(1{*~GdUl$RV6#9O zZ&8ra{%;*MjU%r|=BT=J;9-=GWd%)-&DzrGdd?6}wpw{FLNg*y7gMgueU2~9*kF<4}`NGD;bp56es@1qU>AuUzookjW)Y2tquseP9g zIQF_Vu8BLdIuC3XiMR_kO#1 z4r0Nx7zZ&&kr&>>c~Y8>rZww(9q$(=QK!}@f3&eRmB7+Cl?_@+`fF|B=Zx1^90U+R zFGZ#x*DI5gtxSqJCs6xL(O=cXOIn6QMKm)?{2Yo5grGB;yVpqgErp6PbmB-07GiZ%6^JiM zR^dvM8+iBIVVBF!4|v$5>2+jP^dyRg4fk`6XVC`+3T{yKzD)0!YyE|E&UAiU@ajP^ z^4@+r$Obv~+CgtZ&Mc@=7|Lk;_8iBGh1>HuR*hvgkST^ru`n_6vsB7P8E0HK-BTb` zm;644D~YocMa0%pBz$5{R7$OKv+TN_rZG*!xaP(&nKH7wrpol@t`x)0CF?$P5?_iD z_aWbo?BVXRioW%b`KzcPgcoKE`-u(8fpfmOcs5=TpM`#VJtP$)nGrgS*bhD;qH$7d zJZI0aAGMF3n;#X9x6PMmQi+KNhe=hJ#3b3Cy>)Oy8ZJ=$1e$9ollFTX&d~{n^dmlD z0f%!$hI??2AqEoukw33r8ROF{R+=B~4n7AhxEGxV_eyu&v-?VWB5Y`kE6DvujYO&;z z1Z>{jfHpB46Mrbtu4=ityOJg^sSI*B!UR*NdLY7U#X?FfA2)uq-~_5mIUu8?_=Hv@ zvTHQt;*-!uV$WY$F1(Qj;LT9lq-NLnG1GlbJ;%J@x--v)r}kPfdtt2!o)oK!kxE&< ziFZJxWmJb;cC4MV`hq=Yy;LUWhp0qeRQyOVu>&l3#9GT;F3{nHSL_b`^;c>&3!uyj$7s=+&N=iLy)x{JUqyvI zPS*+_*RE?wC-!hO`K9fZxAlp0V?-r@3QJ~a&pY2+r!t4Vs;htZb_(~1-IbO80NN2YVOC4U*fOdc(Q_EdP&=X|#!^Cc zBiCusi9U55dUW@^{$cH?1wGC08J>n$F*_E?Q`yi@;x|?(r;WQ+jL0Y%-`Zz%B;grw zSh0Ge?6>ZK`N^sC*i1}0VSc~PzO<8&1z~mY_p#i5#>e781A*V(`Az_5*hY3EZ%R$` zR$#W7Hv?2dcHH=_)N0?5qbu?e381v+x@n1k&B<2BBhFGSEHuqcMP5fY0(OBWLT-W} zc0CV`JED7K({Gs9nL%YYC#Q@s_UCKyHkNYvTzs8R^-yc%!VnEa+zMWhslvp^WJMze)sCn1 z`Imkwkj^v>(OH&TtgCoa$o$RG@f*yY>Re>mvC zi`_R&4!%QdsVw!;Rj=`j$k7-0ae@HtViWjfQJKk@r{lzyrvFabSk!C8K?H}$VVgB` zY7MM4ncxYdV6nR&+<8jG)b0PE8b%-6Lu>%iL$Hi#Ih(cKl4%w7*=|lDQMm+wcyP zukEDzb5J`aO5&g&9UWAw%!ipf=27oN^Dlt)PM~+#8{!c=mbq64VTb0cHA?$;P=}?3$xRhinx~TC~0`&MFm^*3rLcCuR95 zD;ZH~Sviz9`%#m7gyu1jp+D#4k|cUfbD+3HGX5q?HB_9oro-tS$Pbc6`CVw}|63%H zAhcod>v^!UE}elZ=NlT=(Z}Kxt|8b#qJmRgM?3jaEA>)`JC0IJ z`Fh;DQLDb;uqe$3BLEa&9A75c^v;ki__Q|=12`Ub0;j91i;^&V6VXKI(K1sxUe*d6 zIbL+rGv#E15JCk|Ri=KRx0q=gZ*A256Gg_v?r~&aAgrVZL@Jx&6;`d$RC=Fywv}XM zi!pwdby!GI+YqJB>caCW&88w+l)p;xXPjlLd2SKMsZm#A8;%iv$3<*Z1@o+sUkNVU z@tL$9zFnxpNdSwews?=cp1jY@tPK^v&UnBGzj|qx=4keV9nFTK8EA=`h#&0-{9n6Z zD>wmDhcBV2n3xQLGpx4%azDcIQ@URl4D+UPsCfT*mEjjXZvHB~tyjT+AJWQyd38>w zaI1M_R6W#Lv%P`SySjaUR^jgykHnmbJoX?6 zG5YhgyobR{1*wNT3IB*x^cec-CFLle`r|FH=`D@{5j)AeAJ{<0iW9I6BqBp03OSmy zDG_2p^o%4aRpZ7ELU-8jumB$ty`F$R<-jPeBkWAfc{yGyq;Rv58(2h!=I|Be)A0Qm z0SO}$N48hF=Mk1QgW8vZ0u5Y_OA)yYwRHwf0p+Tabfci1Tw|X{M~V_P4}oRbxxBG< z&<<6J0$p?)&|JEJVOV*9`m$?!HT_0!AFcRk*7$+|@=UG-rxG_@-gE)J|F zg#8$9!(1BQWPXtwm`yX!&`oIv{80Rf@F;TQ_5CZVHZ&8mps6pN>eX<3E>-Ic=5eE| z)N$gc%IR1S_G?cX=s44~j!<$FfQ!V0vp?LR+%m{8IA=5^!sqJhak0ziY}fdaG8R{9 zl<+fHTsjAN^6iCic-mlKaTV!~?pgxMBkM+v#@Uk04soYp<>y{j;mXX|B3qh92h8mI zoh8Dd_1q!EY#M-K;4{!0$R-PE(IATu3D^nrDKmy^H4pd5i|(SL)0Hn(>>QG z45*RIcF8CU1vFnn(xFKGCSNWW-vrlKk=w=%- zMyC&%MsGdqND&hZ!B%nweWs_tINBe@VG;^;>*|*Keh>M-tD5NQMOVK0>~S&QIv>VN z60JHFJ5#y0!ZVoXTw_r(;+!T5$SqIm5<#NzLQs6#=+p60g!(dZm#Xs9 z8$JvS+ooeuHgFtWwtQ~9XQFiwPlW^}`y&|6lTOtLHly@kQ3(t2k@|KCTK8<)if}G# zEnhuaM+x5axUBJUXO%xo{AR|P&`2M~G}Bh*cetLpJx1mD2V7tw7Q(6e9#`A1ulnzC}t%daOlAP+Y_e2mQyN6f-}_<;d1a>KDY67yPl zwXim-F#!a2PCHBZ+aUm`GybbM>7(l!XWzXm4a!h#m;$p7gY|%gL;%eG8k~F^aeJBKoHAMibJTz!wn!@F%vu?s_vM_Ug zKCO=Urc6iqhM@qd>f#O`$a)D#%;+E-*K8N_1boSB;zR{b){o7)uAX~B?w8CcsNT{uN9abxY3liJ@alK<@gO zh?omc_99{FWsXXv&$(r;^CKYI9C~<#oM>Nj;5{*mFyA}#>)-< z6(ktS-7S0XH#YhXNjm?Ilc=5D*MhQN%Eto_Va4v`|M=8|+Tep35l2{t1>h_4DmSZa zQ%tYQ&Yx?lor4`B9JcJ52`HBQ{%ja`8{La)Rc3ceGN&UYYdKxe5^b;qY%D zgJmJ+2Z5qXgSLK4^kl^<(e%*VoW^fn!d66qw$M`$PN3jgPo$LOF! z&jODA+)=9@oev^C`%@f316b-{&AL!zs1?iCx) zRd_OKD?fPJSZmc=K)_V;%o#z|+)bUX7KYWTBpy+89r_jjWfwuH)E4}r3Lly=W@ zV3GSXZwn2>@uYU_Xjh}`z3svMq;|d0&l#~E-?wfxrr0T-bsS{3-6CbAXq%jDHpeM7 zy#DsQH!mw;5s{!RAnfc#9Fm-y#qR-d(`k{NQ_P9t5^r0#S<|M#MHNES1vkyN$T|El zK|N1pL&$w5+c=2R`4<~$r!Kl9N+T7X=A)~#Dw$j!LC5+D-fq3x( zpOJ)3Yc_Y7s5cvw<8B7uoj-UGr}<)TRA5*)jnnnWeMz?|X-~qXasG)`tWEi@*&B@5 z1;d`i#FqzqWpPhWWA+QQx*9j>XL~%`InFU2t1!d(uhqz#ry%rbFR8NgS@ zI<7mt$>5W;-;3=cQT)AFODG*et_|vSF%mFMONmHX7#zY}E7*@A6 z=f&@UQ(d98+lrg~0R*n>4S-Y;b7*bLzQ(T50g*1v(#DMW@spso zbO0)oO@n0{E$j}$Yz33DivMka7LkDLZ?>VCI2vxPlICuBf=*CafeascD3_v_O$M@o zh6_1{fRLw)B{|bIdZ8=cfLl>Yrj;)T^vepnDsx}<6@iW;#Z>7h;49hDI_yb1KZ~+N zky|`LI9*k40sz1|d$GW|;~{Kq!_MgG&q2{!zDEG?FawW8m~=+D)Wl zK#_Bx_W4S08{M;E?oxv2zXQhqYN8p+cnH0Gj=`U%HpZC(@3HcMW%h zoFiE=3i*l_pl)>P-RQ*L=$!jaRQ-Z1VtzaYy#`AH&z%r`fA_cA`1v4?`6TnD2*&f*bw^l$ zg7qb<$D!MDfPkYMjpX|Ge@wFu_gOlYhrP?HdHa{>=Zk68GT)5*>OaC{N==pgsXkQM$dPIpvSfUu$=4-1A_2JMP|N#74NJoE^vxekkQwW z{x`<2VpJqeSwSXFbPvaw@2QNJ(a#V!=k@%HuQrUfu_zMt-IWCRyP(zEAXI^*YEO`FKgAE1O@*&VOZJkeJkU=v4o?{OR}i4woGZKY4`JXp0=V(8 z`F$iior_C5%bnRf_`#C3LmK|Q!Oa_b9zXN5&R%0=-cU(8)q!@Gs0bjS{qSqKqBkBo z=H9F?xjMHqvu!t9oWn1_K~DH~ zLOcdhslks}C)4#sTM-sasy}bH|Kl;m(ghK#3Wn!HZqp$w71!2<++$2GDJbb;UOFI~ zW5`fb%pCV_B$kT%G!l(TLhlcwO4m~4;vUmCWkY&l;p&sUu){~s=8PMBe5AO9|F(}I z_U_9U)sJOJg(Xt8mx55>_kTMV^Lz53X5$r#rA@#t;KhVX)?6aUm@k5-#OnKr9Qoh4~JRT)&}PyVF9|0w-+FGXnURoiS*+8uK3#wzbY$Tz8tU<3m|R6GHZRWBqB1*?H7;ii33t6{F>WGm2C>XeXL-H4 zj-?ha)l(1QHmMHZ|$Ao*<55Db-^(D*#LcYvJjpO^jW%oXY`NVOp9;}>JUjx zAur~&iE!MJ0^`pLoCAR^{>qI*_?{Oj7T^z3Q}5?Y`e1@dZCmLy?I??)qsa%^7ac{D zcDY(Czk9?v8jKI3CBlNBgJ6e(fxUR&1rAxs@JSK7CN9^+F)5O=zjjyy?};W61z`WI z-Oqz6F%=KbYm6+Fg5(KhH!?A71U@L=#*7CQu|r>jv0tr~<`Y+TsnYAmRV-_(X+F)+ z)?Fw;ny4WB3Uqw46z^;Fj9H*kLljHdfcS}@x3#Z$s9sRpel_t65wAP1dwx|rWt`$S zw<1>HVBRB1>-i;JFtF-I5|;1@ufj|9*%-WX!|vWI3S9C*rb|@I1Vo?`8XBzqS)cbU(Ar=HtVw0yuRFB zGk578*%EHf_pb*`I1hE3Y%cmtpR|bk60l&W9TtCqUP}}2`a9L$`Z7V2P(y`!sZ#bt zitfCkHz&wDweiqwom>R!6h9J`AO0kacOe6nQLT6XeM{Y~kF4<@S~X5D**T>pX2%KYQ}@XbZc(E**QXX^WDi+4&QA!V66x~F} zV{F2iQ()t}aF}h)J$wuiw`C~7F@&f+gI&{&f`bhhAZxKd0fy$~-U>%$f{Td?M+uXK zN;#}Ja|`2h3@`O$NOpa|Fj%L?$qYRXld>iq`T=TbuzZUjaF$-)ght4I7Wa9QcIy72 zXR)6_F7?WwL|cO3uk(hjkp`K+_u$o`%}=dQ3=kURN!h6F*aVEwWR>tw5P2iJz@kzg zwI;2j3&V_`CDlXHa8Dzc$h%SljjgRb(h*Su^WEa+&2D0;Pw(B6R-=Kh=}z#LtxUs| z=6)&wB^1&#;zH=Q2o44|;CwrT=lth1zY9vm&oGkJaqqyK=6bZgpuorXGu;77)oyFh z0X-5AWAKSRhY1w-wn_TuG)2#loXWk!g!qp+AsM>jaO;rB`eUX-?~Qq{UAsO47)GaLZ+1(T;2D?Uf^(*}F%i#r zC#<4gW^2(*ZlB>t(X-L>l3A7+j%J_;n1Gc=Ve-WL7 z!1d``W3ApkieiRKK)vdSkuUUwA99c{5oX=DyG2%j?FMgsH7Fqs_@LzUxo9@=!DPiO}=c(sxZj)qk>DS zODDX8>alz4v4QT`?gv$TlSusFNydkDZD7FrKL@}JdOQt%{v_kbx^~Zam49MADY1U| zduii}N#CP}ru`xrDdbOT7e(YHKW)e~f&DY$n%#htv?})Cy1`ku*~Q>HMdGZSk&3*z0?172R_&M4`BjRvZd_=podwwK!2kruwutr%WU+EPoRjDOm z%ASyr)(RD}agQzVh~05#OIZEST)tZcN~-m{d5h{|sXBP&YifhXY!!OMeh>Vk3LnNM z9^d`E>KiiY_@Cm;zruNp#PDH8Cw`TMG#)v}Cwu@_B|Hf z-+~v+0rTns`Thg^FpC%9+>rP=jBP{qBPzs@<$^s@RNOKq{qU0c5{0vw8Q>Dx!J|rh z7j>3=_#Jv@`J@W!+=W~jkv_N&tLd4G^fXUpZ~>3EOcXPSJCLo|TO9PnBqCt&xc2J& zX@Lt2cM>(SS{26 z(Stf*ZDqT}@GBA5b~iAGA1<+zz~EY6S+{XM{@r-{kN4JZ!<8Rbn?FX1WI^q>;CJ&L z?6|aWz13mjam^^q$mXKnM62X`+fu!hy`USW_T0b1A*;Da7m?NPglfZpG~^}>H0env zK`qAonaD_`c`n(B>C3&zpM;s2x2Oz@U;?OBy)tv&dyDqRgwl$tR3mOpZWWAE^dG0ZEq(MpcOiiwAxSh7SIIRo`4R_oGK0vmE~F1r`4&!%7nWc07e zAEFmE8IQ}z%KCX9FB@iR`H5us+2tJ*7f-U|wSW7(ONi&s{&pw&`qXUP3|il)!p~;j z_gR^j9T-rww+JMKcix?XzL9(PmF`E?lPm2x2+_k0WxuUZm13X` zrwYJsYIx9P_`M_)UuD`ea5i#0BeAz)sp|B=@R{PF*#M}uw&ypNOzemGK<$U!XBR#y zdR+1zAQ>#TdjxR|1r$1iB{p|$NZYK*Dv4H#m+ zBsGP|R#~qoREXi-R5#kfm&w^QFg8P6Cy4SpwWrD2zgpiYq)bOp%7 zIrw7~oO1woDTk%e(NMuBF!u-O3mAIMtLu=t4|I(VW&nrbavwjOD;3UIH?UxaLZ+FW zrSzjwi|KKLpfd3~AYduiq;Ef8tGZJ6Li?+?dvvWF~pC@w3{!T2?rNC_r=O z>Jdszw7)E@yXOw<8g~*7!iR~~a%SIJOO@ABFoiD`cY5#6{4lvr>=9WzcND2?C@lz| z+cDQd@F>G`WCGK)uXF-P72JM8G#-OjXEl|l=FS|Zh=wW0H%CwS@2TpRP_wHXI$yGx zXz{%#7>X4KJtCBuJUZBuSvkJstFr@Z0IbVBAOWP+6xKR8bl%4V1LFY4`tAiiike{; z(_5#dkzwAPfcfv617NHW@oZY<_-kKcmTk?ga!T_*<7XZ;#Fn3PT?pi0+z-?I2piNKi_MvU zZKxDatrh=a*f{RFPdi~JA#*%8?E<{3JpThmG2f+A_4^v!W9?Q>%{W)=9q3Fwi(eoW z&QsGP%PB12q(jXMC|6aO1MtOt3ps|95x}VxSQ&cm-=l0G z;)zb(AZTXckmCU&b}%*q?%+Xtq$*V*Bccr4^}wx`?kcYpN!4C4yK{uDIu$rb_Yoaz zD4wKMiR+9_GTwZZ(}f%n`G5hC)t@-o?_Jaa2l%W9nu?CWHV&GYW&L`x8yuztM0Sa! zX}6FGni9mR%lZ)?NA?Qd)JqD={J$AG<+Mo49TlHF7zAh|fWAQElXQPKAe_@=^kR4L zs`M#j9at+C#n5Fa8X|D{Ok#U;-QAmRJ%>HbbHXD1y6EktOT z*RcQrXIy1aSUtRasZfW8CDco$^(BH=N|w6pkfhJ~1L!Yp6lP(6Y0|eg+gu3^x$v9; zN1TQJQ_K6;w_6HU_28qL_RW%%H$E#{|I@s``uw-8Px}~r1zJh>^#5>Drb|+$eUvhB zXHTGhBorK}QS9lFHn5a2(2y}$lLp%KRRhj|A<)QxLoKDFA)JFxXG>4(TlBn*p;+GG zZ_?PSVE5i0R=s^6^Xr<@wbzPCXaLCu_L?*VvI?EfnSw#!EM!Lolg}f>Xbba+HGDmU z+Ce|5`jNd$G!6?S6Bvb)HX`MoZJ(=!SqDaW$h@XkSy&L=W34P!>np4H+#7>ZPCJ`j z$9CMbJG+@bZZA+{>X2sD9^A9u7w`i--2P{Ug3Y4&o^F>m()U4am3hb8X?H6kDxT$QrNA) zKR8EoRkZG3(tzrQcHaQAOB)8M+7(o7bQYZRH-OsD=rjUtwt$|lj2=%!_aF4K_>eDA z!$%@i$?1d-bqu7caef$N00~x-+#BfB_$W$SP(T?(_wAXS*=uF1*b#-f{fv*4lY2t< z`r2AX>)g8ajR9L`B*PXxU`N9UXCw)~B4iGtsIdxu-yXo)TVx>zQ@7jdMQqQh3ZA|@ zI_@C;I|)6g3(@q#c4t=%A1vP4Q_IArOtW|qyUu zSxvsD&Mx!AAf5L%m2vvy(9@U!!wde0yP@wvEte|dTFIdXHRrtRicp5u7I+NCDr(m+ zi2$@Z0n`tAFTAcJDAALeM~haXv?|Z;bdH0c+f{{WSi^&7?-E4o#oYR`G_XCoGub-! zALUmLbvMjj2Hk!~1=mv)d*1Kyuf5dpG?_Us`4MD?ZpE-L_GXsh5dr=Y>;_9%{?wjL z?p{k)(*wM;m(iKd5g>fEAW6N3S}ZQB)AFMvJCT!3HPXvhgx?X5|Hyoo@Tk3_W5fIO zr1#cagK6o`=FKad%`46LE4+X9{({>T+`zM(iC;g6mQ4TKD*GDp{kt?n76Ik7#lS?G^@nAoY{T zRB)bAS;WQxTi&KYjyXDuEaU!qwX@xU|h?n0!b8rM)hP)$6w}RJFhxV#6 zC7&5OJWsTsoCw;E@G801CT(%$(zv!g$j(Ik1D#(V^pMwfXknkF{viv4L;eqP@*lZ< z2!mROSb#$!0W3rd0N7I6Yj^?U^Bt7WYM_wZ{trWjlbNxyy1tr;+ zS5T!Y7J6-4$RC^tUWgwGY!Sa+!H2OKQ(AYI5AEi-k2V>;bBZT@BKmoh7>S8p94aa} zx%rz|TzXGBV^=EZ=7dRu@>6UNjJhjKyz9VxBcM;RcreYzO{r2N16UUV?wEa{xjZfzv@@vP#Z_an%wZlyRH z@-{RHusR#oQlJ|v6gS%~2#tUxQS+w}X6AzYd_RJ40cPDTFo_M|FUoW*8F|M(1MNSd zv!~KhwDMW?q?C*W3-8m6MCjM}#A+kw>p%IA!~88OZQ^%n~-%rGzeUp9^ZoSX!C z*l(yxRu(wx|8};gOK}PU0a4KjIBjwayE(Pv1hqG7^%r&fZtMc^t4HsTrz{5}!_S-^ zaP*|DCGO+b8=^i=dkdCH9Vg(TKGlwoq5kJIhi$Tv9T!h)fPrFpcWZMuWzD|5H)J;W zX%+4R@K@!9-$2?1v|nq)&nOxUlz%L-d4RIMb4Eto@@+TLHf8;HQ_C=w~ zkXz#UJxeVz7Q(I|9Mt`3B02uV3uKr~pB>ltPb3@I9PE zwDBpe+o9IFQhH=u^<{-+V5WNOEw9n2FgJqo@Wa171rtJ!c6HflUO-c!h!i=t|;qP2K|9VYs-=E(*L##}0YfGlvZGj<{G?xa)!I%A-C@ zM1VCQ{h*qspyB#`O|chAYcJ^w0^N!|JHcU8k8d&}_45;pLVUeQIxNSzb~Lf8VNVU+ z?;!d_;BNdoz!+6hq!NVQ3w|>A!}-JtYJzi)8om+0fbu(eoPk9xp8SR3*{mXw6$E2i zYT6^;M0}NTmij2)iK&7KwPkT@Nin|IE}h0WLODZUdYM}K$Ps&oQ;q{M+&w4Z) z^kggDnZ3J_nLxB9xubwe+R9s@CH@&(mI{+{9#o9^fRyc>9+i%U0|G^UxW>Nz13G~k zYT8@#VR+1%pKci$eK)r_;xvXqLiPQnKsBtRB_7bY%M;y;JEpqdbM5vXJ|wwsRTn(F zNmuAGmdXZ@G`XDfXZMagwlxgkYua`XpEkONmT8wTS+yK#wHDh8Ja3C(@!6h_hb4yV ziTnzy9;}?P7sfcNaDOvfF^=q^7Q!mjva)%ilBoD0S9+qJPiZ|5V^4b9!V{i!i;TYJ zUkTqe=d&=i8p?kCFtpKzaFmqgi;`cShJ`yeCd}cnY{ziN<^)fwZv@RpCZtR~G`tMd z-$C>$)9F1x7bJ=X4ub7q1p_a8-P2d;;f^sc$^gJ5@z5$W#4+Z1+02RRI?pScgl88x zwP76?w&TI9<|Dh$tm59`Pn;5iUpjC8^!=9#y|j1Uf`g)htUs3tLy&qLuX1kiT;geC814;E2uN#*t^*d8q` z8MjDJNb8rGPmI8N&Uq-rV+84*Kv}BA$A5lTxjO&esQRK6HX z>*J}d*dOm+{mK0O??1m6FaCbx`ummZ&li9HEO&K2SM>LvN#{Gj-R`iDr)0~ie_~HA z{Mh-lY35J$&ac1ktzY}G^Znbj(|`SHbFNe8L}&K1&drRC$q}62|ctk6+q4$;((0l2;OL3~VV43APX}Qh2xy`%j zavyj^>tI7~w-eC2>%2`|0iwM<)ZU(5tVxmW*}vXY(p|Q$C)ROxizC*dm?g-4zOoMV z_I=wXe*p6A(>D2cn`~^8!&hwhp~mG7_n)tfN`$s;Udw%cBy-9wVM)t|U;DjCuIJF3 zXt9ovlK|`7HfwR4^;jXJ!TLbuOu)GxKB-mF7k>Cqs{&dEo%YNgJoDbK|bwRNB4RRLqb)a!$1zL-322BwA{SgwW>Ge55HUEqWr|NUM!s(HMZtnxy3?fSbU z$xr1h@yFfK|E6mEsT*^B_xbU`pQ)OEj*MQscyRR7VcXxC?bfc(Yj-9*Ebm>q7y2c( z<9pZhpTP;y?Y(BtLsb%tOL~>YLS|A4J)aLwNN(@7 zdmj29_PMdpU9laPx}HA?PKayowR#?^mS9}k`(O5A*Yow@gv|C{r{|$s3C88U=kA3* zi0$|<`(S&o#q&_rgpQKl{bQkqu^nf-p5G5n_%B;Cp`)yK|Gm(**p6pi&sTyI(%O3+ zo`?R2eJHl$WpIMc^V-th|3}w9;jfS}*TK(^|N5D#@<-#I>*ddnGk>P4{t3J13jE%& z(A3zD(gZQrPPw1`HlN;3510Rc4gR#s{oblN^#|CrA5Z9NKT)+8c4aRv>g*+haMC(!OuB zB({Add2#OE*}R=W@_&Wd|NH+w_`Sz|=FzKAN1vtDJ+3pUXYB6<=e;$!Q{E=!+KK+z zfBMt^9-ORM?z}~{b@-t50{&Onu78t_-?;X2J8}}NyG)p{?T?+lQ*J2j+Nt-mzwy)m zZE*4Q{Qlkq-!6wL;JJ*q19!^bOCP&_@@_ohlh(#*t)|yG$)&I{Yof{vl{b50XCNxi z4Pw9E!IWA3Mr3a4-q=@Hl#NOoi{2w|%eXUgG{A0$y8qZT)$-^-m5ryb(OYS3i6PUh z)9p?_2$ERgD*5-~<0i|WW}WV|Z`WPBI{p`1Zvhm?^F@s&1cF0=03pF0f+V;T+}+*X z-C0}{7ALq{aCa7WcXxMRY~gM4`+rsMtM{t5YPP0lW^3nGpFZc@+ug?sL_aPZ`l@<& z6>5H5Fqhmgmf+t$|CFQeD*cRDVM#v!{lFxF4E=k#L{}pv;&ux8PpjAurk*INgu~HB z_054YoLkl|{W8E@hF{;x6}uWG5w~e6dRVZ&jl!M*(O`>p8{lHl)w@BN6D1XXHb=}vJ zLl0YxvEkd2lu=)kIr!+qx2Iz{$_=)lO$>1=_(}7$gsjZKap|r55%OjU<#5|bT9<+E za~txeuO?Fj-y=e@5BF|`@av3pToB;$)ieQIQW>ux0&NUnc?6b z&jmlMEi{KF!%7X$)jlu;oEyjnKH#3rYWbogf2L~>k?;PL=((`k&lD$3#b=cSZp#2i zKl-mgVg}2FM~3&gCR%{5rd5#FX5Yr2f^?ADeoDK*3(O zxU+>HyB9tCF6evS2uTTmpyXMDV3gSRVFm1p?%))r2YQDG{Yj?za=G&rYo?2 zsH*%)lxsrPNQlGx<*i;}sY0qUz=UDCb8lZB4<2NS)*WJo+>C`nofUER1lq+2`+RyEeO zhMZ3K=#7fv3~=FYmfAkI%+7mE!QPaPnHu7CpdNwR;^g&f7Dp@r;kT z7tQ)PN@i^8@B108vvR4oi5)SGZl!aAzLI~<9HDuf#wl&P`6DDQXjL@EE$sR*(6^c? z)U|KeEV))}lRi+)uRd2W_f z>i6f(RXaQc$p3n~z6L6#7_X_;a0*eQd+Y~1>;oX<%XFaf{)ICqdocR}puDd1sihEC zSnJE`Z)&(;bD1kDVNN9BWwl>Mq@eXrUZjsx>vBt&K=7>eD)6}Xhm}erT_%8Y&cJKb z40fG0zthb}{DSQWB9VEW#a>XhLZ5jY*{nCeTfgS0R!;eCgr21KOFVpHrB5dtWkkV; zd`<<$uzH{h73D63U^3~&cPmj1WH)o{tG%3;A;jpxvEPCur7Uf%7XMxjVeP%nR+)&6 zw8PhrYq+3WtCQmBS{_YSCPF6}^AT2p{Lknb0u2~|T+sX5INkS3Ai&DmvnKjsQkDnW ze8zK(cIfgtR;+d?tX=sw>?`5YI9L6sN040|Pn*QhF|WIt6zgcx(LQvAKa{y=&j=2Z zB_a(x3>!Vjcvo0l*i{sIk@7sZNvP0zA^J15OoAv$0*%RB~*Bf)2$Tl-Zv?_7}RZH-Mq68N-Z6+hGSr%wU;wj6vZ{Qd0mBI$ez#n^odN#do&l{VgRrl)&|9< z2L4@pABUIeGW!vWS80MmC}i`gq5ADD%1I19S~hM#IdozR*&DOGPQe*NEQHVJDs+GfdJ07eA_kb~ES5C=IbrA;`k?MUQ>f@8eeZ0w0z= z`JHk{PwUf(^0&#lS0*Zc0k57@zlENAp6~5o0-8S)o806g7&--V_^!~b?M660$%i8j zfN+D5+;k%$)Pxod;Q)lyz;nag!Q%UI8Iq3R`ArKtCxv;8th*g|iknw!Vt&sz)>mcv z9wq$~I=VlW8gHQ^eSd9pRDtGQ%<=A{D&2LWDq%MYyH_ptSR2Q3wT0l(i-cfimfgV9 z97xppxMFzxbv#qgvu5FcX&CBFwF_3PUAsE+*k^* zRod07%^B35w(77n`59TU-H_lG#$i@ng0p*Js&}InflYwZa=55oTfbH)s5?EW{1=iI<=rdLAmM_-wKlcr$R1AI3z` z_`#lHR< z0nlY3vqwHsdK?(@V-|i47lh%K7gJIG5fE*TF~IVEDq~Z@_|kd|)mo9IazmWEGW97L z?G%v}lj~jO7CyK0j{|YoWcC4{(VR2FbG{1WnHAnXJy$6Bfei1mUz!1F{@aW#{h8~B zM9Em!MG(7v*~kf(q^J#pVY8=dJGdk<0>YrB7!Pe&K=^lK*$n79Z&C2c08?mAG#LRV z>_7+n2T#QtygsK8*N(hRNTb z)eW0CpHE;p0(WcEej2Q@+p&O}gc(^%6hl$X#cY+89bWd>OYaRq9WF=TP9et=QrJwl z4RgMxMLc#_hcAve%F)2wP|a2#`5!x z{blA(#;l2DwG&49*B}W%)$IyM>8Si`0@G{JX#$9}c3v@=)5*$9p<}Uw+*Kns2n|7| z?|1ZqR|{g=Z=Qw%5jQsich++a$Ej?{^Pg()0HsEMJA~ymdadDnUgm)6IK>(6NW5rS zY!Ale8;t0PI1ve1Et$Do-$Bd*p-k?r&p@1P9a^cggVs84Ss;c>nd10MK^PG$yTi3K zJB&SYP$!}Q8`(_`@)S-Y>=-P*|3rI>^MHSFJ{02C)DoG*fpk6oMN|H{^5;!_L~!N? z@JGL=f+FengnB$_3>z!AUg*`GeLahCm(NmCeMK;E$)E|{WWRTKn}nU%&JDf1xOvN= zsvXENWS<3bgT@e0-{a{(yQ3BNg}1@&0r7&15I5)M|R4u3i^jj+o!YW zoC+t0Wg8pcM;EmfB_c$8goStZ+@4CJ3sGyZ&R@yk1T@R2{F!6OsGx7`6p>4X3CPVM ztrh5X!Q<>|ZWo}#?)+Bq>1WY9K`-L4uMzz2r@b=IorIx#%T^9@3pv0659)&-6RV_| zk*j46Z>9SdVmLmF6&l+(EhskLF}Yp^dS(y}4ldPQed$2M=vgybB~paPr*H ztyXsIP1?WIceX9SVB>C1pTl&FZY4^VYCy~Bq7Yo4b}Sa z`PXD`@&deukq+PfJ^fw^n}BiY)A4@zg9{0O{O z570s)JC?{i(y3aQJh3Zzz)d+_+}@|nSfYL3vQCxc8=#bo zNR!QhU&gP=!;NyKGU17ju|q6bRQt~MN-jfrq2G3!*lUnFnr`Pug=}Sc-H)h_aW$8z zl_%QBRY08-G{MTag!{qDfBd-Uy_7T8@fT8Bs}uXYeXWePhv3_FxOA|FcLf>{+$V0$9`+> zA^OptSRcJ(w+L7qWp`_@Irw<|2C2D>+eF^U(nfxM9P5+kqkemCcM&%-4qFZvGQ+`c zm<79McI(4Ffm4H*nD#mEHH6R>}bo-MuCa(cpv*K zZSd7b?hs!fVI}~xIkx!6OnMWAu`Ob<7U^DMSQCZ33GIfs=z@lp;2h=Z24zkVq$c)- z_&~70P}WCN5acn)p8M0u0neqT=0T<^JsojlDzLE5T-2Ojgs6}lp)SRqdXX_S%+#aZ zj6&YY0m2w@EKpa9zsJ!2x~1ZCF6vQ0MR!ovwq4kukN|_jEvWqHcd7I3g%P2Th=ua#Dk;R!} z`bUvh>Nqj|^n@%(E05h1S`Ams%c3ziyC!(l4otYa&(n$MWnAax&9s;*`;5(sl8%+>*B^#01ygUqFJo4hB{ z%qoY~E*RooiV4{&mji@xL}QOX=Zn2e<+92UX^Gm=A6tOLSQEuW0-&E~H1LX%n6jzp zBirqH-r49ViIda73jTL?v60aj7}Yn7#zEKVutupA?L#+5@L^!nDI4Xz6nzEjX7_IN36d47A%iM4UZ;~?o~43 zXqXW5*2GT^CbFoJFf!&XafV}Zg0I|2vEXBCk}QhTuw*z1ZTK_liHS2{x0Ej^uK5-- z`9ln?U=krcydqrM-(v3HQ5Oqt5@+9j{iI21 zLAUWamDoYXTR``;kBav>)=a=oo16(Pu?urUz(^Uf)7PFAr0)$df27~8XlMz{sYcgf z4=%C9Pd%%=5SzbKB9YHboUqfqx&?NpCWB&{p*;}K%gn6Hzx8&*!sv&{0d!m`BuA`E zx#=>0>;;Pl`=)cU;)2ij9%jUKj}Uq9#e8)Y1i1swbQ2UO5_lZd5ICSWdZS&#`*D}S zT{*|fKRZ_ljTUpGBG2%V)`}ezFNhJqUlf?zn}>7Q1D8VPsI=Y?5rSjaiBy8_#7PKg zdH^7|J&|eo#??y&ra}-7yIu(z4_}+i7#-pv4_XsH>2|^= zvQ}mtxHtVuJB;n8-!bALoZ|FOCOU3p&-V-nhdxB|=wVZZt_7LVzfEJ(7*6 zcmy@&9DX%_L`rEFEU1V+{A&D&RP@$cA>en?ohrGSMzj$mzn}E1_%IO72cO#9zRPAT zthq+tKrXjNACADYme2*R@-Gl@4@bM&2!C`lbtE{Kus}=K6qcpW31(k!KkWN7NSp5V z-Q`e@oV7WKuYIT#KA)NsH$QUFOtDGwK)L`%!EFyGx(UwM*8jH_@gB|(i9de4pR>8M zT&&`vE=80{wTLjeVv2t&{TJC$>b4hqf6>*GkgwKRS8Xze4P9rjy z4g+p=PMprT8qWT#6YG3cCXaz(88IoH@4$vtUFx^8iA4{0J<((O-;D*Dp&Uk=A?XOP|%$q%iMFW)` zFMqr4w}JnSofI1|#%DiuE$F9yB=1OLa>ZFdN2gJ-kG^C`plj5au>-QfI#LH14CAyZ z1mMy%ueEY)VORlU)*-U_BTRDpj{?T%L*%UYVFE~oQ+vO5Xx}-OhND=@mZ2VTp~12= zKJ209p3$i7oOKK$_5Q&^Kk0F1Y{7W zqa9u@il+Hc>4+^aI_P8U6z)=FLAHG;VcBxbm0u*wqKw^jq^_5c;zYUFxa<$ww|_hD zwYlg=Tj&tK-}71?er+y8^#0bXcv*Yo>-m@;KH^;0ndE->M`z-LF%E(&k!yj1{~t2s zNcoox4F-s@fwC@IvM#vSH4lFJk~GZ;rgaE1jlq=x;XD>ZBrRa0EZD~Kf zf^zQWG4{tl$DK+?!CByjB~~aGLV2%&`8M=#FkSxN!Mwvgqc{pE;uU0sP5&>PhWTeT zsz2#45Kld8c@|+BW!8~0@Re#0m4X<=N#JPm8X0TnrG+-f=5kHAX@{o2O&PPdA zg*lNf_|f@Uuw;&t$oOF@43}Qx4da_M)PWVewhO@qgg@kFu@ec>?{dzp`EoB(74FmR z=$%C~1T;aPI5SAV`6|&X;}=xGn0+W^{D_&{E?mIq|2d1CCQM?PIJQK3 zpz440=$IpVV&ne`D)es>xG zYjeOECNVG|HYqJ~DqWfMk2cwrT842BMsljq-d=PQr=e}s?^H61;y1bj(3m>?7gOws zIk6w@^1mZEZ!HiZYZU8v&#hSSiVeEC53HS|V;}7gI;Xp4$!=g^Eku*^*(>6!>U6*F zsxDPWm#M+6(qzTbs%O;`*j)eO`^xJsnT`RSoBG3C?)~8#cffa_cXC3-qwKldWup!7 zT=|GD5h8*F2rgv^>HpIvjH;!hnu1co0!f5ra`kVbc-9fm{ByFcKHZ%~h~!nUZX51LFS+4TOv4JVUN)XbYHt1U{K zK_VPWFXHCd_|Gohbu)Xl@-|FsbcI96?s2#>Xmx`^j&RZuwuJy96Es zUZ%I@UJvDfACvm8>`C}m2;`O+_aslhQiDAMip(S(hH3#Qv3C{83}HE`kvp~`DI3d> zFSr2Cr$fCpP&O~KOnk$-D02WiYF&39MtgYfW-5o5o*#7-sgIHqqWt4zZO=pP33w`> z#Zc0zz*)Z;n`T4=sex1`B$^^s7QQueDpc#S8}oO?7UZ3a!US8Tt2S3{#K6U2$GNje ztu3MgK76l3!~2hVo~{qN;|{OgRX)7W&$zhKUx3WvB`)#2uf5@4Z4?)~*O~Lvi@m?g zTs&Y^v)r%Uc#)Vb<|KX%#5kvVtkU7X{_h?jlA7afIyna*WvaTjjB2v&>W(jT=Om+O z?w2{9c)bT%+jH6+4j!R5BHePQ(9$(chp&dha zz7F~7mO1rdIXKv@+m#Op+7~*Uu{NO`~=SBn5Z5=FnkfpE24jkb=C#Ei{zgrzuz`T*aAhB;7@fEXSCm0GpB(6&6~w@96dmKOp3iGzb!($7XDg zTh#?mMr#G=LbpN=CT}Ucw}6h#46)>uh=P#MTQ%#o@}4;|wVK1y7iFZJe}GG zB+o5%+Lm_z`h{6wT@kRjG(9EAVNuVYa791r%WvqIjGw^I6?Z^qV9UmjbwhufRLqCU z+GD~K&l}aM2W)!uIvpqYX<_NcZ*&rWM}3%PU(o=0A)Rb1COEw^3&1G?PA$dMq$aao z1>ehldc^x$(!UC5irw02T1SV~iK?jm@HnKmwo#$pjY2xpnZn^~Tf@iZ zU(OV$l4Xxs#8V0ZJB&@_Au3H@7b9NtDo|7u3xr*gOVe9rtpS>zksr8KLF)`HwdH(+ z_hDF!iWxE)&awT^d-aBjQ`x-Y?RvUjxTV%5;u)q2WpcddqO}6MUWPg9mfm$g;SF5E z+~iBdGb&cum=1Y(1UJM+#1=kG)GF^CM%o2WetAt;v=N*|&OVZoQ;~RjesNrUq8M|S zS$o+OgD!?kZF|BHnj?BwT(HBKf)<7P2do|FBU-N%~b9>zpo%aXA02UMWqizgYk$Q%j`IJd!A=0 zO+h;(m3&B|I0wm?cAY*E#d8(x^YJL3)s=S#^6hguU6j;kz zzS72-b^_tq#gtQ-%kAFG61Ggbak{z2a>aT{()M*e+Yz4D_TJKqxdHj|sTM|IL zsnmq)TX#~Zg8r({J@sVGr7NM!7RnUUx+1gN(BR{_gg9H=Mfgd?MenflQ+YHP$+mZ< z*If1W=0;|FvQ{~p^ESr2%FXQhlKLi8aZGHmT9<<#yCE(886l&6YHj@oAf5|Dj1TkT4SitpB5N($mvu2T5 zI|;vKn&r3b;DVqyU4Mz_g6XV|j3LI5daWDI&t5(lVzpsp)ZgTnwmU!TbEd~m#M6b5?4=q z-;ORh%8RCYJT>S8eVAD90fkA{6f{&(Npmhh;&-xo%Z5S zAxmQ4T?rMEt3Udiobn9h@($fEx-IiR44bvo&_s@EOj)*h)Y7N&&9#7scBc!h9hGpX zDy<>QxyfswpN?hWr#+YjbOQPwKD}&)4-4g1L>B4l(8uf4X!|>9IlKOzcsO~Lo@kiS z!%3Q#8FX+Hw^r%*LGE9BXu=aULwDMKNY1h=2BF+pl#>8kgcOI3uWTw8L6w)MPI48C zYvZu=@Zay9$wbzS+iy>>IaK@&CUU62&GpInp)8EVi1anEG%z zv9i^K_PVsMf9_qvut-+}qRS*hbp}!B-89FSnqC4aT3 ze6oux4r>vNXtB2_nMc~qG1$S&o+JL)$C}4K8=b8^D_O!C>NxogQ_q(6V{!aa>-f{S zc0y>07vjH5SLfc;zp^>;w@A@lcEz;4NH=RYSHwv6syDbwalx-9btH{J@~i#b)`hH{ z&M5Rs50erSN}}(of95F5(HA5*ZW`+CX;vtvCxxrz(^)o+9Y)5mhqD7XqZOCrx=}2M zLfQF$jh4B7%HE&xL0Xn9;T&2T|oup8bs3Zw)RkQzE#voebSybru8CW2NoA_X# z^4;duo{up2r4g=DJn^>cp}28#XD{^Pd6B8y_NVa0dSJta$(@x>e)vI`YWCa2fV+wpmk-6mWiL6XHM*x99FD!O4 zB3t4#Ezx>p{}3&$CkpN-ikAIfWy%F~Hi7Kx)1|8jLWw@F$D9xY8q zwSWYz)yK(Gizmw#PP36M*u>MlsL7C1zVWB8xUNe&D+~;uYha-$Bm9YQ?^La357O~e zyV$%s%w;M8Gdw54%$2`XQN65ZP&3W9=L%f?osU4b3?UFY^+jnoal=Wgvr@uIt!cH3 zBdDxpK7@>wVuh#1HcG`x@z-j3$c7%KjYGy^eWV~JcFU?~jcR#1ulPf!m*X$eW2QLi ztRph}|LDn8BImv@V(GY8V6xWyf7eeQCwaT9EX8Ui$+n$)KysN|!#fFnUYo&WU=anK zmXGqSMsCi3_;mEJQMPpC)opH*6o-Wl9$G*5r#t=mS_&~UUx&hiwYs*?8kA(5oco@K zXMVA>4DFfK%R@{R#&wHmrKg~#5w@U3a(a?J4Z8O>n=-=Q-WYV^ zv41axdye9AF0xVJLP*AIjg_JkD|b!DO)~oLSGY2dR3iRD3{mxJ@0xGQ4#121?g=B= zVdJjJ<;{#|%y-+hy&V3XWELCb^?2v0bMQs`dMBQl2A|uU4KCsVZM@D+C{In{5`<+; z7UHXQ_e7ED(7da~3ho2sb1qk9(=?eQe+Y!l4$hDh{0lH^O)@<>#u@ZIXfVde>zOkh zP?8g_u0n81=H$f2h9Zu+xV*FAAn22!6rUz|4Zd>+{c zda-dE$NphnSEWQdcke=iw{0AND|5CDwgm~>BvQ-3ozYN@@l3BH?YvdXtD&Ahjv?vH zDo=t2)LdtEh;O9_qvvs#)F+A?k;e06!h7?V+Kl|AHkQRTm5!VGdVQJ|SE)(+;5cpHjxmCK?_7s{_kl)q*@L720)R0E?`&@s0*mc$Ev*tzyTgJ;4 zIHigsmln!vmQyeGLFTCnK&oSXv=_~@q>|(T8#k#&#qARxq-s-T59sQp;Md-~0 zzsT)$Etq1x9rwu&70(EgzkT+9apy^;NcG%&R@UZj0+Y0Q=eL6VU#MM37=*E!OFj=d z1WQ|@2wl^6Uccqb%w&*oF)x~VWU)ID0nY6{#Qv#E$Ykna9yi3G8UOufc?zSjFP(|h zp%jmPhwd>Bdq24^W*fd{+c(JqiY{qhuivx;UJlB9v)=WujapsP46b=NY1dc z!uwvb3u{eun02^8;ia&iU$LzUm>hBv@Kon$$|D-$kM)LSBM) zplT?iD;yJpy>>b#X+EIFkJZCgo?CH^keFu_XHO=6I`cFc+^0acbdab-n z$2u=HR9Fnf!X}ojT5;sGtsXPyTpx$lUEa30^k+mrc2^Q74A)_4whKLC0lXHq&Zbj<;%bOfQhCk}my!!x=JPcc9(N?VROo)I7mKaS>3mvAKDAet;tuumc zUN6Yvb@Ga#Gpou3_D%f=m7$^<=*afe(0t{dSnR^wYHbd&e(ox{*0?nQYPKRu|)rWl1w{ zQ@gY-=zAY+gV<1NmUeExj=b=2S=my0b;Axy0!A{IU%B4gan}7%l=L6CD9f;^cRaZ0v#s<`d1~M%Jbs6~9EOR&U`& zd|fN7;S*+SWqOd-O}28$vOmN;vUD!JhyawKg1b@ zdz$lbtAI{cUxS_lP2=v`e3@N9j?Q2Rvs{BgXS)5+cK2KM_2TPaQ6uE2Z!)%cCdAA= z^04ybKlI4`c^tLWc-wWyHqUV&y_nkRs&^*x^!WF3-8EF!ZIoZk(q%{H0sPE21h+|x z{J;1f4GP80y{0aAl2(=wtEcX-J+vfCkfU-b&hBUyR_$BW)VvJLEJA^6Iz7)x;`=pC zjUFJVWZ|3e_|e&6#Z7egLh9un?tBURt4!AZ)g(=$u|A?}M!o@XhjGY_F5w_Ulmo;q zNyf(gouUbk9!!I- zL8XKXUlGbOjmeWm+Lw^Av?HE8J1B6dv<*=xqF)dlSMkKF%;u1d$a^W0c22 zkM;fp_rP0C_17H~-+q8h&!3}D3|t~~*6&+h*)k$Vk=B(q8Pb-H8Vnl`J{G$~iagmF zf#!yW_W2ttZ)a1Cpl7R+awEF=9>eGy0zp4qGn&652$y?$WN{Cz?sna#% zf!0Re71Hk_{wK|RT!Wzg!GV2T|H@jw3kkqTTIo!7h5s6mW{ZLaR3ahO)+V+_kG-79UMg$ z1E)W~ynoD{5ycOutPTF3I&x^oZY0>~dY(}_%Rx=hT<3*2xKWwU&0qP*%uX#;d|0FP|Ee{ZBc$PwQJlsJ_{P8Kh6i3BTxtS;s9~LnJk7#;iTFQG z%+Y^N48Em2GF4PioUFf1s@zmo*9!rn3fx-m_~gQHq`E}(mf%GB%O$b}aDM*H$YI`% zaE_W&^OKDvBNE2PWH*t(T21u#>$8LEP&>xCa223x9xjGd4Ygz7#7mchN+L?QX9}Bp zkhne^EtmOq+YTPDMVZu+TrHy1%ndrMHA_2X)N6f#7hbL-5Xu;LoqKWj=Bj}@y33uT zV3y@J0texmibKfamb+oqUngZ{$^2V08}A8F;C%f<27>_ln2bhRM>Xqb6pcHbS_s|s z$bU|XM&&Q_rMIiT*Zqervl~-s)Dps4B_jtlT=RrnulSjnY*IS^+?tw=>?k*6TgHLR z|GeF#C<`}O2K)jS+jsm}Q2vTg#W2FD8O$8Z{Rtwde10|EV|Sx9^COZ7|PX+OsqiiHpJrE~6(XTyW% zJqBY&szeEQRIYDHo2HFg{R+7GBr`E30R57yDV#-P&86N4H#H68nahM0yHEeiNh4QtzklI(eEfk}81*Iln)21{imfw3|B{phot>f*<-?q>#*jpAsM~^gl4#l% zBst83i(G#DIbF)%tok!!V28?|sT>J>?cQ0^1gmszhbD2@hG{pN?=}W*A6~V@Uw4rI zhbg}q&f1r(bL-cko4KAKNt|^Rmf3!#d~HNhwjy2vd}*mu)!=*WYyhl0Zm8ufM}MGC zkLY5aY_^;;!I{V+tg5`cu3P(dbdjhbkeSC zD$8h8CfPP?B3t-Hi2cv4MnR<1?AkU$?zx?2R~?XIW&IBhBW>baZ4&;I>U^y!ET{ov z$6v{?N}%i z*k$ocrbjblr{ z3&!vFf|ssCv9*)`IE$;w%DBBsIx|=fryas@4K;ds!F-1G5uUHAzX@JqL$8m1(sqHB zG>e?t4fy}0{rQ%iUmzT>8z>P&iQ(EG6b|#iN$%xCAXXnmR>UfQwcW|2pPU|_2X%Q( z-9S%=DkLA1jkX5s2tTCl@ZqSc_g!Do(lyW2AgyKykOt<>*^o)v?#WjkF^MV8(QG`8 z`gbo5x?c91A5Q@82DYd^XR@QU{mb^)n11qE{`lP9UB~z`y%&f6SFBjG`~JM+0;gBj zt{XcpW!?N!D|NpNZVWUop4yMs(!96`uS|v%p~lNm%4FMSXM;~&o7|x@y88ti6;m*^ zHQ4uOy%hXWoQ z51N6-Be;d`2Fs~qxppe2%iR4uzpEKm+JV?LEeJ2EJh(*uPp4VbUKHOK2)3~J*^Sm^ z(`rECZ z65myE4MU;RbD7kW5V5gIaIp}PIBC=)T`I4U@A&V zRw=%-MEj%rp=>;o{?d~=zji$&S?!C2`WDYp!`(?QP=i&ufA+FGO5^LRTrd zalp0L+XRknN5Hp-HW2PQ=qG^3VpIRqi{?#bQ&RZBrY#>R{r*c3z z?5n_lZhe-L23iZI6b3|%y>5%WT1fYU`^U#^(QZy<<*vML7?l1ikK6#|6^uvGwfA)Ua63n$^bM<(3~CSCFWj~qgkXG9|L2q`a`jRMWx9hydY72#`@b|oJiT_JLE9|*!Td$yFNwpN2TpaBarJp)eGB;HGyJN`8 zX$&IrIND07>cY~QiTIfKID9hS(sJC0L3w(3i1i>6Lv#!RHNrv;J;ATO6nZa??Q$13 zvU52HPg#}Ck@oFKj(o0CF3jae3G$$)R&~fqo)A?uNE}VopP~G_22gp4al0ow{dN8u z`^ZET@YwB}7wtweNslMr2#v+Bd53uZ6T8DR67IR>XDfh6Rekxd$h7=+s2%*Ep`N=7 zB|2X%?PQcY%|cxH#bls+1XE5vxL-VE)|o9fkYDb?SSwUdSL!)_vPq`WUgq~6HXasX zXigr@G0vrTY=yjV&<5WncX7&=F6uU-T&Wd{AXf#duXll|*e|$WtO!+A#99tWG%^h} zW#-b@uv-L2bU12f%|u$vA?i=l8EEdWHYd~d9ak^RFI`h=Mp3Slk5%m^m(GgN9JG-g zdYyWsJ#UFq_}|mID#}7nHe23ZYm7#hUBCWiiJG8UA~^L1XSv?E3Oj#B9jLF8TOxKe zSf}+rHT3qc8Y=#+DO~f{zlA1=uF{giCGzE^oJ(~-X!xx5xPJfe^|a8yb4F*L4>(dR z)iJ&PV|Bj_B67j}*S|%ce|GPo_u+x`o~sx+h^oB&=qmJNd|oaM1ym9;>jCH=hF7J@ z8(RJfpgl_EOJz%_{>fLIM1+=pLKD*YbF=1Ge-+T+Uj@Xt^FIY-R{k2<g=w zlHX_cF1vxn1|WvU@EO%zf8m!G>Zcbk_+s@u!x(|@)mM#{(LW5o;)qCml(^K;iDv~x zYB`7MU+?XoN?k(UZJet&u>b4{Whp5wUbP$CtNX5--f(>F4d4`h1#`A)9%&tUy$3Wz zz!Kf=_EsEz4{18{^&I^A`%!zHv5#SV?>31&{XFX0IzawcT4Y&;t)nZ`$9snM4%TBQ+WdifQWp5DNej8e2`_ucaND?+a^4Q`YlqGZw>@xcCDXjA{|{4d8CAFQ z^>5=Y#fv)}+$ru*+)JUjySux)ySux?!5xY_6pFjMKIhx}|6A)>Yw~82OlHkYu6*`R zvNxa*Bm4qf9{*jW`T;TUaydM@?v%yd)8k`UbmCajPUQyid>?w)CqrEm9((I`A-4YT z^y6UnyGrlWF9>0%68wBGEB$v!i4JJ#H4!Nkz!zyfDwgC}%1ZA%cKBked`wtOB=7nx z++!UNZpy=l^74`O#zxm=%#&%}8Dnf$-P)``%(7tf~(1_pI zYzdxo0?@LN1=obE`(G%0n%>@%A2CH#>iulorKa_~9%)nvu6p3uJknR-6YQ*g%)5Ll z;h!95o`^PjxVvwBenGp#k;}!@M&b1-P)3sH&KZz-Dq2t3x!8Mdd|m^8iLvb*(6Szf z7t>ej_|uAn)TS;6^n5w!+i!Q(o`_V;j*yC8>Iobf ziDQU(6?q;f?NAfbh04f~t!f}K#8*a|4ol8gd?BY~^72c{L(|-ih*H|r9a8>USYc-7 z#wxx2o&SJ}BlaZ)o7KXz8piiYxPk_On5-DeCrcUkvD~vsIB5n)*_&zjI+VDmqd<^s zU5QNa_e2PRo?DWPYAIt;i0C10c067L4}v5#<=yT=u^)We{vme0LhJ7`WwmxTnDojB zdR~_kKB+}?_RS#5;9~lPhtnD@v6l}SM7fG2)gSQats!+rN*_uXWZs|7U+NYq0r|wm zqUeh5=$I_3C0`0yGAr|~+DpO_sv$X2^MZVm#(K@HM9+gcxhaC5 z!8~b%;orH6@!^>9*6VT;%rdH&8@T0^YA>|Rula^kI`JbgJ23Q<+ou`W+C2H898rI? z&nJ#&P|Z;pvrnIf8~-vxh|Jzw6@ciMGa=Bhv3@ia2 z@a7&A0f(lJS1qvA1<)-m5~Q%)Tc01u$&Vp z9(lw)G;2gXDRW#eO!i*R;k%iz!}!hAz&6NBC!So79q`M=EuelEglST}bAzp_Ufw zCi~9bUk7={w1(AM6eA!JpfJ-8o+SF1b5qdKCD$R$JxPQbO=8pw%cv{fNdP_33`zB& zbMYn&o(9wz?{1Dp_K!p@iUE)aGgj>RUSXU*d1COC*7+2K5ho{a%~_`oIqQv|t6p8O zUWRwo=fVy$ubeipz|xr9spZ(b9)N@2`80}xd67kyu0Y1_SlH%3w9dmIh#4R(gxI2b zrfC^xlR+9j&TdT~Si&Chb{wNPB0~z{{w%mtdq8@fDLFj3wcs`UtDAaY;^>X*A-!k+_10Q_)Wr zwe8QLGb#xl)xAdASKbu}LsiUd#NT2(B*KrqgcXdzRV>oZwN=}wf?Pku!y&Vho)Qvg z>{Byj1_~VOIHYDuraw^bt-Y%4ImE=0&PCT^{{(}phG!x+RuPIX*#~TX2{%DY7^lpll-14RItRvKS zQ&qrj2x&3}|CmMj4;2!22$VERL_$Z@3^;5nsS4%SAyC1y;B0hK;Wt7eaC|0gyh)tP z>`Lu0(6Ng87u1fBAL53ckwTeS3B$?q!zu~r`~FDmH!C45KM*t}HT3NrGYbBkw9oCh zdowKma)J%sh7)VE(DJoO$J$qdUQUhHc(qs3P=VT{h&pg*x~9$O_oS|Ok-JZaI`Dw4 zzewzW00>8YUrvd~i%mnoC?&Dpk~F+#xZ8sDk|FjCdV2q%1$+V4(X2&kTZ!r3dh24F zEtrbp_59Hj7-u_i%dFrhHm3^oCf7Ekn)#R&%fckHkJ!@U3?>9z138cMXR8wez4&@< zC5|krO>T;&EIRZKuzi|qttRVr)rscOxGN}d(ztY zJaJAtt95MTeTNR!2^|<)dOAnsT_CoGTs1#p?t8d$?@G;HxAso>*uplke$ApVja|8} zXx@P2zszQzeNmQV}b*2QE~!naEj_)dpz~Iv*B%6 zee&D7dRG+CHV5{XOv{P4K14!#+COx+{?L=F3koxg-8+k?P=6Xr!Yvb#~l3580W%+4* zxWsv%4a|$(ud~l#OFIblCEy--gz17W|^^Br)@iVo1stReDCHq1*5&eU<;8#=zIJZ`dVoBe9d3zD6^8p-xw>jCJ$j z)a4c0x@Pc96Jt4!{Qql=BGm?MU|=cT^Q_D;{FtE?&4ql9U}h~LNRhRX%xLSd?s=-zqBR?RzzMj&#+ zbPK0d%yX!UI|8@IR&I<}aetX^&wh(24t9>w+40xovd;pG?Wi(mT5D@<9y!*f{j<%|A9THhxs1?cTs9dJ>7=AF-yg#W7zS}yu=5P;Qpj2;Ecasln z?byzG<`M0k(rvr`egk_0?t<)*uK#C`Tw6)GgBXF{@$Kr`k|w(F6aDaKDp!x2UYD}x zP9*P@e5qqOHRF{|_Qk3gZnmT<>hHIN+sZ{B{i}DLRgx@S(zCUlllhQa?6SY2Plx`9 zQSa<56_Ja{IJK{@11k&@+QfpwI)sX_P-yDT%D30`!NI7D5v=9UaGC&2NjrjRJ(84O zTBOX_SQ2w-m(h-@Ff;Pkma z`Rm`#fPVsk`S|@rCL}2VK@AC^ff+t7Tlm{OqhG_?Fxh%xgthdEjQJEad>MjTsB7^# zKF)yOdVRGa+n|bx9wOQreX0X*0y_ObdgReic3JKVa}j3B7;> z2Vp9C-JpSUjKP%Oih=vZ*+7y{ov8ZV1GpRnOF~X37@>5G@#GR)8b?Y7L6cXVOq&lP zURkH^bdQW6aT47$D5nGIV$h45>qNzt*UVT%PSBHND2bDY0-wRDB87$w1B%ahGJ}PZ z6XReR?TA{f4s! z7+>@cC3gRZlKuZsqI;dKV6RN6`yAIe}|ZBP3O@sB-Y=k5n+>zYkht#>gfzL5jskKrA4v9@`K+h9IhH?5jq zb+kEB#WY-)x#~1pXCMVWO58l(eo5~=?GO=zVs2g^R9{OxhBMXl@echiEp+Sk#Nr*W z!Od2elv~+2`T25>nEz#K`^-}l;pcIuYwG;$cFDmvizwpVZ*yBiSN)kIALrR`5=4Pu0}X)S>8vwSOvb>O7R41W&D=h{Y1|2He1QW7+To>QV`r=UDE_3dKK4*! z*y!BG!Y!cp0lEQ&hCfj*)1) z2i1qhR}a*en9G#`q%$_DKGC1wSl?E?ZT&tAe4FrGc~vRmPkse4`#+^Sd}zaC!GC3# zt5!rCi+gn}lT;77-v>VvMtcd1y_@WlJdBSP5vs{0dZZv);ic#4@`v#MN+aKe)D$#?4p*L;!nPOiZh@jNr^e7BXeWmF%us&iv4DbgE4u?nmz<=IO#M*>IQzi(6 zF9Jlbcwk7)%@Jy`(|^ShpB4exF9yI1*?Tj6dJgHwjip|ndmXH9Yogd4N4|UPjq(Gf z6UET>ItvtWY6pO-Z3H$~y>eF4aT{l)r_-P;GQG^D=WLANTizm8G5TsOIt@CLJTo7j z=|Kys_Zb$;+h5r7{G&3z1w}G(d1%Bm|HXzlEOpfuD&<`}GoyHo11?NsEUCk*^2*7I z*zUHMGE${P!aS7zjP)x(DZMuXhaaVIqXHA9;)$n82p(2 z6Y>G)8FOsmRh>jKUE12<>?E>AWr(=Zp;p@A*|3ImMFR%j1fNhxot&?5Dqh&B)4BwPDP zM)k^wKH=|-SFUU>Eo!RqGS+IU(4MW#T11PB&14`OrLpCOF_eV)^(cKaGq;tA;R)5R z$8b}p9s_5tsw>2$hbHrI#Lf9n&Ghd1?fWymw540~LhHgK(uWNfyue9hWMhB*B5tXtLE8E%r ztzllCHwF}(Zt4@z*CThljv!|!4#2h*GOWm`z?;?L+%NzRIfg-ETQ}WGiHvV|>A-+Uyy-(0G z(nKMyo;AR{_dDs5(r=lM_t#S%;Ipt}O|f=tyQp9FZRE`nDY^56?u47@osS!R<`4?% z=8GGGl?fC{UV1BSr3s*mL%0p zRVZLnSD0r>^krS1Gm@bFmw!+>LWx$a>8&$dWK}kTOtO9G%nqSl!teI5tT+j)YQHvp zegdN$GDA!(1_&1AH#e*&(&!aDnCn50BL3!*!LQyE?O%oB%R+aqElHNl#k8HCQqJz( z7+DsullKDU)i5arzaO*A2*u5XRr66wl%3(4k4GsfB{2+2+LMRuc5p5hM$~VYN$BC| zuBd*ktN_@$@kFe%5IYuT$TUtwsjgS@xOdyi%|fHmP%1(hh}c(l$f#(+bzK^J%176q zMA&ez#_p{0anS8S4ivhXL`>F>tW+9+EEY9UB~`S_yr2l74fR7(&B!TCF13NbisR_3 zO*NN2cRz}<2MX&C_Sc9#!;^0vu2IFwgKTgO-R@MddsC=-`}vvvvaCt z)jE|m`*f#8enZLCs#Kl!ygOCA^E9ZJL}*LMe)1$VFwUfhWM-qP$xlQ018S1DngdTD zzt$h*544gedd6ID-Obyz3_2Yo*)2Aot<2lsRzk(PwQ;c{Y&Vh{)cToh4HB$UWG8Jn zMs)Za6Z85$w;PFDHbP^EZNfN}YKsI;dl0^CjWCwtz2)+Z|49z~9UpO7W%n_ts850? zPcK!c+2#L?7lr^3L`wf3M6&THDMTm9U z-sVp`j}pd1!GNV?W`QFiJx?ZSDcIK^Qc{S>mqbK0h3OGmsE?ULWjw` z#y_G%xh~j?A&`&Bo<(=|cp^fxAoNs+JZEY&y-`4Yi?(TIZhPRdZAO%@jkPlnkGSp& zpSH^rgV3?WAz^HwCM`bJyatz^=EYPX;z#8f_sqW1nU4cSuKF1{$S0Jg+p4Lw#9AJQU>*nz92rA)1)t82eXk#sQjy+MUPDj ztm1hrC=E6qbT#akQgMJ^zx}2aDv1jlqEP+9X;mbjWiPh78%vE#zCafuP&^%`SFD&> zRXXvrU)@Dk^!i3A$y540p;=yWA@Ey8a-pK+i;(?JGz9I?sm_Z~yuL(0#Jfk+v(V6= z%e;?Q-%sMtQ?K67T~LIF&$pic!aUUaZV0~}eqQU|3VyB&e(?CvFjazfeY}1a+k3=a zgA&JoK<*6x-N(yAoO{1~`X)o32F3Gt7d`gStpDh<$xRTsQ7`Ir{$j*gV(&SxBNb~c za!T5!Y%%t<3UlYB=_z$za78iH7xt}f31`B>2kI?}LzAdOVCrH%Vz#HMDZk2Az8)8N z22MrJ?V5lLJ1Mzl%bI{2viIxE%|7-$s)*3{8~O9IC)XIt+0~`6Z@o5?4W=uA4Q64y9VYw!y1Jr6tjL|Bj$tu#w z+HLa_nZMf6h;sOt3T%-cBn#oGLzrl_}P0FW#14HeKdTZum%rGt6z4y z-a4_~dE>@&o3q72MMHZulM~)FtM;gld_Rb!K5t>g-w|Q1Jwao3sZS;78_7 zX=2Z#H^%Soh0^bD{2dF^#405|sl{(yZfBr=)n?}kK5jhA<=lYcnLT^nmFM~@=PRd= zQ={(-e$V6#~H+`tBCW{DGE(RB5?d85Od)<$HOxpADe=nS{UR1*rV9@Y#ET zCHi$L(m!$PHF>U-o;&6|AvGosJFg2??E1-_4ONgw0jtP2j$IgdRHmL)ajs+$il}^~DY@}ltxjfg_Ix$U zC}}@^&o$DtXKI2K%MjbHWzQ?AZ^b07?tmN#UVfe~gwH5x-lMQlG zoFkkGA%1B4^wL-3=P$&4{FZTSAhs(J`W{_U)fj)_XZ1%7W#n+u4S|De#^#x5N}_=C ztDnTGu3W-LJ{Pu-SH9t(W6KH-J{*buBxdAL(o^eTX)w_6tE8&z1!}{?U|2$H{^L!6GgrgV%~kg zksp6_nJTWst?P(Mi}{Q80#zT^ocE{Lie!=8nFu5=FP^(|KAxUdd)TF~=t-Sa9h4hw zP_+Bf&EPlKIfT~@5yO5(ljr5aN?wohf;PsaIiljbusIv1HSe9x2*TXj2?t??S^-_V z%gg^2rf)u7qCQ-`wJV-L-C5%4B7&D32wq{lzwt@CXpgRBJYd0UEnk~=z%d_XB4cIN z&&BS(XnEZ}chF8BUWZIhnWd5b9*{(*goLdy}NjY_MU#Us_tLnHm>yKQ~qoK-!bg;wo)7^V+WSM zNh{JD^?mGw&|rLb?w({CDR|b%g~)MQUGR60?@4eOtC1 zH+hMlK<_03ygfs^4{xELA5h$<4-qfk3IA92hf#s``|0!}iN$uUEA`)Yy@fwl19UkL z3Ed>S*T_Gog+ARI3J$!ppznps|6YC3(-Pdu;qFxS+8$#(hU_sQe%Q8ztEAz)L^0Ml z^E?vdy*mBV1&PX(%5XEG1`Gv?`)ocx#n=$!)@ovG#mn8rA-BiXBhIH_)JGQj@Qzyb zq(J$ybzF2G6!xUMY5#O@XPkaK?bo`(x%1v)`?#n4U)g+UO+9LLHCp6bxhtKvby@Ci zEW7R61Z8x1_j%=Z&!v3Iq+frncXZ>pZm79-(5|^m4Q>ZcgIaW8 z)a4w#eeYn#d3!)79u_3LymIyK*}e?ivU%zf-ZFfxdAz#lcIK(t))m>pe@&T!CnB2v zNZmcSIiSP37d~&u8PX+E)>W_5nZlBAs4?aSZbG72`Q7FA zw#(-NOjpMz_vrQDMWA-8N4S*#l6|mdppxwIEL`WZNai3XdHWuo)~$b;P82~J9Zkey zAWH^wUN}wYVno+I(JaDvQ1Fp-tFqz~Hik6q*6#CVxRsMp3D}K99o3|%erKGf_;mJjd+QBV>K$+2tDm1~eg&K35(=ynFl`e!BHXD=_EtUd+ z%hyYJ^LP9&JS_Z&mzfkFhT2upH53r`yCUl{m}IVngH}_E&?+pZ0wR)UzbzGx!Z@(QFxDJwXz`>+t|4Gw{SR_ERsD3 zlA@#W1HfI(gi<6}T3!G(42j*ISd4HunS{E&+fEpU)FVL%`WoLX4`1I@xRGZ}Xo7I# zPy`{+e#TKqxKikjj0Ec&mLM8>qX2YeouG((15#3W1%W<%47t&Te3k+M$zB}TAstn< z3bs@sojRt$ryl~*ys@qjG$o;X01qGhSom5#rh7WC+Xkys+d8I{u+U&NRH(ViOjboC znbj?&)%qb##Mk^TUAu5tx znxV>&2A&~W&;fWQqvWz^{tH}t_k26f{Lzs@3=*jc&>Sd~-z^jXnE65{86wn%wDHh6 zcdt^s@wE=h4EgyP0#_(J*=z5jT34Z77_0 zuoD_`99OdvL;3aEy!fH>>M>%a>3+Wzt+TsDV#~-G7=iX zN1DTjp{qo(MapStYO?rg5{9x=iKW7vX_eYd6r{a(zMD=-Z?8jP@#Wj5>l$$Y_7kbf z22_M-C_Mm6qEgr5ipFjUUKsaSQ^tTFNGDV*oGww)7An@TBU~z(wJ{63_Ei)8Y zcA!!_fv>g?iP>S*@4qKHiEdw7Q4POuD^jbB<0p|S#7q3Rx%|c~dcS!kWD;7TV^5Js zkZewNfgQzN<9j5g!%e%4T@Ik;mJ4&cV?Jn`BfVm$EyIwVN;n>|oX~o6=KdPpt;UyD zuqi>Yr&aY*t$j6-5$V8KcggYdTtXhNa*1B5t~aC7rJpO(;c~#4c50v@RVKZ8@X($1 z=7jiGK8M`h_ijSE!-H~Lm5A}9H-B&Y&g;6d?FoM2#EAANT#Iudn3smCYAVkU;uVKs77TM~b`@E6V(dk97ZWtvDq)tZ z*FhHX)4%G7AY&O|I;jFB0qo+cWnMPP{Z)r2dZYHxPeK+_2+dQ;Ml3R2Cwnq@FkL!a6h7RB8Ctw3}NcZC|%rAFKOl6?O}7NwhOba_UggB@5~L zH?3~(;aKnQWxOWOa3i(ol>Lc5%pA%xQ=~>ftKhU_`K+UHN~T7k!Ygs1w}D#g|YSaKf3Dh`roV#7A9r84MKX34c`Pr@Z4H59=S zZAxfgAKY!4rTIOBK#6D7;D0Lvrwf*Bf!RtX5d1P6_?XY+S8<$DCaI{zDp;|nex|CG zJK+k6^J=Hggelg!`8~~?!83<0Aa|QyavjoFM=eN!;?$~#{{*__z*QEhRETH;^w=TmC(ytYg5qkm+M zT_ivXb5ZZlCvX<|$e`v?m%PE9QG0jX?LG58O+iFtX=$+&c7zOTV9W?6#=S<6EuAXc zC=N0?qZ}Vf*;uk*;;X*hFF)@Eb_PbQK|n0sao+EJ=kn?Y7CC1V3f8GPDVh`3m}U?5 zFLRQRgvkZ|6bnN1I$Bb7Msu*nRt!afXJ=pIZ&d-kB55pS*fR8LZ614=5rckE(t578 zcG$uzNiTc_76$7{jbB{Zpa+{>#EVh&5n^oMLMOq~yyV~Uw;WHelPrGnwd)Jec9P<= z{^UB4N^r7WZNDe-XA(4-wdq$1cu9U2( zk_ZHmAm|`Bz9*{?1dBDNKo8Djxjua9-NrFd{!EMwuDc0%D1Q1~VO7S%nJ1PrZ$jbD zEJ-tRbp#QtR7a@$xXzdDoK(lh?V1F0TGWfLhhtG?@XTGA(=#v*zr%iKE?o|E4$mI+e#&t^qr^6j%Q>f}1 zxQXZZkzr8UaYb1W+7%T)+;ZL$U!X{UYzfC2swbN?8Py`fAVU_+F%~$49obS^=%p%& z!ioWlKXJzyOaI>MoP!pH%ZacL08;x4ab^_(s%p03XVW;xzV5`GdKm8 z$Y09xL(t4%{j_Y{JL8p7e6tzhtAkccUm|<(#({E&L4NP8Uw&PwIOkw&4G1=v<}m)% ze61B3$IxQhvR9&=Cqg3UaS~sIz)Z|cc%ZbMvrtRTrPVZr$Sgt)p#7)#Tq{?ZpwS(Y zel6|E9>{MzuYjLJl6SZ<#NY7gjn1^ z>k&FrIczeKnL@^9C6(i}YBk4*{kDg01kx3U3 zkNfX&P+plWbSu(uK;X&~LerNdnHVT6qbTjcW+;MNX1_ovtFZC+?*RzXE1;ik>x`KX zwvqkk5H%&ogCznG=0+hgAuwmoDrEQANhSUyHC$rIA|jB74)n>;m&<`=(l92Yo}gj+)5R7MD#8)nc9z`~5z4w4Wl)lb=|Y88k4;%-Kuj-W zyw95YmNE;W$2TSP93gzf6K%53^gxAD6n-`Y(%LOUqO&81!W?u%OvHx#Rou~|*ArhF zV50b7hLUmY4l{p9l8&rj=*~k0@7PZlV9NX(aPEr%2X+RD;JX8dBCQkT*y41lEV0z= zM|zqh_E?Dw13f|go(zqVfa9q09`SPza+Yl7#sJ7ka6^0Fd(onA?)2k}xeG;u7%5Ts zO9uCK&>KL@jEaqYDLH9A(j1vVmJxnbP#hiu72)jf)eB*1p^5hN+yHC-tQrD&Q8&@< z+{A)VtaeTcHfz@P?#az%f)_hsd8q*#u6mwNGvvu9iv0cC=qiL(ipww zmX|P-q8AZ~tZjyx)& zI1YttO9(NHks(IE)cDExUPL+cmk7^BU4}8_OZkC(qRq%HHaWxoE>kq;_EqNd-dNS+ zj0MP_B;@arjJ1e^TKYFF@b}Wdm@t1lKN+43Z(!B~ za)X>wvERIsUHl`8uG2XZnEW7!l;ihU85L(C#AQl5+NCIT_E}|EDd;+BRrCYWB)!pA zf3yc7sDV4s<~`A!GC}e0edJcw>-jT&Cq* zMw24xc}BqrtdO+sfyLzj0lHYyOIa8|pylPZnec&YeaHa7CBqBT*K_u#9jqUco z!E>YPXoUWv%)BP=t*$^WCEF||@;)>zr2tECL60tsDJ~(}se2j~WI~f-xxYp-VASJ< zL7(r-2laWH4mhz802PX-ngaq|JkOaSU zqrjRKYc&W6QL(zFP~vYm99*+UxGCcY)97Gc(~HEe8dB>Tas zP>>bF8#ziCgWomnZI}$rnhYiHVJ}x)pteE_fv2f)m>TyU!bDq_Xe=?3Bbi#?n{fYT z#W=F(OW^T?V6LWhpiuK#WS`g`p1+zXfsfP-u@Y9)s3iL?j}oiqNSFDo@n?ocm+WEi z7eE#$!Xy5|&sfk{i?Zg3l2jy7I9H(mh^L5qhhciPkVfxVj;4@GPAJlzH%r*tqnCsz zp&$irJXr;C!lSwCrPM}nuA)v71+f_7T@3UlQC$wF&9j%wQLQvahz`@Ma;LY*8r>PB z#yBN7syL0IK+V{lxnt92SJxImUFfvTzJ|64{zUZsiYuD-{_L97SpKq;H_E|2DVm+WM<+g({y$V-|d;;;;WYl5^Kyv*%EA zU6l|7;Gw^a_xm>IPxQZF`YU1e?2X`W?(%Brgc?Hg0S-!_#-=pxu#!&cUvB5-;u)2d z*N~D=>7!&40j^mIp_!5=FsU?{K26KboK0@(OCpf_@{qG{JOr`5wpl02HW|gvbvC1D z8#}+iL82%l$wN;;e7}TanmwHX(0`o$TD+ky4&|VWKflC5i@PxD4(_}3D zQG8V4=pcx_cywBcxxGe%R4e^d7=?<9RFJd~tK>L>0|w%}*TyE;$MnPqeU% zj`W-(0d*?mwB$ERz%ggwZ;2BA#|fWVEO;LIB`6&(w)1rI7MSimqct|8rs2dyXK_;E z(ma^yu=GdSMZ8@S;m!TUugmPpkpj~ z)*PvNoOf{iB|U$CfeM&cHOAvgj{(6(Rrhr}5ltGF9(Ms}6gM@VZ#x&V9<5VhE`C}+ z;1@OCO8riT8K42;*^Pim;I~{Brs7ZH_@&I7Gr1LYRsIn<>Ib8C4H z?f(gu(7h`E9Kii?+BW7tDrZ*Vu=c#xQIzG9DfgqQ)CZwe=UeW%+%QYf+x@2XZ+oS* zCfEmu?7(I-6dNjBin)uvnT3%Hk|jo_)<8u_+llkH!e^G_aEQBTe>q>{x_&fP*SNoR zsU$mSUzRTZuvTG??{-5gf|Znm-@@{En@{G15cXJ0MwLclF-C#YGHm7&*${%(nKd8- zOw3ZmX$LMxW2JjTOjVDl(baFZm=hI9yAZ3u;|9YiPd5f3w#hcyol~|B?8ez$|xaj!pV+5;l3)aD#fY(5pyj~sT10~7> zXjK?Ho%u8#|#IUxjH z8pkCSc~O0Ek=^6J44eG;`$t6l`-7KrFSjaPQawRIV1(5QxEMIx5bZry8nkDCx-+^; zhum%a$R<~alb5$^W}}vB5|&quW8H(o1Gc#+Bc8t%3K@eRQJH1-qszzaTUtRb)Dix- zc8cXN>~B(*q8XvDPC@TVLigSQWSMA1KT&LGC3nikkR{Mo6QIMyD7Zr$5)m)q0GfW1LJjJc2_7(< zyJJ&)YGh(_k_~kl*rN;*ic29XkW+Scr%v^M)g`F&=|;fBSp)F75jxfVk@TUA;n#b$ zi`;5+f*Brl1uh62v0Bg~RY)EsX#j7C?vcqoy|OvH$~1WnqD)Ho2rVIrzNogBsR$)vUB^CF5Ba=wCRuYS^JN%0rJ*CW%!(RyTL{HO`BsxZpN zQyy$W91~3k&--4PVpH&oG8u;ylX3<(Pcm+w(!iCE23cD4FJHb@OleJCPHgE*OsN2| zLN8lcN-BdA0mC9X#vdL))|C?+#@oRc7=>#mILf{EiPpHyd;{~1&{U@W@l3>#I`oms zm=e&uTLWNjZsj2Tho&l02Iuwcu9FMN0)uD=1`y2Y`=DIR8InO z3cc&jLpQb~;tSs6rcaYF*7Q5~wP`nC*?d)d7zq;0lllwcK>%}Sp?cd*lM#5pt zKv+$kyFtZwcT4V0IO?e zS5Bf{H5itE6dYM1uvPZMFR?Uu@6r(h+ z{_UfqI6q(x3&AoZ$Z&eT4nBsJrK9Xjbz3}Q9uRYOt0%;8-iKam)mePh&WON^HHsN4 z)Ewbe4SSNnuYQyK9-S0EE3RD%(Z0hKom9&uGel~bGHtCxh33JO_7h{~R&gmoDg8_h zH@jauhYrK9?PvxSrzBh&U{+lw>rxpbuU}|doS06V`tcmfWJkS_lG|f4woa7JhFJz_ z-9#tuLGoF#{X(A!H`3T5VL9{PQ@>n3e9+M%5`{!b9*%mv4wz|YX|;siQop7+f2ve| z;hpzKR@6e!?FJbGEy6?CyT9(IEWF@5Gq#t&#^0z4^UQ)W17##oem_lmTZR1Eyc~sm z-BQJKl_M{NExuCMjS~x=Hc2m63pt86O+{29Lb8L7eu$$M`X81@t>iHeBO~}T$wlgv zyS`s`pcU}fgYZjrFupCGXtj%{jqD^-6B*%{WWk2@D@y?tfhm9==m04DepYS?DKWhy zNK$SX(0#{m!41GtDe3%S8(G@dbSy)ShSe&a;eNSEi>5Ye^<#ZE7*-Ojn69~#Om!NN zJ#wbO%=;QxKf~Kg?;_2mh?JvmJjZaPuaSWCh=K#KytWc85d)H)4hq2|KpAICQ4#tR zA&FxK(!^=TT;6CjbO$Du9_+ea9`-<^5A@lfDuDOY#$E zDQgXF&_s?dk6M+K?W=tLulo$zOBD0yoe&5LKLhfizw(wA5zVvYf`+;F-ztC1(AsbE zifDJ4f=>E|AL!2KO7D;m|0l#3?fr{TBVF}FVs8ul9%+qUarDzmK9K)0` z&j`yG9TbQ8;a)kraF|CVtaSQQ6kLhMFW4mp4Mu-W;#N{~aJh^7enrXz#0++Q+zj?=I+sqA+){|sP2*+ayi1llYOA1HL>?g}A zl^)v_Wk;6HhbO{3wBJ(iMT={4E;}tf^ z&8Hke<7C#S6()VgWbF`Q;>C19cfGSt&$-GdnW7Ya<%Nlb|(&k**( zQgVNkoO-%UA?64XJPci2I zIs6)qkWXPn$#Ssav1%b_eh7Y|lj0j`qCO0LceIuK$pc-TcZYu$HBhn2VErk|r7&0t-PyJ>yvTtC6d7i~pn5K$r9 z{>E*9pEi+ji;O}lKWU;?nor_FidDcQTj6r^=oq4Mn{(#vA)))8TAF77buc;xBP$s$ zjMyR>uSmOlsKi=l^93_eQ`aJb=Cg$RG0~(QF;HHubcDo;-yKF3SHn6Yj%z(6K*noW ze#9U3+)U=Wrr{Qm4zAaIp5j&MF&Ytv6=u9^vTI5(9CmE0$9sn3M3HUrtZlcU;#H#l z(TX~0AoRP02(Jq7Ih+^vu>o>}Od88)LjA_%NlyV3QpKzV8_*QYYb1&%;b{|(r6`w7 z86i6cS|~K-E)7*lx*HC>99Cfj(-*ZZsyk*5M2*{pvL{usa{#wOspm(bNP~XFLd1F;R@P zAj!}ZhB@cD&iG~L3tN8q8As~wGnuY6>CSy65MGgi< zEt>_^;tZtN0mXPf^3udY35N~S;X)7x4aZ?MKK322N={MjD`vk@k&&;`0U@XmR!zWF z>}a5+hz(Ne)aE6n(gMlHPMq-Q)h?f68%*#>cT+@;0Ii5&*YFlUqvNWFV68uB3XVhB z=QXnF6Awu;^KWvupnjDKKH=Z|`bre7xeawtflp1DNt5;vsU3?likdzOeMDRQh62rz z1ifpAwCgUA3O|fpG16Z%K?w5;pO%2?9qZ;SjL_7;uvsp^RFGmLeT1UhPR;jWAnZHq z*3={)(p<7hWbS@h1R`zm2fTyUf>yA_(WpgUsCG=7DnX{qw;#_knVT|{a^-U=VtXdO* z1m;hjdYaD2Z-+k-v@|h_pe9TRBAA$rJN48d%o%)A`mr1`1BdnaX{gX~82ziwQiZ>y z_7!c*Mig(-$;>Pt<&x0YE8o#U*hab;1>7a0&xE|I}N1!UuIMipB~4w&&V#1;3J(Lxy<0WHaeFdfW+Oig_T z@usKx-ZjG^jCex}QTp4Y%Kp#AmV1)T`t3i4>=mZ9_EIX9lzqQ2U2a9C#^CZ2OhIhV zWr?-+*nN%&Ezq25#!Nt+`fRv$hcZ^qLzpJ1h2kg8JqzIDnB&&3H3IDa#9v{`E=H~7 zme&ZGB10jx!Ngzqnd(Oz^DV#Hu5LE7Y~6$mD9hZ;p8 z6#8z(>^`*vqa~~DnZkz&T1@5^$EaiTA46g#;;j&tO<%@ZyPEqzF*HS|-ylzImD=uK zhjJhms_FBrQ|ARTtz8ipEV1uoOTqXiOypwbQZH=nrnpYL7h856->Xvb zA&kZoh4P!7^Q!3GEm0{rF}+?1GsGi?at|ft|H>|!6;o5v4Ws)}OxG>*_bU=XD7QsH zCjwgF(J4fs#uMBE*v1`n_JYxEQ8@xNX`{oiNTJbl3KpKR4}%A?2N3^| zv_0iiG96MC;SFozxDS{jK|66-Bh6W$+rLfeWO&6hxu;KU#$%=pT6l?$s{ZLmQnMS2 z=1~}*imxxkY%6;5 ze=jbfSjyhANa}2L{L|WnWpt9HqE0xywk7^8BFjTYhg<3XW}*B31V4lpmC@JQetBwH zvNUR4^rXpi<#s_dDg=)2;fhGO0kUS(0U^D)|RLnB>K%Nz!1^Jj;<>(b^bKtRuqBPKUDlO{9?JZjr$|dvG4KZb$ukGi7u5bM37~%!^CA<7|TSzb-UXR z6i{0*T{NsKrA-#>H%F;Dg$3Mt?B(HMVDZY+VzTP+x)RwQ*jb)=4b$}%kLX&X=~3w8 z*cc8{+2PcMu<<34EBRs`z_JSr#hS$Dl(qp&Vs=Jc%$`?^hdDweVAuqPP(GnKdSZyF z=;xYC(@v$(AqF2)b&EyeGZG0CBv@?AvnUIyo`eghOG*{F1^6*63Mrm5M;uox$=a1SeWIm-FXkTYC@Y3Xk+x!(eA^b3?MOezjX3H=mjXxNGddqBuScFHANMa9P!X+1)V7=c2wj;PT3 z2@Y>4irJ>nH*}$qs1qNPULT8zJkvKnirh>b0M(q?D>F>Wt92TTa1Si-vH$2U5 z*b4mrUOpZ7bWy_ws%)mDehV)hcQC_ijt!H^wAKyNd?*n2daV!VDu(ZZb(yi* zv#C;X@l?z4g&YZ49Q9kwlmp~WO{nrheyN;6?1GPrq^DS94%WwA^JDA^DJ_3V7g268 z8*uxSGxp&7Q=1HNb}{4VsH)lSHZoq|D1!go&3tt@yo+cQl_E97ntTvx#7>Py!TNomPOdPJN8*ru@h8-RTKU-u+N16Rs zKN5!zcO+H;sN-{woai`FsmhE9)+0k9A#2LvZ4rV&S3o9_C4?L$uU%V7wZiDB zw&FbwvJ*0#q7q^l=rx+QPG@t&QCrN&lmRM92gX>pbkNr>V71Y*JnX13Ghaqa9?(6~ z8_u0%f>~rYYpN`-kc#*{p*WIT81d6x*e0{LZi-!C50)|_G5g`Q7YYy-iBhMOHQpOI zmOg;`ny1a&kD4S-rHe$}`pbLs?-=D~wbZ0eGLul6fQ)Q)p&$=K5cjvu{7%ibNNOXe zq;v9`mi5To#SdFPfA2O|`t|W(q zWo2S0D2TMh(@%Cog$p1voSJ#hsoFR{X;Bc#7f~OO81_JKyIpX&6ekW!9X8ntv{{n~kXCM2Wux^kej~RNB z+T9!()Lzwwnyweo)y9wcPJKhk~tR)en+%fsF_PA8ZL2oyM>`YdIPJauBabl zxc#(AvHw7uJ*v=DdP@t>{rp0fXgUc$j?%&S`%GKVAbeBCAQ5@OK2_06wcciW(oW$vU}Ka~OWLmhBmOT2|^;xH8mdG#10hHNQW%a6gBP5VA%wW|wEi)E2t} zzvhW<-Y%F&C;&-~3E6d=kAo#j8BUFVw!?1hihw;CXFC^Z!JgDNMUiMf)ALbx3ELfT z-MyUr{N6tZ!gU&we0ko)=NM@8`XHtJTRsk5`j_wi(6-XO%B$D*#@UiuKLbK*3iK2( za0!K(UD6ntR9aj#uIWjum^E6FCve#Dyl{m#jSe!Q#5FWCZHog0)_d3o;UR?NmdU6eiXQH zMw0U!R(RR^z9bR9kg|XJJb1}J?g^U^s0M%PNB(LhR=alGiHCqOdnm>n2b&e}_95Wy zE9mVyZ9;L}x@$8b-ce3F?cda(D4sfJq9-;!LCniXp_?}IgL0v&11u8&m z;vB=Kyf17pW(aLUi*C7Axu!E0pV)<+xKnhoQM^i`yUV^iaLpep3nOWIEB&b#ien6A z51ba{eI}`h#WMh;ei94pL@d?*92f(8g&8sJ$+>=Ri?&roS_1b9JR>)=IEEo^7~7;#mx>8oUd;(7=zCD?_*+Ff@0vdmttPX zC+ztEqWD9M7gx0TA7ziB;)@^!vZytgtS6qMr))jojq(&&dMuT;kt;_SiBD7tR7cmo zj;tq|ycV(xW2p!A`r`l^VEGR^LS1rXkSRK-m1ls{G&sIZ=ffGuiu-Z~KjI^xH*cwa zbWELNtvbM~92_g)W&pFT29g-lT!Up1>QxvJ#E>UWR-0fV@*mwliQx;MyF0lw+Zz$V zU~P_5iQx3sA5^9Qjw7=An;qh>px8IZr)R^HVd(C@y@cD{ni)Fl^hy0_*PK3oew&>{ z5AbQkorVQ`FZ|anRSDw5cFl@fhR^ioIQo+vZP*xaGZ0htR6~1TTBLObXXR;IN5nD540#caHG`iGi}V;Hap+Sdw3F8Sh?M&G<3FM`6q2 z4V^epdcz3$t1@=B@s%tEa!uN{fxlO-_ZLMXZOHcp9`~hZh>O$7N9WrK7K~9(|9hY@ z^mp8*oBRkt9Ql18uSVV3gTTM<$M8+%hD(uUAvsg#ecwBl##F7_;cy`ZLD$K%r|dd3 zZ?jMm0wzD_<>PqEXhvC0YlWRDtJlKj#E=r~bbT#!_Yl~mHJd?lOa)Tqej@eKblqCs zeIE~Z?#C|Tz2uM80P;+I9rVxxi@ioQZ<+eCxiB1S;mVi^KFBCw(B=IxUZgSl^yL$+ZEh}fA>sI94WXF&5B;&M zVEiR(;*9pB*Fa!jl14TI8$AVk9*ahTiQyA(C20kxe&qHq@%Q$ie=y&8j8ASx;W1y@ zgFf!9y+h@s?=`1X1GhV-5Ma#z3?)KjV-1Vixp#f0M#uj904h2O8JYD@aiyHJ35kpl zaVt(Xq-Z{CT*C@&5|YR&qL|IO$G*dcN?*4)Z+nBd(|d`v{J54b^JGtVmg=rsUbC}Bau zaoAyK5Ac2a{1RIJoz3ScF&i4s^{Syzlwh`LzcJ_oM(_16yJ5SJrq#8P>vSOacb}wQ z@V`#nV1^}D*Gm@Dvm)adWR^~SHCM+b8syDrtRtelMv zW>|t6q#f1vO%1QaOHo=&t5Gsq3$>8unwa@gUsX{*QNz4=NOT#m=35b1jH1a4RFg&cFn;tlP6z z+Um+3lA!U;DH)l*ENPH1xn=SLF|RM#XRM%mu52m*F`8A>ADv`PZuJiqc`2}rgc{Np zp~T}s#6AK#39Z`S4OEy{cwNa84*h!-iUe#8-uZ5Xq>>Utd�T8)t@c9s$!n^02c| zHE?tlGAA3n4KCpdwt487{<>LCNEkb)JoVS2d9`W#?t=&t&$P6~zwN!vekgYlU~x~Z zP^v&bdO-7tVQpFzn39*QVh)GXP|2XVpm9AnS2Ycqc2I$?5S=Ht$1KJRxT>*!>znuO z=X6&!v1!B~!dSTp491G&k1vQaW?;dWP|xK+9qn;n0F`~V@WYv|9UK84-6q7^L6To4S>g*$7nc}O`<{#ksa@=O#e z!On7PgR@Uv(S;u0*spjS-Wxcl;(!CoEe3T(pg;*~pQq#CgamneJK)#}NHZk%)8!@$ zkq|myc_SI&0!2H2Z14%vmsCTEo2*A0>+t3I21rw5N(9m?vSqvzqKK2E|LG`FV{*dm zD!+!56j31AF%r$ZsQ=)=eD4|P&qwm{YHb90F zS8VDxwdmTL_5HoK{5ER3vEu+5>PxNb+5RtHF5o0Uu3j^5%*SNY2@wlE_Id2(ugRVy zD^O!(+ekgxN|P<}cYF*~LS=n+(;z6a*^z-i#`&OsaZh=9=?;f|qY-I(FIklTjIVSu zU!=8g8smR8?*Vd8^4TVR%mWGGmg`b$lv>y+O7=A1zCGzCj=nBn7r)NwP)uwY@;lRv z3A*UKQpawF3mH)*)juSMFc3H;5)ttpX6fRWJxxx=Q01naQ`XnT0(?NPH1;wUObciDk*#vn z8qqm_(g-qBEVsNfIhE0rG&=!PUR6srJ7Z;t5GB#%>^XJy$d$g9Jhhp`gIl7aybBS0?MjGby{lb_m6}1JFr)BqHr0%>ztsVr_C%c-O7Oy>+PY*7~;7e6s9qNVTHtih? z_Lmi70k8NsE%TPujXJ)LnsdLk8DWG6CmS_$xiX|cKDOG$50lf3eR=mleTG=KpAmT? zXv{Ji>cQy(>5m8Q1+f;RV!A#Kc4&2mk3zX+#qS;7@=psA)4twx7xC6B| z;;Zh8cB$}xyEKel=5|){Z`QJ^;rR10Kd<(IC>6RXhO8HGEWHqr=A^;s?5e=#+qXP!!8(gUq=(poK!;46KsXQycrpjg&>N$aE^yUl17$W;WEDYFz3}DQ&RhXnihPx^pFZ2 z-!Dv)S>~Ak9LehEx|h8$;soBnHu}P&Qr&B9)-P4tm-8VeOqbdaof@ulOEK7@i+p2D zPIPBbX*?$Tth}W2Q|z;i#ZG``wn;d#4B`{Sj( zu)FO${bYMs5Z}=bub`>l^MRF?w2a7aC30y1MtO{j>TNDWd=NdyR3$*0rdTk)llH{x zSW}b0^G?pVaamCatyL2LQ@SlZndCs!PMVAz!zKV1q#CMfGWA@do5ZrRC=tc?$TV}n zK*VRbtCg!}+N$mnjo^kAVg<6k>uzP9Z9JY_s=8xSkpgkl7_e>4R=PMOdE&fy28@ns zai|~q4!=smF43Mmpc7BImzWs}oNT27BQg%q#V2638(N(48+Ig<8PG_M*g5pOUAmb@ zc9cN)#morxI&mEpO>D+0y#Q8h8h&0$hu!FdIx$2kP+}kkNqqFAFsEOK;ue~jRSlAw zKX&GIP{m)-JeY-}S{QeguumbQ<&s-d2?Pob(i$uzzPl>|kZGg;dZ3f6Qz!^? z|4RFtR=n>oZ?Ej9kS ze{l3zQ;PsTbH(8XB*2bdNU(?N>kaMaA~0;^kM}gIyHc90bIJsb5kyUZ-yky~Tn6D2 zs}C;Vi8{o^Joq`2Lku}FJ$4TdA+BGFhvA#g;RQv~)~sM-WQHrb#l&6$U)Y=-V6Z*W zNxH^POHh@NT8fb=4e9Vi5Th>n(;lIUqC-6z^f|`KMDhzZzvmdIcV;6jkQrUf#+A*o zYFX%HUu7>Ind5WG**0%VVfnJ`27Ft(zj5FO-79Q|KS=du-cH5&{IE2yrb#7XG2U-k zmY3lELlepn+HqS}V_3%nrR&3{Ib~Hh%bkTsMYtvcs$Gi4RVOW9e2n}k;_=t2iR>xt z!W_1^1jt>54-DUTzZqky6mMf(-=e!?xlCC(ld;X4+`84l*uh=34^TI#gucC`#ZMldUi?ATZ;GZ?B<2XcVPX7xfls^_dAupTpEMt$tY5!|LdnN zQwtnM0i8XhVz=iI&4nKqi1EG&f%K9+8XBaIa(e|{nFj=G`+VNbFO}i(gc|>#3k7rpM5783rzx8ig7^% z|GsPUT#JJevZ$ZeMR&x(e^IIg^Gh$lxoZp>gFAbG(Fs8rEw2l5yrT3H)<+uo*%nb$ zh^A~P_BjWdsCc6b=tC%XDI47wLPQe%<#u>J{QC=mC>g^N{Y3?nxge1nEh_(JnOTuM zBDW2_3oI-zM(vfjf=&1ciJQihYB1s(TPDYc*AbdUNbg z!}@cmi+(_0FJm4yQ&{Mp^t)HNitW+9fnlH$V0^3Xi-h z1%C_d-s7o(dW2>2$9J;w^&oIHLDtV{WKzf+0aN$G?JM{!VHhCC)s8ouxUwEK-mHK% zzRr+^u|tcZy814?#zsmeb<&#2M z>b~s597=3>kwu0x+CMk$U*DliCX(luQ`+eX*KrF-s+8ce4Z; zh?_xi|DkSXEuupMM3Fs*P#1F^Czpzd6Va3gVuZ~~4dY5445F!WecLAchGqEg&Tm8A z?VaAvGion!EN9>RzI-%5DKa+ECqgXy!z0l@8ga7y;HEE%f5~9Q3BaKdq#ETkA-0egywHj&>&;b_YxN1EK7#t(l+7Pozv|DW%77*Td zl5<6-4(RG~diDXrie(5zCY6eB1!Mml z)3h~^jU;CquwwOpLCI_gW0eNJTIlQvS)(a5lmm|mEx5p#5B24L+Anir6h7&i+ti?W zinLWhqs~sZn%@c>A14(1eF`yzUb3g-Xb5X+Y%^(SyH5b_3iCV8Xy)*W9mMn)1-Kt+vud78jydWj0|6zSW4OYB+*DH@m`jgE15C+ADX0J@1lMEb`9k~xCV2- zNkuEWovECtL2H$%KWs;ht5FuYJPyxycpf{TdxR6eMf5n z7u^x}p38^!YU~j#6hIycpW)TW6+2jk5gQm`X`I)iV10d?(-S3?K~t@&Qg=!$w->*^ zW0LON4E1#+G?pQDiZDUYy5yOdA7~dDQ-gI{@w0`g%<}Zc0Bw=mE=7-Js5rO7m`UNY znCPxBPT2iFhqP)9tQhW(ST8#H1I2h?ft_nLG*JveLK$-q9%hAHjvm48cg^q(`IN%p z5zQz&qpH7ZPLYIpfefhUnd-yPU**2m_|B2VG8m6z-}PylkMk5$Nzr*}Ocs4QOsHAn zTTycNW?DHWRf1a zSe06;?9^|>v7dF2L!UB?l~ABYk;%(R+m=}K_K(rL@TjIii%w8ctRU=Fw{%!+nFa$|iEgCd2d)%Dzot zARv70CNs6w08fc2p#VQw#}>0TZV*ZSRf2w94;4-UnPtFq`J$F6Vlp3xazK<=(rEBb zbG*%g{?qUeYur|{nr?>$z1zpdMFKWYS2lu>Bq?fk62O-^6`(^w_{JKQN-oS1W6s~E znDYgnmG{tR+roM>E=99tND){8YyGr!3ZL7(*pQAqrC`&Ir(}ceDOR*m!WS$4BPOvN zKQ@C)9>s)ZvOxS-7Tu#jeWc#}GcANB@*fuKeuTv@LR+3Iu?*B~9RKelx11{2)Gv*P z?z6#4gyrY#WhNyy{kcqTYXkI`cdzg%tKlmI-em>kP}F~NNDM=zGm*}UpAcD6n>fU zXEP%|d>y!XQ_kWmlFf!o_lt=Vy!UTxd*ezuZT}?XdGEJpFxF!rravkt3AzTRn54fL zQ4+WRYo4}cZ2T0~>rHoMPyNUTQ&CN5l#&*noc6n>Q8lGW0%b zDO0d^H3lR(R*5yIg1ItFnfv@e4cNZVMZFmjH+fF5%3`OZERm4kKDf8k%`a>@wgFt9 z#!gfMCn^Juo)*FcKS`N-M~OVUgBndX$(?2`7*tp1D4PS_f>I+2>_(q_E5@|dEsOFW z+cS7;_WiP7{!9nHVGZVR*5Pk!A3i;j$*me}%R3)w)6f1vx4X|$`eKR&Xw>R9nut-o zWM3E>(~bt9*WQ^;3Y{Oe@2=e{6wV9&SoapcP)I@Q;CxPC#ZEmK`mpJ_J}DM9`SCDD zzLv(K{U+v0Oz{sV@WHpFG{5|7<7U&&dvTQ)&8sE!$SlJ2z9F$Uu;bn!@<#vmcDvPl zD9tIac|8=5t1KLCv?H1diEJDHQkMvpIZypR^)!teyHLD>`0`J6JMPC44hY{cdzN;yI>{ zw~D9rCMOM4N{rS%Zbji+wZgwYz5XFz05#+;Pe^X2bR_G4EF9CSCN%qGCHhQ; zzRHw6ahk}DOu>i%B8s{nb`tt{NP6>a3?B{j4O08R(^_4Bhs$L0Jw6~^m@$=q1wFm1 z@?zUl!5*e%-3coSka3Fp?0=7+X@>ke)8?>RupB#Z?TuB;Q+_2hP`3mfa?|Kc%dr00 zv^E2e=8O+>p_@Qc?H_P2%Ok_iHwwzy7avN4qil)F6EZnpCeYbOz_~KoKl%07Nq(BY zCyY&uvw*YW{fipGWd6FNNYRtH@_?nt#S^%%Q+ah;Ty4t?!(7gm30%fhuirJV=GNceNdIYY#MbY{1(#F$HD6%}G$Wi%8Hn)POF>$&6m z)4ve>d(Vk~*uu(5q-@?E3z)BdK1-;66&YC1_ji6^0(N_A{P!!3LfcsUU-2z1cEw6H z1S%L=RLK@UkqoK)3f%UE#NIiCvdefgG=fO_m$~MXDv610C-O36iO7wv-b;#DZ+~`F@EeS#pWS zCOtnhJaLTUP7YCJWm!ZpW$?U|M+EfJ-(D8j zu-fP~fiFFG{#%^HAEcc}*CjN-#2%zxmkYc=>sR z%T>nN%EPTJ86;32wbKWW-7dZ}9A8QgFw;5HjiXcwxAZ`JopEtb2fcMa((cvQ+jhlA z*oO;-P>%d^l{eu#|I;v_>&Nsbl~=Y;z0_}I%9o=*-p>d3!Gmi4b^DHJdRHKq4^6GE zelkI}7oRm|i=aK-F!s%N?EnfpC!@)Mp~4cgC%~T{XGBMZz1if>ilSeMt!&qM`KEKY z*>`YAo^f)k#Flra+4U0NyG8jT@}kExaXP)#^mE7F7YP?nB3oW3cN*1=d7gd2lP$Jm zJX}g?DzC{c>4=Mw1-63BKnurp)!L<_q>4u}ysn$$bpT?V#UhA{eLGp;YtF+stR9Vj zx!y`%dHy8RnGd+DJOIH%!L)u&vSRDNEWvhg>i2SFb;WWEtCzV#TOiH~3ip&mAUFG# zhq≪uasJvis6}_P<<=GI~P@?R9!$9)atzZu`=goSXOZ#D^qY)uN>Q1HOm1_a9#S ztxMdbpMturo);7vm5H~y*fS85kcg)R%cf1`ty*k(3{8JZRxForUs9JgL(6t`;E#1= z{=V{URV5g2s$0~~wvd*bL^rwj)*@z$MJw3kJSpaw$l(~%4)+!Y9(q>PdL7m)>SdDY zq&B>CVoU3Pfy^Zc-J*;xrH5wv)S6kt5}!DTDN9>|*(mmg0okFO<6E1;Vs>kg(gU{G zlU}WGBR%^8cuRnSjGXh2s|ETJBZ!=286-QDGn?7=y3Ba1?zV8AMIxZC$F(buwXTBw zlxJ!fW$0wrP4g1*z6}Cmm zd#PVUx%6B%e#tb}cgPHA)l&VxxVbt|@Y4&ii|o6VSt>);9krdE81?jw)L#bNb84%= z8I9#ghswuDygVe93sU6aQ7=RlLrlT4Z+LLxR5XRow2l-=?;F_enCY$a(cVXtuKOO>{sPe9N&myea~HW1GG= z<~4W<5YR}Rt*+c<&|qq1gbmGP9In%*#|10|jRq_OL_Howe;p273FB&$W*6x5NMEFG z#hy2+c@jQ9 z_AfKR1_pe5u7( zQK!1j_I)#O?0dPe%1%_rEY>z3d*r$6eXh=68n_6f!90%XW^(IzAFbyo=y*R9nGv?> z2)=G6AQbsQ>#O1D;&V09c|v^Vui|==E`!`&kEf?^&oQt8A^U5T*JM_s`v@Q=1*P2+ zk7ooPUHQpR@`(Eo%a7(Q#lYX%qO`Bo&okIOXS_?C=eiaZ6$l9MvyyBObh@N zxRU-`>&!c5yV4Y3A@@e!6_x7&+b{=UyDx&HS<_?c;>{5pRwyk8J+9y#zqarA;THST z@hFCUQ&2yVciw!b#y;svrrvVH&d=r0_4_mjJEg>fP=^e0UD7kT)yg$EHP0q1$3M}v zG;5@R@!baTVm`EUt0mocA)RE2%>VMh=05Vz#fn^8lfNcl<8Gq62W&f8^1Ap9Z42aY9p`qBUp&kRrhvDzy!zb^?n?+W&5g-NR z!`r%;FV7=t4(=rGs<#F~F?~j8rT=Y|BXBOCHxzdaVSKVTKG?Fj4XsZ4TnwO-SIk#% znqN{FV-~w-r<5K0=m#2oWY*uUwBOdg6R=yU<-aBuZt;z+h3V3m!63BTK0_5BwiVACu5^poOTXabg0jYBK8&7(Oy88R(B_6-4 zzv_k`8Byd*lqKXGa(v`eZfm~t^-QWDZ@(}2w236ith7&?UrcPyyfFz(>SAy9(n2PaqFT^{xNTq$N*ujW~flMXiuHCi$oeBm>%npBR%-?)DlBXvp02K&C&?@UaAwH?O^H$7bDQ8|_AUkeWJ+NU)B5<2H6 z+#c}Fy3O<oj{-jHsCkcpa>F9m8E9({z|eOyP|yHE|{s#5-Y8kkW`!_a1RvnVkRo zQ3?3xVhwR^KOJ9WXV#pMHme4_&puZCDAcj9=Ebj{cIn1y|G-hb$G0W% zZ&H09I|={oxYY%#0+oK?gW-sA5Oy=H!~t6Z+C87fPc<+7fb1CILdpzAdS}H^fa@xw zja*Pfnp@`ocB4WW4@Jk_pzImoc+9z`O*>yl>Xt__A4TFF-Bm@!!7kgg@k|oREYNw? zZ+mt)_B@a)Mk!&}y>mOji7YMZL`Mm;Q==(5xmZz&FTZ?)S<7Nn0o*1g^i?r0c@Vek z=$&LR{W7`8h@@t*)>#t~a3zjUpy8|4_TRfJN8fNwfAa(GLRM#;@CSb7sE`WrGu>pv}`p zw`{*l-&Vt&GH^T4-Ot8_VI&^Z>e7of;Q3Ed?wo0v+D&1*a4m@||jC_Iwfu`$+^ z+>d?J=IC^ORPG9c997?>>>(aNtj?JZKI{SMo`YAKg7F&0NnzG z|8TIHw!B5=Jn(EOT+n&!#iu5};x=9(5?Oddlw#N`;zkU>m{F)Bs?e+2!;SDK?Fdfo zflYONEIRu%af-O~wgBU-NO(}k_zs&SV}zCux}0jcdLw?R3w=T#OnnV znW;YG&8z&=#In=R+`jk~SA-(McD8s>=0Y6@0iS93Q3yUlS>&Av9dy!HEo_?^u0jP<|$Qa68aWq_;y z1)`IUt3Q(3%Y3Xi#GjY>Mg0!D87cHWQj)(NUvldgkF#m?PeZixu-5su_v8m1q6N|G zC=9lUljC!*8^tQ7kp0XhRz=61zRX`sZ;vVil) z;ocfKBxEW=YwbZx%*e0ppLr;A^{;qSLEjdl5bsTFIr4EC5K}OF8v3=L3rwaP0>JMp z>HInV5nC4VtFHKk%z+J_-*x`VL2+f7 zX*3}+Df4_tDx0_V3qxtkOPK*_{9tLz#`?%CGo$d#?$&Mv_ZaZ+E3csi2Dfg$LPt~* zfHaV~PgIb;52I(@HN{Y1u&HRK#u&IBqYPm8X}_+FzC`)c?qwv2>?$ zyLC7n^~4Ma;Ig57G2%~n;JSw`N-qa8#*65^uHwBTg;KD|YqWNrR`Fl1i z&qt>{NGv`FYc^@ZsxjA{axi=CSKWOc2sd%m=EA9BaTWl*E@I%r?rPqzum%ZkVpPs+ z2P}@8t4LoR({F|L14qN0MLG_sZFr@G$w_8c=Afx<>?Cen#@F5_31 z)g5Xoq?#ZkJucaK{P$xn;N9bu6rv!(y<=csDg2*mC5-OS6-o@{uRo9DY0F6w>En4# zW|AhRyAODgK3$Wi>+NI@2R9s3cBgoy!cW*39PoB$BHgi7iILt3qh)p_c7;%g)k2`% zMg=fZ>!(cyY1!N;4_NpwCN4sI>OniYF{JUSkV8C4;uXiit{_qMzQ?#fS7Z%BIHr!y zm$IS|Jw}VIeQNIb?Em4o5L=o#?1m%VX*7bHv4X{q*Af3q?`@{u)ghncranW`XPac5 z>uFR^d{6VrRBjb2-R7>@`M~F-&nNRGXdxg~_Ww}zj^ULwLD+Dx(Z<$^wXuzjZQHiZ z-E3?-8{4*R^TbY0>}--R&&%)qGuPdBcTHFKoSsuxbxoHxn>Tf&TjuOB*}aJ8MBG6~ zwMI#b+`k)rng-nu8JcY|U(cSB+YXx=H3JweCz+HxeA>{mWTgw*MM}SISCN&M24dQc zlw=c3DjG!^8=#CCzz$7*$m2=*p`8|^h1`9*&&VC5(xP6hQS(dB!!^4nGJ9_{QD}aO zW%@8^uSgPmDHLDhSg5N41NYtI%fd1+8I3`J`JSLm-7gaMhwKR#$3I@|EKDl`ZDXu% zCa8|}gh@Tmt>e3K?JvuoJEPH+&{$?~2;kDue5YsTv*%2MTFl&^I8d$-PwX@DyfkMKWN+*Amp$G4huq&G`KK4TxZq%vR>d%>N*!@nDWvESq{`ci~MkXRD% z19vCBNG3C}_>|MWL~b~|vCas9lr?0NnTlCXB2uGW7o0b`Si+vDF$?{N-Q3&s0T)c- znR-jB>%IoA_Oj`zZYiAzG6nC>ql!~X+eBjIFzm?;vymv)&s8R7T|L?qR_Fg|$A8wveB{c0z zb24`aUZfH@xS0lj_#cy>n;`6Pm719vulRSo-dQvv9UA?Kkh-^ewd4|@l*xMD3%!lp z?|SDO9ryOMZu7L)fUd1Mc4t2SaOu2idq6calhaWjelZqEfsroqWS+^5VC=-$E|Iyd zO`h%`r6rWoWyV74{_}qEfJq(2LU3(@r<^qxCxq@9!A*GY6t!XFmFC&>k5cdRar@)- z=jWr~gTd!VOV7vo=W9#PzY&Aa!>doRkKw}sA}_WdcpD4jY7jMsR`=Zi?tD4sO4g^p zevheu4o|m%8cPX8FCw@symeQ{f<(208l$O#m&-Va>{XgNe-g`?12$_lGc_)sZTi|b z0|Vr^nH-tBm5LCKDS2g@^+A#hi;nN`b_^DeX+m~S`BhewaVj=6HRhlI!`cmln$0x5 zf8Hvy#cMe7Lm6Dz-iNFQw7E{X};6#|%V5Q#TF)Iw2aGClSL7IY*mq_^$I2 z`&>6@iTS~*D{ctN@fQ2%BXtbr%HhZqYas`iptRdjYvUs2@{neMS#<(Ca`|*EexXM) zaSF_b=m>{`RQ#-5#OA7@qB#aTw!Q$OL@y|OvZ1$=?-f)2vKQRn`QqRT3d{Li8V!Mw-k#F?uxF9lH6$~gFzBEYXs(O{Op_9Gg^_;8 zCplkkssv1#x%;Kk9^7|a_Qv#)V^ajX@rLs&BL8bv=V+k-i6edKt3`AorV(cC(jG0^aMTe5tIrU;BobH%%tfC3sF zgJnq(%6hCOJ~Brs$n(x26fGUyM8vHW zc3!I(JXl1B=}k|*Dl;)Vtp*+WhE#Uew#YA)O2ZI!m$_ER4)qPNI4`DG%uYGMz58bO zEnBop7%0K)0#=6FFU4zuL!+9QP323Bq4dz)N$&Y9HW@Z-O}hCme{nDj@%MgE{QFB&`1`MGLV6+RVH7>B}59hHH&C!oDuQfFm!l+ZT{`>-TW9l>TskXeN!(Rc& zp`UCP_wWQw=!6kHO#}Jf+#GOh0=HSWmRxi%sSCwKU7+FU{5-h|HNB&e@0fOkiLT-! zQwgq&7kLitU>ydF3HW)!H3eW>0q31>W`k*|{QUkLRx4l+ors>ovK{wmg}) zAiJa@+dtfEjk&q35ztr6o#`(7lIbhW_S>=mR@Kok3IX{(E7b%$)nSV@hD<}Ae{A++ z-)d|*){pcEFcQUXgmIZwToDWjTp|&z(p&~(Y%kXFI`Cwmib!%2l?6M!iX3hFYlXY+ zkiluh4-BIu9JC_Y%yt_L&>6SV906q>j10cN0%W0gz@Ng21G@wWN2Y|Q@Z~O>jX8EfJd5G%t61Nac+z<8&SKgq&bL9qWgK2^+I9h zO-b}J&Jl}{_`9%ujJ)pQ@%4W*!0)RW;z*w5+;G)>P{OseCE9%Xk5Xwk4`mzc3Y(v} zF;|I`7pi$En+m4?N?_R8<8rlRYoQQhMU79Xr-$j`d@eCcP&7LOi1vjt1`6|sHq?&O zg6&`lfDNy4lT~S~2!zVl0>YQso46A22p%#FEu<(P{wrA#xP)-a*^8dC&R!ko2=Irp zF%);!SvQTIM+R1?d$<%J1P=uUiJY~n6TGe43#CdIBQYrw%A^S~BwSc4dHj|bQE7_~ zFg;iN9&pMFNm+(L+ucKp-d_MXbp(17*C@xEFkee8h<}d$(>yq6>Q8w@?R;Cg8d9Lw zeULArnw92Er3EWVHne>e>3Y{GTjO2&jmxhW3U3l3QON80u|b-h-PbK?h<5>YLxIK? zks|ftZ-8E%Ppt$o9xe^j@af+^&!cw8>e~APXT7sTH$iW{L>dUet@obkNVtI?VH{hm z=J+JQm)(&IVTpCY-q9(apZ^@;a}0zMv4A;UP!h!Cs|t0S-yFU+kI}TY3n;f%%pv)) z&ch`#rsl+xhb+?@a!Xm#t@&1u;2;7~gr!o8V)+Fnm2IDN-l0QnR;`#LyBVfkpj-+IjP@ytL| zPf}vF=l~)O?i7W~vE2;-{40zUm;nl7QKdjbiU=RXM|3G(s0#Xznh!q zIxP7;Uc>Q<7$bD3hIqSVWGd=UrQ4Y$+Bv$_`qjhQ%fsS2oXD$N>_ZGPALS8Dyi9Ji zVlL=T?}f0F`=11-^GYU{Q>G|3eNVV=?j`5;I{TW*<&>3C^Yz>s*&>R-T$*z&H(cXe zl1%36P|z$&U1Zkv19UgMdp2CjI%{v^%L0*5WQZS%714W<-=<~DnzAu%H21^`6w}auH)t)8f?2vR+mk}E88jaHE5vpE4ZcG=Gf&A9m+v5D2 zgB9P@Uotbe9E6ir1jp)lhe8Y9$1{_GVr$XWPQv+_CQm zK^Zr1lM`xNwr{*oPdDY5Um2uD_6fWNux;>%tei;&3+)!U<(0OnU{8VV%ay}dBt6Fi zo{`m@XYYP$%@6_&?#W&M+#*40>Mt{&w>1G>%PKja$FZm`Hdh{tcN>;OOIv>~UZM-_ zecv8^{kz{g<{o<-x|3a;cR(#Pe_lX39lQuL4(|XA=QnyjiKXoTgyX@6x7b2DvcaF@ zVeeaaY}tB_S3i#$#17s^jvLnA9hO~ocHT$)k!m`(NB4bK+CHBRg@JZ=2>VaK5zpc0 ztGVI^gO~Ra-{$L937sUpbb^rmOU4cEl)Vqej{e|K`nF>`-)8OhPc9kx@yoQqhU?c4 zg~a|%Pjz(rkK4Zd_V=msYX@@DMS5&DtfIfQmTWE?-|ZvT4RRQpo@At6rh|R__*B3- ziOxm(-JMx5gx7D}U4>718!gr(*LS9NFDBeRO@9hhwP(8Q&mwoZ65 zq}6^>LD)@Bh!l8f=Dx4u>1SXOz@#^u(|4I)+IBxSd|ZE=kCsjPM8;y^XA>?@f6NmM zsAH6ivkc_m*C>xot(0$em{hHAKQ@@$yss2$PZxk3R<+9;rfk>!3G{^bA8j&FI%-}3 z)?F{JTrhqPDL=ax`Hzfn?Rt>TOB}MJ_yEQA?|7I%9{JS|XFM85cdX5ScHAx(9058r zM$4HsavKFN2o1n@rM#BorP}Oqcd>!`?W;K^z@rb_MFoFu31ZWyo?8G>$ovOZL3!Ie zTfO5~&8<~)hNJ67Rx|>q!H9Q@GN)}>dx^Ddz{aP2=BxcvlR|X!3lCkf2`#={2W$xk zjSf&?oawRJcOt@v<*K*+bK^COy5lA%(>*Q(f1^2yaESX&4sX2eq9>tQ%H-eJXjXv3 zLw7fo9eQYd6y$xXY9h0y4^M~sY3BX6;4OZLGa50tWtta{zr#1R5z>|M7d`%fh=k1@o3D2@oZ|9CEcL*$(6yCf1OHF8!_}}zyRPVG zrdQYYM#(Arq6kvWhZBbgpNWr;{6cA?RI(fjti3DtOrjunnyk=-Z9`&NPbb|AFst_=aLxO%f@)@XSJ$_X`)&DUbx zeVlXA^H!xCkzJ(Bxbi)B0=J#cK><%j(vP*kKO<9%vF+~}pQVj{M))Dd>)rWEe*f&Y zKkPIJO%^U-JKr}#Cz@kBif}D9olUySFMB9K!AN8-=LLnO-PA}6YA-$n2C zLeeR7c(NS4*u%POyluYf7b&o%k7S!)?k9AawvTKBf-bm-W+ zVQV+I8hAbT@gn>k@T%?*^|5JG@pYIjcD(qE_4+4hpP``Yk+4~G`*N-paOaLaoW0$W z5pWXKImB1l^G?s5;WzuZY`K4Vxlv=%HS$=|zExb^QgIGC^9}`i*cvFS1T<@{``I5S zogrTOcRSi9aK^Z3ZXcby{M$XErDi^3-qCvjI{sjrS&MwzMl77;yJ!YkjgnY_Cj)NR zI82^iNOY{Ibhx90phq6h2js`!dI+N5zn<7dVM2?+0QZ~MUGj9eTV~Bo*38!`-@%L1V52auWWpd~qb~(5{vf(L_w(mZ23EMleNq4Bn zx6gXF+2_bC%dL{+$R&DGi{*_a`$?BgxbS%Xo5B*sC>Fe_etITQ7 zQiI7z`r@{W@nhZ{DakkRSfR<^mhK?G!_jOD^wO=X6N+Dg!Ewp%# z5x49#xR?}{oQ}AMCmWXTxJm?vHfr__EL&h!3U?ya{f`b3_FcE^Kh~%Uq^1Q3x!#@u z8^J5-20foVr2aYru}w4v6=+s;`=?A78f<w7xy(p&b?&PENjiS3W8fS1^we-F7I zuMVF#Edigo4ef_7M6nKEUW>0h#sUAnDr0*-7k)Uyy~PT>Nv@BS`h9uHEB)x!N6P(d z*GH;Zge>C63;wcDm+F3}$^125@|T6CH0wJ}#jkN%WiPRIzOqizWR1ex2vz;~|H07I zNFJ)GdSR;Ri@jf$bw<$CQ`RX>Q!5Usj^OMnwpI9isIYy{{wY2{s&ckTVBz5MpM&1Uh)5jnfW2~<@g1m_R)mx+}`A#fT*5HVSqCizfpKn`i^2J(eh2T--P|=BZe?<2We96C>Rm^<#9hzsI z1rQKf;^J1xWtT^q$tyz*zd0y(a(+gZ+dpt5$rv8n6=VDAJl+zI>dx0`9&A{o?Tb_T zk1IRDqY5>cTRNHg;j-}6Z)CNTGZ&8D{=sDS*Znu6zKR@Jvs_w74Zoq8oMYJJm$m4M z!6&)upqa`U*yLmI+P{>~4u8QDBy`!|Sc&T?P{eh7XS^xp;gHh8ifzQB8hKtW6h9hK zsTv-;fhc?7DnLtSBeLjxj6d3s+OwVa&AJ(u%7|q}gOI#)5;tM_BIfpkzgnnjDXAMU zi}z=KRjX~_1%9L%b(-TKW4&g6JDowoh~~t5j~5T{B7Q#&x^ID*CnAyz@FRYI3A%s! zDiBKs1pPJTvpdyYAR>_r_(S}T`|I8Vc0LzRGC+>_oja)hrnsa=CqRk#T`H))&R$RZ zUIS|W>p1TK4dQpBp!-y)c_L)V03zb|pul@*4*DX)OK=1@Fz=``(|Y@d5L{-wGw3q>!%?3Abat zqXf>FUrR?$3J42gy-@_tgq}+!)=ZdKuw2IlFmEl99+Vj}O$Ficp9}(?K=xz;^XYMkK zpcKt$Uphadb|9Kt2gQHP0#3gDvgnt<7nK=rUCb!k!k2IFCCYzFd{!*RCL3u_Hz}FF z&~V~9KzQkrU zLVVLQoU%Ed71!VYiO(0PO0}#c5Ee}tcvPL`~1(DI)^Rhp{~^J%m3yxq`ZG!0k*f?y5gY*kmKj*k{+nKP3$ z%Ki2-q?A@mYrVab8E|jBeJI&2lJ*=+W0}6XQb#vEY92A$=8Jszp|(7r_$5>n_`Doinq&U6?4Cy6YA$&a9R&!jphSDv4#D#lqR?P~*bGxK?V z74SLn^YhK%^KJX%HY?}VAkL}GBhlgK$h5!Jz7u1jYqZd8?tTr31n4E#J_7B{I~*MF zCs#N#hMl-eo3(caVPu8KZ%W^A91FqG1b%vO`qKt)V7ca)760)?qos#I;#&{L3ZT4u zIX8k^(TmyeAQ7+DtS^In@E=-@d9`i0P~%t;l+C!1ZOz&WkUWpEkrG>2vld9G(M4(P zp)y#oYJlPT5h%o{An$N=YL-)Em^;?{Z)vTAn9AS8?)*AqKJE-JxQpb`+tUte+&I$~ zF@rR+weAD^V6etyYOvpPwKsCh)Ws(I0Ss)vmV41a`RAFZ0SzNyO%%Y`yX@XbqgI2o zsn6-a_p8b0Mzejgn6w&HF(%yU$^1DgDC{jEg}ceMoQ6~Dv1Fril$&0fT4Z%)q@9_DywMLAX>I*Tt-H<#rusATAp~eVE)g&` z@{jD!lQEn_!DD{_QPR~wJl@W_&I(qOX+l75YPhp;iV$7Iq;)3CLQ-Uj21MM_VX>U|{=8#zy%2a@D{eWEnmj8XWPx)w)9Ud)AYW9RjO zaLksa42#YAlmg+HvxJ?|&C?aTsn4tnrCRygcG(&$Lt==n1K4NAG;v?<1rbHY?XI}! zjIU7ah6C@i1=GxVtFi}(AB(PoP}#O{T75~7Vg5>5r3KL$r-C^B&T<^quU{(hu-JqT zsr#A{41XIPVX?Ct6dhgtRy(z+J5lA z=2qXa&M-NoDKgVkwDg-_zGL%l@5A+W_80G8Rl-F7;qkzKSWkWNz&bk&IfDMHZ_NK8 zFQJ$6nUFYjHmPxEG%g`8Q;wW@=1hmpiHZNv{w?PFU;UQ&clk_K6+N&;-@Y_e?8hh? zVjr7u$~{e77jUMUmP+e_qaA7JF#XiKf4uMy`8<%SHGb&<7E%wl7;u79gzL||`vkf4 z*JR+gb=9{xc8k94q=DXl&PWB>iEws8xSwx2);smR30kqRU76KXFw(yC6@~*ln>7E` z6+Q#4S<}O+NaZg1JC?N53Gf2WLM7GAfj%g#Ylh7=+2UH zpXv#E$InijiBSvb4cvpyjKjk&T+?4YJP=T0sU!V}s#@;(Lo$+trU;Py2mfWGY_Q1erA#IYsn|2;;E;QIE5ZWu0 zZX06;Uy0bD1iPjK<=EYp^8``6D0Y?Tn^h)wFdX?;NQmEne`tEvArvakZ|IKAspRQ= zussDP(*Mj%3u|tqHPHKdm6h1`uv_@s$isz|*WiS|FK4ajxIid7l7{lzE-rEtN5XD9 z--CY3pZ}F0j-_=DoSt4IkzXGZ4CZkemS|C8yh4wUdjQ~rG68g47{f7M+O}&s6Wl`k}=I-wtQTd=&qmZ0B!D-{>aERP%&7@>Pc1{tI> zy=QA@||iyC?USE=R$Ck!773n6^zaWf=NCd-F2+!W2Wchtp_fSkx;yxF_TA@ zFyV1*GC;--?H)0$W|8?drdI0^>_u8`pg+l>4&kfWUz(n*ifE5q`M&&2g&BGTj{rAk zQ6RQFv?$tozGMI|pe$Z8!T=$rkY9dIHjoBmO@(6#&;-pgBb^B6?}%j0qSBE`b(660 z({4~!6rKx}!`3PXW04r$=xS!HH(_aEc%mAU3R$x2(5>fGqUXFo z%DgO{*?hv4YOgLB!Iui+_Z-%_SgR{BdaUtQR zXRJ6CisULf?F{b_3lzIVRClw^5!lOkp%H2&&GchO=1 zEuaQ;5ui($8w+ofOrQ*xrco$oNoXE#8)r>i9`qair^Sj`Gm)f;-abaB!AFvL@s`|B z9KN@I-?5fow3*{Bse$|HYQFtSvOV(vrQA~;0VmNYT^8( zph6P0@{%TX3A9qOw(#4@rf{Tq5Bc^Z{tB4BR-{X;n2A@w0ZkKVx+OOP&`lw8@`&+; z2u%A~WnsYRo|X994*P<q;V&}DcWf4Rjv^r<}H~g3R-UaMqJ2I`#tX8?OAj}9^DvrE{Q524##L3q`*xWBM z%FzeLtV<|oG_0daJj6Q(qjK1;#IIC7feV!HA7}_UR1*Be#t&g;eQe6kvz|~XO_XGqM(mar^W?c?Dn2;8>9Rb@1E* z>&I2>b1*(2HXVbhDkBG9tc1~YrDq9TWkXO#QHXyV+(IhSq(+1=W|0huG-an#;yQC3 zSP8?V`HV~paB)6!+_P|=EVE|HhP4E^WL*d;&yy)POe?$x<}oJR2W1*#!cR^*p}YA{ zcpxi&1pN9@=3sRSK0dFo)-XQinPgiC76^}e`=F?MIdD@}?hsvXUBDxmbqe@)dsd|> zoWOOH6q5k!SSM`=6K*E6*Q=5tZ|qayCuG$~ASkrQK<@itsf74#dLuTldLQB!>}p?q z0=TAM%ISl-u#Fe(cUZ;vZzO%HsHPB;;cDa8(jzeE;-rq%2_@2`(mRZ;{uJiO1h|57 zo@-%+1MbyBXa$immJ9J)XI_HBu!{Vy$aK;F+RRQbK~JV$7cIHa*n4`!ySiekvHq>( z=Q=VeYfsC&7|HOIRKMxOYY7pzzyE+xl@#uEfnNzlNeTsSNn`hx<87E3sBS!v%ibY4 z6cq78mGpH}r=vqLGSqi4IWtnhK)Ls!u&$7xxTnfggRk?ODqw#wxN`zOIwaE4p*`+y z{Z1j;-`Z|k&hX`u&|aV(lV#iuj*XXToG894%k)t&OL~1tkzdPxLw8sLnrg{@jXWT~e5Mr%w#;-af3umFrXX&ekYP@E z+|9Wg12?@@Y8f$oRwxA`eKxf6GDssmaCu}CZT~tBF)yZG8=(jiLV&}~5*x0lB~#_x+}FG0*qT zxCEkVHb{MK(;<98*phUJw*l%oa4vh0vYweRwifdr#(954R8vT9mijCtL7*9kKpqB6 z7og@RJCcOy`Ul0)34+md zbJ2V5jzL2Amzt4#E4__^H;#W)ZW(<~4A7_2?+3`i|D|IIHXi-<$AUPJ1}_Aid!1GU z^iqAr;y7SM-a5lynAiU3Cd`_EIX0Df>ezTRwWtRQttcpP6vxw7wg1?fB5WewXH%)9CaTSg8lu>1$e=wT>Y1>dyxKe2+>)0n?rg zq-o)ta(}b6*USK^r*2jifyn`|Fx@}ZFK=^5x6awA`a4>VY&j37(Uwt$9Yx`Q2yH@& z@@Z7g8!jlls4(KBUhp_lC#WVThMkW(HJaJ{VKKQ`Fpl-^#xUepvy_|=`q+;A=z51Y zpO}LPHZG}NyQKZ%orWMOpIzrQ9k@p4*pr1h_(-8+ZLm|f5h?)|@AIiO|ftXz==;$^_)ERK0PzM=H z@F+w(Wqx1SRabY)%kU9mO#2HT|9G>R>w_d5cn45-PzmeMJ z%~|jX2JS^V53OZT5Sc3!b_57&`$Ec=0_Ryhu7hYNyH0xr$>Br0K;I#NR zZ(*1Bna`K7Q0Aqg(CozM^57bdV!TzhHKedXClK z%SaHtQn$@wef9(n;nE0(k+REV3&0pSn2y(0jrRMsdV81ZOKWQ?2O)tM>CNF5Cu|ZO zyRe0Ejx9&9o?4rM+@$e0nEFw1bT_UuJ14{V=ew4*_(A506ZE4oF?qP2@j6xN;Bq60 zzv8IE=)Quvp(OBb%nho3$hn|D%p3O>ETeT{Oi}hk!>F!pOw|<53G8LHBX@EPKMY%_ zIC);H!)zN*_PafD9T>Dq*yp=lNa!k%QLlgJsgW8eR+OwPHX$?XPkL=4n(OvoMrAH) zm8o3T`hM%GDG|Q?8Z>)$U-nGNk@vfkS?)wcKm91OW<+v)Qv%#e_RHN$-E>x);5;_Z z$DEhgs33dt0|bknQAlD`USl8}>qTniI1?L#ph_1r|M?ZqkAJ(F1Xxy>KB(npkSFeA zpw*|b758H>V=@N~z1+V1!K@bRcyK+yB$mjDk}ZVPG#?w_ibraeXkxMjN62A4{?wwU|_AQ@$SKpG~*F4u2 ztKrrgATG4}5@Si%D&5o!^H0&One>7V2i&8z&L9V6FS2<)4;OM0knUu^$z2M!onvE*_ndCiqqO5 z=a48Fy*L%3&ancqg}R!h6?GvC`Vc*f;>24+NFrh@4Axc|@mio_HbEr8(*_26G58Cv zCsNJf_s1V2vlC$LV`o6(S#>Wka>p^TDYFgF_FlXU#ii_$NY5~s7Dm`Z*!r|F_$;Gw zXN=Y#xGz{~^}WYD)4?%aYGDMfsTyzMF+E5pNfS7Ekk6Evi-BlH!hh`2*Sq0TGR648 zz25&Gn2SxZv4|5`OeN1^l;FVN+a`s40rnj9!dE1LNdUyO1)Q<765qO+I-c$9Q$7SR zg2L65^#g+wICG5LTo;?|jAzfm$MVzfYdBbYjp_y>bM(u9_U`Keka zp#jh7PtwDo#LMSH zDdT^)g_PQpJ1;cNyKyg0YqG;TmzZI71Ha1xU);iJiNT*DDw@e^Y59Q65a{7p1cF_s z+N9t!+|+fRV0r`^-ynCkGJKhXs;CrmmQ0SJB(z9u3Jshi^~ur6cGK?aapNB-q@au@ z3iLQ1WtgX5_S?lL`JfObzex=#1^H^>ayxVM%r+{Se%C&V2iC3DkWbBR{)YK(#yfHV zl7pJ2UZ3IZ9R7xnf^Pd9riF!2`1@3iY0Ace!ef=s9*#&bZWV#veeL{q@dBtBg1ZCF zs3hJ=*4~>6R2~kMuQcGNUI9F3ht9L+t5wI>iFX6xpvF%oEYn_Kf9Gqe zhF=w)+Jc^K)b97s>s85Z58O51tJ_EHF?n*O{+ZS5$hf!jn>}o2P=CgicIPsMG4X(p z5-EYcBw?e6WEW2Uxmhm^^9^!6&pC^!uNF1zf^IcxK}NFab-b!@06Yr`nJw-c>B$Mw z&Ivd)pRM~HEfRj9?mE`Bye<7s)sl8E5uB%}_kdB*Q!y4Gqi9bp559T#uVnNtDG85Z z(7tSpIh(F&DnVFgXjm8|q#gYW`*&_!q@6*B%q8X)D2Qo@RqqB0-i<&hijhR!2-D-_ z^e_iWii0yz;cdWq)5a`a&OA6@aOe&(W}89!G74a@TM>We5!JK#xRR*w(}>(R4B^*n zh;CR*Ac{T|mcZVRDpc%X43Mj)P!%FwSySFmj%Z@s0mYu0IpYmkxsU$J1Iv~WE{6RC z$7-`olT_r1s}St7{0!*lm^b0B{{Fd zh#|ngeQvl=x^Vk@_)hx==P+~(bsY?m6IAA5n0G7|%p`&rYn=4aNJo^c}ak@ND1Zn-FEp%nK8ChXu0Z!Exi`e z;f7}Ah?peGX=Q15Z1#Ao5H{qU4?cGXv_6!=Td!iI{#85XIZPU1#aT)M_i%gNXxKpcPL{V; z9`7Ok%-K>U&+2W+!T<{Uj8OJ{{;c^T17sfX_06X?LYJDoW~)JpC2lC#R6l$P|Na`F z|IBF&17p_0>qSF;L3PZfh|>KHb8~6GT?9k6S5$~kXvvDa?WmUj<7(Ys8gj8E4yS?w zW)^G#@Z|GNgf8Cp8bMGx1+IG1kM%wlO3YCMt$z_~@*T~n+i~9?I-!5i!}KBErbw^t}driuNo6gH%=QP>)BH@{apW?nQhx3 zLW5x`FCJ^c1V4m)8|2Lrk3<#MU>uBYOohXd(`(!qcd_i@M*)NFF!!lYhjjx;OMjDp z(I3#&XwGhoI%nNXgMXtn1hca2e}tsEhOqcI@!G#osCh-zZ1Dt_W&=;$*Sqm#DU^-m zKsKO$%0{3>P#l6&q;Z7tE8W&{kw+ma`&Ev895ZPj2!{;gAh_Q=kR^6=gEcMQcnzbP zXV_|$8)3?N&{Io85TXzDL^cIb5TgMN^Yx_TIXaK?6qLUbrQ-rFpdD&)Vk8xgDtoEd)Mo}j-MfUs{w z`uk-YP~mgH)Ba>Z0)Lt2QgoP6#0sw}fiCX`6L$jrgJeMs3&%5gM>hqJD2q*Au*P$j zY#g1T)XhU+_=8tuYZw|x11(U3lCHhC_N`br1nyv90NGV!rxr-RfMSsw_Z_&d==e2N zkdO8mZwt1&5A=#0h9hQF1f#S)0KaV(y7rKkC<+d0`A$O0B(p<`PZ-Zy#&r^IvvItKTjEEuAo7z&Mh^FfoM( z1^GPA`g*FvBCH}oT`6P7n1UP7#X;~D2Oo>-2_FSPxakB@;gKz1AR#+mgBke9;D12O zq6JAoSvyH_*adrmsm-r?l~Qy4;D^|x)wxcJ6E~IUlM=(@VX0DB#HnLkOqqbaPd79t zDJbzY0U^!7p5Z$)GlK=k0pQUk0EO&ardVm-$)n(OWl)Me4tPc|5W?A0AA1_jVs~<4 zwNngY0auAJ&Qrs5Y0zw@y#2*S9YgGf8E-~PeuqrTqhmiBLbd;DiE3Us{nE z+5svGe*4e^_Omcj9kyg1%#eM|`WBIw(av5e?; zneC>p6uA;>d ztgduOR^r;kA!p#1scl)`l)!7rbUi~E93r2O?BuVm!&S!r3I70jYJW!um(@U51&j#| zqcD-y!{%$a?2~y`y-(1s%<} z{tsJ5gXORH9_Pa%r#;gJG-CC{j~!_oEQ7dBh@rViiAi6qRGCSp#8*kMwmzeoZYwL* zZYGts0chSt@R!Fh8z-k4KL1Rh5I&xe=?v*LS0t)M5j-e}*N{{j!qvh9R=T3P;_12+ zhcx!%0FUgTP{nlHV2y3dLOetIBbTe(nKH9k51Y(J@7t>| zn{Q>lNWkHaVjVPFj)RTV$O(g( zDsdwhVd=ZpD_+B_Do8QG*a1~3X#ynR-!di4(pXe3PztnIf5sG=`Vu2k;BSfywB2zW zBmAr8bW1#d@L;pi6%srVIFj=Rn(eko@3xO6_&nF`?a^c*)m*?(JR>wXHoy}V5LCzj zEpWkMLBHSYrKL4D?N?Oqi(NYCTIP3<MCE@3T|j%Bv|t=YYK3cBEaEDq`@4=Kd?d0 zLhA^ZqA}tmhT;@cPNl<;0QBWG2;xY51+om*1)~< z!2qlb?t-w@tyzQeF+Ob7N2Ouj;qQ(o)2%#%qRt-7 zFHGY3Z6(oGM~t4!!C+B!$uu>1uyLHw!N53#eijno=zUP}pgSCA8%{&0A#X1#ZMU}9 zX0oUy%;C-}YxXNzq&HUN}Ev=~*vtjX;A^dDGhbmOeD4DtO@!PBn;-`$wigrK5;M&OblD>*NqRMQsVmrG~ zxHbOb!`b36TLZt-MgXQ8F-U^_tQsgpk}?1-?5GqM#p#yq<_ekVco!7%c(D z8mUCtOKNPL_^x;=LSL=lOFo4(xfc=aESiu_Mp|vT)2IGVz)LG?<2wh*95`*uK$Gw$ z0+^vnv*FJJp#A5Y1rMeJRSwg%aK!PKE$;JWi~B*Zs9`t~AZ#eCcKz{eT_ZCkq@AEJ zPJ4iuq&<9pdKT*ieu<|@$1|p%V1bnO73nqTf5xEWI76u z=Wu_T>L#8dHZfNzB3xmsB3$QPSog3^b(!uqYolPXNWdR z^xmQyeT3-Ii7p{V?;?YU5;7?moqMgb@4feRU;8?Hd#8`# z{K+C+0htig|57#;TZ?+r1{|YkGZBs8Kh3 zcw_e9u#NFfDp>W8eQX|I%@cHmTv7JNJr|XFby`lxILUE6bgAui;%AaGxhp@Un_FRB z18nNWZ@sJgPx9&%1Sn$7xCj3>MSOb)1Y{=OQ~gs~I>@M#`}xUF`WS1upBAMM1b=|y zp#O#9IzW{H_LbKWLEs0eScdwDAWs>n=S5{tdKGc-p<+1QokshpmQ9g2R^C;vZ@bP6 z&^_-|eo;P^Ed&-iJM&JZNMf%`c}kunGX#8&*oO#=eGmGKZA*WWO_akUIPP}#D{o9< zw zT(}Fs+@vePj{fP=XD~p{YNV656jsO^NzW?nj{e&sTB!?f(c6p zU0Oae|9sRN=hlO}nIF%tl~2LzK;!M@p6CTZioP}Fmv)g25}*x=yL#%-Z?Y>}e=9Zs zRI?4VpipR~rSbMqfKxZHS|=)lK(d`88gyCj@C$sk@~N<9r-XTFF%8rJ(R9j9bG@%g zYWB3sCv4P~W4+jBW@C@2MVK+Dm3^N9Lm4t&f`ke%SFETF^?&#CK3TwC1m9E@J+j+H zaDMYuam|W->@%w9t*@x4ZWV`v;nSc)rEDS7?bxImq)Xn`b7Ft>LssIp1PkOngTXsP zzF&q-sbqhw{+r7@{}#a$(w$Pyk_s&?L<=h^x+Dx3{ryNm(dLi$n>YlfRoARdGq-MH zYw7{UxGDZ_8K~Ri=+T|zIZS48xDD@}>RH>h^f;?&Y11G?CRi19ep;5VPCUfhM@&IB z!aKFY>#G81aR6`-xO3g)-19++ZM_kujlt#6vwu+jHa^8hQy6hJ| zh31lSsGcTwJxL^MEBP^<_J_9b4^tbu@F%}W^lJ`dn+3Imec?_a?P)_%7o}RhT|xbH zlzW97Z{k=}m&K9fRt}ZXtFNksKP|O3@Uh=D(l2%}m$XovYznTmB_D8q&&j zdnFhA#tX_2w=Sc!VXA9cN{yRK_M-%Aqf9z7$Crt|M;Vnx_2$3%H|ZI%bqq`Mz>wsm;gG%{M%G3I`lT}t%;Zzi;j~O1=fBy19r`O zd<&$N4#!mCTQ0_?KpU1$=J%u&paOkCO81Q=Qu?fGVEJPYBI;7+l{8s0`cj_XfOENi znJDbQJI1y;nFqFl`8x>YM`?KKU0fm+i2%`82ZS5Z8<9GJL!D_AK+%OGZevt4`!MD% z(UU@LLB4=YTX;5JKCpL|yF&pt$-(!xjx6s3y2p`PButxAa*>5j+K#@qia!3f^}3I- zHKx;@?@5z97B2n2i<8w&!5|YrBo;33pJ=DB^XY;5v{f!3a~?Nmk}=m!xzuAf+HLDXV?mk$NDDfR=`?%w{uwa4>4aP8Lr;o7k&lKA>tXalFlKDsNMdqnbG zl0u`QE1ssoB8flkuB4wQyT?B8T~xWLkcKoF%%_$~(pF*(pHIL19`#k!(mFmw#;lJg zqRwjC&MtSfL(X-5viQ+9e@#h!HMk|ugJgmYe*%q<>s;L~0(dIRZVev<%g&cXz%>njVN5Igz;w2p;&)F4qvCmz zJwnLFrlwVbl%6sJeUZAh6=sSf(BbFRiB#?{Ox(49fixW=!adTEx1*j~mR-E ze02Fp3aL?Vpr`Rr1HqXeo@5_9EEMA)XKru^w~Tn-A2CVOT-g0TyBI>{x++UMJpwJ8?c5h(KzLWnKidWV z%PXL@`ab%{?B7^gt1c$KmUJS3?Y@ChaX0o{A7#@9HCYlfNecsfd1(DK%epIBC27%j zT!w$YH|$DsG}FpU!WIf;v@bs(O?_{bU|Q@?ImPsgy}E|6NJ@k;UkPGXHoUfUBi&=nol%DY?Z*IqV5de1V~ZVN;U<%ellSFvV+Uv&9G;W4gb%-x?wRteVLf*xB&BL$Z}E{(%Zav1vzpHa_OMpcV()U zvkG4Mi$@1j!Z2heW&#@J8m-Mw@uaiFI<(<}k>kk4A)n(}S5R2n@;=QW~cZR&Kti7BEW+>l2_jW}oAp zyX6CEa-USr4|v6yX?;_9l^&r@l1D5|7RpOqAk{K>8@c%&SwROld(=t_2d=ggJoU5H zdBMXENIL+56nFsp$lF=L@Df7B+gimqheg+K-CV;vwJXMNjy|vdB7NwF%pkG*hj211 zPWh}ckv3`U2UoImdm&4Al*e>Tjh&>)mK>D>EUH5Zs%^M1cYO1{)KO_R6kD2 z`%iVk?xDI=XO6VuiaFaI$K@|>>G|G1>fM|dUs=3)yfTEt3v|F(@l^Tj0={^9WMOgu zy6|CeuIbF$st%wi&ghMeQHoQt{yt6!$mitawbdKhRZ+zo^}4=}r~sjMHr(r^kkcpz zOeJL1eXZdCZRLuC$Ct##=;M=kfd4?nlS9+DrUigs4sFU1}RAXUS) zwlpxCop&lGJb|BW_kDD zELl&!)rdL9*baFs-3|`hEAwgm5Z>lOWfj1wb>=p+Y=&KX2POS9CNtQ>j^a z2KAvXVpYa{=Jw=a^E?J>)uDWovQW;Gxs1{VmBg~Kq4h#rTsGj_S}ZM*2CQ!ji0M{Altm0+WyY76yltxtUT#_n&PobRIiH?OufxMwl_i%7%P9YUc#-vX8Q=XWCtI6ogt^?`Lw|Sa0ygkp4>VBp*Q?hO*=CvuW)Wx`4qj%@Qo+1p&w2d zNeAQ4e^klfL8@r|e^R@~7mqC*^X=)e_^u{>ud_+uh`e2&JEZ^X`0S_dUpRV43APy&Gm2ljV&jF}-7E3;Zjg}oVwNnNc=k9aw1YD|Q<6G7mB4RMFvYF@?NmT+d}kZY{lhk)8L87S$2@-D~zv7n8K`Trxs|6*;{}_UvD9`Kqg!lu0}@LdiXR z^tEb}ci3q7QJ?bZ__+Y19&YgQ59QhDl!$oeuRO;D7K@Ac1P>J*$>{iJ30ly9cu1<@ zMRkuA4mSJx20qdy3!<#_46;NsrH?Wwkrndo*AV4;yj5}19N9z1H%5$@0b=!1%5+6B zL3g%cw7Q9zHz1qVLkTilgt;k3#c@tPK0ae75%JR^#s2QVf#;q^Z?7m&G*EaOhRD`O z`0BN8ZkO3QnS}^B(Tej@kfJoy3zf!r$kmVnT`k-|OVHtO0@#ut`h8y9NG6zc;bH0& zlR2{h8}Y!~$2*(f`QLpiG(%x816;-`5ep~mQB4+@^bcSt!gO$5)Y zRlob!-)P5fB?*S^1;23!N+R`=JRlSSFZC1yPL+HpOm#^~f20(KDZC)0ad?=yQ;+N8 zS(w0Y|Ch9`@^c5w{Xl0jwVufNJ;_N9Rrr-V;K>x2K?e3@Bixrax%>z7M}GnaoIGeG zjHJdo7FzYFOJk~55i*10q7fMLJ>dn+^RooF8Ypzv{XSUUG9}2Vreng58Haq5#m)$L z`EOapIY6F=I24Ba%s{%Me^mg1+tcOxj&E{GsZstNQL?kb+MV&_K&l#rskE10fn+JC z9}Xc4#@MwOfB4$3B^)sT%=@+asHU)u8|*c&%xMLX2>#K!T-13gREYsx(|uKS@y6y4 ziTlN)|19t~KEJXme>2ZfG{V(w2=ty4D-Zp9*Pf$e8|A8FaRJ_W4?huYp_PZ&#azu5 zbxJ)aOQ|LL9E-+(yQ9|M^pAsN%PG|xR1L&?H3_rnJBw1F?qe}Ib1yNa?<(HsL8qid zGrYsWH|Z+=JLZr`o*8mcvutq&aR2I_4&4+d*5TpT;eqJz5F1SGuf`uFW$*4a>sUm7 zWYji!XMY}Lxui&``YPy z?6&o+&lYtOxFfw^;|46k)Hu5Il-kzMNFy})clN{iiG?Vns_ql`=PEd7cWb6fX30vL z>XfOyJr(Szy^j~LA56GWLzf$zKh{Tec6P_Kk<_$uG)5;V-q>cv?>r&jQcu_>QIMK? zxHaB;OrTLP3&zZWO-&~Z8OL-}SVu@~3Mi0QPshlF(F}8<6q)kU5YPyOakV>$@x3x6 z%1V(Mm${pWH8DJv|2-Mw9Xm?~5LZ*S$mHSm6jx7A=2qXcP=qGR$mMqGktnu$}&BR0GTvBxv;9yvHLrg%!on1v_b45oAz>7 z@K2kd#If@)bWHJgaZ~nRrjYXBhkh{xMTuIy!&4$B9`eRQ5qrx2;GNzG!x?o`b2%fk@&Y^ld#v|s{Es8z!gVxTxUrQt-{X~0PPOaK9KjxE8~UU zc<2p|RqBSQ8qQ8q1|w!c8u)R*DCBKE+xi6Nf9mwUs;iB_UBus4aG$>j;osY=$ z4+6}o@nnsm_>3=@07JTwk7<(Zr|^w-7IiEzpKe#>w;V^n>P#={ z?7sf1U1AKR=L!b(az%57c~S5r4gjw&i@Vu(s#wR zP4om4Rxk$yM=%|SNrvyLqxtI@4C4iSyOj+MV|C$KCUDwzUR;f(Vt)#zBd^u;=BgPNG4-*M6VBcA%-UCrAzf9)kF#QkZy^p z{v@W|_QrB#TG=ICt2FA)pv7U-*!e+}%epcV5BrhT_aHz?WL|j-7D*&4GOhxA^jBhe zJdvP!+QFx)x`O8qvxHMepuh6l6g$U3nt+%tutox9*$ovQu{QAlk53QqkuNGru$ohs zjoYTQ4u&vgC@#aYu|`?OAZv3;@LfcGEo|%xa>$yk!MT&)ij$LMrH9CvTFd>kMVJRh ze97}tvLhTnW*j>P5$!}a!r1QKoXz#8)iZlBd-WQeTY-uO_G~b+PWjF>rUEh-Hfp7)b>2+0Y zlFqI%7X={O!4eFRmH6t!>Js9~#xMK2(tf1q(+Yd*GXOP-JJsVH%mA=s>jzt1mWEh{ zKz1fl_;h1VqHKEFa6rvT)M1mH5OnS=^y9oV55-O~gfAqq|K5tCB?z}gGLi`Sj-TRa zcw?-Xei+n=HH9w-FV#YJr{D@H5q(yd9sjBi$p^vtu!lN`ji|3 zI{)?*M65fFrPm(;`JS#-sEj<9npm@FXxA3p#q-v(e(4JL-#P;rGN4$;h}h77Ppozm zm*t(C0z;~*nd`%+6+Q!JG+Jjb!KMPH!V}>k88H{hHkKcQlFufxIhCWKnBFs9jgda> zy+;{KUI6V)>J!K_-mO-yzS_Jm+!bstnE6I|DS6chH zb!HcGPwRMEi)k`8E;C8Wt8~(PP5P7JFUdaX<@x(XiC60ms(OX46%kI9C3e;dP9F2^ zhXcfaE~JbtCXbQ2IHY3GqAH`TE9yP$JCsMQiTD9HSjbC8(yk5&h#4_M;N>f?m8FDl z>4H_5uo3=%pGf9})-j6zhIV{T7pffQ)*p%!3aSbX_!<&NZ{PKTKW(rYhvIF0s7_gfMCV;AsgjODN zg8776b!Q^p046{XBm<1g9i`j{u^+-I^ak|VaIky6iJY6!JG)wv^@d~5>8Zz=^cgd@LjYI zLb2~p4lY&Ao}uq}vZ*ZrwIFL`&~m!FF>cu^S?B`vc~wv!^tn7^2Vo-s$2AC_k#Q_* z|Jo&IMiTSy^dvW9%-af|?1ve$g)x&$PKN=FM^4I!TOETJI5y1)>hvEE9+n6qrC(Ik+#E_kZ zuoo=RuKWvA*k%l4WT*h;!ygf+nI_w|cX^bRCMOVrBnEEX@q-s4hZ*{BBOKXm`z7t4 zCu~(*fel-%GWye==(JDmL-;C7=ynuYb>0-H5=uH}+~4osF8iI`h06KGeq;UP`BKOp zjyS#75QzzybmzY35{dD$ATwcuEZ4=Ztu}5TR_KndjQf#RI}^w8RNq3#F&jm!eg$Oo zs`7B$IaKTk^9+qQ7S5KkrqwQ^AmHsc7h2fxG5_EhY!UtP590@YRp)eODhtZYdrOq% zdXj0Nr$iII@I|@{YN%0N!u_dPh0qT+6SvXQR&B6Z=3x7Mlmchq5);W)&S!;IY7t3W zyaxpTx81WY@TmIBIT;{6bffV-xF2Nf3Pxr#lA{u~ii+C{eu`FtPvWgK6CxTPpwIr= z>^_lq%yxj{PPCwoMWuhT8sjL>Dj~%H=QFX|lY56hM7|sSE`m4wflI&&m|7a-`-A9I z9)vZg?CUkuUfy0|mLerG{HHn3WaKWo?D^XweaB-Yg*PDSrX!ythyl3sJA}j-<{OLd zW~$_&@~@!Hy!@=cidt0~-#@c(=n&Zg8%^ zRU)gYlxkYl&zPc_4n?Zk+H#Z$mPWm%%l@WQa(X#SZV(pAS@xpXN-3=#gHyY39^_BOI^%=mb$-HR?9i+uPMQG07-PI z*-NEK`6&eFd^q1IGNG^sYhBMzJt{P!wg(%i-pMMD38afHu?hrIuQ`m(<*)@N&Tljr zlU-44u8;cdy&jur&(okZ!KPA)M7lE; z`XYO@eucy+bFrZ5H82!qZLvXuywC#Jt7<0*QRJp7J5%XXLysg%n{v zO(G3bfa3roiRUwJPO7=-l(4MP{wz1%fIPa`AWd*!eR615tBc8&+tv8Mo$CmPS|8O9 zj@OlMl^%`1rkI3~;E_j6`j5t69G3LIRjyV@(=o3+b}4e8>*HkA<2LFd-zHyVdo^J* zD7#X*#E;Qa6ndS&C0$OUT+M8G%#xlV?(*-mUjC;`?b8Yuh1LoAS{*x4iY1E_p;nl9 zZ2Ge-&unhV;Sjcrj;}1QMYGr$Bs}8U2SSbiTBP4(u;0IaSRPw!)t}Zp694emX!^m; z%DbhrC)oLQcT>~xr{$D?9gxoPk9oB|w}B5(KZvP2yYZuCknMnsm$a*o&y=OOyj@8= zweeupz;_`vR(bGS+}s`FR1E(HisR#P5LQlFBzegBGM2K+_&M27?s*8^Tk%mZI#2FL zt#u?`o9+2L^mOoD1-Kzyq8r5~M`nPgB7Y) zpv)_-fLn#G5iN&N684rQwhsp16|jqblqC<+n65F0cg&`axkAjkvKLyo>jv~fDH!Dp zM7k!J2J}QDI1(>jdZ*g7!{D(aE?#)|by8WW`QMyaK5h5K|NIeOD5 zd)d;XOs#a2jL5%dmTV-I_+i#M1?vo?Uo_rnhETY!Q0=6J(kK3Je(;!RRXk|mee{qb z##QjgU+T2;;I!U=LPmv$Idny%ie|LcxvDq+9Zo-c=hXrE^)r*4haTwi;9bS2dEkgCB+iAZ{k2HB$zZ!@?+uL|ouK>BG`c17sar(X zsh-=#BRSpn<^rFA23e*Itl z6Y4LrPaBGLha%SphS#EoC|jONDr#FVCD47mdRdfH^gI!<)o^j+kw2*$ljODd+gq4; zd9@RFD1|g7R}$J0!zSSF{iYJ$H92iolq38dJroSq>eYaW)*;00$`NPO}aC$|-~iU|J>z30BAar*^DEwCq{RBtuw zS;lkTt{2GQ7wJ((KhJ(=uJq8bKVK61jucNbGY>-V>n0w+G~AnxYnA%65D~TYR?c*W2$r~S9f|AJCpzJn z=L$b@a?NF%=aqaFkA`E`emK9LW)4uk%OU@Q7tXjpj((DMDwx35)#Hfx@JDv&T%_06 zwNV)Tlk(+iQWYrhJ@!W7=H6}7%jYz`T{2&wJ#M+0Q0g#j|8RA(H2y(;EEFU?WCQsj z!xXu*dDGWrVkr}v0V<`=Uw(o6b?M@pa-#0z-^uJUZ()gxsyAOe9{2ugTi^;lTkUVww{IEP8k+H3uATIT;YgI3RPEWCvzi6Igyd6f!>Fjkb)VU*sJop1*xm^E5TAdviu{!856vHHN-r96Ar zRbS~MadIAZ06%rCbL#2Hi>*VRT*NHc502pem2H(MnIhe+$_!7j9)B3?p#K)%AT+kx zW>i`OV8^aXlL2*8Rh#-lAVcX=%fj~`Bz61j@v`yLHT;Y3J#R)7kCkll9}kobvB22` z9AO!R^Z(5uW_YZ^-)$!r+}dk0+}g>hU8pr>@%9<=J7Urf!yzt&%GDg{XjrB@hwp?p z^{D-Q!^fAywr}SE9X#$=h{*e!tG?yVo4u3e`@fezwwLd30;R$GnaCh>Dx!!M7ZZ>$g#*q)`^9@!7^m(<`_~amd=ND+V0k*;{eWywS zwaL@I{P#rWNE;pbG{!*Y$eJ4^)kovk&H>8{z!uWc3d9y#l`bOE>HB=f)cMPynyE9J zb(g`KG)jiG0#Lbiz_7lD8o6HWJC`!_8iY-^b~nsC%u~De`T9DIi+*dKE~2Gwv4wnO zG05Z{O@=1A6e-fb>BTS%Ld%c1nLf&-5;=1fC&_#)5@Hu_v32kjGQ z<~-696!?Xc`E9L*cEi>8MHfT+YjkGo95;4t;13t(pNW^`f;gE(j>$n=ok$DJ=_Xtal9}a{Kh}gd*@OsJ>w1KyE$&dUrgKmvqrc-ixH*kzfbdCDmTY zeEW9|5K&F(6CZs-;Ua2So)}5pn*T19uDh&s?&v}7pFIV%i}a7;|E~C5a5i5{B!F52 z^YN^X&8uTHz#55JA&J*aAy>p3Y#18E;U1hc;tK$0wiPUWK~>!v>#$^Un|&`Ha=*7N*SU1J`or!1-_?(Dt@}F?1zGo)nN|kC F{{d=+q^JM@ literal 0 HcmV?d00001 diff --git a/research/direct-mixed-flow/vendor/p7-NATIVE.md b/research/direct-mixed-flow/vendor/p7-NATIVE.md new file mode 100644 index 0000000000..394d9a03c1 --- /dev/null +++ b/research/direct-mixed-flow/vendor/p7-NATIVE.md @@ -0,0 +1,180 @@ +# Complete all-fresh p7 native controller + +This package extends PR4359's exact local construction at +`da637c87c89482bc4c86be36bd0071b3d400dbed`. It uses the newly regenerated p7/keep232127 +Laurent word, the authenticated THREE-base full-identity native supplier, +and the source whole-job helper normalizers. The new checks establish finite +physical contacts and complete inventories. The native all-column semantics, +permitted scalar/routing primitives, uniform compiler and outer analytic +transfer remain explicit inherited premises. + +## 1. Literal word and actual arbitrary inputs + +The selected p7 controller has 15 chronological native calls, seven main pairs, +and 112 ports in each side of a pair. Its right scalar program runs first, +then its literal LOCAL/IDLE/ADD/SIGNED_SWAP program, then its left scalar +program. An independent exact Laurent interpreter replays this entire order +and checks every coefficient of the resulting diagonal operator on all 14 +formal input roles. Changing one backward local orientation to forward must +fail that equality. + +`factor_receipt.py` authenticates the exact original factor generator and its +two imported dependencies, regenerates only mask 232127, and compares every +serialized coefficient, boundary word, diagonal monomial and literal event +with `P7-FACTOR.json`. The independent Laurent replay then checks the complete +word separately. This is one admitted mask, not an exhaustive p7 census or +an optimality claim. + +There are 1,568 independent main input arrays. Each of the 15 native calls +also gets 408 distinct fresh arbitrary helper fields, named by stage and +native helper role. The total is 6,120 additional independent inputs. A +helper is never a copy, a main idle field or another stage's helper. The +source native word accepts every persistent input arbitrarily, returns each +helper autonomously, and has no external cleanup bank. Its one owned center +is initialized and erased and receives no productive credit. + +Apply helper normalizers only around a whole local native invocation. Their +actual endpoint widths are 5,6,7,8,9 with counts 28,18,56,93,213 per invocation. +The source gate authenticates the underlying word, both orientations, +helper boundaries and arbitrary-input receipt. It also restores the original +eight rank-eight center jobs per invocation; their former 3+5 split is +unnecessary before the new tensor strictification. The exact midpoint and +absolute phase remain checked against the original native receipt. + +## 2. Native owner maps at ambient rank 121 + +The old source utility used a fixed 73-axis container. Its owner formula has +a dimension-independent extension, which is checked here at every one of +15 stages and 112 ports rather than assuming that the old container extends. + +For port normal q, let b_1,...,b_8 be the actual first eight orthogonal axes +from its pinned initial idle recipe. The checker establishes + +``` +b_i dot b_j = delta_ij, b_i dot q = 0. +``` + +At stage s>0, let e_i be the fresh coordinate axes in positions +`9+8*(s-1),...,9+8*s-1`. Put `v_i=b_i+e_i` over F2 and define + +``` +G_s(x) = x + sum_i (v_i dot x)*v_i. +``` + +The v_i are mutually orthogonal isotropic vectors. Hence G_s is orthogonal +and involutive, swaps each b_i with its corresponding fresh e_i, and fixes q. +Stage zero uses the identity. The checker verifies the complete 121-column +matrix and its involution, orthogonality and q action in every stage/port. +All coordinates outside the original nine-axis block and that stage's fresh +eight-axis block are fixed. This supplies a legal full-field coordinate map. + +Write C_a for the source Gaussian factor on a nonzero binary axis a. Its +Fourier multiplier is a Z4 phase. The phase polynomial of a product of C_a +factors has linear terms modulo4 and quadratic coefficients modulo2; +higher parity terms vanish modulo4. A physical translation adds an even +linear phase. Every C_a product and translation has multiplier one at +Fourier address zero, so its constant phase is independently fixed to zero. +Comparing the stored linear and quadratic parts therefore proves the full +phase, rather than merely the polar rank. + +Let `F_s` denote the positive product on the first `9+8*s` axes and let + +``` +D_0 = F_0*C_q^(-1), +D_s = product of positive factors on fresh block s (s>0). +``` + +For each forward/backward native call the checker constructs the four +entry/exit coordinate-and-translation maps between its actual main references +and a shared spectator frame. It verifies both map directions, the exact +raw diagonal difference D_s, and the cross operator D_s*C_q^(-1) for a +forward call or D_s*C_q for a backward call. Thus the raw local contracts are + +``` +forward: D_s * [[1,0],[C_q^(-1),1]], +backward: D_s * [[1,-C_q],[0,1]]. +``` + +These are raw-input operator equalities, so they remain valid after the +controller's earlier scalar basis changes and on arbitrary correlated data. +The exact audit covers all 6,720 main contacts (15*112*4), with inverse maps. +The all-column lift replaces each coordinate by its common column block; +this is the inherited native generator substitution, not an assertion that +tensor powers distribute over addition of matrices. + +## 3. Endpoint targets and all full idle jobs + +Every literal diagonal Laurent monomial has Q exponent +1 or -1 and stage +exponents zero or one. For each of all 1,568 main outputs, the checker builds +its actual positive target axes, proves their binary independence, and checks +the full Gaussian phase after the specified translation. The 784 endpoints +that require a nonzero translation reject its omission. + +The main target profile is `{25:448,41:448,57:448,121:224}`. The exponent +factorization alone is not used as physical admission: each target has the +separate 121-dimensional axis/phase check above. + +The controller retains twelve complete idle windows. All are paid at their +literal event on both main sides and every port: + +| Window index | Pair | Stages | Rank | Physical fields | +| --- | --- | --- | --- | --- | +|0|1|0,1|16|224| +|1|1|2|8|224| +|2|2|0,1,2,3|32|224| +|3|2|4|8|224| +|4|3|0,1,2,3,4,5|48|224| +|5|3|6|8|224| +|7|4|8|8|224| +|9|5|10|8|224| +|11|6|12|8|224| +|15|3|9,10,11,12,13,14|48|224| +|16|4|11,12,13,14|32|224| +|17|5|13,14|16|224| + +A Counter equality checks a bijection between this paid inventory and the +literal IDLE events; no omitted or duplicated metadata window can alter the +bill. Every emitted recipe retains its pair, stage list, port and both +physical owner names. + +For an initial window, begin with the source's exact rank16 axis list and +translation and append its later disjoint fresh blocks. For every other +window, use precisely its listed fresh blocks with zero translation. The +checker proves rank, independence and the complete phase identity against +the product of its D_s operators. A whole-job coordinate conjugation sends +these independent axes to a canonical rank-r call. Helpers are all fresh, +so there is no partially completed borrowed idle input and no helper/bridge +chronology to assume. The entire original idle operator runs at its original +literal event. + +## 4. Complete bill and new fixed constants + +The final raw inventory is + +``` +T = {5:420,6:270,7:840,8:1395,9:3195,25:448,41:448,57:448,121:224}, +P = {1:37305,2:10695,3:3360,4:1530,5:300,8:1464,16:448,32:448,48:448}. +``` + +There are 7,688 independent productive fields and 55,998 paid calls. Target +rank mass 131,723 minus paid rank mass 131,115 gives exact surplus 608. Maximum +paid rank 48 exceeds minimum target 5, so this raw word requires the separate +tensor construction, target completion and paid-call splitting before the +original compiler applies. + +The scalar bill includes the 15 oriented native words, every boundary ADD +and SCALE, every boundary swap as three additions plus one negation, all +literal bridges and all seven terminal signed swaps. Its conservative allowance +is 2,490,856. Every coefficient in the boundary word is a unit. Coordinate +routes, inverse routes and phase translations are additional finite movement +operations and must be counted in the newly expanded word. No old p3 movement, +prefix-growth, row-stock or precision constant is reused. + +Give every instantiated raw unit its own owned center for as long as that +unit is suspended. In every product or uniform compilation, retain all actual +scalar operations, native calls, whole-job routes and inverse routes, with +all owned initialization and erasure. The new full-word counts determine +replacement precision and storage constants. The finite construction is +specified algorithmically; its enormous final tensor/uniform word has not +been materialized. This is a conditional supplier construction, not an +unconditional integer-multiplication theorem. diff --git a/research/direct-mixed-flow/verify.py b/research/direct-mixed-flow/verify.py index c0dd794858..9bb5e4b310 100644 --- a/research/direct-mixed-flow/verify.py +++ b/research/direct-mixed-flow/verify.py @@ -9,6 +9,7 @@ from fractions import Fraction as Q from hashlib import sha1, sha256 import json +import gzip from pathlib import Path HERE = Path(__file__).resolve().parent @@ -147,13 +148,50 @@ def inherited_rank_size_bound(): D = 1950+2702*(H+1) need(sum(k*n for k, n in T.items())-sum(k*n for k, n in P.items()) == 608, 'underlying raw p7 rank-one surplus') + native_bytes = gzip.decompress((HERE/'vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz').read_bytes()) + native = json.loads(native_bytes) + factor_bytes = (HERE/'vendor/P7-FACTOR.json').read_bytes() + factor = json.loads(factor_bytes) + need(sha256(factor_bytes).hexdigest() == p7['native_inventory']['factor_receipt_sha256'], + 'actual p7 factor receipt') + need(set(native) == {'forward', 'backward'} and + all(len(w) == 22633 for w in native.values()), 'actual raw native record counts') + # Macro description allowance: 15 exact local words, both serialized + # orientations as an overcount, literal controller, source scalar + # allowance, every productive/paid/contact/helper/idle slot, with 32 + # records per extra routing/ownership slot and literal payload bits. + ni = p7['native_inventory'] + slots = (ni['productive_fields']+ni['paid_calls']+ni['contacts']+ + ni['fresh_helper_fields']+ni['main_fields']+sum(ni['whole_idle_profile'].values())) + raw_allowance = (15*8*len(native_bytes)+8*len(factor_bytes)+ + 32*(ni['scalar_allowance']+slots+15*max(map(len,native.values())))) + need(raw_allowance < 2**40, 'complete raw macro/serialized-input allowance') + W0, P0 = sum(T.values()), sum(P.values()) + Uproduct = sum(W0**(v-1-i)*P0**i for i in range(v)) + need(Uproduct < 2**2392, 'chronological product raw-instance count') + product_allowance = (2**40+32*v*(W0+P0+1))*Uproduct+32*v*P0**v + completed_allowance = product_allowance+32*(paid_mass_upper+W+P0**v) + # Include each dense binary chart/quadratic phase descriptor and role + # indices in the fixed completed-unit allowance, not just opcodes. + ambient = 121**v + serialized_unit_upper = completed_allowance*64*ambient**2 + need(serialized_unit_upper < 2**5000, 'fixed completed-unit description allowance') + need(2**5000+32*(W+paid_mass_upper)+1 < 2**5001, 'compiled record coefficient') + need(2*D*(H+1) > 7*H+30049, 'explicit closure exponent absorption') return {'kappa': old['kappa'], 'H': H, 'N': '2^'+str(H), 'D': D, 'width_bound': 'B_N < 2^(D * 2^H)', 'paid_leaf_bound': 'P_N < B_N * 2^H', 'raw_p7_instance_bound': 'U_raw <= (B_N * 2^H - P_N)/608', 'owned_p7_center_bound': 'one per raw instance; <= B_N * 2^H / 608', 'routing_macro_record_bound': - 'R <= (A + 16*(W+P) + 1) * B_N * N; A is the complete fixed-unit record allowance', + 'R <= (A + 32*(W+P) + 1) * B_N * N; A < 2^5000', + 'raw_native_record_counts': {k:len(w) for k,w in native.items()}, + 'raw_macro_and_payload_allowance': raw_allowance, + 'raw_macro_allowance_upper': '2^40', + 'completed_unit_description_upper': '2^5000', + 'compiled_record_upper': 'R < 2^(D*2^H + H + 5001)', + 'source_precision_E_upper': 'E < 2^(3*D*2^H + 3*H + 15021)', + 'source_C0_upper': 'C0 < 2^(8*D*2^H)', 'routing_slot_bound': 'slots <= 2*(W+P)*V, V completed-unit instances', 'physical_scope': 'Encoded whole-job adapter/move records. Their permitted physical implementation and tariffs remain inherited, separately priced premises.', 'winning_uniform_word_materialized': False} From 199ced56720601ab8986091436eba65c2046871e Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 15:18:55 -0400 Subject: [PATCH 03/26] Verify expanded raw-column accounting and record standalone checks --- research/direct-mixed-flow/README.md | 20 +++++++++++++++----- research/direct-mixed-flow/RESULT.json | 2 +- research/direct-mixed-flow/TASK.json | 18 ++++++++++++++++++ research/direct-mixed-flow/verify.py | 4 ++++ 4 files changed, 38 insertions(+), 6 deletions(-) diff --git a/research/direct-mixed-flow/README.md b/research/direct-mixed-flow/README.md index 68af46c23d..2c6c576bc1 100644 --- a/research/direct-mixed-flow/README.md +++ b/research/direct-mixed-flow/README.md @@ -16,9 +16,10 @@ Two results are established under the source native-word hypotheses: unmatched job as an exit. All recursive ranks decrease. This gives a finite uniform compiler, **without a proved near-root saving**. 2. Choosing **nested divisible widths** gives `B_N <= exp(O(N log N))`. - Exact rank-one accounting also bounds raw instances, owned centers and - routing slots. This batching choice preserves the normalized leaf cost - and therefore applies to the already supported PR4433 supplier. + Exact rank-one accounting also bounds raw instances, owned centers, + routing slots and the source finite-constant envelopes. This batching + choice preserves the normalized leaf cost and therefore applies to the + already supported PR4433 supplier. The main exponent target remains open. Exact compilation at rank 1,000 on the raw p7 profile fails the desired saving. That finite failure is not an @@ -248,8 +249,8 @@ record allowances. Every owned bank has an explicit initialization record, so total allocated owned banks can also be bounded by R_bar; the sharper raw-center bound remains separate. This is a **description/record bound**, not a new tariff for executing a -general matrix or permutation. A dense binary address matrix and quadratic -phase have O(N^2) descriptor bits. Explicit role indices add O(log B_N) +general matrix or permutation. A Gaussian monomial adapter's dense binary +address matrix and quadratic phase have O(N^2) descriptor bits. Explicit role indices add O(log B_N) bits. Thus an encoding of this finite word still has `exp(O(N log N))` bits for a fixed unit and its finite coefficient alphabet. If physical expansion of one adapter needs F(N) native records, multiply @@ -449,6 +450,15 @@ unchanged exports by commit, full path, Git blob and SHA256. Their bytes and notices are preserved; direct replay needs no foreign Git objects. The source theorem and earlier finite compiler remain attributed hypotheses, not new work. +Local validation used Python 3.12.8 on macOS arm64. The registered replay, +metadata/pin check and committed-byte preflight passed. A separate Git-free +copy passed with `python3.12 -I -O -B verify.py`; changed-native-source and +changed-receipt controls both rejected. Replay uses exact integer arithmetic +and source hashes, with no network or foreign Git objects. The repository is +shallow, so a full source-history preflight was not attempted. No Lean, Docker, +full native/all-column admission, physical adapter expansion or historical +suite was run. Independent mathematical acceptance remains open. + The overlap refresh at 18:48 UTC covered 538 open PR bodies and 3,280 discussion/comment records, with complete reported pagination. Specific searches for direct overlapping-rank compilers, Pascal matching and nested diff --git a/research/direct-mixed-flow/RESULT.json b/research/direct-mixed-flow/RESULT.json index 4f305a54c0..e657f58b5a 100644 --- a/research/direct-mixed-flow/RESULT.json +++ b/research/direct-mixed-flow/RESULT.json @@ -480,7 +480,7 @@ ], "new_code_sha256": { "flow.py": "460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a", - "verify.py": "80ba21844b4f77b865091969edf9b8826362754df5efe714d366ee245ebf182f" + "verify.py": "9ae067eadf17ff9d97737805eb642a69375a5ff2ddb08988fef59aa0771f9b7c" }, "rejected_mutations": [ "whole integer subprogram batches", diff --git a/research/direct-mixed-flow/TASK.json b/research/direct-mixed-flow/TASK.json index 2164fdf04b..840f5deb45 100644 --- a/research/direct-mixed-flow/TASK.json +++ b/research/direct-mixed-flow/TASK.json @@ -126,5 +126,23 @@ "full_finite_size_bounds": "proved in declared encoded native-record grammar; explicit bounds for the existing PR4433 supplier", "direct_near_root_exponent": "open; requires a uniform boundary-exit/complement estimate", "scientific_significance_target": "in progress; not claimed achieved" + }, + "validation": { + "python": "3.12.8", + "platform": "macOS arm64", + "registered_replay": "pass", + "metadata_and_pins": "pass", + "committed_bytes": "pass", + "git_free_optimized": "pass", + "changed_native_source": "rejected", + "changed_receipt": "rejected", + "unrun": [ + "full source history (shallow checkout)", + "independent mathematical review", + "native all-column/physical/analytic/recovery admission", + "Lean", + "Docker", + "historical suites" + ] } } diff --git a/research/direct-mixed-flow/verify.py b/research/direct-mixed-flow/verify.py index 9bb5e4b310..df9ca12ad0 100644 --- a/research/direct-mixed-flow/verify.py +++ b/research/direct-mixed-flow/verify.py @@ -169,6 +169,10 @@ def inherited_rank_size_bound(): W0, P0 = sum(T.values()), sum(P.values()) Uproduct = sum(W0**(v-1-i)*P0**i for i in range(v)) need(Uproduct < 2**2392, 'chronological product raw-instance count') + strict_surplus = (sum(k*n for k,n in T.items())**v- + sum(k*n for k,n in P.items())**v) + need(strict_surplus > 0 and strict_surplus % 608 == 0 + and strict_surplus//608 >= Uproduct, 'expanded product raw-column identity') product_allowance = (2**40+32*v*(W0+P0+1))*Uproduct+32*v*P0**v completed_allowance = product_allowance+32*(paid_mass_upper+W+P0**v) # Include each dense binary chart/quadratic phase descriptor and role From daa027690db412c22d6674b7098c9e31fdbd62f7 Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 15:29:34 -0400 Subject: [PATCH 04/26] Record authorized publication of partial compiler checkpoint --- research/direct-mixed-flow/README.md | 3 ++- research/direct-mixed-flow/TASK.json | 2 +- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/research/direct-mixed-flow/README.md b/research/direct-mixed-flow/README.md index 2c6c576bc1..3be00f754b 100644 --- a/research/direct-mixed-flow/README.md +++ b/research/direct-mixed-flow/README.md @@ -1,6 +1,7 @@ # Direct mixed flow and explicit compiler size: a partial research checkpoint -**Local work for user review. Do not push or submit a PR yet.** +**Publication authorized by the user on October 21, 2026.** This is a partial +compiler/resource checkpoint; the direct exponent gate remains open. The target is a structural successor to [PR4433](https://github.com/CrocSwap/integer-mult-bounds/pull/4433): remove the diff --git a/research/direct-mixed-flow/TASK.json b/research/direct-mixed-flow/TASK.json index 840f5deb45..e232fd2674 100644 --- a/research/direct-mixed-flow/TASK.json +++ b/research/direct-mixed-flow/TASK.json @@ -93,7 +93,7 @@ "blocked_by": "Inherited native/physical/analytic premises remain outside this mathematical count proof." } ], - "publication_policy": "LOCAL ONLY until user review. Do not push, submit another PR or post Discussions.", + "publication_policy": "User explicitly authorized posting this PR on October 21, 2026. Subsequent research remains local for user review before submission; no Discussion posting is authorized by this checkpoint.", "significance_target": { "relative_to": "PR4433 higher-moment strictification", "requested_multiplier": 2, From 56003680aee2871773de408e5f01cc5dd46b144c Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 15:46:16 -0400 Subject: [PATCH 05/26] Align status and CI navigation with selected PR4359 --- docs/ci-verification.md | 19 +++++++++++++++++++ docs/research/current-status.md | 6 ++++-- 2 files changed, 23 insertions(+), 2 deletions(-) diff --git a/docs/ci-verification.md b/docs/ci-verification.md index 582e416aaf..4541cfa0e8 100644 --- a/docs/ci-verification.md +++ b/docs/ci-verification.md @@ -5,6 +5,25 @@ Start with the [selected record](../certificates/selected-result.json). Its `reproduce`, `review`, `source_manifest` and `validation` fields identify the replay command, scoped assessment, source bindings and integration evidence. +The selected checkpoint is #4359, documented in +[the proof review](research/pr-intake-evidence/pr4359/PROOF-REVIEW.md), +[the source manifest](../certificates/frontier4359-source.json) and +[the validation receipt](research/pr-intake-evidence/pr4359/VALIDATION.json). +The public cold replay is `make frontier4359-verify`; the configured +[frontier4359 workflow](../.github/workflows/frontier4359.yml) executes it +on Ubuntu 24.04 with Python 3.12 and the pinned requirements. Consult +[the integration receipt](research/pr-intake-evidence/pr4359/INTEGRATION.json) +and [workflow runs](https://github.com/CrocSwap/integer-mult-bounds/actions/workflows/frontier4359.yml) +for dated evidence and exact tested heads. + +`make selected-record-check` checks metadata and source/proof hashes. The +finite replay and changed-interface review retain the native/physical, +analytic, precision, fixed-tape and recovery hypotheses in the selected +record; they are not a full formal multiplication theorem. The winning +uniform templates are algorithm-defined and are not materialized. + +## Historical checkpoint through #1094 + At this checkpoint, the selected composition is #589 with #1094, documented in [the review](research/community-batch1099-review.md), [the source manifest](../research/community-frontier1094-audit/SELECTED-SOURCE.json) diff --git a/docs/research/current-status.md b/docs/research/current-status.md index 62a8cbb097..043a8cd78a 100644 --- a/docs/research/current-status.md +++ b/docs/research/current-status.md @@ -1,12 +1,14 @@ # Current reviewed status -Selected conditional κ: **0.0023 = 23/10000**, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. +Selected conditional κ: **0.0023** = 23/10000, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. [Selected record](../../certificates/selected-result.json) · [Proof review](pr-intake-evidence/pr4359/PROOF-REVIEW.md) · [Integration receipt](pr-intake-evidence/pr4359/INTEGRATION.json) · [Contributors](community-productive4359-contributors.md). Cold replay: `make frontier4359-verify`. The fresh 23-stage replay and 59 normalized artifacts pass; the changed interfaces have an AI-assisted proof review under retained analytic/native/fixed-tape hypotheses. Winning uniform templates are not materialized. This is not a complete formal or independent human verification. #4404 independently checks a narrower arithmetic/flow scope. -## Historical selected status through #1094 +The sections below are a historical snapshot; consult the selected record above for present status. + +## Historical checkpoint through #1094 Historical selected conditional κ: **0.001672660197076918**, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555. From 914a53a2300a1c2ea9ece15022e3f4d6c6be6272 Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 15:07:46 -0500 Subject: [PATCH 06/26] Construct query-thinned productive controllers at conditional kappa 0.00296 --- .../BIT-CONTROLLER.json | 2175 ++++++ .../COMPLEX-CONTROLLER.json | 5801 +++++++++++++++++ research/query-thinned-controllers/PROOF.md | 278 + research/query-thinned-controllers/README.md | 39 + .../query-thinned-controllers/RESULT.json | 356 + .../query-thinned-controllers/SOURCES.json | 120 + research/query-thinned-controllers/TASK.json | 86 + .../query-thinned-controllers/VALIDATION.md | 43 + .../query-thinned-controllers/VERIFY.json | 36 + .../query-thinned-controllers/controller.py | 208 + research/query-thinned-controllers/verify.py | 202 + 11 files changed, 9344 insertions(+) create mode 100644 research/query-thinned-controllers/BIT-CONTROLLER.json create mode 100644 research/query-thinned-controllers/COMPLEX-CONTROLLER.json create mode 100644 research/query-thinned-controllers/PROOF.md create mode 100644 research/query-thinned-controllers/README.md create mode 100644 research/query-thinned-controllers/RESULT.json create mode 100644 research/query-thinned-controllers/SOURCES.json create mode 100644 research/query-thinned-controllers/TASK.json create mode 100644 research/query-thinned-controllers/VALIDATION.md create mode 100644 research/query-thinned-controllers/VERIFY.json create mode 100644 research/query-thinned-controllers/controller.py create mode 100644 research/query-thinned-controllers/verify.py diff --git a/research/query-thinned-controllers/BIT-CONTROLLER.json b/research/query-thinned-controllers/BIT-CONTROLLER.json new file mode 100644 index 0000000000..89c400d597 --- /dev/null +++ b/research/query-thinned-controllers/BIT-CONTROLLER.json @@ -0,0 +1,2175 @@ +{ + "ambient_rank": 127, + "boundaries": { + "boundary_unit_ADDs_per_port": 160, + "coefficient_projectors": { + "12884901889": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1073741824, + 2147483648 + ], + "1367": [ + 1280, + 0, + 1280, + 0, + 1280, + 0, + 1280, + 0, + 1280, + 682, + 0, + 682, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "13958643713": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 268435456, + 536870912, + 0, + 0 + ], + "14227079169": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 67108864, + 134217728, + 0, + 0, + 0, + 0 + ], + "14294188033": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 16777216, + 33554432, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "14310965249": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 4194304, + 8388608, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "14315159553": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1048576, + 2097152, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "14316208129": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 262144, + 524288, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "14316470273": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 65536, + 131072, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "14316557655": [ + 16384, + 0, + 16384, + 0, + 16384, + 0, + 16384, + 0, + 16384, + 0, + 16384, + 0, + 16384, + 0, + 16384, + 43690, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "21847": [ + 20480, + 0, + 20480, + 0, + 20480, + 0, + 20480, + 0, + 20480, + 0, + 20480, + 0, + 20480, + 10922, + 0, + 10922, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "23": [ + 20, + 0, + 20, + 10, + 0, + 10, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "343": [ + 320, + 0, + 320, + 0, + 320, + 0, + 320, + 170, + 0, + 170, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "5463": [ + 5120, + 0, + 5120, + 0, + 5120, + 0, + 5120, + 0, + 5120, + 0, + 5120, + 2730, + 0, + 2730, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "7": [ + 5, + 2, + 0, + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "87": [ + 80, + 0, + 80, + 0, + 80, + 42, + 0, + 42, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "diagonal_monomials": [ + 7, + 7, + 23, + 23, + 87, + 87, + 343, + 343, + 1367, + 1367, + 5463, + 5463, + 21847, + 21847, + 12884901889, + 12884901889, + 13958643713, + 13958643713, + 14227079169, + 14227079169, + 14294188033, + 14294188033, + 14310965249, + 14310965249, + 14315159553, + 14315159553, + 14316208129, + 14316208129, + 14316470273, + 14316470273, + 14316557655, + 14316557655 + ], + "full_coefficient_endpoint_sha256": "0164c424ad261c955e105330fcec5942d9a863d1b6030f70e786f5cdafb2acef", + "left_program": [ + [ + "SWAP", + 30, + 31 + ], + [ + "SWAP", + 21, + 25 + ], + [ + "SWAP", + 20, + 24 + ], + [ + "SWAP", + 19, + 27 + ], + [ + "SWAP", + 18, + 26 + ], + [ + "SWAP", + 17, + 29 + ], + [ + "SWAP", + 16, + 28 + ], + [ + "SWAP", + 15, + 30 + ], + [ + "ADD", + 12, + 14 + ], + [ + "ADD", + 10, + 14 + ], + [ + "ADD", + 8, + 14 + ], + [ + "ADD", + 6, + 14 + ], + [ + "ADD", + 4, + 14 + ], + [ + "ADD", + 2, + 14 + ], + [ + "ADD", + 0, + 14 + ], + [ + "SWAP", + 14, + 31 + ], + [ + "ADD", + 30, + 13 + ], + [ + "ADD", + 10, + 12 + ], + [ + "ADD", + 8, + 12 + ], + [ + "ADD", + 6, + 12 + ], + [ + "ADD", + 4, + 12 + ], + [ + "ADD", + 2, + 12 + ], + [ + "ADD", + 0, + 12 + ], + [ + "SWAP", + 12, + 13 + ], + [ + "ADD", + 30, + 11 + ], + [ + "ADD", + 12, + 11 + ], + [ + "ADD", + 8, + 10 + ], + [ + "ADD", + 6, + 10 + ], + [ + "ADD", + 4, + 10 + ], + [ + "ADD", + 2, + 10 + ], + [ + "ADD", + 0, + 10 + ], + [ + "SWAP", + 10, + 11 + ], + [ + "ADD", + 30, + 9 + ], + [ + "ADD", + 12, + 9 + ], + [ + "ADD", + 10, + 9 + ], + [ + "ADD", + 6, + 8 + ], + [ + "ADD", + 4, + 8 + ], + [ + "ADD", + 2, + 8 + ], + [ + "ADD", + 0, + 8 + ], + [ + "SWAP", + 8, + 9 + ], + [ + "ADD", + 30, + 7 + ], + [ + "ADD", + 12, + 7 + ], + [ + "ADD", + 10, + 7 + ], + [ + "ADD", + 8, + 7 + ], + [ + "ADD", + 4, + 6 + ], + [ + "ADD", + 2, + 6 + ], + [ + "ADD", + 0, + 6 + ], + [ + "SWAP", + 6, + 7 + ], + [ + "ADD", + 30, + 5 + ], + [ + "ADD", + 12, + 5 + ], + [ + "ADD", + 10, + 5 + ], + [ + "ADD", + 8, + 5 + ], + [ + "ADD", + 6, + 5 + ], + [ + "ADD", + 2, + 4 + ], + [ + "ADD", + 0, + 4 + ], + [ + "SWAP", + 4, + 5 + ], + [ + "ADD", + 30, + 3 + ], + [ + "ADD", + 12, + 3 + ], + [ + "ADD", + 10, + 3 + ], + [ + "ADD", + 8, + 3 + ], + [ + "ADD", + 6, + 3 + ], + [ + "ADD", + 4, + 3 + ], + [ + "ADD", + 0, + 2 + ], + [ + "SWAP", + 2, + 3 + ], + [ + "ADD", + 30, + 1 + ], + [ + "ADD", + 12, + 1 + ], + [ + "ADD", + 10, + 1 + ], + [ + "ADD", + 8, + 1 + ], + [ + "ADD", + 6, + 1 + ], + [ + "ADD", + 4, + 1 + ], + [ + "ADD", + 2, + 1 + ] + ], + "left_rows": [ + 5, + 2, + 10, + 20, + 42, + 80, + 170, + 320, + 682, + 1280, + 2730, + 5120, + 10922, + 20480, + 1073741824, + 2147483648, + 268435456, + 536870912, + 67108864, + 134217728, + 16777216, + 33554432, + 4194304, + 8388608, + 1048576, + 2097152, + 262144, + 524288, + 65536, + 131072, + 43690, + 16384 + ], + "right_program": [ + [ + "ADD", + 13, + 31 + ], + [ + "SWAP", + 30, + 31 + ], + [ + "SWAP", + 21, + 25 + ], + [ + "SWAP", + 20, + 24 + ], + [ + "SWAP", + 19, + 27 + ], + [ + "SWAP", + 18, + 26 + ], + [ + "SWAP", + 17, + 29 + ], + [ + "SWAP", + 16, + 28 + ], + [ + "SWAP", + 15, + 31 + ], + [ + "SWAP", + 14, + 30 + ], + [ + "ADD", + 11, + 13 + ], + [ + "ADD", + 15, + 12 + ], + [ + "SWAP", + 12, + 13 + ], + [ + "ADD", + 9, + 11 + ], + [ + "ADD", + 13, + 10 + ], + [ + "SWAP", + 10, + 11 + ], + [ + "ADD", + 7, + 9 + ], + [ + "ADD", + 11, + 8 + ], + [ + "SWAP", + 8, + 9 + ], + [ + "ADD", + 5, + 7 + ], + [ + "ADD", + 9, + 6 + ], + [ + "SWAP", + 6, + 7 + ], + [ + "ADD", + 3, + 5 + ], + [ + "ADD", + 7, + 4 + ], + [ + "SWAP", + 4, + 5 + ], + [ + "ADD", + 0, + 3 + ], + [ + "ADD", + 5, + 2 + ], + [ + "SWAP", + 2, + 3 + ], + [ + "ADD", + 3, + 1 + ] + ], + "right_rows": [ + 2147494569, + 2, + 2147494568, + 6, + 2147494560, + 20, + 2147494528, + 80, + 2147494400, + 320, + 2147493888, + 1280, + 2147491840, + 5120, + 2147483648, + 1073745920, + 268435456, + 536870912, + 67108864, + 134217728, + 16777216, + 33554432, + 4194304, + 8388608, + 1048576, + 2097152, + 262144, + 524288, + 65536, + 131072, + 16384, + 32768 + ] + }, + "diagonal": [ + 7, + 7, + 23, + 23, + 87, + 87, + 343, + 343, + 1367, + 1367, + 5463, + 5463, + 21847, + 21847, + 12884901889, + 12884901889, + 13958643713, + 13958643713, + 14227079169, + 14227079169, + 14294188033, + 14294188033, + 14310965249, + 14310965249, + 14315159553, + 14315159553, + 14316208129, + 14316208129, + 14316470273, + 14316470273, + 14316557655, + 14316557655 + ], + "invoice": { + "main": { + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 25479, + "2": 24156, + "3": 1422, + "4": 792, + "5": 1836, + "6": 198, + "7": 342, + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + }, + "paid_calls": 57555, + "productive_fields": 11454, + "rank_surplus": 753, + "raw_scalar_record_bound": 1000000000, + "targets": { + "8": 7902, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "127": 222 + }, + "thick_calls": 18, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ], + "thin_queries": 1665, + "whole_idle": { + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + } + }, + "keep_mask": 35047648968703, + "kind": "bit", + "pairs": 16, + "physical_events": [ + [ + "LOCAL", + 0, + 0, + false + ], + [ + "LOCAL", + 1, + 0, + true + ], + [ + "IDLE", + 1, + [ + 0, + 1 + ] + ], + [ + "ADD", + 0, + 2 + ], + [ + "ADD", + 3, + 1 + ], + [ + "QUERY_SHEAR", + 2, + 0, + false + ], + [ + "ADD", + 0, + 2 + ], + [ + "ADD", + 3, + 1 + ], + [ + "LOCAL", + 3, + 1, + true + ], + [ + "IDLE", + 2, + [ + 0, + 1, + 3 + ] + ], + [ + "ADD", + 2, + 4 + ], + [ + "ADD", + 5, + 3 + ], + [ + "QUERY_SHEAR", + 4, + 1, + false + ], + [ + "ADD", + 2, + 4 + ], + [ + "ADD", + 5, + 3 + ], + [ + "LOCAL", + 5, + 2, + true + ], + [ + "IDLE", + 3, + [ + 0, + 1, + 3, + 5 + ] + ], + [ + "ADD", + 4, + 6 + ], + [ + "ADD", + 7, + 5 + ], + [ + "QUERY_SHEAR", + 6, + 2, + false + ], + [ + "ADD", + 4, + 6 + ], + [ + "ADD", + 7, + 5 + ], + [ + "LOCAL", + 7, + 3, + true + ], + [ + "IDLE", + 4, + [ + 0, + 1, + 3, + 5, + 7 + ] + ], + [ + "ADD", + 6, + 8 + ], + [ + "ADD", + 9, + 7 + ], + [ + "QUERY_SHEAR", + 8, + 3, + false + ], + [ + "ADD", + 6, + 8 + ], + [ + "ADD", + 9, + 7 + ], + [ + "LOCAL", + 9, + 4, + true + ], + [ + "IDLE", + 5, + [ + 0, + 1, + 3, + 5, + 7, + 9 + ] + ], + [ + "ADD", + 8, + 10 + ], + [ + "ADD", + 11, + 9 + ], + [ + "QUERY_SHEAR", + 10, + 4, + false + ], + [ + "ADD", + 8, + 10 + ], + [ + "ADD", + 11, + 9 + ], + [ + "LOCAL", + 11, + 5, + true + ], + [ + "IDLE", + 6, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11 + ] + ], + [ + "ADD", + 10, + 12 + ], + [ + "ADD", + 13, + 11 + ], + [ + "QUERY_SHEAR", + 12, + 5, + false + ], + [ + "ADD", + 10, + 12 + ], + [ + "ADD", + 13, + 11 + ], + [ + "LOCAL", + 13, + 6, + true + ], + [ + "IDLE", + 7, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13 + ] + ], + [ + "ADD", + 12, + 14 + ], + [ + "ADD", + 15, + 13 + ], + [ + "QUERY_SHEAR", + 14, + 6, + false + ], + [ + "ADD", + 12, + 14 + ], + [ + "ADD", + 15, + 13 + ], + [ + "LOCAL", + 15, + 7, + true + ], + [ + "ADD", + 14, + 16 + ], + [ + "ADD", + 17, + 15 + ], + [ + "QUERY_SHEAR", + 16, + 7, + false + ], + [ + "ADD", + 14, + 16 + ], + [ + "ADD", + 17, + 15 + ], + [ + "LOCAL", + 17, + 8, + true + ], + [ + "ADD", + 16, + 18 + ], + [ + "ADD", + 19, + 17 + ], + [ + "QUERY_SHEAR", + 18, + 8, + false + ], + [ + "ADD", + 16, + 18 + ], + [ + "ADD", + 19, + 17 + ], + [ + "LOCAL", + 19, + 9, + true + ], + [ + "ADD", + 18, + 20 + ], + [ + "ADD", + 21, + 19 + ], + [ + "QUERY_SHEAR", + 20, + 9, + false + ], + [ + "ADD", + 18, + 20 + ], + [ + "ADD", + 21, + 19 + ], + [ + "LOCAL", + 21, + 10, + true + ], + [ + "ADD", + 20, + 22 + ], + [ + "ADD", + 23, + 21 + ], + [ + "QUERY_SHEAR", + 22, + 10, + false + ], + [ + "ADD", + 20, + 22 + ], + [ + "ADD", + 23, + 21 + ], + [ + "LOCAL", + 23, + 11, + true + ], + [ + "ADD", + 22, + 24 + ], + [ + "ADD", + 25, + 23 + ], + [ + "QUERY_SHEAR", + 24, + 11, + false + ], + [ + "ADD", + 22, + 24 + ], + [ + "ADD", + 25, + 23 + ], + [ + "LOCAL", + 25, + 12, + true + ], + [ + "ADD", + 24, + 26 + ], + [ + "ADD", + 27, + 25 + ], + [ + "QUERY_SHEAR", + 26, + 12, + false + ], + [ + "ADD", + 24, + 26 + ], + [ + "ADD", + 27, + 25 + ], + [ + "LOCAL", + 27, + 13, + true + ], + [ + "ADD", + 26, + 28 + ], + [ + "ADD", + 29, + 27 + ], + [ + "QUERY_SHEAR", + 28, + 13, + false + ], + [ + "ADD", + 26, + 28 + ], + [ + "ADD", + 29, + 27 + ], + [ + "LOCAL", + 29, + 14, + true + ], + [ + "ADD", + 28, + 30 + ], + [ + "ADD", + 31, + 29 + ], + [ + "QUERY_SHEAR", + 30, + 14, + false + ], + [ + "ADD", + 28, + 30 + ], + [ + "ADD", + 31, + 29 + ], + [ + "LOCAL", + 31, + 15, + true + ], + [ + "LOCAL", + 32, + 15, + false + ], + [ + "IDLE", + 7, + [ + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 8, + [ + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 9, + [ + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 10, + [ + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 11, + [ + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 12, + [ + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 13, + [ + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 14, + [ + 31, + 32 + ] + ], + [ + "ADD", + 30, + 28 + ], + [ + "ADD", + 29, + 31 + ], + [ + "ADD", + 28, + 26 + ], + [ + "ADD", + 27, + 29 + ], + [ + "ADD", + 26, + 24 + ], + [ + "ADD", + 25, + 27 + ], + [ + "ADD", + 24, + 22 + ], + [ + "ADD", + 23, + 25 + ], + [ + "ADD", + 22, + 20 + ], + [ + "ADD", + 21, + 23 + ], + [ + "ADD", + 20, + 18 + ], + [ + "ADD", + 19, + 21 + ], + [ + "ADD", + 18, + 16 + ], + [ + "ADD", + 17, + 19 + ], + [ + "ADD", + 16, + 14 + ], + [ + "ADD", + 15, + 17 + ], + [ + "ADD", + 14, + 12 + ], + [ + "ADD", + 13, + 15 + ], + [ + "ADD", + 12, + 10 + ], + [ + "ADD", + 11, + 13 + ], + [ + "ADD", + 10, + 8 + ], + [ + "ADD", + 9, + 11 + ], + [ + "ADD", + 8, + 6 + ], + [ + "ADD", + 7, + 9 + ], + [ + "ADD", + 6, + 4 + ], + [ + "ADD", + 5, + 7 + ], + [ + "ADD", + 4, + 2 + ], + [ + "ADD", + 3, + 5 + ], + [ + "ADD", + 2, + 0 + ], + [ + "ADD", + 1, + 3 + ], + [ + "SWAP", + 0, + 1 + ], + [ + "SWAP", + 2, + 3 + ], + [ + "SWAP", + 4, + 5 + ], + [ + "SWAP", + 6, + 7 + ], + [ + "SWAP", + 8, + 9 + ], + [ + "SWAP", + 10, + 11 + ], + [ + "SWAP", + 12, + 13 + ], + [ + "SWAP", + 14, + 15 + ], + [ + "SWAP", + 16, + 17 + ], + [ + "SWAP", + 18, + 19 + ], + [ + "SWAP", + 20, + 21 + ], + [ + "SWAP", + 22, + 23 + ], + [ + "SWAP", + 24, + 25 + ], + [ + "SWAP", + 26, + 27 + ], + [ + "SWAP", + 28, + 29 + ], + [ + "SWAP", + 30, + 31 + ] + ], + "prefix_pairs": 7 +} diff --git a/research/query-thinned-controllers/COMPLEX-CONTROLLER.json b/research/query-thinned-controllers/COMPLEX-CONTROLLER.json new file mode 100644 index 0000000000..39318f6ad9 --- /dev/null +++ b/research/query-thinned-controllers/COMPLEX-CONTROLLER.json @@ -0,0 +1,5801 @@ +{ + "ambient_rank": 153, + "boundaries": { + "left": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "left_program": [ + [ + "SWAP", + 29, + 31 + ], + [ + "SWAP", + 28, + 29 + ], + [ + "SWAP", + 27, + 30 + ], + [ + "SWAP", + 25, + 27 + ], + [ + "SWAP", + 24, + 31 + ], + [ + "SWAP", + 23, + 27 + ], + [ + "SWAP", + 22, + 27 + ], + [ + "SWAP", + 21, + 23 + ], + [ + "SWAP", + 20, + 30 + ], + [ + "SWAP", + 19, + 24 + ], + [ + "SWAP", + 18, + 28 + ], + [ + "SWAP", + 17, + 33 + ], + [ + "ADD", + 14, + 16, + "1" + ], + [ + "ADD", + 12, + 16, + "-1" + ], + [ + "ADD", + 10, + 16, + "1" + ], + [ + "ADD", + 8, + 16, + "-1" + ], + [ + "ADD", + 6, + 16, + "1" + ], + [ + "ADD", + 4, + 16, + "-1" + ], + [ + "ADD", + 2, + 16, + "1" + ], + [ + "ADD", + 0, + 16, + "-1" + ], + [ + "ADD", + 33, + 15, + "-1" + ], + [ + "SCALE", + 15, + "-1" + ], + [ + "SWAP", + 15, + 32 + ], + [ + "ADD", + 12, + 14, + "1" + ], + [ + "ADD", + 10, + 14, + "-1" + ], + [ + "ADD", + 8, + 14, + "1" + ], + [ + "ADD", + 6, + 14, + "-1" + ], + [ + "ADD", + 4, + 14, + "1" + ], + [ + "ADD", + 2, + 14, + "-1" + ], + [ + "ADD", + 0, + 14, + "1" + ], + [ + "SWAP", + 14, + 15 + ], + [ + "ADD", + 33, + 13, + "1" + ], + [ + "ADD", + 32, + 13, + "1" + ], + [ + "SWAP", + 13, + 31 + ], + [ + "ADD", + 10, + 12, + "1" + ], + [ + "ADD", + 8, + 12, + "-1" + ], + [ + "ADD", + 6, + 12, + "1" + ], + [ + "ADD", + 4, + 12, + "-1" + ], + [ + "ADD", + 2, + 12, + "1" + ], + [ + "ADD", + 0, + 12, + "-1" + ], + [ + "SWAP", + 12, + 14 + ], + [ + "ADD", + 33, + 11, + "-1" + ], + [ + "ADD", + 32, + 11, + "-1" + ], + [ + "ADD", + 31, + 11, + "-1" + ], + [ + "SCALE", + 11, + "-1" + ], + [ + "SWAP", + 11, + 30 + ], + [ + "ADD", + 8, + 10, + "1" + ], + [ + "ADD", + 6, + 10, + "-1" + ], + [ + "ADD", + 4, + 10, + "1" + ], + [ + "ADD", + 2, + 10, + "-1" + ], + [ + "ADD", + 0, + 10, + "1" + ], + [ + "SWAP", + 10, + 13 + ], + [ + "ADD", + 33, + 9, + "1" + ], + [ + "ADD", + 32, + 9, + "1" + ], + [ + "ADD", + 31, + 9, + "1" + ], + [ + "ADD", + 30, + 9, + "1" + ], + [ + "SWAP", + 9, + 29 + ], + [ + "ADD", + 6, + 8, + "1" + ], + [ + "ADD", + 4, + 8, + "-1" + ], + [ + "ADD", + 2, + 8, + "1" + ], + [ + "ADD", + 0, + 8, + "-1" + ], + [ + "SWAP", + 8, + 12 + ], + [ + "ADD", + 33, + 7, + "-1" + ], + [ + "ADD", + 32, + 7, + "-1" + ], + [ + "ADD", + 31, + 7, + "-1" + ], + [ + "ADD", + 30, + 7, + "-1" + ], + [ + "ADD", + 29, + 7, + "-1" + ], + [ + "SCALE", + 7, + "-1" + ], + [ + "SWAP", + 7, + 28 + ], + [ + "ADD", + 4, + 6, + "1" + ], + [ + "ADD", + 2, + 6, + "-1" + ], + [ + "ADD", + 0, + 6, + "1" + ], + [ + "SWAP", + 6, + 11 + ], + [ + "ADD", + 33, + 5, + "1" + ], + [ + "ADD", + 32, + 5, + "1" + ], + [ + "ADD", + 31, + 5, + "1" + ], + [ + "ADD", + 30, + 5, + "1" + ], + [ + "ADD", + 29, + 5, + "1" + ], + [ + "ADD", + 28, + 5, + "1" + ], + [ + "SWAP", + 5, + 27 + ], + [ + "ADD", + 2, + 4, + "1" + ], + [ + "ADD", + 0, + 4, + "-1" + ], + [ + "SWAP", + 4, + 10 + ], + [ + "ADD", + 33, + 3, + "-1" + ], + [ + "ADD", + 32, + 3, + "-1" + ], + [ + "ADD", + 31, + 3, + "-1" + ], + [ + "ADD", + 30, + 3, + "-1" + ], + [ + "ADD", + 29, + 3, + "-1" + ], + [ + "ADD", + 28, + 3, + "-1" + ], + [ + "ADD", + 27, + 3, + "-1" + ], + [ + "SCALE", + 3, + "-1" + ], + [ + "SWAP", + 3, + 26 + ], + [ + "ADD", + 0, + 2, + "1" + ], + [ + "SWAP", + 2, + 9 + ], + [ + "ADD", + 33, + 1, + "1" + ], + [ + "ADD", + 32, + 1, + "1" + ], + [ + "ADD", + 31, + 1, + "1" + ], + [ + "ADD", + 30, + 1, + "1" + ], + [ + "ADD", + 29, + 1, + "1" + ], + [ + "ADD", + 28, + 1, + "1" + ], + [ + "ADD", + 27, + 1, + "1" + ], + [ + "ADD", + 26, + 1, + "1" + ], + [ + "SWAP", + 1, + 25 + ], + [ + "SWAP", + 0, + 8 + ] + ], + "right": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "right_program": [ + [ + "ADD", + 33, + 32, + "-1" + ], + [ + "SCALE", + 32, + "-1" + ], + [ + "ADD", + 32, + 31, + "1" + ], + [ + "ADD", + 30, + 31, + "-1" + ], + [ + "ADD", + 29, + 31, + "-1" + ], + [ + "ADD", + 28, + 31, + "-1" + ], + [ + "SCALE", + 31, + "-1" + ], + [ + "ADD", + 31, + 30, + "-1" + ], + [ + "ADD", + 29, + 30, + "-1" + ], + [ + "ADD", + 28, + 30, + "-1" + ], + [ + "SCALE", + 30, + "-1" + ], + [ + "ADD", + 31, + 29, + "-1" + ], + [ + "ADD", + 28, + 29, + "-1" + ], + [ + "SWAP", + 29, + 30 + ], + [ + "ADD", + 31, + 28, + "-1" + ], + [ + "SCALE", + 28, + "-1" + ], + [ + "ADD", + 31, + 27, + "1" + ], + [ + "ADD", + 26, + 27, + "-1" + ], + [ + "ADD", + 25, + 27, + "-1" + ], + [ + "SWAP", + 27, + 30 + ], + [ + "ADD", + 30, + 26, + "1" + ], + [ + "ADD", + 25, + 26, + "-1" + ], + [ + "SCALE", + 26, + "-1" + ], + [ + "ADD", + 30, + 25, + "1" + ], + [ + "SWAP", + 25, + 26 + ], + [ + "SWAP", + 24, + 29 + ], + [ + "SWAP", + 23, + 25 + ], + [ + "SWAP", + 22, + 23 + ], + [ + "SWAP", + 21, + 25 + ], + [ + "SWAP", + 20, + 27 + ], + [ + "SWAP", + 19, + 29 + ], + [ + "SWAP", + 18, + 31 + ], + [ + "SWAP", + 17, + 33 + ], + [ + "ADD", + 15, + 16, + "-1" + ], + [ + "ADD", + 14, + 15, + "-1" + ], + [ + "SWAP", + 15, + 32 + ], + [ + "ADD", + 13, + 14, + "-1" + ], + [ + "SWAP", + 14, + 32 + ], + [ + "ADD", + 12, + 13, + "-1" + ], + [ + "SWAP", + 13, + 24 + ], + [ + "ADD", + 11, + 12, + "-1" + ], + [ + "SWAP", + 12, + 32 + ], + [ + "ADD", + 10, + 11, + "-1" + ], + [ + "SWAP", + 11, + 20 + ], + [ + "ADD", + 9, + 10, + "-1" + ], + [ + "SWAP", + 10, + 24 + ], + [ + "ADD", + 8, + 9, + "-1" + ], + [ + "SWAP", + 9, + 28 + ], + [ + "SWAP", + 8, + 32 + ], + [ + "SWAP", + 7, + 18 + ], + [ + "SWAP", + 6, + 20 + ], + [ + "SWAP", + 5, + 22 + ], + [ + "SWAP", + 4, + 24 + ], + [ + "SWAP", + 3, + 26 + ], + [ + "SWAP", + 2, + 28 + ], + [ + "SWAP", + 1, + 30 + ], + [ + "SWAP", + 0, + 32 + ] + ] + }, + "diagonal": [ + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ] + ], + "invoice": { + "main": { + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "153": 224 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 49045, + "2": 13547, + "3": 4256, + "4": 1938, + "5": 380, + "8": 152, + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 448 + }, + "paid_calls": 72902, + "productive_fields": 11560, + "rank_surplus": 800, + "raw_scalar_record_bound": 1000000000, + "targets": { + "5": 532, + "6": 342, + "7": 1064, + "8": 1767, + "9": 4047, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448, + "153": 224 + }, + "thick_calls": 19, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 34 + ], + "thin_queries": 1792, + "whole_idle": { + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 448 + } + }, + "keep_mask": 280378328416255, + "kind": "complex", + "pairs": 17, + "physical_events": [ + [ + "LOCAL", + 0, + 0, + false + ], + [ + "LOCAL", + 1, + 0, + true + ], + [ + "IDLE", + 1, + [ + 0, + 1 + ] + ], + [ + "ADD", + 0, + 2, + 1 + ], + [ + "ADD", + 3, + 1, + -1 + ], + [ + "QUERY_SHEAR", + 2, + 0, + false + ], + [ + "ADD", + 0, + 2, + -1 + ], + [ + "ADD", + 3, + 1, + 1 + ], + [ + "LOCAL", + 3, + 1, + true + ], + [ + "IDLE", + 2, + [ + 0, + 1, + 3 + ] + ], + [ + "ADD", + 2, + 4, + 1 + ], + [ + "ADD", + 5, + 3, + -1 + ], + [ + "QUERY_SHEAR", + 4, + 1, + false + ], + [ + "ADD", + 2, + 4, + -1 + ], + [ + "ADD", + 5, + 3, + 1 + ], + [ + "LOCAL", + 5, + 2, + true + ], + [ + "IDLE", + 3, + [ + 0, + 1, + 3, + 5 + ] + ], + [ + "ADD", + 4, + 6, + 1 + ], + [ + "ADD", + 7, + 5, + -1 + ], + [ + "QUERY_SHEAR", + 6, + 2, + false + ], + [ + "ADD", + 4, + 6, + -1 + ], + [ + "ADD", + 7, + 5, + 1 + ], + [ + "LOCAL", + 7, + 3, + true + ], + [ + "IDLE", + 4, + [ + 0, + 1, + 3, + 5, + 7 + ] + ], + [ + "ADD", + 6, + 8, + 1 + ], + [ + "ADD", + 9, + 7, + -1 + ], + [ + "QUERY_SHEAR", + 8, + 3, + false + ], + [ + "ADD", + 6, + 8, + -1 + ], + [ + "ADD", + 9, + 7, + 1 + ], + [ + "LOCAL", + 9, + 4, + true + ], + [ + "IDLE", + 5, + [ + 0, + 1, + 3, + 5, + 7, + 9 + ] + ], + [ + "ADD", + 8, + 10, + 1 + ], + [ + "ADD", + 11, + 9, + -1 + ], + [ + "QUERY_SHEAR", + 10, + 4, + false + ], + [ + "ADD", + 8, + 10, + -1 + ], + [ + "ADD", + 11, + 9, + 1 + ], + [ + "LOCAL", + 11, + 5, + true + ], + [ + "IDLE", + 6, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11 + ] + ], + [ + "ADD", + 10, + 12, + 1 + ], + [ + "ADD", + 13, + 11, + -1 + ], + [ + "QUERY_SHEAR", + 12, + 5, + false + ], + [ + "ADD", + 10, + 12, + -1 + ], + [ + "ADD", + 13, + 11, + 1 + ], + [ + "LOCAL", + 13, + 6, + true + ], + [ + "IDLE", + 7, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13 + ] + ], + [ + "ADD", + 12, + 14, + 1 + ], + [ + "ADD", + 15, + 13, + -1 + ], + [ + "QUERY_SHEAR", + 14, + 6, + false + ], + [ + "ADD", + 12, + 14, + -1 + ], + [ + "ADD", + 15, + 13, + 1 + ], + [ + "LOCAL", + 15, + 7, + true + ], + [ + "IDLE", + 8, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15 + ] + ], + [ + "ADD", + 14, + 16, + 1 + ], + [ + "ADD", + 17, + 15, + -1 + ], + [ + "QUERY_SHEAR", + 16, + 7, + false + ], + [ + "ADD", + 14, + 16, + -1 + ], + [ + "ADD", + 17, + 15, + 1 + ], + [ + "LOCAL", + 17, + 8, + true + ], + [ + "ADD", + 16, + 18, + 1 + ], + [ + "ADD", + 19, + 17, + -1 + ], + [ + "QUERY_SHEAR", + 18, + 8, + false + ], + [ + "ADD", + 16, + 18, + -1 + ], + [ + "ADD", + 19, + 17, + 1 + ], + [ + "LOCAL", + 19, + 9, + true + ], + [ + "ADD", + 18, + 20, + 1 + ], + [ + "ADD", + 21, + 19, + -1 + ], + [ + "QUERY_SHEAR", + 20, + 9, + false + ], + [ + "ADD", + 18, + 20, + -1 + ], + [ + "ADD", + 21, + 19, + 1 + ], + [ + "LOCAL", + 21, + 10, + true + ], + [ + "ADD", + 20, + 22, + 1 + ], + [ + "ADD", + 23, + 21, + -1 + ], + [ + "QUERY_SHEAR", + 22, + 10, + false + ], + [ + "ADD", + 20, + 22, + -1 + ], + [ + "ADD", + 23, + 21, + 1 + ], + [ + "LOCAL", + 23, + 11, + true + ], + [ + "ADD", + 22, + 24, + 1 + ], + [ + "ADD", + 25, + 23, + -1 + ], + [ + "QUERY_SHEAR", + 24, + 11, + false + ], + [ + "ADD", + 22, + 24, + -1 + ], + [ + "ADD", + 25, + 23, + 1 + ], + [ + "LOCAL", + 25, + 12, + true + ], + [ + "ADD", + 24, + 26, + 1 + ], + [ + "ADD", + 27, + 25, + -1 + ], + [ + "QUERY_SHEAR", + 26, + 12, + false + ], + [ + "ADD", + 24, + 26, + -1 + ], + [ + "ADD", + 27, + 25, + 1 + ], + [ + "LOCAL", + 27, + 13, + true + ], + [ + "ADD", + 26, + 28, + 1 + ], + [ + "ADD", + 29, + 27, + -1 + ], + [ + "QUERY_SHEAR", + 28, + 13, + false + ], + [ + "ADD", + 26, + 28, + -1 + ], + [ + "ADD", + 29, + 27, + 1 + ], + [ + "LOCAL", + 29, + 14, + true + ], + [ + "ADD", + 28, + 30, + 1 + ], + [ + "ADD", + 31, + 29, + -1 + ], + [ + "QUERY_SHEAR", + 30, + 14, + false + ], + [ + "ADD", + 28, + 30, + -1 + ], + [ + "ADD", + 31, + 29, + 1 + ], + [ + "LOCAL", + 31, + 15, + true + ], + [ + "ADD", + 30, + 32, + 1 + ], + [ + "ADD", + 33, + 31, + -1 + ], + [ + "QUERY_SHEAR", + 32, + 15, + false + ], + [ + "ADD", + 30, + 32, + -1 + ], + [ + "ADD", + 33, + 31, + 1 + ], + [ + "LOCAL", + 33, + 16, + true + ], + [ + "LOCAL", + 34, + 16, + false + ], + [ + "IDLE", + 8, + [ + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 34 + ] + ], + [ + "IDLE", + 9, + [ + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 34 + ] + ], + [ + "IDLE", + 10, + [ + 23, + 25, + 27, + 29, + 31, + 33, + 34 + ] + ], + [ + "IDLE", + 11, + [ + 25, + 27, + 29, + 31, + 33, + 34 + ] + ], + [ + "IDLE", + 12, + [ + 27, + 29, + 31, + 33, + 34 + ] + ], + [ + "IDLE", + 13, + [ + 29, + 31, + 33, + 34 + ] + ], + [ + "IDLE", + 14, + [ + 31, + 33, + 34 + ] + ], + [ + "IDLE", + 15, + [ + 33, + 34 + ] + ], + [ + "ADD", + 32, + 30, + 1 + ], + [ + "ADD", + 31, + 33, + -1 + ], + [ + "ADD", + 30, + 28, + 1 + ], + [ + "ADD", + 29, + 31, + -1 + ], + [ + "ADD", + 28, + 26, + 1 + ], + [ + "ADD", + 27, + 29, + -1 + ], + [ + "ADD", + 26, + 24, + 1 + ], + [ + "ADD", + 25, + 27, + -1 + ], + [ + "ADD", + 24, + 22, + 1 + ], + [ + "ADD", + 23, + 25, + -1 + ], + [ + "ADD", + 22, + 20, + 1 + ], + [ + "ADD", + 21, + 23, + -1 + ], + [ + "ADD", + 20, + 18, + 1 + ], + [ + "ADD", + 19, + 21, + -1 + ], + [ + "ADD", + 18, + 16, + 1 + ], + [ + "ADD", + 17, + 19, + -1 + ], + [ + "ADD", + 16, + 14, + 1 + ], + [ + "ADD", + 15, + 17, + -1 + ], + [ + "ADD", + 14, + 12, + 1 + ], + [ + "ADD", + 13, + 15, + -1 + ], + [ + "ADD", + 12, + 10, + 1 + ], + [ + "ADD", + 11, + 13, + -1 + ], + [ + "ADD", + 10, + 8, + 1 + ], + [ + "ADD", + 9, + 11, + -1 + ], + [ + "ADD", + 8, + 6, + 1 + ], + [ + "ADD", + 7, + 9, + -1 + ], + [ + "ADD", + 6, + 4, + 1 + ], + [ + "ADD", + 5, + 7, + -1 + ], + [ + "ADD", + 4, + 2, + 1 + ], + [ + "ADD", + 3, + 5, + -1 + ], + [ + "ADD", + 2, + 0, + 1 + ], + [ + "ADD", + 1, + 3, + -1 + ], + [ + "SIGNED_SWAP", + 0, + 1 + ], + [ + "SIGNED_SWAP", + 2, + 3 + ], + [ + "SIGNED_SWAP", + 4, + 5 + ], + [ + "SIGNED_SWAP", + 6, + 7 + ], + [ + "SIGNED_SWAP", + 8, + 9 + ], + [ + "SIGNED_SWAP", + 10, + 11 + ], + [ + "SIGNED_SWAP", + 12, + 13 + ], + [ + "SIGNED_SWAP", + 14, + 15 + ], + [ + "SIGNED_SWAP", + 16, + 17 + ], + [ + "SIGNED_SWAP", + 18, + 19 + ], + [ + "SIGNED_SWAP", + 20, + 21 + ], + [ + "SIGNED_SWAP", + 22, + 23 + ], + [ + "SIGNED_SWAP", + 24, + 25 + ], + [ + "SIGNED_SWAP", + 26, + 27 + ], + [ + "SIGNED_SWAP", + 28, + 29 + ], + [ + "SIGNED_SWAP", + 30, + 31 + ], + [ + "SIGNED_SWAP", + 32, + 33 + ] + ], + "prefix_pairs": 8 +} diff --git a/research/query-thinned-controllers/PROOF.md b/research/query-thinned-controllers/PROOF.md new file mode 100644 index 0000000000..9068f42989 --- /dev/null +++ b/research/query-thinned-controllers/PROOF.md @@ -0,0 +1,278 @@ +# Query-thinned productive controllers + +## Conditional result + +Under the retained native, whole-job matching, owned-erasure, tape, analytic, +precision and exact-recovery contracts of #4359/#4416, the construction below +gives + + T(n) = O(n (log n)^(1 - kappa)), kappa = 37/12500 = 0.00296. + +This is a new author-checked conditional construction. It is not an +unconditional theorem, a formal-kernel proof, a practical implementation or a +change to the selected record. It improves #4416/#4433's conditional 0.00268647 +by about 10.1818%, and the selected 0.0023 checkpoint by about 28.6957%. +Those percentages compare exponent savings, not running times. + +The new mechanism replaces selected full native invocations by copied +rank-one query shears. Losing their productive helpers is charged. Removing +their stage multipliers also removes the corresponding parts of every idle +transform and main target. These coupled changes improve the complete moment; +merely deleting a local bill would not. + +## 1. Exact local interfaces + +Retain the source local word's all-column interpretation. For complex data, +on each of 112 ports write Q for its central rank-one Gaussian and D_s for +the commuting fresh eight-axis multiplier at stage s. Stage zero instead +uses the source nine-axis multiplier times Q^-1. The forward and backward +physical local maps are + + D_s S_y(Q^-1), D_s S_x(-Q). + +The complete THREE-base supplier has independent helper targets + + {5:28, 6:18, 7:56, 8:93, 9:213} + +and unsplit paid profile + + {1:2487, 2:713, 3:224, 4:102, 5:20, 8:8}. + +Its 408 helpers are arbitrary original fields. The one sequentially reused +owned center receives no productive credit. These source words and their +all-column/phase evidence are retained unchanged; this contribution does not +repeat their full historical physical replay. + +For BIT, retain the PR589 local word on 111 ports and 439 arbitrary helpers. +Each helper target has rank 8, D_s has rank 7, Q is the port's rank-one +projector involution, and the paid profile is + + {1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19}. + +Its nine copied-center episodes remain in that profile. Its rational charts +and common-weight delayed-cover interpretation remain explicit premises. + +### The new query-only call + +To implement S_y(Q^-1) on arbitrary X,Y, clear one owned stream Z, copy X +into Z, perform Q^-1 on Z, add Z to Y, and erase Z. Return X unchanged and +Z zero. Backward uses Q and subtracts from X. Each port costs exactly one +paid rank-one job, plus the copy/add/erase and fixed matching/routing work. +There is no independent input or output credit for Z. + +For complex data Q^-1 is one positive Gaussian followed by its physical +Pauli translation: the Z4 phases -q and q+2q agree. It is not replaced by Q +using an order-two assumption. For BIT Q^-1=Q. The same construction at +column multiplicity f makes a rank-f request; this cost is never treated as +a scalar operation. Erasure is the inherited owned-stream erasure operation, +not a claim about reversible or dirty-borrowed erasure. + +## 2. The two actual finite controller words + +Start with the credited paired path controller, keeping all middle idle +windows and splitting the initial/terminal windows at a. Let p be the pair +count, with 2p+1 local stages. Keep the full native call at stages + + S = {0, 2p} union {1,3,...,2p-1}. + +Replace each other local call by its query-only shear. In every idle word, +remove those same stage multipliers. Every scalar bridge and signed exchange +remains in its original chronological place. Thus there are p+2 full native +calls and p-1 query shears. Thin stages have no fresh axes or helpers. + +`controller.py` constructs the words and constant scalar boundaries. The +verifier replays the emitted LOCAL, QUERY_SHEAR, IDLE, ADD and exchange events +directly, compares with the original polynomial specialized by D_s=1 on thin +stages, and checks every coefficient of L A R against the advertised diagonal. +The complex check is over rational Laurent polynomials, with all Q signs +retained. BIT has a separate exact binary group-ring factorization. + +Only two finite words are needed: + +| Family | p | a | Full native calls | Query shears | Active ambient rank | +|---|---:|---:|---:|---:|---:| +| Complex | 17 | 8 | 19 | 16 | 153 | +| BIT | 16 | 7 | 18 | 15 | 127 | + +Unused fresh blocks can be removed by an injective relabeling. All noninitial +complex native contacts occur on the same old-nine plus fresh-eight space; +other blocks are fixed spectators. Exact forward/inverse phase checks on +all 112 ports establish this contact independently of the number of stages. +The initial native call is unchanged. The binary rational 15-dimensional +charts are likewise checked on all 111 ports. Tensoring these identities with +I_f preserves them for each positive column multiplicity under the inherited +all-column implementation contract. + +For block rank d and port count v, the main targets are two v-field copies +of rank 1+d(p+2), and two v-field copies of rank 1+d(j+1) for j=1..a and +j=1..p-1-a. The corresponding whole idle ranks are d(j+1), each with 2v +calls. The old one-stage middle idles have become identities. In addition, +there are (p+2) fresh helper inventories, (p+2) native paid inventories, and +v(p-1) paid rank-one queries. Literal and formula-derived ledgers agree. + +All helper identities are allocated freshly per full invocation. The main +fields, helpers and suspended centers have distinct physical slots. Scalar +boundary changes are invertible, so independent arbitrary main inputs remain +independent. Thin copies introduce no new sources. Center/query ownership is +retained until the relevant call returns, and every matcher is undone. + +The exact invoices are in RESULT.json. Their basic resource counts are: + +| Family | Productive fields | Paid jobs | Productive rank mass | Paid rank mass | Surplus | +|---|---:|---:|---:|---:|---:| +| Complex | 11,560 | 72,902 | 258,271 | 257,471 | 800 | +| BIT | 11,454 | 57,555 | 217,506 | 216,753 | 753 | + +Both paid and target ranks overlap. They are not directly admitted to the +strict compiler. Raw numerical roots near 0.002960345565 and 0.003464248972 +were discovery aids; the argument uses the exact strict tests below. + +## 3. Charged tensor completion and splitting + +Apply #4416's chronological product construction and #4433's higher-moment +tail theorem to each new native unit. This is composition of actual programs: +copies are paused at the same paid position, a complete child unit runs on +distinct current owners, and it returns before any parent resumes. Correlated +values in distinct slots are allowed. No product of sums of operator matrices +is substituted for this schedule. + +Write T_t,P_t for the raw moments, B for the productive field count, +t=1-C, and choose cutoff c, target floor b, u>=C and integer power v. +After the product finishes, complete every rank K2^26*N^5, also avoiding the finite denominators and +rank witnesses, exceeds 256/(C0-C1)*N^5 and pays the complete fallback. + +Change the atom power to delta=0.004. With retained old ordinary saving +a_old=0.0000384599, the ordinary saving is exactly + + (1-delta)*C1+delta*a_old = 0.0034363538396 > 0.0034. + +Admit 0.0034. The linear adapter has saving delta>0.0034363538396; stock +is sublinear because delta<1-0.0034363538396. The old delta=0.003 fails +this adapter comparison and is explicitly rejected. All compiled dimensions, +role counts, routes, centers and leaf counts replace the old p3 constants in +the delayed-cover stock formulas. For fixed compiled N,B,P, the borrowed +digits remain O(w log e)=o(e), with w=ceil(e^0.004). + +Put kappa=0.00296, C=0.00296030, d=(C-kappa)/7, and + + complex_uniform = kappa+6d, b=kappa+5d, + a=kappa+4d, q=kappa+3d, + epsilon=1-d, beta=1-3d, r0=d/10, stop=layout=d. + +Use the admitted BIT saving 0.0034 in the unchanged nine-row outer ledger. +All 54 named strict predicates and the three retained functional predicates +pass. An additional functional predicate binds the new BIT atom explicitly, +beta*(1-0.004)>0. The smallest outer saving exceeds kappa by +629378373/4900000000000000. Old BIT admission, zero layout, closed epsilon, +closed complex slack and an unfunded endpoint each fail their intended checks. + +## 5. Finite constants, precision and scope + +No new operation is declared free. Raw scalar programs, signed swaps, copy/ +erase records, affine port charts and inverse routes are finite emitted lists. +The conservative raw scalar record bound is 10^9, above the checked local, +query and boundary bills. Every query adds its own paid job and its own +fixed routing records. Initial/end charts and target normalizers are retained. + +For a raw unit with productive count B, paid count P and scalar bound L0, +a v-fold chronological product has at most +L0*v*(B+P)^v nonrecursive records before final completion. Its old paid rank +mass is P1^v, and added completion rank is at most B^v*b^v. Bound all new +completion/splitting records by their integer rank masses, then multiply by +10*m^(2v)+10 to cover whole-job normalizers and inverse routes. This is a +constructive finite overestimate, not a claim that those movements vanish. +Allocate a distinct center to each simultaneously suspended instance; a +bound by the total expanded record count suffices. The integer compiler adds +only finitely many effective classes and clears their batch denominators. + +Apply the retained semantic-precision and stock prescriptions to these new +finite lists, coefficient heights, prefix row norms, owned centers and +matchers. They are fixed constants before the asymptotic input size varies. +All raw complex boundary coefficients are unit signed scalars; native dyadic +coefficients and BIT rational cover entries retain their pinned bounds. A +brute-force product of per-record row-mass bounds supplies an effective +prefix bound if a sharper bound is unnecessary. Increase the fixed precision +constant and fixed stock coefficient accordingly. The outer slack conditions +are strict, so absorbing these fixed constants does not change their powers. +This inherits the same all-column, physical tape, native movement/repair, +precision, analytic and recovery contracts as the reviewed source; it does +not independently prove that historical implementation stack. + +## 6. Sources, attribution, validation and next questions + +Canonical baseline: 3a23e9d9d2e67833515d1c60a17e966bcdcab43c, priority +revision 7. Refreshed main and PR checks are recorded in TASK.json. Live +overlap covered all open PR bodies and Discussion pages; sparse local README +coverage and closed-PR-body coverage are incomplete. No novelty theorem is +claimed. #4194's coded/clean local hybrid addresses a different interface; +this construction uses complete native calls and copied rank-one shears. + +Credit: zxv for the retained controller/native construction and higher-moment +tail proof (#4359/#4433); Jacob Alan Sussman for mixed-target integer flow +(#4268); Cinna Davis for the p7 paid-completion/native construction (#4416); +DreamingOfClouds, eumemic and their retained PR589/PR555 BIT lineage; +David Ganz, Jeremy Kothe, Rohan Arun, Marius-Paul Dumitrean, Erwan Secousses +and the native/outer contributors named in the unchanged source notices and +the selected contributor map. New query-thinning construction, proofs and +checks were prepared for Cinna Davis with substantial OpenAI Codex assistance. +Apache-2.0. No subagents were used. + +Reproduce with the registered command in README.md. Finite source, physical +operator, phase, interval, invoice and outer checks support this written +conditional proof; they do not constitute formal verification. Full old native +word replays, Lean and Docker were not rerun for this contribution. + +Open next questions, with first steps and blockers, are in TASK.json. The +next useful audit is the whole-job/owned-query lowering at arbitrary column +multiplicity. The next improvement question is a changed local query/native +alphabet or controller topology. A larger path census alone gives no global +optimality or assurance of a stronger complete construction. diff --git a/research/query-thinned-controllers/README.md b/research/query-thinned-controllers/README.md new file mode 100644 index 0000000000..6d1099e9a5 --- /dev/null +++ b/research/query-thinned-controllers/README.md @@ -0,0 +1,39 @@ +# Conditional κ = 0.00296 through query-thinned productive controllers + +The new construction replaces selected full native calls by paid rank-one +query shears, charging the lost productive helpers and removing the same +stage multipliers from the idle and main transforms. It gives an author-checked +conditional multiplication saving **κ = 37/12500 = 0.00296**, approximately +**10.18% above #4416/#4433's 0.00268647**. + +The complex controller uses 17 pairs, 19 full native calls and 16 query shears. +The accompanying BIT controller uses 16 pairs, 18 full calls and 15 query +shears, supporting a stronger ordinary BIT saving of 0.0034 after all cover +and atom-conversion charges. The complete outer ledger passes at κ=0.00296. + +[PROOF.md](PROOF.md) gives the native query implementation, chronological +product and paid completion, effective compiler ranks, changed BIT stock +parameters, full cost/precision obligations, attribution and conditional scope. +[RESULT.json](RESULT.json) records the exact arithmetic and rejection controls. +The two controller JSON files contain their actual emitted event lists and +constant scalar boundary programs. `controller.py` regenerates them; normal +verification directly replays them without repeating factor discovery. + +```sh +python3.12 -B scripts/research_package.py --package research/query-thinned-controllers +python3.12 -O -B research/query-thinned-controllers/verify.py +``` + +See VALIDATION.md for the exact executed environments and commands. + +This retains the reviewed source's all-column native, owned-erasure, +whole-job matching, fixed-tape, precision, analytic, prime and recovery +premises. It claims no unconditional theorem, formal verification, practical +speedup, global controller optimum or selected-frontier change. + +## Open next questions + +Open next questions are recorded in [TASK.json](TASK.json), with relevance, +first steps and blockers. Prepared for Cinna Davis with substantial OpenAI +Codex assistance; no subagents. Apache-2.0. Source attribution is in PROOF.md +and the unchanged pinned predecessor notices. diff --git a/research/query-thinned-controllers/RESULT.json b/research/query-thinned-controllers/RESULT.json new file mode 100644 index 0000000000..e0695152c9 --- /dev/null +++ b/research/query-thinned-controllers/RESULT.json @@ -0,0 +1,356 @@ +{ + "bit_invoice": { + "main": { + "127": 222, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 25479, + "14": 444, + "2": 24156, + "21": 444, + "28": 444, + "3": 1422, + "35": 444, + "4": 792, + "42": 444, + "49": 444, + "5": 1836, + "56": 444, + "6": 198, + "63": 222, + "7": 342 + }, + "paid_calls": 57555, + "productive_fields": 11454, + "rank_surplus": 753, + "raw_scalar_record_bound": 1000000000, + "targets": { + "127": 222, + "15": 444, + "22": 444, + "29": 444, + "36": 444, + "43": 444, + "50": 444, + "57": 444, + "64": 222, + "8": 7902 + }, + "thick_calls": 18, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ], + "thin_queries": 1665, + "whole_idle": { + "14": 444, + "21": 444, + "28": 444, + "35": 444, + "42": 444, + "49": 444, + "56": 444, + "63": 222 + } + }, + "bit_strictification": { + "alpha": { + "lower": "0.999995735238059506641600561767", + "upper": "0.999995735238059506641600561768" + }, + "compiler_H0": 3755884544, + "cutoff_base": 17, + "delta": { + "lower": "0.949707924144871179442776557218", + "upper": "0.949707924144871179442776557219" + }, + "gamma": { + "lower": "0.957429821066420278606254392110", + "upper": "0.957429821066420278606254392111" + }, + "normalized_surplus_lower": "68719461047/16845935476736", + "tail_exponent": "1/5", + "target_floor_base": 18, + "tensor_power": 1024, + "tested_saving": "173/50000", + "uniform_H1": 25986965159937, + "uniform_N": "2^25986965159937", + "uniform_saving": "3459/1000000", + "winning_word_materialized": false + }, + "complex_invoice": { + "main": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 448 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 49045, + "16": 448, + "2": 13547, + "24": 448, + "3": 4256, + "32": 448, + "4": 1938, + "40": 448, + "48": 448, + "5": 380, + "56": 448, + "64": 448, + "72": 448, + "8": 152 + }, + "paid_calls": 72902, + "productive_fields": 11560, + "rank_surplus": 800, + "raw_scalar_record_bound": 1000000000, + "targets": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "5": 532, + "57": 448, + "6": 342, + "65": 448, + "7": 1064, + "73": 448, + "8": 1767, + "9": 4047 + }, + "thick_calls": 19, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 33, + 34 + ], + "thin_queries": 1792, + "whole_idle": { + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 448 + } + }, + "complex_strictification": { + "alpha": { + "lower": "0.999999952117240859760145478345", + "upper": "0.999999952117240859760145478346" + }, + "compiler_H0": 75415467350, + "cutoff_base": 20, + "delta": { + "lower": "0.941649713484853845388929204840", + "upper": "0.941649713484853845388929204841" + }, + "gamma": { + "lower": "0.967466409565147920980822933859", + "upper": "0.967466409565147920980822933860" + }, + "normalized_surplus_lower": "8589700209/251666829934592", + "tail_exponent": "1/5", + "target_floor_base": 21, + "tensor_power": 1024, + "tested_saving": "29603/10000000", + "uniform_H1": 10418370291022217, + "uniform_N": "2^10418370291022217", + "uniform_saving": "103609/35000000", + "winning_word_materialized": false + }, + "kappa": "37/12500", + "minimum_outer_margin_minus_kappa": "629378373/4900000000000000", + "native": { + "binary_charts": 111, + "complex_contacts_and_inverses": 896, + "owned_stream_restored_zero": true, + "thin_paid_rank_per_port": 1, + "thin_productive_credit": 0 + }, + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform_gap": [ + "new_complex_uniform_saving_above_b" + ], + "missing_layout": [ + "positive_layout_slack" + ], + "old_BIT_cap": [ + "actual_bit_above_effective" + ], + "unfunded_kappa": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "old_atom_rejected": true, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "17429997759/17500000000", + "fixed_halo_explicit_metadata_branch": "1347500003/17500000", + "new_BIT_row_stock_sublinear_in_active_group": "69789991027/70000000000", + "new_semantic_group_guard": "9/70000000" + }, + "margins": { + "boundary_algebraic_matrix": "14504839378373/4900000000000000", + "fused_gaussian": "14504838135119/4900000000000000", + "global_coordinate_router": "51803/17500000", + "group_bit_router": "3626262033773/1225000000000000", + "group_scans": "34999997/35000000", + "main_transform": "14504629378373/4900000000000000", + "microbox_face_corrections": "1347500003/17500000", + "polynomial_products": "69999997/70000000", + "sparse_union_movement": "2005129839378373/4900000000000000" + }, + "parameters": { + "a": "51803/17500000", + "b": "41443/14000000", + "beta": "69999991/70000000", + "bit_saving": "17/5000", + "cap_xi": "4455129629378373/4900000000000000", + "complex_uniform_saving": "103609/35000000", + "d": "3/70000000", + "epsilon": "69999997/70000000", + "kappa": "37/12500", + "lambda_": "19940797/20000000", + "lambda_prime": "69792791/70000000", + "layout": "3/70000000", + "q": "207209/70000000", + "r0": "3/700000000", + "stop": "3/70000000", + "tested_saving": "29603/10000000" + }, + "strict_checks": { + "actual_bit_above_effective": "7697/17500000", + "actual_logarithmic_gamma_guard": "3/70000000", + "actual_logarithmic_group_guard": "444870685621627/2450000000000000", + "alpha_logarithm_absorption": "3/700000000", + "boundary_algebraic_matrix_above_kappa": "839378373/4900000000000000", + "cap_above_band": "2005129629378373/4900000000000000", + "cap_below_cell": "444870160621627/4900000000000000", + "cap_below_phase_cell_power": "5344870370621627/4900000000000000", + "complex_above_effective": "3/70000000", + "complex_below_one_over_32": "396057/14000000", + "complex_endpoint": "3/35000000", + "epsilon_below_one": "3/70000000", + "epsilon_positive": "69999997/70000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "838135119/4900000000000000", + "gaussian_above_main": "104378373/2450000000000000", + "global_coordinate_router_above_kappa": "3/17500000", + "global_gamma_power_slack": "27/700000000", + "group_below_dimension": "3/35000000", + "group_bit_router_above_kappa": "262033773/1225000000000000", + "group_gauge_power_slack": "444870675121627/2450000000000000", + "group_key_fits_record": "3/35000000", + "group_positive": "69999991/70000000", + "group_scans_above_kappa": "34896397/35000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "614514790400418148631/500000000000000000000000", + "lambda_above_internal": "3/140000000", + "lambda_above_sigma": "9/140000000", + "lambda_above_tau": "3/140000000", + "lambda_prime_above_lambda": "3/140000000", + "lambda_prime_above_leaf": "83875671/980000000000000", + "leaf_saving_above_effective": "41875671/980000000000000", + "main_transform_above_kappa": "629378373/4900000000000000", + "membership_arithmetic_fits_record": "3/70000000", + "microbox_face_corrections_above_kappa": "1347448203/17500000", + "microbox_halo_volume": "5530000009/70000000", + "new_complex_uniform_saving_above_b": "3/70000000", + "new_semantic_guard_with_C1_one": "3/70000000", + "polynomial_products_above_kappa": "69792797/70000000", + "positive_layout_slack": "3/70000000", + "q_below_effective": "3/70000000", + "q_below_internal": "3/70000000", + "q_below_leaf": "83875671/980000000000000", + "q_positive": "207209/70000000", + "short_record_fallback": "13958557/14000000", + "source_axis_superpolynomial": "3/70000000", + "sparse_union_movement_above_kappa": "1990625839378373/4900000000000000", + "stop_below_one": "69999997/70000000", + "stop_positive": "3/70000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "9/70000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "9/70000000", + "union_tag_work_per_visit_fits_record": "9/70000000" + } + }, + "relative_gain_over_p7": "27353/268647", + "schema": "query-thinned-productive-controllers/1", + "scope": "Conditional native construction; all-column, erasure, whole-job matching, fixed-tape, precision, analytic, prime and exact-recovery premises retained. No unconditional theorem or selected promotion.", + "source_inputs_authenticated": 17, + "status": "PASS_CONDITIONAL_QUERY_THINNED_KAPPA_00296" +} diff --git a/research/query-thinned-controllers/SOURCES.json b/research/query-thinned-controllers/SOURCES.json new file mode 100644 index 0000000000..0f061c87ff --- /dev/null +++ b/research/query-thinned-controllers/SOURCES.json @@ -0,0 +1,120 @@ +{ + "schema_version": 1, + "base_commit": "3a23e9d9d2e67833515d1c60a17e966bcdcab43c", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/higher-moment-strictification/README.md", + "usage": "input", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "usage": "input", + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "usage": "input", + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef" + }, + { + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "usage": "input", + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0" + }, + { + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "usage": "input", + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "usage": "input", + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf" + }, + { + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "usage": "input", + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7" + }, + { + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "usage": "input", + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497" + }, + { + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "usage": "input", + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e" + }, + { + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "usage": "input", + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "usage": "input", + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6" + }, + { + "path": "research/pr4359-p7-padding/TENSOR.md", + "usage": "input", + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/pr4359-p7-padding/native_inventory.py", + "usage": "input", + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32" + }, + { + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "usage": "input", + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + } + ] +} diff --git a/research/query-thinned-controllers/TASK.json b/research/query-thinned-controllers/TASK.json new file mode 100644 index 0000000000..ebba49a09c --- /dev/null +++ b/research/query-thinned-controllers/TASK.json @@ -0,0 +1,86 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "priority_revision": 7, + "base_commit": "3a23e9d9d2e67833515d1c60a17e966bcdcab43c", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "changed", + "actual_scope": "Construct query-thinned complex and BIT productive controllers and carry their exact physical words, paid tails, ordinary BIT conversion and complete outer costs to conditional kappa 0.00296.", + "scope_change_reason": "Explicit user assignment to improve kappa using the new productive-helper mechanism. The current card predates the selected changed interface; this replaces its frozen local-packing question with a complete global native/query construction.", + "bottleneck_link": "Selected full-native path calls impose stage and idle transforms even where a paid rank-one shear suffices. Removing them changes the full target/paid moment; a stronger BIT admission is needed above the prior cap.", + "budget_minutes": 60, + "stop_rule": "Finish the two actual finite native/query words and all caller costs; reject the endpoint if physical query ownership, full invoice, paid completion, BIT cover/stock or any outer predicate fails.", + "outcome": "completed", + "evidence": "PROOF.md, RESULT.json, COMPLEX-CONTROLLER.json, BIT-CONTROLLER.json, VALIDATION.md", + "author": "Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in derivation, implementation, audit and writing; no subagents.", + "open_questions": [ + { + "question": "Can the arbitrary-column owned-query lowering receive an independent native/tape audit?", + "why_it_matters": "It is the new primitive interface connecting the physical word to the changed exponent.", + "first_step": "Replay one complex inverse query and one binary cover query at two column multiplicities, charging copy, matching, read and erasure.", + "blocked_by": "Independent native/tape review of the retained all-column contracts." + }, + { + "question": "Can a changed local query/native alphabet or branching controller exceed this complete moment?", + "why_it_matters": "The old all-native p7 screen does not constrain this changed alphabet.", + "first_step": "Define a different complete finite physical word and screen its full invoice before larger native reconstruction.", + "blocked_by": "No stronger complete native/query construction has been established." + } + ], + "upstream_checkpoint": { + "main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "checked_at_utc": "2026-10-21T20:06:00Z", + "priority_revision": 7, + "selected_kappa": "0.0023", + "stronger_reviewed_conditional_kappa": "0.00268647" + }, + "overlap_coverage": { + "open_prs": "296 bodies, complete pagination, 2026-10-21T19:50:54Z", + "discussions": "3284 records, complete pagination, 2026-10-21T19:51:43Z", + "local_readmes": "sparse; incomplete", + "closed_pr_bodies": "not exhaustively searched", + "additional_checks": "PR4194 coded/clean hybrid differs; PR4433 higher-moment theorem adopted. Frontier rechecked at 19:33, 19:51 and 20:06 UTC, through #4439; no higher kappa found." + } +} diff --git a/research/query-thinned-controllers/VALIDATION.md b/research/query-thinned-controllers/VALIDATION.md new file mode 100644 index 0000000000..2924d84be3 --- /dev/null +++ b/research/query-thinned-controllers/VALIDATION.md @@ -0,0 +1,43 @@ +# Validation and limits + +Environment: Linux x86_64, CPython **3.12.14** (bundled runtime). Initial +factor discovery also ran on CPython 3.14.8. Standard library only. No +subagents, Lean build, Docker run or full historical suite. + +Completed on 2026-10-21: + +- `python3.12 -B scripts/research_package.py --package research/query-thinned-controllers --check-only` + passes metadata and all 17 input pins. +- `python3.12 -B scripts/research_package.py --package research/query-thinned-controllers` + passes the complete registered replay. +- `python3.12 -O -B research/query-thinned-controllers/verify.py` passes + from a separate **Git-free export** containing this package and exactly the + declared input files. Its RESULT.json agrees with the normal replay. +- The two external rejection controls also run in that Git-free export under + optimized Python. Appending a comment to the pinned interval source rejects + with `Changed source`. Changing an emitted QUERY_SHEAR to LOCAL rejects the + physical-event equality check. Both altered export files were restored; + no canonical predecessor file was changed. +- Internal controls execute omitted-clear and omitted-erase query words, + reverse a query's actual orientation, change a Laurent coefficient, retain + the old BIT cap or atom, close the complex/epsilon gap, omit layout, and + request the unfunded outer endpoint. Their intended gates reject. + +The exact native contacts include 896 complex forward/inverse checks and +111 rational binary charts. Both complete physical event lists are replayed. +Two rational interval implementations agree on the strict native moments. +The complete charged tensor tails, effective compiler ranks, ordinary BIT +cover/conversion and nine-row outer ledger pass. All 54 strict outer +predicates, three inherited functional predicates and the added stock guard +are retained. + +The actual local full-native words and their all-column implementation are +reused from the pinned reviewed lineage. Their entire historical physical +stack was not rerun. New winning tensor/uniform words are specified by +finite algorithms; their enormous instruction lists have not been emitted. +No finite pass establishes an unconditional theorem or formal verification. + +The exact-commit preflight and source-history check are run after committing +the package; the submitted PR describes their result and hosted CI separately. +All reports retain the inherited native, whole-job, owned-erasure, fixed-tape, +precision, analytic, prime-supply and exact-recovery proof boundaries. diff --git a/research/query-thinned-controllers/VERIFY.json b/research/query-thinned-controllers/VERIFY.json new file mode 100644 index 0000000000..768aad6d68 --- /dev/null +++ b/research/query-thinned-controllers/VERIFY.json @@ -0,0 +1,36 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/verify.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "research/kappa-rebuild/bit/bit_native_binding.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-rebuild/bit/mixed_productive_bit.py", + "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "research/pr4359-p7-padding/TENSOR.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/pr4359-p7-padding/native_inventory.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Authenticate source blobs; replay both emitted physical controller words and exact boundary programs; native phase and rational chart checks; full query, completion, compiler, BIT cover and outer costs with negative controls." + } + ] +} diff --git a/research/query-thinned-controllers/controller.py b/research/query-thinned-controllers/controller.py new file mode 100644 index 0000000000..d4557e08cf --- /dev/null +++ b/research/query-thinned-controllers/controller.py @@ -0,0 +1,208 @@ +#!/usr/bin/env python3 +"""Exact native/query controller construction. Apache-2.0; Codex assistance.""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def engines(): + reference = ROOT/'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py' + load(reference, 'joint_pair_dag') + base = ROOT/'research/kappa-rebuild/bit' + bit = load(base/'mixed_productive_bit.py', 'mixed_productive_bit') + complex_ = load(base/'complex_controller_factor.py', 'query_complex_factor') + return bit, complex_ + + +def keep_mask(p, a): + b = p-1-a + return sum(1 << i for i in list(range(1, 2*p-2, 2))+ + list(range(0, 2*a, 2))+list(range(3*(p-1)-b, 3*(p-1)))) + + +def thick_stages(p): + return {0, 2*p, *range(1, 2*p, 2)} + + +def specialize_complex(coefficients, thick): + result = {} + for term, matrix in coefficients.items(): + key = (term[0],)+tuple(x if s in thick else 0 for s, x in enumerate(term[1:])) + out = result.setdefault(key, [[Q(0)]*len(matrix) for _ in matrix]) + for i, row in enumerate(matrix): + for j, value in enumerate(row): + out[i][j] += value + return {k: m for k, m in result.items() if any(any(row) for row in m)} + + +def specialize_bit(coefficients, thick): + keep = 1+sum(1 << (s+1) for s in thick) + out = {} + for term, matrix in coefficients.items(): + key = term & keep + old = out.setdefault(key, [0]*len(matrix)) + for i, row in enumerate(matrix): + old[i] ^= row + return {k: m for k, m in out.items() if any(m)} + + +def replay_events(events, p, kind): + """Literal second replay of the emitted word, including query-only gates.""" + _, engine = engines() + size, stages = 2*p, 2*p+1 + zero = (0,)*(stages+1) + matrix = [[{zero: Q(i == j)} if i == j else {} for j in range(size)] for i in range(size)] + for event in events: + op = event[0] + if op in ('LOCAL', 'QUERY_SHEAR'): + _, stage, pair, backward = event + x, y = 2*pair, 2*pair+1 + if backward: x, y = y, x + term = (1 if backward else -1,)+(0,)*stages + matrix[y] = [engine.plus(a, engine.monomial_times(b, term, -1 if backward else 1)) for a, b in zip(matrix[y], matrix[x])] + if op == 'LOCAL': + term = (0,)+tuple(int(s == stage) for s in range(stages)) + for role in (x, y): matrix[role] = [engine.monomial_times(a, term) for a in matrix[role]] + elif op == 'IDLE': + _, pair, selected = event + term = (0,)+tuple(int(s in selected) for s in range(stages)) + for role in (2*pair, 2*pair+1): matrix[role] = [engine.monomial_times(a, term) for a in matrix[role]] + elif op == 'ADD': + _, dst, src, *coefficient = event + c = coefficient[0] if coefficient else 1 + matrix[dst] = [engine.plus(a, b, c) for a, b in zip(matrix[dst], matrix[src])] + elif op in ('SWAP', 'SIGNED_SWAP'): + _, x, y = event + matrix[x], matrix[y] = matrix[y], [engine.monomial_times(a, zero, -1 if op == 'SIGNED_SWAP' else 1) for a in matrix[x]] + else: + raise ValueError('Unknown emitted event: '+op) + result = {} + for i, row in enumerate(matrix): + for j, poly in enumerate(row): + for key, value in poly.items(): + if kind == 'complex': + result.setdefault(key, [[Q(0)]*size for _ in range(size)])[i][j] += value + elif value.numerator % 2: + need(value.denominator == 1, 'Integral binary replay coefficient') + term = (key[0] % 2)+sum((exponent % 2) << (s+1) for s, exponent in enumerate(key[1:])) + result.setdefault(term, [0]*size)[i] ^= 1 << j + return {k: m for k, m in result.items() if any(any(r) for r in m)} if kind == 'complex' else {k: m for k, m in result.items() if any(m)} + + +def inventories(kind, p, a, diagonal, idles): + thick = thick_stages(p) + ports, block = (112, 8) if kind == 'complex' else (111, 7) + if kind == 'complex': + local = json.loads((ROOT/'research/kappa-rebuild/complex/full-identity-certificates/RESULT.json').read_text())['providers']['THREE-base'] + helpers = {int(k): v for k, v in local['helper_boundary']['widths'].items()} + children = {int(k): v for k, v in local['unsplit_replays']['forward']['paid_profile'].items()} + selected = [[s for s, x in enumerate(term[1:]) if x] for term in diagonal] + need(all(term[0] in (-1, 1) for term in diagonal), 'Only legal central Gaussian normalizers') + else: + helpers = {8: 439} + children = {1: 1323, 2: 1342, 3: 79, 4: 44, 5: 102, 6: 11, 7: 19} + selected = [[s for s in range(2*p+1) if term >> (s+1) & 1] for term in diagonal] + need(all(term & 1 for term in diagonal), 'Every binary main output retains its central rank-one factor') + targets = Counter({r: len(thick)*n for r, n in helpers.items()}) + paid = Counter({r: len(thick)*n for r, n in children.items()}) + thin_calls = ports*(2*p+1-len(thick)) + paid[1] += thin_calls + main = Counter() + for stages in selected: + need(set(stages) <= thick, 'No removed stage receives output credit') + main[1+block*len(stages)] += ports + targets.update(main) + idle = Counter() + for row in idles: + if row['retained']: + rank = block*len(thick.intersection(row['stages'])) + if rank: + idle[rank] += 2*ports + paid.update(idle) + # A second derivation uses only the declared prefix/suffix intervals. + expected_main = Counter({1+block*(p+2): 2*ports}) + expected_idle = Counter() + for length in (a, p-1-a): + for j in range(1, length+1): + expected_main[1+block*(j+1)] += 2*ports + expected_idle[block*(j+1)] += 2*ports + need(main == expected_main and idle == expected_idle, 'Literal and interval-derived complete invoices agree') + surplus = sum(r*n for r, n in targets.items())-sum(r*n for r, n in paid.items()) + need(surplus == (48*len(thick)-112 if kind == 'complex' else 48*len(thick)-111), 'Rank mass includes every query and lost helper') + return {'targets': dict(sorted(targets.items())), 'paid': dict(sorted(paid.items())), + 'main': dict(sorted(main.items())), 'whole_idle': dict(sorted(idle.items())), + 'productive_fields': sum(targets.values()), 'paid_calls': sum(paid.values()), + 'rank_surplus': surplus, 'thin_queries': thin_calls, + 'thick_calls': len(thick), 'thick_stages': sorted(thick), + 'raw_scalar_record_bound': 10**9, 'owned_streams_reused_sequentially': 1} + + +def run(kind, p, a): + bit, complex_ = engines() + mask = keep_mask(p, a) + thick = thick_stages(p) + if kind == 'complex': + coefficients, events, idles = complex_.controller(p, mask) + coefficients = specialize_complex(coefficients, thick) + factor = complex_.factor(coefficients) + need(factor is not None, 'Exact rational Laurent simultaneous factorization') + diagonal = factor['diagonal'] + boundaries = {'left': complex_.serialize_matrix(factor['left']), + 'right': complex_.serialize_matrix(factor['right']), + 'left_program': factor['left_program'], 'right_program': factor['right_program']} + need(all(Q(row[-1]) in (1, -1) for program in (factor['left_program'], factor['right_program']) + for row in program if row[0] in ('ADD', 'SCALE')), 'Unit scalar boundary coefficients') + else: + coefficients, events, idles = bit.physical_controller(p, mask) + coefficients = specialize_bit(coefficients, thick) + factor = bit.simultaneous_monomial_factor(coefficients) + need(factor is not None, 'Exact binary group-ring simultaneous factorization') + diagonal = factor['diagonal_monomials'] + boundaries = factor + invoice = inventories(kind, p, a, diagonal, idles) + new_events = [] + for row in events: + if row[0] == 'LOCAL' and row[1] not in thick: + new_events.append(['QUERY_SHEAR', *row[1:]]) + elif row[0] == 'IDLE': + selected = ([s for s in row[2] if s in thick] if kind == 'complex' else + [s for s in range(2*p+1) if row[2] >> (s+1) & 1 and s in thick]) + if selected: + new_events.append(['IDLE', row[1], selected]) + else: + new_events.append(row) + need(sum(row[0] == 'LOCAL' for row in new_events) == p+2, 'Exactly p+2 full native calls') + need(sum(row[0] == 'QUERY_SHEAR' for row in new_events) == p-1, 'Exactly p-1 copied-query shears') + return {'kind': kind, 'pairs': p, 'prefix_pairs': a, 'keep_mask': mask, + 'ambient_rank': 1+(8 if kind == 'complex' else 7)*(p+2), + 'diagonal': diagonal, 'boundaries': boundaries, + 'physical_events': new_events, 'invoice': invoice} + + +if __name__ == '__main__': + for kind, p, a in [('complex', 17, 8), ('bit', 16, 7)]: + row = run(kind, p, a) + path = HERE/(kind.upper()+'-CONTROLLER.json') + path.write_text(json.dumps(row, indent=2, sort_keys=True)+'\n') + print(kind, row['invoice'], flush=True) diff --git a/research/query-thinned-controllers/verify.py b/research/query-thinned-controllers/verify.py new file mode 100644 index 0000000000..f1114036ff --- /dev/null +++ b/research/query-thinned-controllers/verify.py @@ -0,0 +1,202 @@ +#!/usr/bin/env python3 +"""Exact finite replay for the conditional query-thinned construction. + +Apache-2.0. Prepared for Cinna Davis with substantial OpenAI Codex assistance. +Retains zxv's native/factor/tail work and Jacob Alan Sussman's integer flow. +""" +from fractions import Fraction as Q +from hashlib import sha1, sha256 +import argparse +import json +import sys +sys.dont_write_bytecode = True +import controller as C +HERE, ROOT, need = C.HERE, C.ROOT, C.need + + +def encode(x): + if isinstance(x, Q): return str(x) + if isinstance(x, dict): return {str(k): encode(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): return [encode(v) for v in x] + return x + + +def authenticate(): + count = 0 + for row in json.loads((HERE/'SOURCES.json').read_text())['files']: + if row['usage'] != 'input': continue + path = ROOT/row['path']; raw = path.read_bytes() + need(not path.is_symlink(), 'No source alias') + need(sha256(raw).hexdigest() == row['sha256'], 'Changed source: '+row['path']) + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], 'Changed Git blob') + count += 1 + return count + + +def controllers(): + B, E = C.engines(); result = {} + for kind, p, a in [('complex', 17, 8), ('bit', 16, 7)]: + row = json.loads((HERE/(kind.upper()+'-CONTROLLER.json')).read_text()) + thick, mask = C.thick_stages(p), C.keep_mask(p, a) + if kind == 'complex': + coefficients, events, idles = E.controller(p, mask) + coefficients = C.specialize_complex(coefficients, thick) + left = [[Q(x) for x in r] for r in row['boundaries']['left']] + right = [[Q(x) for x in r] for r in row['boundaries']['right']] + diagonal = [tuple(term) for term in row['diagonal']] + transformed = {k: B.matrix_multiply(B.matrix_multiply(left, m), right) for k, m in coefficients.items()} + expected = {k: [[Q(i == j and diagonal[i] == k) for j in range(2*p)] for i in range(2*p)] for k in set(diagonal)} + need(transformed == expected, 'All exact rational Laurent coefficients, including signs and Q powers') + for name, matrix in [('left', left), ('right', right)]: + need(E.scalar_program(matrix) == row['boundaries'][name+'_program'], 'Literal unit scalar boundary program') + changed = dict(coefficients) + k = next(iter(changed)); changed[k] = [r[:] for r in changed[k]]; changed[k][0][0] += 1 + need(B.matrix_multiply(B.matrix_multiply(left, changed[k]), right) != expected.get(k), 'A changed physical coefficient is rejected') + else: + coefficients, events, idles = B.physical_controller(p, mask) + coefficients = C.specialize_bit(coefficients, thick) + fresh = B.simultaneous_monomial_factor(coefficients) + need(fresh == row['boundaries'], 'Exact binary physical operator and scalar boundaries') + diagonal = fresh['diagonal_monomials'] + need(C.replay_events(row['physical_events'], p, kind) == coefficients, + 'Emitted native/query/idle word equals the specialized physical source') + mutant = json.loads(json.dumps(row['physical_events'])) + # Every removed stage is forward; changing its direction must change + # the actual operator rather than merely a tariff field. + next(ev for ev in mutant if ev[0] == 'QUERY_SHEAR')[3] = True + need(C.replay_events(mutant, p, kind) != coefficients, 'Wrong query orientation rejected') + invoice = C.inventories(kind, p, a, diagonal, idles) + ports = 112 if kind == 'complex' else 111 + boundary_records = (sum(len(row['boundaries'][name+'_program']) for name in ('left', 'right')) + if kind == 'complex' else row['boundaries']['boundary_unit_ADDs_per_port']) + scalar_upper = (p+2)*10**6+16*invoice['thin_queries']+32*ports*(len(row['physical_events'])+boundary_records) + need(scalar_upper < invoice['raw_scalar_record_bound'], 'Conservative complete scalar/route count fits') + need(encode(invoice) == row['invoice'], 'Literal and closed-form complete '+kind+' invoice') + result[kind] = invoice + return result + + +def native_contacts(): + n = C.load(ROOT/'research/pr4359-p7-padding/native_inventory.py', 'thinned_native_phases') + phases = json.loads((ROOT/'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json').read_text()) + axes = tuple(1 << i for i in range(17)); old = [(a, 1) for a in axes[:9]]; fresh = [(a, 1) for a in axes[9:]] + checks = 0 + for recipe in phases['recipes']: + q = recipe['q']; basis = recipe['idle_children'][0]['orthogonal_axes'][:8] + need(all((b&q).bit_count() % 2 == 0 for b in basis), 'Old eight-space perpendicular to q') + swaps = [b ^ axes[9+i] for i, b in enumerate(basis)] + route = tuple(e ^ n.act(swaps, sum(((e&v).bit_count() % 2) << i for i, v in enumerate(swaps))) for e in axes) + need(all(n.act(route, route[i]) == axes[i] for i in range(17)), 'Exact physical route inverse') + need(all((a&b).bit_count() % 2 == int(i == j) for i, a in enumerate(route) for j, b in enumerate(route)), 'Orthogonal physical route') + need(n.act(route, q) == q, 'Central query direction fixed') + need(n.polynomial(n.norm([(q, -1)]), 17) == n.polynomial(n.norm([(q, 1), (q, 2)]), 17), + 'Inverse thin Gaussian is one positive query and a physical translation') + for sign in (-1, 1): + raw = (n.norm(old), n.norm(old+[(q, -1)])) + entry = (n.norm(fresh+[(q, sign)]), n.norm(fresh)) + out0 = n.norm(fresh+[(a, sign) for a in axes[:9]]) + local_out = (out0, n.norm(list(out0)+[(q, -sign)])) + out = (n.norm(old+fresh), n.norm(old+fresh+[(q, -1)])) + for x, y in list(zip(raw, entry))+list(zip(local_out, out)): + n.contact(x, y, route, 17); checks += 1 + for x, y in zip(raw, out): + need(n.polynomial(n.norm(list(y)+[(a, -c) for a, c in x]), 17) == n.polynomial(n.norm(fresh), 17), 'Exactly the fresh eight-axis multiplier') + bit = C.load(ROOT/'research/kappa-rebuild/bit/bit_native_binding.py', 'thinned_binary_charts') + ports = json.loads((ROOT/'research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json').read_text())['ports'] + local = json.loads((ROOT/'research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json').read_text())['local'] + for direction in local['signed_directions']: + need({int(k): v for k, v in direction['profile'].items()} == C.engines()[0].LOCAL, + 'Every actual binary local child remains charged') + need(direction['unit_ADDs'] < 10**6 and direction['owned_COPY_episodes'] == 9, + 'Native binary scalar and owned-center bills retained') + for row in ports: + p = [[Q(x) for x in r] for r in row['central_projector']]; rho = [[Q(x) for x in r] for r in row['chart_15']] + active = [[p[i][j] if i < 8 and j < 8 else Q(i == j and i >= 8) for j in range(15)] for i in range(15)] + full = [[Q(i == j and i < 8) for j in range(15)] for i in range(15)] + need(bit.multiply(rho, rho) == bit.ident(15) and bit.multiply(bit.multiply(rho, active), rho) == full, 'BIT exact arbitrary-column chart') + need(bit.multiply(p, p) == p and sum(p[i][i] for i in range(8)) == 1, 'BIT query rank one') + # Formal independent X,Y,Z columns. Mutants execute the same word with + # an actual omitted operation; they are not merely different receipts. + for e in (-1, 1): + def execute(clear=True, erase=True): + x, y, z = {('X', 0): 1}, {('Y', 0): 1}, {('Z', 0): 1} + if clear: z = {} + for key, value in x.items(): z[key] = z.get(key, 0)+value + z = {(name, power+e): value for (name, power), value in z.items()} + for key, value in z.items(): y[key] = y.get(key, 0)+(-1 if e == 1 else 1)*value + if erase: z = {} + return x, y, z + expected = ({('X', 0): 1}, {('Y', 0): 1, ('X', e): -1 if e == 1 else 1}, {}) + need(execute() == expected, 'Completed arbitrary-input owned-query shear') + need(execute(clear=False) != expected and execute(erase=False) != expected, 'Clear/erase omission controls rejected') + return {'complex_contacts_and_inverses': checks, 'binary_charts': len(ports), + 'thin_paid_rank_per_port': 1, 'thin_productive_credit': 0, 'owned_stream_restored_zero': True} + + +def tail(E, invoice, tested, uniform, cutoff, floor, alpha_gap): + T, P = invoice['targets'], invoice['paid']; t, u, v = 1-tested, Q(1, 5), 1024 + target, paid = E.moment(T, t), E.moment(P, t) + alpha = E.divide(paid, target) + other = C.load(ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py', 'separate_rational_moment_engine') + tl, th = other.moment(T, tested); pl, ph = other.moment(P, tested) + need(tl > ph and max(target[0], tl) <= min(target[1], th) + and max(paid[0], pl) <= min(paid[1], ph), 'Separate rational interval engine agrees') + gamma = E.divide(E.moment(P, t+u), E.mul(E.power(cutoff, u), target)) + delta = E.divide((Q(sum(T.values())*floor),)*2, E.mul(E.power(cutoff, tested), target)) + need(alpha[1] < 1-alpha_gap and gamma[1] < Q(31, 32) and delta[1] < Q(19, 20), 'Three completely charged tail ratios') + need(Q(31, 32)**128 < Q(1, 16) and Q(19, 20)**128 < Q(1, 16), 'Exact decay blocks') + surplus = 1-Q(1)/(1+v*alpha_gap)-Q(4, 2**32) + need(surplus > 0, 'Original and completion tails both fit') + need(cutoff**64 < floor**63 and max(T) < 256, 'Strict ranks after completion and splitting') + h = Q(1, 64); z, z0 = 1-uniform, (t+1-uniform)/2; gap = z0-t + B, debt = (5+8*h)*v, 1+8*v*(1-z0) + x = (gap*B+debt)/(h*gap); H0 = -((-x.numerator)//x.denominator) + x = H0*(1-z0)/(z-z0); H1 = x.numerator//x.denominator+1 + need(H0 >= 8*v and H0*h*gap >= gap*B+debt and H1*(z-z0) > H0*(1-z0), 'Effective integer compiler bound') + return {'tested_saving': tested, 'uniform_saving': uniform, 'alpha': E.display(alpha), + 'gamma': E.display(gamma), 'delta': E.display(delta), 'tensor_power': v, + 'cutoff_base': cutoff, 'target_floor_base': floor, 'tail_exponent': u, + 'normalized_surplus_lower': surplus, 'compiler_H0': H0, 'uniform_H1': H1, + 'uniform_N': '2^'+str(H1), 'winning_word_materialized': False} + + +def run(): + count = authenticate(); rows = controllers(); native = native_contacts() + E = C.load(ROOT/'research/higher-moment-strictification/verify.py', 'credited_exact_intervals') + kappa, tested = Q('.00296'), Q('.00296030'); d = (tested-kappa)/7 + complex_ = tail(E, rows['complex'], tested, kappa+6*d, 20, 21, Q(1, 30000000)) + bit = tail(E, rows['bit'], Q('.00346'), Q('.003459'), 17, 18, Q(1, 250000)) + before, after, atom, old = Q('.003459'), Q('.00345'), Q('.004'), Q('.0000384599') + ordinary, admitted = (1-atom)*after+atom*old, Q('.0034') + need(before > after and atom > ordinary > admitted and atom < 1-ordinary, 'Complete ordinary BIT conversion') + need(Q('.003') < ordinary and 2**26 > 256/(before-after), 'Old atom rejected and finite prime bound') + L = C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'complete_outer_ledger') + params = {'kappa': kappa, 'tested_saving': tested, 'complex_uniform_saving': kappa+6*d, + 'b': kappa+5*d, 'a': kappa+4*d, 'q': kappa+3*d, 'bit_saving': admitted, + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, 'stop': d, 'layout': d, 'd': d} + outer = L.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta']*(1-atom) + need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete predicate inventory') + need(all(x > 0 for group in ('strict_checks', 'functional_checks') for x in outer[group].values()), 'All outer predicates') + controls = {} + for label, changes in [('old_BIT_cap', {'bit_saving': Q('.0027')}), ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('unfunded_kappa', {'kappa': tested}), ('closed_epsilon', {'epsilon': Q(1)}), ('missing_layout', {'layout': Q(0)})]: + bad = L.ledger(dict(params, **changes)); failed = [k for k, v in bad['strict_checks'].items() if v <= 0] + need(failed, 'Reject '+label); controls[label] = failed + return encode({'schema': 'query-thinned-productive-controllers/1', 'status': 'PASS_CONDITIONAL_QUERY_THINNED_KAPPA_00296', + 'kappa': kappa, 'relative_gain_over_p7': kappa/Q('.00268647')-1, + 'source_inputs_authenticated': count, 'native': native, 'complex_invoice': rows['complex'], 'bit_invoice': rows['bit'], + 'complex_strictification': complex_, 'bit_strictification': bit, + 'ordinary_BIT': {'before_cover': before, 'after_cover': after, 'atom': atom, 'ordinary_saving': ordinary, + 'admitted': admitted, 'prime_rule': 'odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses'}, + 'outer': outer, 'minimum_outer_margin_minus_kappa': min(outer['margins'].values())-kappa, + 'negative_controls': controls, 'old_atom_rejected': True, + 'scope': 'Conditional native construction; all-column, erasure, whole-job matching, fixed-tape, precision, analytic, prime and exact-recovery premises retained. No unconditional theorem or selected promotion.'}) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__); parser.add_argument('--write', action='store_true'); args = parser.parse_args() + result = run(); output = HERE/'RESULT.json' + if args.write: output.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: need(result == json.loads(output.read_text()), 'Complete receipt matches exact replay') + print(json.dumps({k: result[k] for k in ('status', 'kappa', 'source_inputs_authenticated', 'minimum_outer_margin_minus_kappa')}, sort_keys=True)) From 40e22a83ed660d3d6074c4f2dbf14bfb621eee51 Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 15:08:04 -0500 Subject: [PATCH 07/26] Record committed-byte and source-history validation --- research/query-thinned-controllers/VALIDATION.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/research/query-thinned-controllers/VALIDATION.md b/research/query-thinned-controllers/VALIDATION.md index 2924d84be3..8e9598ece7 100644 --- a/research/query-thinned-controllers/VALIDATION.md +++ b/research/query-thinned-controllers/VALIDATION.md @@ -37,7 +37,8 @@ stack was not rerun. New winning tensor/uniform words are specified by finite algorithms; their enormous instruction lists have not been emitted. No finite pass establishes an unconditional theorem or formal verification. -The exact-commit preflight and source-history check are run after committing -the package; the submitted PR describes their result and hosted CI separately. +The committed-byte preflight and source-history check both pass after +committing the package, with all 28 package/input files matching and the pinned +canonical base in publication ancestry. Hosted CI is reported separately. All reports retain the inherited native, whole-job, owned-erasure, fixed-tape, precision, analytic, prime-supply and exact-recovery proof boundaries. From ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9 Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 15:08:06 -0500 Subject: [PATCH 08/26] Raise conditional kappa to 0.00272124 by retiming fresh helper boundaries --- .../ARITHMETIC-RESULT.json | 219 +++++++ research/fresh-helper-boundary/ATTEMPTS.md | 44 ++ research/fresh-helper-boundary/CHANGES.json | 562 ++++++++++++++++++ .../FRONTIER-CHECKS.json | 14 + .../NATIVE-RESULT.json.gz | Bin 0 -> 29131 bytes research/fresh-helper-boundary/PROOF.md | 224 +++++++ research/fresh-helper-boundary/README.md | 155 +++++ research/fresh-helper-boundary/RESULT.json | 18 + research/fresh-helper-boundary/SOURCES.json | 96 +++ research/fresh-helper-boundary/TASK.json | 102 ++++ research/fresh-helper-boundary/VALIDATION.md | 34 ++ research/fresh-helper-boundary/VERIFY.json | 32 + research/fresh-helper-boundary/arithmetic.py | 152 +++++ .../fresh-helper-boundary/discover-cut.cpp | 35 ++ research/fresh-helper-boundary/discover.py | 75 +++ research/fresh-helper-boundary/native.py | 183 ++++++ research/fresh-helper-boundary/verify.py | 99 +++ 17 files changed, 2044 insertions(+) create mode 100644 research/fresh-helper-boundary/ARITHMETIC-RESULT.json create mode 100644 research/fresh-helper-boundary/ATTEMPTS.md create mode 100644 research/fresh-helper-boundary/CHANGES.json create mode 100644 research/fresh-helper-boundary/FRONTIER-CHECKS.json create mode 100644 research/fresh-helper-boundary/NATIVE-RESULT.json.gz create mode 100644 research/fresh-helper-boundary/PROOF.md create mode 100644 research/fresh-helper-boundary/README.md create mode 100644 research/fresh-helper-boundary/RESULT.json create mode 100644 research/fresh-helper-boundary/SOURCES.json create mode 100644 research/fresh-helper-boundary/TASK.json create mode 100644 research/fresh-helper-boundary/VALIDATION.md create mode 100644 research/fresh-helper-boundary/VERIFY.json create mode 100644 research/fresh-helper-boundary/arithmetic.py create mode 100644 research/fresh-helper-boundary/discover-cut.cpp create mode 100644 research/fresh-helper-boundary/discover.py create mode 100644 research/fresh-helper-boundary/native.py create mode 100644 research/fresh-helper-boundary/verify.py diff --git a/research/fresh-helper-boundary/ARITHMETIC-RESULT.json b/research/fresh-helper-boundary/ARITHMETIC-RESULT.json new file mode 100644 index 0000000000..686c36fb19 --- /dev/null +++ b/research/fresh-helper-boundary/ARITHMETIC-RESULT.json @@ -0,0 +1,219 @@ +{ + "BIT": { + "admitted": "273/100000", + "gap": "118653797/10000000000000", + "inherited_unrelaxed_saving": "27418653797/10000000000000" + }, + "compiler": { + "H": 349300000000, + "N": "2^349300000000", + "eta": { + "lower": "0.140815224484524968848722108625", + "upper": "0.140815224484524968848722108626" + }, + "gap": "1/700000000", + "integer_test_exponent": 499, + "logarithm_power": 13, + "theta_upper": "6/7", + "uniform_saving": "952437/350000000", + "word_materialized": false + }, + "fixed_profile_ceiling": { + "decreasing_C_interval": [ + "0", + "1/20" + ], + "negative_derivative_upper": { + "lower": "-178315.972608883259749333049784629374", + "upper": "-178315.972608883259749333049784629373" + }, + "negative_moment_upper": { + "lower": "-8137.901782546330185425252976230749", + "upper": "-8137.901782546330185425252976230748" + }, + "remaining_C_interval": [ + "1/20", + "1" + ] + }, + "gain_over_PR4416": "3477/100000000", + "headroom_from_declared_to_root": [ + "8051/400000000000", + "50319/2500000000000" + ], + "kappa": "68031/25000000", + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform_gap": [ + "new_complex_uniform_saving_above_b" + ], + "old_BIT_relaxation": [ + "actual_bit_above_effective" + ], + "unfunded_outer": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "outer": { + "functional_checks": { + "fixed_halo_explicit_metadata_branch": "13475000001/175000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000", + "new_semantic_group_guard": "3/700000000" + }, + "margins": { + "boundary_algebraic_matrix": "1333410398095129/490000000000000000", + "fused_gaussian": "1333410394285387/490000000000000000", + "global_coordinate_router": "238109/87500000", + "group_bit_router": "166676386785673/61250000000000000", + "group_scans": "349999999/350000000", + "main_transform": "1333409698095129/490000000000000000", + "microbox_face_corrections": "13475000001/175000000", + "polynomial_products": "699999999/700000000", + "sparse_union_movement": "200395910398095129/490000000000000000" + }, + "parameters": { + "a": "238109/87500000", + "b": "1904873/700000000", + "beta": "699999997/700000000", + "bit_saving": "273/100000", + "cap_xi": "445395909698095129/490000000000000000", + "complex_uniform_saving": "952437/350000000", + "d": "1/700000000", + "epsilon": "699999999/700000000", + "kappa": "68031/25000000", + "lambda_": "199455751/200000000", + "lambda_prime": "698095129/700000000", + "layout": "1/700000000", + "q": "1904871/700000000", + "r0": "1/7000000000", + "stop": "1/700000000", + "tested_saving": "2177/800000" + }, + "strict_checks": { + "actual_bit_above_effective": "383/43750000", + "actual_logarithmic_gamma_guard": "1/700000000", + "actual_logarithmic_group_guard": "44604091351904871/245000000000000000", + "alpha_logarithm_absorption": "1/7000000000", + "boundary_algebraic_matrix_above_kappa": "2798095129/490000000000000000", + "cap_above_band": "200395909698095129/490000000000000000", + "cap_below_cell": "44604089601904871/490000000000000000", + "cap_below_phase_cell_power": "534604090301904871/490000000000000000", + "complex_above_effective": "1/700000000", + "complex_below_one_over_32": "19970127/700000000", + "complex_endpoint": "1/350000000", + "epsilon_below_one": "1/700000000", + "epsilon_positive": "699999999/700000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "2794285387/490000000000000000", + "gaussian_above_main": "348095129/245000000000000000", + "global_coordinate_router_above_kappa": "1/175000000", + "global_gamma_power_slack": "9/7000000000", + "group_below_dimension": "1/350000000", + "group_bit_router_above_kappa": "436785673/61250000000000000", + "group_gauge_power_slack": "44604091316904871/245000000000000000", + "group_key_fits_record": "1/350000000", + "group_positive": "699999997/700000000", + "group_scans_above_kappa": "69809513/70000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "495134790400418148631/500000000000000000000000", + "lambda_above_internal": "1/1400000000", + "lambda_above_sigma": "3/1400000000", + "lambda_above_tau": "1/1400000000", + "lambda_prime_above_lambda": "1/1400000000", + "lambda_prime_above_leaf": "1398095127/490000000000000000", + "leaf_saving_above_effective": "698095127/490000000000000000", + "main_transform_above_kappa": "2098095129/490000000000000000", + "membership_arithmetic_fits_record": "1/700000000", + "microbox_face_corrections_above_kappa": "1684315473/21875000", + "microbox_halo_volume": "55300000003/700000000", + "new_complex_uniform_saving_above_b": "1/700000000", + "new_semantic_guard_with_C1_one": "1/700000000", + "polynomial_products_above_kappa": "698095131/700000000", + "positive_layout_slack": "1/700000000", + "q_below_effective": "1/700000000", + "q_below_internal": "1/700000000", + "q_below_leaf": "1398095127/490000000000000000", + "q_positive": "1904871/700000000", + "short_record_fallback": "698095127/700000000", + "source_axis_superpolynomial": "1/700000000", + "sparse_union_movement_above_kappa": "199062502798095129/490000000000000000", + "stop_below_one": "699999999/700000000", + "stop_positive": "1/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000", + "union_tag_work_per_visit_fits_record": "3/700000000" + } + }, + "paid": { + "1": 33795, + "16": 448, + "2": 7725, + "3": 6675, + "32": 448, + "4": 1530, + "48": 448, + "5": 600, + "8": 1464 + }, + "paid_calls": 53133, + "productive_fields": 7688, + "relative_gain_over_PR4416": "1159/89549", + "root_bracket": [ + "1088504051/400000000000", + "6803150319/2500000000000" + ], + "status": "PASS_CHANGED_NATIVE_PROFILE_STRICTIFICATION_AND_COMPLETE_OUTER", + "strictification": { + "alpha": { + "lower": "0.999999983026163231936831206184", + "upper": "0.999999983026163231936831206185" + }, + "cutoff_base": 10, + "delta": { + "lower": "0.864870069524004068270352709182", + "upper": "0.864870069524004068270352709183" + }, + "gamma": { + "lower": "0.910935673068185945998089027910", + "upper": "0.910935673068185945998089027911" + }, + "gap": { + "lower": "0.000000705775426641554341705594", + "upper": "0.000000705775426641554341705595" + }, + "normalized_paid_upper": "312500529444649842944287051245464084985300648225953097729364854469515503029278664568874151635979493066877292627151728507225829268936433948299379518726558518343844530884174444838473561069623983608689185814338090148572417036912296673977860237369051387753314848294993638501683424262073636500572764166420861283708720335677094583332070847074689861555558356543552667138912721443073650953550760942655945597474686732201711464952735742366374988690440592748048891939/312500750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "rational_upper_limits": [ + "62499999/62500000", + "911/1000", + "173/200" + ], + "tail_offset": "3/10", + "target_floor_base": 15, + "tensor_power": 150 + }, + "targets": { + "121": 224, + "25": 448, + "4": 390, + "41": 448, + "5": 30, + "57": 448, + "7": 435, + "8": 630, + "9": 4635 + }, + "tested_saving": "2177/800000" +} diff --git a/research/fresh-helper-boundary/ATTEMPTS.md b/research/fresh-helper-boundary/ATTEMPTS.md new file mode 100644 index 0000000000..61dd1812f5 --- /dev/null +++ b/research/fresh-helper-boundary/ATTEMPTS.md @@ -0,0 +1,44 @@ +# Scope of discovery + +The new contribution changes helper entrances and exits jointly with scalar +contact frames. The old choice was optimized for a hosted owner fill. Once +all helper fields are fresh independent inputs, that objective is different: +price the paid moment minus the actual productive helper moment. + +Exploratory checks before this pivot (compiled C++ discovery, not registered +proofs or global optimality certificates): + +- All 262,144 paired p7 masks: 256 modular candidates; none passes the numerical test C=.00268649. + The old rank profile and root were reproduced. +- All 2,097,152 paired p8 masks: 576 modular candidates; none passes C=.00268649. +- 2,391,496 masks within six individual-bank toggles of the selected p7 mask: + 6,278 modular candidates; none passes the numerical test C=.00268649. +- No untouched consecutive native transports fuse. Single common-frame + components, and alpha expansions over the 1,159 existing frame spaces with + all boundaries fixed, gave no improvement at C=.003. + +The rank-sum modular test is a discovery filter. If a polynomial matrix A has +invertible A(1), a constant-basis diagonal monomial factorization implies that +the sum of ranks of its nonzero coefficient matrices equals the dimension. +A necessary mod-2 screen is particularly cheap here because A(1) stays +invertible mod 2. Scientific acceptance of the selected word uses rational +Laurent replay and full native replay, not this filter. + +Allowing helper boundary frames changes the result. A binary alpha-expansion +cut changes a selected set of scalar contacts to one frame, while hard +constraints preserve every nested chronological path and every warp contact. +The energy is the complete paid moment minus productive helper moment. Entry +and exit moves are optimized separately because their joint concave reward +is not a submodular binary cost. The submitted finite choices are recorded +explicitly in CHANGES.json; replay needs no optimizer or C++ compiler. + +The optimizer is a discovery aid. Passing every tested label does not prove +global optimality. In particular, simultaneous different-label moves, changed +scalar order, new operators, center sharing and new geometry remain open. + +A subsequent scan added all binary lines, all hyperplanes and all coordinate +subspaces of F2^9: 1,264 new distinct labels, for 2,423 tested spaces. Separate +entry and exit alpha-expansion sweeps from the submitted profile found no +negative move at C=.003. The registered proof uses only the final finite +choices and exact native/moment replay; no claim of global optimality or +exact mathematical acceptance is drawn from floating discovery costs. diff --git a/research/fresh-helper-boundary/CHANGES.json b/research/fresh-helper-boundary/CHANGES.json new file mode 100644 index 0000000000..45744fedd0 --- /dev/null +++ b/research/fresh-helper-boundary/CHANGES.json @@ -0,0 +1,562 @@ +{ + "entrances": [ + [448, 114, 0], + [449, 114, 0], + [450, 115, 0], + [451, 115, 0], + [452, 115, 0], + [453, 115, 0], + [454, 114, 0], + [455, 114, 0], + [457, 116, 0], + [458, 116, 0], + [460, 117, 0], + [462, 117, 0], + [473, 114, 0], + [474, 118, 0], + [475, 118, 0], + [476, 119, 0], + [477, 119, 0], + [478, 120, 0], + [480, 120, 0], + [482, 114, 0], + [483, 114, 0], + [484, 121, 0], + [485, 121, 0], + [486, 122, 0], + [487, 122, 0], + [492, 115, 0], + [493, 115, 0], + [502, 115, 0], + [503, 115, 0], + [504, 115, 0], + [513, 115, 0], + [514, 115, 0], + [515, 115, 0], + [516, 123, 0], + [517, 123, 0], + [518, 124, 0], + [519, 124, 0], + [520, 125, 0], + [521, 125, 0], + [522, 126, 0], + [523, 126, 0], + [524, 115, 0], + [525, 115, 0], + [526, 115, 0], + [527, 115, 0], + [528, 127, 0], + [529, 127, 0], + [530, 128, 0], + [531, 128, 0], + [532, 129, 0], + [533, 129, 0], + [534, 130, 0], + [535, 130, 0], + [536, 115, 0], + [537, 115, 0], + [538, 131, 114], + [539, 114, 0], + [544, 132, 0], + [545, 132, 0], + [546, 133, 0], + [547, 133, 0], + [548, 114, 0], + [549, 114, 0], + [550, 114, 0], + [551, 114, 0], + [553, 134, 0], + [555, 134, 0], + [556, 135, 0], + [557, 135, 0], + [558, 136, 0], + [559, 136, 0], + [563, 134, 0], + [565, 134, 0], + [570, 134, 0], + [571, 134, 0], + [572, 134, 0], + [573, 134, 0], + [578, 114, 0], + [579, 114, 0], + [580, 115, 0], + [581, 115, 0], + [582, 115, 0], + [583, 115, 0], + [585, 114, 0], + [586, 137, 0], + [587, 137, 0], + [588, 137, 0], + [589, 137, 0], + [590, 138, 0], + [591, 137, 0], + [592, 137, 0], + [593, 137, 0], + [596, 137, 0], + [597, 137, 0], + [598, 114, 0], + [599, 114, 0], + [600, 114, 0], + [601, 114, 0], + [606, 115, 0], + [607, 115, 0], + [608, 115, 0], + [609, 115, 0], + [610, 115, 0], + [611, 115, 0], + [612, 115, 0], + [614, 115, 0], + [615, 115, 0], + [616, 115, 0], + [617, 115, 0], + [618, 115, 0], + [619, 115, 0], + [620, 115, 0], + [621, 140, 0], + [622, 114, 0], + [623, 114, 0], + [624, 114, 0], + [625, 114, 0] + ], + "exits": [ + [277, 256, 299], + [282, 257, 299], + [293, 258, 301], + [298, 258, 301], + [307, 261, 303], + [309, 261, 303], + [311, 262, 1], + [314, 263, 303], + [323, 265, 304], + [325, 266, 304], + [327, 267, 1], + [330, 268, 304], + [337, 270, 305], + [339, 270, 305], + [341, 271, 305], + [346, 271, 305], + [353, 272, 307], + [355, 272, 307], + [357, 273, 307], + [362, 273, 307], + [369, 275, 308], + [371, 275, 308], + [373, 275, 308], + [378, 276, 308], + [385, 277, 309], + [387, 277, 309], + [389, 278, 309], + [394, 278, 309], + [494, 262, 1], + [495, 262, 1], + [505, 267, 1], + [506, 267, 1], + [548, 285, 1], + [560, 285, 1], + [566, 286, 279], + [567, 286, 279], + [568, 287, 280], + [569, 287, 280], + [574, 288, 279], + [575, 288, 279], + [576, 289, 281], + [577, 289, 281] + ], + "gates": [ + ["A", 626, 115, 0], + ["A", 627, 115, 0], + ["A", 628, 115, 0], + ["A", 629, 114, 0], + ["A", 630, 114, 0], + ["A", 631, 114, 0], + ["A", 632, 114, 0], + ["A", 633, 114, 0], + ["A", 1762, 134, 0], + ["A", 1763, 134, 0], + ["A", 1764, 134, 0], + ["A", 1765, 134, 0], + ["A", 1766, 134, 0], + ["A", 1767, 134, 0], + ["A", 1768, 134, 0], + ["A", 1769, 134, 0], + ["A", 1770, 134, 0], + ["A", 1771, 134, 0], + ["A", 1772, 134, 0], + ["A", 1773, 134, 0], + ["A", 1774, 134, 0], + ["A", 1775, 134, 0], + ["A", 1776, 134, 0], + ["A", 1777, 134, 0], + ["A", 1778, 134, 0], + ["A", 1779, 134, 0], + ["A", 1780, 134, 0], + ["A", 1781, 134, 0], + ["A", 1782, 134, 0], + ["A", 1783, 134, 0], + ["A", 1784, 134, 0], + ["A", 1785, 134, 0], + ["A", 1786, 134, 0], + ["A", 1787, 116, 0], + ["A", 1788, 119, 0], + ["A", 1789, 119, 0], + ["A", 1790, 119, 0], + ["A", 1791, 119, 0], + ["A", 1792, 117, 0], + ["A", 1793, 124, 0], + ["A", 1794, 124, 0], + ["A", 1795, 120, 0], + ["A", 1796, 124, 0], + ["A", 1797, 124, 0], + ["A", 1798, 125, 0], + ["A", 1799, 125, 0], + ["A", 1800, 125, 0], + ["A", 1801, 125, 0], + ["A", 1802, 135, 0], + ["A", 1803, 135, 0], + ["A", 1804, 117, 0], + ["A", 1805, 128, 0], + ["A", 1806, 128, 0], + ["A", 1807, 128, 0], + ["A", 1808, 128, 0], + ["A", 1809, 120, 0], + ["A", 1810, 130, 0], + ["A", 1811, 130, 0], + ["A", 1812, 130, 0], + ["A", 1813, 130, 0], + ["A", 1814, 133, 0], + ["A", 1815, 133, 0], + ["A", 1816, 116, 0], + ["A", 1817, 122, 0], + ["A", 1818, 122, 0], + ["A", 1819, 122, 0], + ["A", 1820, 122, 0], + ["A", 1821, 129, 0], + ["A", 1822, 129, 0], + ["A", 1823, 129, 0], + ["A", 1824, 129, 0], + ["A", 1825, 132, 0], + ["A", 1826, 132, 0], + ["A", 1827, 126, 0], + ["A", 1828, 126, 0], + ["A", 1829, 126, 0], + ["A", 1830, 126, 0], + ["A", 1831, 136, 0], + ["A", 1832, 136, 0], + ["A", 1833, 118, 0], + ["A", 1834, 118, 0], + ["A", 1835, 118, 0], + ["A", 1836, 118, 0], + ["A", 1837, 127, 0], + ["A", 1838, 127, 0], + ["A", 1839, 127, 0], + ["A", 1840, 127, 0], + ["A", 1841, 123, 0], + ["A", 1842, 123, 0], + ["A", 1843, 123, 0], + ["A", 1844, 123, 0], + ["A", 1845, 121, 0], + ["A", 1846, 121, 0], + ["A", 1847, 121, 0], + ["A", 1848, 121, 0], + ["A", 4031, 620, 621], + ["A", 4037, 622, 280], + ["B", 0, 115, 0], + ["B", 1, 115, 0], + ["B", 2, 115, 0], + ["B", 3, 115, 0], + ["B", 4, 115, 0], + ["B", 5, 115, 0], + ["B", 6, 115, 0], + ["B", 7, 115, 0], + ["B", 8, 114, 0], + ["B", 9, 114, 0], + ["B", 10, 114, 0], + ["B", 15, 114, 0], + ["B", 16, 114, 0], + ["B", 17, 114, 0], + ["B", 18, 114, 0], + ["B", 19, 115, 0], + ["B", 20, 115, 0], + ["B", 21, 115, 0], + ["B", 22, 115, 0], + ["B", 23, 115, 0], + ["B", 24, 115, 0], + ["B", 25, 115, 0], + ["B", 26, 115, 0], + ["B", 27, 114, 0], + ["B", 28, 114, 0], + ["B", 29, 114, 0], + ["B", 30, 114, 0], + ["B", 32, 114, 0], + ["B", 33, 114, 0], + ["B", 34, 114, 0], + ["B", 35, 115, 0], + ["B", 36, 115, 0], + ["B", 37, 115, 0], + ["B", 38, 115, 0], + ["B", 39, 115, 0], + ["B", 40, 115, 0], + ["B", 41, 115, 0], + ["B", 42, 115, 0], + ["B", 43, 114, 0], + ["B", 44, 114, 0], + ["B", 45, 114, 0], + ["B", 46, 114, 0], + ["B", 47, 114, 0], + ["B", 48, 114, 0], + ["B", 49, 115, 0], + ["B", 50, 115, 0], + ["B", 51, 115, 0], + ["B", 52, 115, 0], + ["B", 53, 115, 0], + ["B", 54, 115, 0], + ["B", 55, 115, 0], + ["B", 56, 115, 0], + ["B", 57, 114, 0], + ["B", 60, 114, 0], + ["B", 61, 137, 0], + ["B", 62, 137, 0], + ["B", 63, 137, 0], + ["B", 64, 137, 0], + ["B", 65, 137, 0], + ["B", 66, 137, 0], + ["B", 67, 137, 0], + ["B", 68, 137, 0], + ["B", 69, 137, 0], + ["B", 70, 137, 0], + ["B", 71, 137, 0], + ["B", 72, 137, 0], + ["B", 73, 137, 0], + ["B", 74, 137, 0], + ["B", 75, 137, 0], + ["B", 76, 137, 0], + ["B", 77, 137, 0], + ["B", 78, 137, 0], + ["B", 79, 137, 0], + ["B", 80, 137, 0], + ["B", 81, 137, 0], + ["B", 82, 137, 0], + ["B", 83, 137, 0], + ["B", 84, 137, 0], + ["B", 85, 137, 0], + ["B", 86, 137, 0], + ["B", 87, 137, 0], + ["B", 88, 137, 0], + ["B", 89, 137, 0], + ["B", 90, 137, 0], + ["B", 91, 137, 0], + ["B", 92, 137, 0], + ["B", 93, 137, 0], + ["B", 94, 137, 0], + ["B", 95, 137, 0], + ["B", 96, 137, 0], + ["B", 97, 114, 0], + ["B", 98, 114, 0], + ["B", 99, 114, 0], + ["B", 100, 114, 0], + ["B", 101, 114, 0], + ["B", 102, 114, 0], + ["B", 103, 114, 0], + ["B", 104, 114, 0], + ["B", 105, 114, 0], + ["B", 106, 114, 0], + ["B", 107, 114, 0], + ["B", 108, 114, 0], + ["B", 109, 114, 0], + ["B", 110, 114, 0], + ["B", 111, 114, 0], + ["B", 112, 114, 0], + ["B", 113, 114, 0], + ["B", 114, 114, 0], + ["B", 135, 115, 0], + ["B", 136, 115, 0], + ["B", 137, 115, 0], + ["B", 138, 115, 0], + ["B", 139, 115, 0], + ["B", 140, 115, 0], + ["B", 141, 115, 0], + ["B", 142, 115, 0], + ["B", 143, 115, 0], + ["B", 144, 115, 0], + ["B", 145, 115, 0], + ["B", 146, 115, 0], + ["B", 147, 115, 0], + ["B", 148, 115, 0], + ["B", 149, 115, 0], + ["B", 150, 115, 0], + ["B", 151, 115, 0], + ["B", 152, 115, 0], + ["B", 153, 115, 0], + ["B", 154, 115, 0], + ["B", 155, 115, 0], + ["B", 156, 115, 0], + ["B", 157, 115, 0], + ["B", 158, 115, 0], + ["B", 159, 115, 0], + ["B", 160, 115, 0], + ["B", 161, 115, 0], + ["B", 162, 115, 0], + ["B", 163, 115, 0], + ["B", 164, 115, 0], + ["B", 165, 115, 0], + ["B", 166, 115, 0], + ["B", 167, 115, 0], + ["B", 168, 115, 0], + ["B", 169, 115, 0], + ["B", 170, 115, 0], + ["B", 171, 115, 0], + ["B", 172, 115, 0], + ["B", 173, 115, 0], + ["B", 174, 115, 0], + ["B", 175, 115, 0], + ["B", 176, 115, 0], + ["B", 177, 115, 0], + ["B", 178, 115, 0], + ["B", 179, 115, 0], + ["B", 180, 115, 0], + ["B", 181, 115, 0], + ["B", 182, 115, 0], + ["B", 183, 115, 0], + ["B", 184, 115, 0], + ["B", 185, 115, 0], + ["B", 186, 115, 0], + ["B", 187, 115, 0], + ["B", 188, 115, 0], + ["B", 189, 115, 0], + ["B", 190, 115, 0], + ["B", 191, 115, 0], + ["B", 192, 115, 0], + ["B", 193, 115, 0], + ["B", 194, 115, 0], + ["B", 195, 115, 0], + ["B", 196, 115, 0], + ["B", 197, 115, 0], + ["B", 198, 115, 0], + ["B", 199, 114, 0], + ["B", 200, 114, 0], + ["B", 201, 114, 0], + ["B", 202, 114, 0], + ["B", 203, 114, 0], + ["B", 204, 114, 0], + ["B", 205, 114, 0], + ["B", 206, 114, 0], + ["B", 207, 114, 0], + ["B", 208, 114, 0], + ["B", 209, 114, 0], + ["B", 210, 114, 0], + ["B", 211, 114, 0], + ["B", 212, 114, 0], + ["B", 213, 114, 0], + ["B", 214, 114, 0], + ["B", 234, 114, 0], + ["B", 235, 114, 0], + ["B", 236, 114, 0], + ["B", 237, 114, 0], + ["B", 474, 138, 0], + ["B", 475, 731, 360], + ["B", 503, 743, 371], + ["B", 504, 744, 372], + ["B", 505, 745, 373], + ["B", 506, 746, 374], + ["B", 507, 747, 375], + ["B", 508, 748, 376], + ["B", 509, 749, 377], + ["B", 510, 750, 378], + ["B", 511, 751, 391], + ["B", 512, 752, 392], + ["B", 513, 753, 393], + ["B", 514, 754, 394], + ["B", 515, 755, 395], + ["B", 516, 756, 396], + ["B", 517, 757, 397], + ["B", 518, 758, 398], + ["B", 521, 256, 299], + ["B", 526, 257, 299], + ["B", 533, 765, 411], + ["B", 534, 766, 412], + ["B", 535, 767, 413], + ["B", 536, 768, 414], + ["B", 537, 769, 415], + ["B", 538, 770, 416], + ["B", 539, 771, 417], + ["B", 540, 772, 418], + ["B", 559, 779, 431], + ["B", 560, 780, 432], + ["B", 561, 781, 433], + ["B", 562, 782, 434], + ["B", 563, 783, 435], + ["B", 564, 784, 436], + ["B", 565, 785, 437], + ["B", 566, 786, 438], + ["B", 571, 261, 303], + ["B", 575, 263, 303], + ["B", 576, 263, 303], + ["B", 601, 268, 304], + ["B", 602, 268, 304], + ["B", 622, 271, 305], + ["B", 624, 270, 305], + ["B", 627, 271, 305], + ["B", 629, 270, 305], + ["B", 630, 140, 0], + ["B", 635, 801, 491], + ["B", 636, 802, 492], + ["B", 637, 803, 493], + ["B", 638, 804, 494], + ["B", 639, 805, 495], + ["B", 640, 806, 496], + ["B", 641, 807, 497], + ["B", 642, 808, 498], + ["B", 661, 813, 511], + ["B", 662, 814, 512], + ["B", 663, 815, 513], + ["B", 664, 816, 514], + ["B", 665, 817, 515], + ["B", 666, 818, 516], + ["B", 667, 819, 517], + ["B", 668, 820, 518], + ["B", 673, 275, 308], + ["B", 678, 276, 308], + ["B", 684, 131, 114], + ["cleanup_tail", 0, 286, 279], + ["cleanup_tail", 1, 286, 279], + ["cleanup_tail", 2, 286, 279], + ["cleanup_tail", 3, 287, 280], + ["cleanup_tail", 4, 287, 280], + ["cleanup_tail", 5, 287, 280], + ["cleanup_tail", 6, 288, 279], + ["cleanup_tail", 7, 288, 279], + ["cleanup_tail", 8, 288, 279], + ["cleanup_tail", 9, 289, 281], + ["cleanup_tail", 10, 289, 281], + ["cleanup_tail", 11, 289, 281], + ["cleanup_tail", 12, 262, 1], + ["cleanup_tail", 13, 262, 1], + ["cleanup_tail", 14, 262, 1], + ["cleanup_tail", 15, 267, 1], + ["cleanup_tail", 16, 267, 1], + ["cleanup_tail", 17, 267, 1], + ["cleanup_tail", 18, 267, 1], + ["cleanup_tail", 19, 267, 1], + ["cleanup_tail", 40, 262, 1], + ["cleanup_tail", 41, 262, 1], + ["cleanup_tail", 42, 262, 1], + ["cleanup_tail", 43, 262, 1], + ["cleanup_tail", 44, 262, 1], + ["cleanup_tail", 45, 262, 1], + ["cleanup_tail", 46, 262, 1], + ["cleanup_tail", 53, 267, 1], + ["cleanup_tail", 54, 267, 1], + ["cleanup_tail", 67, 285, 1], + ["cleanup_tail", 68, 285, 1], + ["cleanup_tail", 69, 285, 1], + ["cleanup_tail", 77, 285, 1], + ["cleanup_tail", 78, 285, 1], + ["cleanup_tail", 112, 267, 1], + ["cleanup_tail", 113, 267, 1], + ["cleanup_tail", 114, 267, 1], + ["cleanup_tail", 115, 267, 1], + ["cleanup_tail", 118, 262, 1], + ["cleanup_tail", 119, 262, 1], + ["cleanup_tail", 120, 262, 1] + ] +} diff --git a/research/fresh-helper-boundary/FRONTIER-CHECKS.json b/research/fresh-helper-boundary/FRONTIER-CHECKS.json new file mode 100644 index 0000000000..2bebc81a01 --- /dev/null +++ b/research/fresh-helper-boundary/FRONTIER-CHECKS.json @@ -0,0 +1,14 @@ +{ + "schema": "frontier-watch/1", + "started_utc": "2026-10-21T19:32:20Z", + "interval_minutes": 20, + "checks": [ + { + "utc": "2026-10-21T19:52:05Z", + "latest_pr": 4437, + "highest_conditional_claim_pr": 4416, + "kappa": "0.00268647", + "action": "No stronger new claim found. Continue from p7 and PR4433 tail theorem." + } + ] +} \ No newline at end of file diff --git a/research/fresh-helper-boundary/NATIVE-RESULT.json.gz b/research/fresh-helper-boundary/NATIVE-RESULT.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..e6fdb31624e4eb8c7c770bb4422cd07ea99ab152 GIT binary patch literal 29131 zcmZsCWk8crA1@&wf(&V-1xB|5la!F|?k=T~?oJsUQlcQ;-Cd)kMPhWrV8m$deBbxp zPj{d9oIU%WbN=U7hbHzp%D)fV({YDN9i@!xaSKcZb@O%XbzWxOOnc&@t)j|n-)Z}u zOxy@yk7LGf1}v#EM&Eg;Kc_f9N^ee_Mk00Qt4teu!m>l-Wk}3z;erdo?QsE?D{^;m zDAsv@0;uZrK09dhbTSD*T$a&v-9mG{yM&(xp04t$pdEq2;U>cOn+sgfcE7ugr6#VY zi}j(6G_iYFpx@d9*4BnOdc)lNeaq$!Zzb|?khCOZWJ_UL|JvoUz4c(rZc-?}J zA7E}vGlBP)eX#qJ?Y4!dvxAwc`-jo0rw1-BXu$bdV$qOs=flHc5$V}gm$BbdIxP3G z^J&M}?_p~LjCtjp)I$)@x1BuhuE-RD*e+HrT&0yB9G?6|(Y69{~q@ucAl zzFkIe9bSTAt502dx%%eU*INRQ1182@cPDdTv4E>c5s}9OvD|>2KDQ?L{Y;-zSK#^M zyN5|ISXkr=Y$Eb>Bqljb^K=Leczk-iJFh28i|IkzgZNJ^lyMJs^dGfhGntZ7O zu*wtjW#|l?oZbbu2Ud09eL%Zmgo$CQ*c`TzJ}t~VogR-0h&^ru-aNL^m~=dV0WwzuyMZ?VCzGfB%Sf5P zhj+pc_X1T=-xgC!@Ez=zv?`-kg|?HPsJbI&TM z|8-NqA?(qaBro7<5;-T^EdEdMF7KPZ8LgYs%F4XFzN*fE+kC)NA1R>A`=JQh^;ABX z9e5^oe>#*d7U1P_LJD~LLboc`Sui;{Kl5~P@g~qKa3|^Rde21csqX1KvM3gQq2_;g zFjQ3cc=6>{b z8L^AoHk!x#lik3hbVctcxqyewNa)qGjr73V_3=oPTd}9(Iwn8F0YHqZu_zgFg3Zd6 z8+Cf}z!q>0AM&KBni%^0wC(-yczh@({Az1F)(QC|H~Zk{bpBTbCXC^b7hg$UbG)kSMMBjV^d)@Q! z*J#s;DM#St>RYcF+crDDTlm=l7gxabX5hp1?Y@4y*X1~k@xw*W&BIL5dR97eX1~~p z-H#0|L1w`B8xf}uSx%y2rY0Rv>3P(DL?!1Issg<(2dKnv(#~h7Hs_jPonA)|KdZWY z-#c+VLN5l!*ZZi}Z)gGc8(mMw=}+e~0qfd zgP7}gqERM9t~cZ9@P{VoB^p$R-oAv+xE3UG)pZOcnOHse}43``7sJS}`NL~XYJLa5oLi3$)sxGbSFgS!2ECoewfd_8sH)j_udGv%?V$t>dfU(CDusHUQ@+T_O zw_c2%*?@DsT$HmYK>{8fF=04iQ2={CM}OYaCrl%OM)j)KiB>F=9{R355DX>y zvAxeB?otc!4eGxDGD@FizX4nWCnErVu=x)ie7Hn&^$fQLP-)Dz1x60Zg-^4Vo8Jj0 zDl!m`Nbx2vYX?PUf5N!-`K#&a*ZD;L5+FFU$bO?H8^o${z(tj{@ZPubH@XHny)9>% z_s|SQwy`JN(#&?^RuIR1`#k^ZheS_QoZp&T6xf{`1eGEgfF?w z{z>h*sc<&q)1Ep^c5djE#ZqbiVyQf+WbTFxN_tN2^mL!yw~`KvQ8tY{Uw+}`6z=KW z6cbaf*`?U+?ne04ld!M(z&0Fd&tWIF+F^Joq;OfsRHgsR0-Hw>cQV*4 zx$2u|e>EU>QUA`K_M`mq2JkgaG$u{jdB1m%j!BJj;OQ;_Lhu1~O&J-SwAm?~g#!+VqqF(exTcHzGU9%U@ zSrlI+_j(ppuV-A@Q%1ZvE{T-ca5hrdm)Hy%_b@T>X4d$^K~;Txa-b}-U~kC(#aU%i zU-jE*x3%y2!PmVjDiJX>`+-8uba|pih#0j1x@AiTt6f-@Cu0F0Shd!W<2z&Iei%`+&weok5KK5JMd9GirlS4YaA6DW{JE@g`Vo>oAiRbJM(Pl{0 zqQBIO_4`$yZb=Rd$Gmt}c{3i|&-RwHFx;;slzXfd3(%g__LkE>U9UTtBHcAxb$V3U ze6j2^#h=Ftj$Hx6PXS?MzzF0>&GGB;=k%eW$QL><#C@7rjRGhH2!AxIXi~VRj6z(h zJm(H;FrIc}HT6aa0Zx}b7AJ_B9<_yr2QiNH-*y=KO zAN|6Z%5Na1LZ2rO%P(%Ro}@E{K#s!oyGvX(epm7$_e<-S^K6NC?~WN!^Q6|kHQ$C? zro2QhM1;6Y`qpb1qOww%A?B=gGu+hWfFIt+qCkyb+39v4wI4?L^S5oata$89ASQg9 zV~x^JaMPKRij2413O`$B8?!rUqW4&p9!9-76lfdi(l34rh1 z^}RxVps*0CFZ$n%e6ZEzVztv=tH3aCcl}2EX4dvn>I#r1N&Oqaw~FR>BabG!Tat&R z%ck-1J=z<|MEaT;lCQ?Udb2b!gur zT3nD{$8pO%eU$&RY_q=7FD1&*e3L_{&Gz`T_2Vhe>F(p2Q{rMgMwiU@RAO6}W7T1L z@6^9v?@2u^#7;zq;21#A6n+kz9Yj>l{9gG6D^=Si1N1W29+)*`<@Q!^-F>a?t`@|; zf(Ms!j`#$3&-k`%{sELb_Ru^lfSQt9T()41)BU^!*WW{>J{RSC*fT@4Taxz*p?6J( z?N5Zkz>+t=$|dR(ey50~`Yj5OK6-s`EQgpsl(KgR{YoePj_6Jv%v7U`kKWXCUdGp- zXN+6V6;#$PJ4@amV{LCT18PbDY`*`*NN*5LFO+KjXv$+-Mw3DdfJ}}5j4-Ufe8KVC zR#jUjl>eZTgc)A~pEzbA-TN(z>VABib>YC6st2*o7XwtGm)lO08?3VV5PEGY4c~lx zO_!f$iOoZLXWWotMGNaC96FfvZ1lyL?Ma245>4k2PCf`P7;;Bu7G}a zjY1cSg3*d^0D8Ux_=^U9H|aoF}6QHpB#m$Jz zkGt<0(*FF6CU1*@s`1lzWQQyrWN1(1YZ|y#6B)#$-X4e6o-r6Jp*?zR^BoZ>Y4QB| zTO3FT39Id3H>Y#Dv+#7Yj;Phc{M)V?5pyc_aybcM;Exlih8IzFf?*e2)%|kqqM!lu z5o(Fmwf+{N)nkR=sH8AIub=m~O|A{%0!Q$w_+DTuyK=C|*Oe6*vh@?-kO^p3c^BX+ zBb(|&@{}Kdxh+d#Q4u?j45Iofmx;Bv@3b8dgmJ%7_AvTL`oXTn-he_#25n~yi8+tav<^-t zNxz8?#>tUqAYxxC+X&00U4qJwWa3FiMj{tHKVDxYvY>{7|5dBj8gl$YfUd@0i zqP8~2Kck(6ybm7 zn@OtNam==jnAiUC!B|D$%e>LEFY{8tM)sIhW^d1xvUIdq0`2lJ>hy>cCX6&SZW@}r zm%>JHkEs1=%xoj8D$$C|WZEKZfQoQ@Z2egh0AxBP8jjKI0e{cpBr%cFE@w%w_{Zw^ zS1#{K1xv}IWV`6N6liCw<;d`;OlRr5*sSZ3yi1zlf!t?^Z5lz0dwr3;{|8Z8W4SZ0 zja|ZmH15Cp9ce!>?Z>cM8c4RtwO?dRzVQ_6q-No#r12(4=~ciAnQXKYjehIerxK&3 zU-~U6xo23RHq-v3Z->)P{a0doa@`^)+|^o8^4-n*$~)8S$vt_ugA(iV)aBYmLe#eW zpGCGao9}jf0A-7u!RbAkK_y+@E@e72@+QAozWQ5r^1RD4;Y%)aKwm~v_ji-?=7IAU zOP7B=d@oBzI5_FZM_|iS?5aUlQ(9Hpfzx*)s>DCMjIHBXO-_$@F7xP{Nv55D^;HbBL{5`rfk~0l zwSfWs=u)l-vr@UlIHENkfJTt#J_eQIUHu!gLA>uBJ1+qYqS@3i+NY2RKddf8RK!rh z$)8{4EG-z?r~rAdXBk=5T<$|}*7A9>CGPO6WOw?+ON9D)Yy4Q)^HSQ}bl8`u*6nKI zh&D#%UYv1HT#v9AEZsGxZ{M}e*Cib0ecHx*g}LX|3L=Gtf{t=}zG(*XEv<&|`< zG0J5aLT3&ucDfZFl++vH<`1>+l&0c^yd-c5`*eDoX(MEWI?m0=SnEY_9Qwc`>P{M! z?*7G27^qG|X}+Z@h1Gdp-{vYQM)HElZ$ETKI0LwvCk<*_+;IEUDr_ zIQHxu-_+5TjGxjvGe46w-uMV*#^*fcrdP`26&3=)rYj{AJ%Jmz$o z>VV%LJl)-x&*Gp$n4p_1P`_FZ%IDy4Ezx(c!ul=f$pN`vZW&fm-UTx@*8s2?sF-O>t}u8Evs`0p8>V0 zdO#}9a#(nZ?*%`HekR96n6FP3T#C^uNp(GWLz&SigQ&sEUFM4*&29&-7>+zK(`2i` z0kWqM6+QSuBn`-$@R%~?c6dgXxp~ab=#y3ifOVPpqVF>EUE5UwFriP(`Oq~)xjiFb z5z$_Dy+Ok@)Mv}b9Al1FFH(5*MhyMMNMD8G zEoTo5R*^L?UN&yFwtIe4F~F!zCrDf4Tw}BLX$e8=1^r}jn`dncaV`N*?f6Ixky$e- zQ0=z_6l}X|v|F`U$sx-uGrLq1Svl3Tnwvi0ae0-(9wC2{%Ggv`Ne~Q6sd;bAyj%As z;YUGz`u$>-h+P!IIcPlBcFlg;bB#fcjOFVP?ZWSnxGN>uR|G3`j@p13(F%3*zgtGS zou9T{&3rF$;G?6xXxWy)OwT0H>+kO=g`9bXGRHBMe*yW_<4JdP;z_fAWjLa7Ugu`w zeI2t2*pBomM0sV3fka!IWk;vza)2Qw-P^(m%56~RELC;T>025mxG-Jp$c7DW4MVJN z4wOX?2|qU(^agpz&vcuL<8KNp+n5h8h65f@Xp%u#IFsG&0ttE&PSMU4d0MoxN_^uI z?YSO#&`6th4XOo}1sXlnkScU6{iJ?|v#)aYJiq`A0xZ4?Ur_@3?W>I;qmu03a`Tb5 z3o=&V&bf-x)`oyD27F>PmebD7sq)aDC<0XMacl&V-^=qWE_D3M5S&=fHse@N?d)L zd44sF$84EmaH=~6!oO{=O}5+ipDidAn|Ai`wZgNvBq(JzV8VHXZ?SKa&dRTq@#<$N zhw_|qDE+jI1R%6(#P%LU2-r=cF84`WxYhMR4mIJ+ee+%FGu~i7a#{orT{~L>a@K$t zyqbPYB+v!3hfrwi$n8k1lTAr2^JaklbWp7(-tY$qS5li0WaqJ!n(8z5(K7R-8WF*O z8A`OxIbjP9!SFNQSSPd=n==uXg!~O5x8;JeWP8*`FYW%q(%Cb$2pn!s#A!`yZ+Fv= z@64f&@ba|QWu`!8$8LKwxD3Fr>arpC9lC(jp4=YBZa=oSA~lV%j{(u{Nv^PR(=Lyu z4{6$}zho@qp#TG+5?{f_m-TR67%ncRgG@*2cSFElAdAE0jRft`hgfb=-3#r4S5l%b z-9dEUtC^ipY&xPXHm;*YMmYuXn)+Qjh2ryjeb>83f?mfeepi2+)_b)R{uWjj+0l@8 zi)R1R)`vFXk`z7Umh!4WpzlO|K&z}|vOg9KV38w+>$T*5zAwxqEmD%Tn7&5wO%{LM zH1o&6ZdGHNjI~WCZ6zI5M91eu%Ogvf_|u~zc6FnA(rrR_{Td~=7TNT*m1j`nZmNyd zvj_GzIg4qph}x{T)cHrEd4sZx9eCOLAT#IC`>XxnEzC2QB$w)hajjMA*vbZ`2R(?rjzU>mIaR3X=(%3i>Y*Mc&-~-Hbo3dv|_~!NIvJa zxBo!igvs(K_rl_gJl|R^1R2w z3V4+L1>~I==l94&fi1}w!n^z9r?KsUay}4OdcL}FoI%VG z8!fczQtI8;)BJUc*6d?>8!%NwR@%nPruTujN&X#1Rkqx&yM6{`b-!L5rC#l>@}vx< zALZOLwB9N|G}3*G#iAyceF7qh4#m14nPP#|#-CXSXKhN!a8Jqwd*?yLNMMEZgcr-5 zXm_t{A|j#AAg831ZN>f0Rj@+ZgE=+7Is2dhkcEymm!cR+7Xv#=p%c6DWUEpm-|nbzhZ+*WYd zKeG*cw#TvIq^qt`r*TCDuIe`GAkb+1kudcEmf{U5nRV*T;Lar)oLWN-Y`qr2jvE~} z!zEtvesk;_!dZ0h{E>E&%+?o8G#7o0oO4o0(ZaCqApR!^aI1yAre$bDW$Hov^Yah? zu^zw0-Lnn_@1-=0WS(KIc4ArXiQ3PlW1g(m=$kQ6B(M?&rcrzhzg3Kbl8su^GoK^n zntmLdv(C*3ifZFLe5ZSIqI5aL@g}x*7>NbzFSsY_U-#kqd~;}{wh?nghFBtvqA4%x z->j;ldc|#D34FqSi;zF&)}`zBG9iClw_PRhB?tI5IF-n0g06mf6>Oy~_F8o>_G&^8 znz1&22EUY7n5tu1H`6dIA$r+^o-rva9!*d&kA4Y8?4@Qx7%o%e>bbX*`Ax&+AIU5{ zWv$e`xl%iNI(KxZrOY#b`OGEvES4MCQIiCZh&w6=+BbuxB( z&l=N-6ZBKe3u}7FCz_~I3Umf>2XNAK@YD=Ql>G>iI0ru|YQWNzASY^cBd!@q0&LwgHnKJg|TYW10qctB~uch1-b=Wxl%9!RPzgqt=RnY?b(X_Ak z4E!b0bikx`V84fJG|&a~-Cr zx}RPnB465MN|fNxLehG|*e#z|~%5I6#Pp|F`xH;6HFcI`SLa$iCQd#JnyX0{RCL z%$Adclx@k_CcRMX%eHnZ>>aF4-2&RbZ}9f}dbNL*t5z)se+BE*hSf zW^ztU-BgE*7$07}qpECOCSOe>^x zDt)l4_%RFiI83Y6jE2M~;mR)snW-1{o)5$D&~5YykoY~r6fZOgv`RL%>bU4?{13ms zURd}2h=I9S#N{r@hNQ}Pd#pkweRHTKX`NW-O1o;7PR1jzRa<{3JP5KeY3#qaMGbS| z!XQuzNL-QM#tJ^dgvn6L( zTFh+v-dy@9=LQkOo0mBK#B7iq+Q{Fgc|&z&zhnAioL4N-`@2# zctj_jqijXuB9lRnTdt{ud0B~j-rkgN+#YpdG-qBnnm7;vRatC8^A=9XV@@UzN(aoVST zRK@#HJ;>N8@LT`&MAtsIysUVg26>-G<5}WhyM0vaxlB)%pLwA~!#q{(*4z&B3q3^= znyLIaOzkj#88x7FO(tmlKVDS#bqrpR|mf+vDbauu+XeCv{VqGiuFJ1y=st-pd6ySdIzFWX->Int{sbM35csP(OhuYfRqrzGlcmoJ0-yfS;G7(8F?u~ zs{2N|J|>u#h9@mL`ws6-isjH>C14U^>2(#R-AH6^;Y+;lxWIe0ua8!&6QCxwHaVRo z3TVB{^R?SqpZuds)T~m*oH! zR@_Fu5mCNjiCW)NQZTi_BIoJ%2+Uo8qTu-v4)veC3hsL;xsk)vSv2rJkZZN>Up+`r z@s`Ad)M(-=kwdaQobvkPTM{sCD{=RQU?oRiIByf(%}=b(?d$?`w(5Dw=6qZz0F-U zCDvds^4O-&e~eNgnY9UE1S#Udww-As0h`WUPO*J%NFU{)`SvO-%H-hHfI{q#H(f&? zqodfn@Tl*}L7y$11$%u%KU$6IUgsWI8WlJlV#>0bC1QE8xT`Ui%j-9NPSYBDaZ=43 z^BYY#h3bbKOBa>T-u^h5XH624>+aIJ9o6t-M?sN%zp0KmJ9A7Glq={st>u!)ID={V z6U{_z_j=;BF8Jr9pn(eu8!c57d8?|E(AMh}ma6 zEZ1hz$h(}?bx>T&UvE= z_T`^ZoYQ$qp#ibUEA$P2{I%zdT(-#r`Abp zFgPLOb7Wqp}3nQ57PVv60y#!--7+S|pjH+$CFqb%Lq z@Uf>^EP7Yql-~DK8VA~vnAxEf-(iz!KoHHxP6F+zQR_xaPV=Mz%bItw;F|k*OBWc+ zDfT~HlFNw5zPo~dX5|Tdy;HU3yJ2Cg+l(lgWr1zmQzsp92c1VxLRgh0a_0z+6Lj5> z7?fvR#X7>J>s$yuF8@cCb!hs!UxMguHm~K>*IXkG=C%p%aTD!aG^-$d1$I!|9v*KJ zh z<+NhMpS*LUIMwWJ)qGbED}*|>y{a-SB8~_X3uF);D!>t{G3H9|%q5w-6*ML-7PqYQ zCV9AyprvPLj)E*dVVDN&%xln{nLMm|W275kf_1fD0}wM4^S+_F%{3Y?rK`A{DI*(Y z#nNBgJ7dW)4*0AfC?96Fl#KF+O~vfy-(VUkP=;Fn8xfYoe7G-p(|u=1RjLQ`fn(O+ zbi=}MJ(F6otjlm}C{>x$%vT@A5KFD{_*e6zxp~4HYMe0Jir=9*%0y08Z;TZ;lb6p2 z*+dmD|D8?AXrR}cngqHq`HJj8R-FH%UbVo8%ogA3m6a+N( zW_gB=>iU*lMkkk1CdrVSR!{jL@^Zk($q$^Ke{_A2O||A-{Ldb~TOj9H?53+Hk|`nv zrAI?Oedm3;d1{wJIqsaBb{EOoL`Vo%{3lPQYgM|?rZ5vi=i+CUoW|9az zX-;&L`nH@sk$c_idPYb%GEv=^YDktlJ~}c|6u9l(=VjKhfN?^Z_e7WZ<=gMowxu@( z@S{2kOW=n}Qg%^Ff1h!AheZoa$}gimyNIJiM~Mu4YQkQlUKZ^2P;@t7D7U616Um~8 zd&*1Q^^!^ONG8MOd9|yB&1>?)o-v5KgQ2`Dqe-5IgM#IA-j1d}MOqOn?_;!RL%F&O z)XYkhkPw~zM>C`UV;VD__RNyT4>Fc!0kN?ykLI1?HFZP?hr6e)gB^7>s=U3SC`DgG zza@V4=YfvFPjU5w4~46vDMIhrx*t|j0-M*24-iwe?{wQClUCF%%fKk?4ZRQci6~I# zNBR%<7ZN08R~uop5i!Tz=1WOu%e(ANQ%oT&YJ3!|BgpWrCMMU1c0q zK{i@x<6CUeL90KW2gmT)14g#bN*PDKK0RlkfOM@?89WRT`Fl|4pfDwmY}t^W;T%nu zez9}~*JsOR;-;?I{UGp@@YS^xTcyv{(x?}r_?7Cku|VasjIX$>OoDoBg>jo>(BYNn z8Y`e>Ft*%Un9IO~k#5+fC_AKKe3EaYGHhOZUF#~_$J-8j@59R#J8rGAW67iGY7?KQ zdj)!>!U_t}f)*{n3k1yt)y7v&-{9q5rj5V5**00fe?g`rryD_srNV!v-*`*GBE$F2 z&355}VZs;LPh0}Yu+XteWy!KwSKNA$(mjs5qrwD}X_ZYGfRwY_*(}4X`8V`S)es_s zp+syAaq-ToUoR$RKUCd>mZv{8VyH4G=?tf_2~ zvT`ddpnIv3bWdNaslLsj#L5N1(8^`t@Yzl_Umhgxl|zzy0@l1Q9uE#BlyX+(xF#i0 zh-1IB))}pGtWMS(l}VRAvmoeN$i~b5Z>tu}ulD>nFXg3TI9)?+qj-qAhe}b(t|1T= z)ahu@trF7fqO$JF2}X?ESTHAdHzTD~@u{2~3)TB<)PYaavlh@+kmK<8YiNo{P}oMb zY>m{uJsSDI0lAnEt7tifw`}DN?W=zAc%GRJY>VFO0K2pQ+g(+s#)q##^s_(ExhJ1D znDIbqE$%8kpahCM=z+;vVfrazO%&&w{d$m+fr=y00B#*awA{u_FFUp^hW##) zjJ1iJI*@#rZI)@P%Fr>gQ?i<_KsjN7e+8itvpQ^{mFkvu3Ka2c_7%^ zlngQQeTHMI&P+3?@*Ef%S!V}uzzb9hgmYq0&3Fk}9ogsHkHqHO7>fMetJ zJMww6rWp>%ovX}`fA9SK1Ig|XR~v;fu``e70O4q_e2Msh(L~DjvC+hvN_Uy)jufbg z+noajH5w$Ve!i*#jw!ri7fH@d_f>Aw<^tDm%{;oJ*MwdIrc*DF@Y zDyqp@xnYUsvkLLMK;|<6)HY$)BQ5Gv=3UHWBE!a<hGh*1ZcRi+x+Uk zU>(KCRCnh)ed?9y#Ox@`YLrPzf&J3@VXpN;2Q`@yW7E)c2*!1f#wr9qzt=g7qFO$REN(Xxc8 zQXWTz(zv9s9DTxv4HNy_ZV(A~uy6_vuPzy(g43H!SyAZf)~O!M?!QHXl6|+hP8_-X zgE?TNzSgzcs);z!`Bm_4D!|iTGBj+306e2*dqzK8{W6ozUp6dK za@z4LQ2;DmqXLhtT`&0#l(-4U>Ow#lzgzsFsNF3+_8t*Mn0)GSL&4|lOh@h#Q7Z1x zJQP{>SJ%aiyibc{=S(C73Q$mAgJ@%E6t_CHA$o#E`7&Ba%MQHyo(cuiTguJu4{8*8 zE|M*qEoG1}n4mWkl?1!uGJu=)0@G6!JP+NuHF6_sJl~Li| zz^`|v7-?x}XmD$Wot?pQpHdekir9lj13#R6cfk2=4<^?u*5Qpco3-Ja6^g!+ZXc{K z@2(@N=%0g8K)7O--Xrll^8YMgxN&=ZZ0E@s2X@(D@@d8avK`5HGz|GoCv8ds?Krwc zXmS6X7#=_uxuX4ISGO0Zn{?i1D%a%c2fH<~hT|2qZlOLqP2n|tPO+t!e-#RO_-#dN zp!CR^citSj#=tisjFs7@xyx`)H*mdd838%#cU@Kwak;dkXSU!d2Ll9ff1~7ld0@)r zCKaW;v})(B1u&HS8k=}?5X-egzYfsZs4>pBOPq91Ei|+TBqMtm)2lv7KvhrYPv-Na zKlVgc5(JXl9=XNK@q`k_jeHvsUxYPqwp3tVw+B1!Ep{!(G%{X&=u-snkx}|IjU2dq zvHl+kgWA3`#-`fEpI%*Q6#)tRQn| zy@@AlygR0Y=Jz=(6)%}T;SGSn8=E8_6c)w$M6+txdY17(i~e2#w)q4!VA&* zX#ULzqkoQfU94cBXH97<)BgnbQ7LIe+!9jT2wENbQ+@0vx(ECA$$tIpSeg1^P#k=8 z8znYF*B4$U)OB<<{aUg!84h}p-*Mip4bE#j1twr`jiPu9o+n2K+wVMxa3Bpb-$JYy z#zR8WFAZ~djHp3f(;F#>&^oO&XRwxUtZ+^pmP*ptg$4xM8yEe1T^I&AH!g4Zaa@Ih zH@PrvqikL^5y_g|t7|15$G77D?1q!S2iAWs$dd)9_KD_ zkK)XO*b=fQm)(hvNi1EandCr=<&C9?&%M^J?9qk|Gs(HE`KE0&C#DJ=a*Hw{r3$|l z$kNxwU_Ku3`HDBPgGLu37GEo+g1TiN~ zci%7|0+XQo!&lY4wNVSTvmma#A7Q4pE$(X=Hv3A{$wQIn&Fj}PGfrR6;eso{VQPi!oEDcaUmavb6NOfO3~(%{p+6Dy$Nu&1?&#O^3aSC}P1c3b+q zrBtlfn-DEi`~<;`_Au&gshOFGh!G>c!5XN`3^#KcMuCOn@?Q2B`;_8J^%-6zmxb z$DV|y`vzS;cc{o672z9QCF#9>KAM&^H0-L9a)Udp|B$hi_F-@ol}#L?lCP8fpJ*oq zI!F|6i>`@d=$UJ)$UkSf`ugP4r)`05<@uS}1M_Mp)n+ChazhjiHq$0imhqW$CCt!s zjtDIXI5SfpH2+V?YCk{Xk6KR7z>Oc?^z%gOSe{$8Rw|j&oS^<$U>&!Z!w#e^_QWAO z4@mrBi-`5cE@py&AOU+FE2=IfHB;Suq)atWOf!Ia-sz3Yb}6HaA|;Hiy>F9O(4`$~ z$hzmf#=n>(Ar5RbAy?=U!P@RXI4fV7ENjGX5X9K<5+csIi>1$+XL_TTqLZ)evmN=S zH-KcdpT|X5a$Sj%M%8OF$fDqM^}adWlY0;AYsUAqU}Vhy6?*&Et?5Zu?gNE}mDc4i zS)ydj%>GO`$+gT~a&wMLe|uwp*6!D`N=T{xI*z{rB@$voB-Iuj)hpB6OFzT|SV{G7 zNISUtQr5%x*8PkGhp5@Utxq_|Tc0zz^^vneuyRoVI@Qe~?A8L`Gq=iQ=M<|aj1eyN z84i)xHH4A1?@9!Pz<$s}HNLDCg3v;uC552fnhNMsT}7z2)hk z0KiTv@u|{TBU~w4C*oylt_}Nf`J{IFg8CfE&1);vB4IX;?wACbfJ7QEqHt4Sh7E?B z;Ipx_LDQ4ho*!3=h!@wP@;F*fY%J%$=5P8rFv8mo8G+ zOolG)d3JFx3N`m|*mq-X)Tz(NDcZZjWD{-7g;JP%u`*$96WJ>U4cIRSDcgWr4<^(n zQeX;t!I4{&-llXW9UB)^49K>>nhUMLN?1|)pA_+H*V81~&uT^{Kut-!R-fT$D7+&) zV~gYU&tKIlwJWLTLD*m*8tEQcBsAdQ) z{_t;bHtEpziD1MF*l_RN-es<)C#L#)8dO@5J}O{Z2L)$p$x%f>U%IuX{A=Axn%lJl z9Ih8Ofb@>g=`D8-@UQ~uJb!AT*Ze92Z!~g;H&+td8U;W`+#(`2B6 zx`Je>cD}eS?nhlSH6Jj?%4xvE4#OwAQ~7p_;Sbfudzbo?3R@cZC2PJjM6%?A-IDf4 zBZ8rRmq1ES&~jrfqFs>FbBIUN%Lel#JNHyorjgg7I3aiH)6e166a2*`eto3_rWkb; z=`uTHbwSQHZ2eAlRO!h3{X;q^10iK^E1s@jSt}$)c(&I^I?wDs&IR9poQnYj z(ZAN4y8hnC(|7FZAaNzvxpCTcK^)67ek%H~ZRw{LS&Y3ZM=GorC7SYrV zN*=L)*3@F?#Uav-L<|7m1S%D{# z_fanflLq#&27q}>)A6rqjQvMv!!-k+k@IL;Gv_n8z{8MH{I)v53vQtnrr2>y*nf;u zHiZ)qPnBxUl1Mry5+dW-NX={Tp4$9E8zVI@0Gu3^Qe-oZp$s*t2Zo_Tk*!o%W|3-S zbCd1AL}f|J4DQmqLS1O2LBq)&RYY8C>B4_tV+#Dt#U$M*PRLdi3Hl)6ijUn}h1 zo44sXE$V1Wk%&j3vR4pAGum&?uOP!s_eXD5SM#yr=*{fgtUye0i9haU3}44OqEE2p zp|>n29xB&%H|gGdmUu;K3nII?)Q#SzCJcWWxhUnb=;D!V*e@p?J$5DjKA2at_-Jx8 zCs%|o++*rJyqD|JcB8y`8!}pi1d7PSq=dd+5Hc=V*D%mDU_W$Dc{KQoPK2+M!A${8&1B}R$yR4bbN`QD0N*hMcWg1s&JVmrKkF zPItpUEP94nKFTO(~2i4=Wsd`ygVL{Vn8HT}DJTf~9rz=9e}J`PYTn4u7zf&x|)= z$zQ9&-Kc&LEfXKx$V>Dwf1EjbjPD2PK)m4C{UE6DX)`vGU{2_KjIi2x^>Oat~?Tm8vGi&lkxx(kL&8&D|DMoZT!B5&oH4$Qu#?5 zNu|?ylp?dDq%tbrNC23N)1C@PpxoH~rNAG;ZeaL#72(j)X5GNG{5daI{P~ItF7aw~ zxTj7qh8)*N%!Y*i2wp=keew+sO0{DTOt+|CXtC-^!$%lg1}^Gm(b)Lb^S7cZx3016 zZGS768R0)7Z_B^mvsA1p{K2r<{s-&^h2t@WPY#`VdB8Kr-f=0bhwmNtMK)RepON^u z`j^ryR_Oe~-If!{xO7Jkas}u2dPTJ~`6_Cb;S$SF0x@Lh*d5|)UCX(FGx!bW^XrC0 zb5fc539iYS-&1PFFsen9C*|nCSq2w%sVxR?8ETny4`}eeD zl<>}Q{e<~ad5MFOzgMuby5$&`8`1OFvec0#{+OGoQhNhT~$P*a*JmItUv zUH6`D8bL0}R8lyaY50kpo6>CWnYZj`KYe$QoxcPn;m~}Dr|`2O_~LSq0w3PrrgKIR7hu z`r^>Ft=~g4Al6pb^_mfoQ$>vXwT#FhTmbKm8F1C0;7IXR8zE(NIc9&^0LR$tw#^`7 zX7(Mk0Zu_;XQV@YGQRmolE4$O<#344u8mgG@>eqz%djTWHyeWQpQjA}D-LxSi{qMwgiRhs>qC%l)g~WUMgnmbc)Xjdp$#(uO2J$BO>Hbw1na|7mp)gCXoNr(pg5e(REQ6 zcPs8zthh^&;!dG>aCdKUcXyZKQrsPa1ouKI?ogcIE?;=p_b)3eD-*dh_ndv6y{8!= zV4~bS)8J{d3Z#TFWsFPm)ynXZbzH=o*FE4+M1c0!DnUNpPp1I$yB+CzB0^|&YV}zI@k_onib$m*$16CwH5{1U$FYK0@?H*R~^;{9WqI@6A;COrtHm2W>u5~e9dh!iqq zH{OSN)5cpwN?P>?B<;`Tbg`VlBDxEvN`|S10%!L{@jZhOm*r)^7u+vv zuHfp|WrefaZqm7K%%Aa&fI!o-j1op3IWbMo&5LBSmM=X#soDYJbJxa%!vpUC3O&N5 z9Of$iNKc2}p#zkeRrlpM+<09m+c=mzj@oZ#dnA{|Ycq}Z_9Q)mf9UTWvv^`yx(uJl zcb-Bqk-=eToxJilxA4S}f?za93!f8Y`}EaZLRq1aU2=5}V|5 zUURukk*IXFAwri>w-Q8)Y6%c8-KYh`T(b^HA*hcTE%dRZurB{@ARRq=CMQ{%iS(M- z3r2f}VL{-!3)oNM}cZRPBmk)NGcN zi;-ozgzMP;sk5wVj9OmI1M!!6sF&Zf-1USD6T~@?D(z10<9a@&WBJzT_EUYEH9u{~ zK%uuXta^}vk1vbv8Y^mDf7F<4hKp*vrmoPrj_Qj5*EaBs4~v3risZ4v+o{$pMY0EK z3LDTB`ddmi06EPjTJ#Fz+)+MHtIKXv;IfO4^sbCA43EE05wbnOU4w~;?abH#(Y|g0j-_rS*na-6ePm%;>MdUPxF$b~VhH}W*ESV=B~Ty3 zax{*;xPTKYnPzXZCs5=Q!Ouyin z!H`OLwPtJ^^z(bU^Or_jFaJ%U=+T}h!xf{2&DC@kU0mo%_@~e>A_8pL>9Bh|3F;OS ziMF$|kaMw)Cf)m{-U12^b{qM&iRk#xfYwkMVfG)*Rq!=I#4LeCd+C_3F`0W)Hl%4D zhHK>em0tv%u~yw@R~k5tY9WhkD8o8TZ|6Do)9K;2KGcz;=!t~M^!HVlRTIjVlH!f# znUC@DGWTW6Gif{JU`;`Z2zYkTr0daeAzYisCMOdpC$fl9xIZ2^N?Tn;}^Bu+%Q>t9|?XOp+qEDzv}mB=Zh)0!1++$NRzgf%*ZSs9)U7ma^o;Z zXNgc47OeN2h@!Bl_Y#6=c7=G`mL&?-#LhduYE^cGK6ZfcYPn)yy4d~So!+yAvz@4@ z;A2_lWfLyiG^XRV((fCt=%Q4<*#jo1kGWp0E*myU+9@6q0oNoq4)0XA1elklYd`eD z#gXu%`CXag6UF%1gsZ~1aW>k`E&}Hcky!V@T!`VF! z8qKl-D`6yqVDVRW&m-nIUa#$Y4lHzLpYR1;XMHWGb!s9$F3 z9MyA|uxx~W==*`jTk>d)k?j+WT3Fm>CjV^JqDJ(yY8GlxeXGgitHTKU#dure8pQ7+ z#FPLV=!1~}VhKQt&GGo=#|As?KK#IYkQyKUjE#Us3^NXM;j>fWq_)WSgBD^t_Na1B zRTZ%+n}YsWYrtAr9iTD)_ssJoSmQ$fh;OS7`qQ9%n==fn1scwzXY%mw1*wojK8t5p z_^?~{nc5}cEHFJV3e5CFP*he45YbHfOzUI$AU6IZDOL-DNhJs)D+PaX=ty=?HyXZGRVU{XU*&-=esqT@ z#qshUZO>bhTw?6*v&w~1iFxa668Y0V$OD%>!Hii0am99M2ICGY$6hih6`iKILwpP^ zU@GR{Z}QPD_5_Uo=>VaZO5}GcK#2IR>La*y*zH-Px7_b%YbuB(ns%INCgXVjC;jM3 zsaiP)`sJARm3+}#if$DvxKb+3I$G#=rR_x<<3U)w#@fX8k*lgjefazeKv2ni6&CG^r3z;qWqiU4ET({H29X6!=zAFgeaR771$XHP zy`-zL#RWs8+86qEN6#jQFvjO&65uIe-h~Bl))Ya$!3J9`!ZQ9=G6rL|V|ibv{R+_B zHssX(%ZkzvXf5G7hxqe#y-FS|C0)mSqwPYI0-qtLe^l=hlR_UCY5Me6Dc$6`hCj|? zZsYqlp(=18P#(;L#A2&fiDN9x9_{G|T-J9@n+Y%v-d=T^Tu=SnoSd9xmXbA&}rzx9X`NK zSDsnk`#Y?NN<<#*O7>3D`kl7h=ZguhT#(+_x|x?RCdiJ z);WIT`MV?Lj43^l|15f^ByVT*oV8T-ZV*N2Puu7YCDTT~uL5=^L?zp&Z|M1u zSOBBf=Ia=_-1_NEL72)_jCB2jJK)euu6~cSelTPW9iv$=u4cA3#3w%e5gOdRfaAgo z>sM|Fm;aKp%c-(G@}Kemy%QEFs!aF>w`0cl%10GbAm_-Zvg8|DO-=ztvh>H|W2Fyj zjo(xT?bi11R(|wWfW&>8_@-EY&H0G4K(dVSp6M8&EaR#$rwp3fc!cppufz0VT~FoAwwHF+y{QaZ zvQWiX#1_gYnt~=P7LIT?iAp2-=9G?t)ExZ;$Gl7LqmsC;C6)X4bMA~N9bKN^^O;1b zg+wSbaad)jB(LH=F8#nI>U)Dn$f>6-dxkLKZTTZTYYw~Q()!HawKw&Au_B@Qw!@FH z57Rf&mT2+^89ti7;RxB)StL6j1?RngIzx9EM<>y=LKzcKdG3wH>xLyy&|DRpVF-_q z%Ke)jJ();zp`+s}4pSHgbAA=`LylfD`SS=T9Ww3S@%dO`&i6%0-;->lhb1yj! zf7Ma#)G%p;=CUz5!|#cF3@Nfp?K(GoB;l+ZT|L0icx#wG;7)XXo@P2CxJ-y{Fz$W7jp79k%x zizMr3!h+o;yuI7MotAm(Iy<&62*)SM^pJ=vA5;9{V0vXb3+MVQn4CmN397#;D&^iq za{wI+pCO=lL)0<@%&|jwyua^0s3BH3+0tm+KVV$1gJ#e@LQBul@`@Dv>c}3=lUBR1 zV7T4@!-m<`vh!;Vjzi3c0_$m5j1CU(v{+!Lg6#~B)HGMNzWlhJq+jol8dcDT&P@+t9yptf0Az5K4ZyrDW zZTG!hU6)ya8Omkn#c0jJ9#Z-B%&D?OR?99Q5mFBQLVh#;FUHtr%E)pL`!EfEs=?P% zp^2TxyulH6_D@T5A!2X%L&KIX*?NwCh>^E zky}U^6lbv)!8bodR;{c@?fI1yl^WQl5w6_$d3^%U95Kg6+7*v@X$DjAt_BO$tPnhw z1}c1zaIR4rYwe=y9+VKS?@QuiJ%e7=yVMABCiOm`zZyPdcKF@`&1nu5n6TmHb-BM;c%YD@`J>;DIpi_ zWNJHZKEW#!Uh7}?-#+1GK2I>R{f7QRxA8}*MYmPf-%&MF{R|kjF@M ziHbQc8hX!zZeAi>f^C))C}LSya56FCE__5V7n(;Y5yc|`SW3|zec@(i&B7BN5wDj%Vw7c26OBmO-qK|FMtPj=d919nq*7EArkYzsdU9~B2>J;qH&tf+BX2ZoE17hX z?TwR$iZ9Hq?LP4PYY|&k%B2Wcqgihpi-x+liFV=;eP(w3Q#R~g8(x=Q-4hzQ_Vu33 zo?+5`kSN_tBk2gC%EehG`Wx3xI*Ua~RHfkDs8-`2WluOx7KFIwckIrRU|`hD*=odCo7hLi>^pfObS47&6(^Jm>g{lN{#9WP-K)f19bN0)py)maLwnH z^6ufErAB37KVzA5wu(Vgjr@iv9}uH1Me*MTw*Ro`Tf*Q=Sf_dB7d~ZC*#xv~A2Us& zee28`TWgS6x;bDi-y)Q^mRgEubN%Ix{EaI?v-sqb;iRfRQ%OV8(0m)DT)!V8<`WRg z9}xZ=P8F&fmxBA4^&?EEPBgC`v(HIH6UbP|E`pB#ZMCn3F3Qp_$ft_8cSd{CN&7=Q zpHuKUv-d(Kyqe$S|219*ISlnVaP|SoR0|oL!d<=gbSG=Uf%tDAPUDBZ~ zCrQ%UWMWLprrcL=Hs(I%c=hC;bQH%T)lt=!bZ2?!S%;h6ir(NpUli5jWN(qEaaB>1 zzbT45gN^dYjKN&qx`Q3kA6JE*u#xj>|Dy=<$BRic9Tzp_2+jSCQz#HN(}XwP8`F+$PKwQ0&RF zdiIzxhxW06nW=S^r-7|w$1C<|#v9U08Y^yaMqb}Lke)l6+*QX2%Ni+G4^wv%_yC-} z8c=urq~v{D?{~mi7fFF3?PqhZ>WR7Q9eg;j*nC)S*ERyx91?>{z2%?wGLYnVwmS=hzxBMH|}lz5o-A^mYFmxTd~Jj+VkaR(Mr&Yx~a-F*~7f8j&`6e$I*R| zwArm?7-Cv>0hl`nblNNh@aC&d;~G6!1F(HR= zb|jYxuFcxLkRf-}oW08t3QJ3s4=YP=?CNIy_;u6fx`bk*-}bjRNb> zZOA*dm^d~=9Ypswbd-|XG^9}JdJEr0W*mBr#p)C@9A7$vgaP*BAlrb z+@S@u=Qq?~h-QI<6L<6#Do?o(QHeLVyjc(M#7icWX!so5a9^Z2ZLd^$XAHuoWG(Ww z-HNywd@4izditMbY6h}aBAdW9LSao{PK^tt^1W6}Wq$ABT-EV{!Pdi+0)(QJ0FnR` z#BWeb(9vv5{SV8nF5$;?%?wF@9S3FQrandthMY(}r_d?+0;jC&8GS!g;u;s;olp zXpCbRy=*=ApEW%t=7h*O5Ca)_Vn>u5yzkrwA5R6ZhmlY7&%muE18-v%{}++E;mNlk z&CJGIyP2G3qfHz0F|X76k-uHKRH1N-P3{rwk^Qd*ex} zM&-*xFCTmemagw9JaNW!L$uu75-02Z)KgE%rQVV$)wxqikC1KJqN^ISn2;f!zhA9B zsaV_1hmRf3^qr95<~^fO%lQRW{Flo`T_xA)QPbjk)^X9nJ3RcuRQ}o7202V?<{yb< z>9<=sN8ahtRoKgARSA}~&hF(K?eZ&h!Y9<(ey-8`7n5V^)0>(xEUGscSjQbvmvl4p z?+Zn_j@KDs1jv;ziM?kD$64$<-hL*2>aAKW^-yJI!=m*Us1&Odlq8W8fM4cvf>li` zJH1%l)HxDY>dQ2j8S%I9CZ+tnbH6}a=JOP)y7gs`r#kf}`*mOXr$N`IAo`@c$|4O9PU0;-K_MuR_P@ag^qj&Tk3UV$3n*RM$>cM~#)@ zyu~pP{ykfi1eN-?=-I*Xp|Eh$Da!e$_e*-7ESCwgNKv>QRDj{#aAI10vd73!2g#X| zS_}#A$xA)StqZbVqGUr;OzL`hWl+^RT?2`F z6{Wm`a%qE4C^&Sq=5Cv{n)$OKA4ez$<=~pv0d;c2kjL3EDnjy6d~$%Ph3zCU=LG$i z1tqw`wOWC=?f2%a^0QmGkA2}d<$pPwYHEvX$^8jaWZG5~f z5qpwadsODxW0$@@Q&M#D_d?{?o;`O? z8{Q{M0wq5BB41;)Bd z*-%+EFzVw|8u`62#(BbC3^L@8)5XjTA;+(QyQD`2Ps-osVvj@|{gh$sVe4RJGaL*f z)Py%80_J|(n?7^;>)Tob@N*|(JIr1P@Wg)701nSu^GYs+JT>rEvXo~i;nP`b6$lkS z*Eb}0GWfZ|x0Q}*+~!KtLFi&TB?}qOJShu*dQJ(iHd2X5<`E^~fE2PkbV3!Bn;!`F zvd4B0B@TOeU@AzAf%r5=Q%u863v{2Kyan<$T6Tc4JakF=cJ)-P@}+Om9aHTpet`Z8 ze1yWvrD!7qgk|#4r*^ORK&QEM#9rD6A4#AVQHA#V{kpFTc4FvISX_L|0k|XUKX-KA zej$*eO3D2Ym4Ickg3--v{nrg~$uPFb#|PJ^{At<~&`3)Oq=9*v?hnL$XEzP}JIO(t zke`Rrl8eYkn)2gbYclMoNZX9k>@OwukL*rYmeh;7xQwqSJQH|J&ylVVRo0j60`WiyEyL)-CLf9D}M zV1YXgRzfs)Hz+i$Z;x_~sCC6Xb7@DZ&t_{#G9Wxkm-Ex^j?Hwa=19SfW0fK(mz86L-qS+!nEALWBVM(L>awslyL2KolXgm{pW zDP^x$3ot_VtjE^IZQ2j3b6!xdK&N$ow-lQ@ukJA;Zr{_Bt|)m;N1DoBke6QrEzCGf zVDpYsS4ib-Vwi{OpM82%Oe;Jb?fWp+Vb^>pkBto*KsFj)-o4k9LgYV7?GV}%;T<7m zGY~WSWv9taA0Au|u(NRCq>85M?u;nxoLMnb_8#F&G&nT-i9%6EuK)qPBr z-gJ+1HpZ3~?ruH4leP~?@(q2q5}VClLL0-h40=qtTx0&=F#?@C`GqKu(4U!!Vw`3tlNaAYXF`yQOEK@@aKPAS*GPkg{dHwE>2hXsHrYF+e;Vx z@IFK|_4o2eWB{@)A2Z*m{27Es6*+OmKzkC|73o;`6pClfiVElY1Yakk@wJx1=$VGW zTV|F}wEa7@@5Da?dI?s@*UXd!!X&-KCZHW|xICMcysj;M)AZ3|(p?)wI`CseZVGf6 zZ{#2~U)vE(K_3_O-o=rxch#CM1!Cffz1*uzjKN+3CN$hkn`vLWQ zi%C69G06aW7imI?F?YgWC%~Y_RJ|FExUb?ZKBRS`hF^j``7;MMiY5;!(vd(*UxQ~y z0pb7 zyBvN9k_3s?IiT^k`HfCkjYDtN{p{q?YvBgJTAh#gytPd_D@+F@!F5Q6+ZDFdO2jei zQL=_+6#lxDf5$q%k9>E&4$#=BM=^(AHTe4@X_d)^10;Fz`CaChyI3=Nk*5U1Gyq&^(GO;L4^9A-;M+?_*Yz~q+JAN{i9&CcDDw(^F_FwZ5@SW>5px$$Y}Rmcy<5a+>c;Po2#uhh z>Ej95XELlqmg)v3sMo?y1QESj{m=zqurU{j7Xuq2!Ori|dC$zx`D=(RbO$o&iUkx= zfPJ-sR;ud-x`TaZGNe&+mj_O2xs!|T!HvxEr3%74$a`|K4y(@gnttNyFr>=FlwVLg z`vz57hTR%WJ4Bz*{=@d9UK%evN778zVtUYO9b%ALsQ6Oe|OS# zU5g?Kf)U5PRcB=uJ&ploCuMo%^XSlI~62DJyfWs$%z*56QITF$&vZ5-0KWOLaif4^HmIE9={IfrL z?rupi$gjs0Rb)r#2F!H1Z0JySO9HKkOfXjE_P$Jyy*o0LvBalpy7o&h+`bb_WVvI9 zx*Kl^SB?}mg=aYUSWm9}eK0GpgfdR`U8QY_U>-AGGycJo`>#62@Go1fTGnV)7liim zK$*E`0!aF_BG@+_ja zyQD}d;~NA1G+`p)wGPrtz{}PDs@cbUqM9{1s=Pu6(oAXi>bHzHuH&in^HOuhH~})a zb`NTYuAoZ`ZbfM1Yb4CUpGd#}#_GjQ|LWR(lySE%@`Iz!A1d-A+7`|!++T7sWXJGK zu+(^@VG_N*{KF)BqWr>kMenAK&L})lo!gLjfABV48X+jV~BWXqs()r%{s;-)xRLz3b&gdS0l-@V~zz7CN7)p@8L#dY9Ke(J6f z082|&hbt>W4(mFi@mVwSKP2*p!|~G=>iKIBfMr_8mPFxW-RYOXPpWBV9Qi z`tLt~{!UPLG)8-@h`?T<>pp!qvweDl-Asu!x}JU1KW964Bd8DA%Uz&=*gxO@X02f4#4M zm^wPeN29Mz3(N5RHIzcTbVRy=LzLNDfJdxU|WFO=V2=@TWjuY%R zeE;2d08=L-tco()jS}(&_5{4{0 z%0y{_yy(K7;mKp~QA-wm!+TCA;!M zB0fmIFD8R5T^85UKuRBJ$6Fc}$?N<9Z-ojR<}@6GcZAt!`tfI~{vVRgIZKSmLeGD% zKX3hD*Fw`vYVA_%J0|Ct94x75=_|y4z>wgyF zF)h4>$rue?_=eF7^G`U-k{U}YIja#TuBik?8gu}A058$Vmt4RCIE8|u5AMrVA zL}wqX;6$~d&0-ouQ?uKYL&c&TOpOP}^-0iQpzlF24gN*khtU#^Gf9B@B(!znkeh(t z^K*OTttXHPA0z^i?-k&0NGjuRO3H_~&V&lKmdl%N@ufY)r1j-)_SMLlz`bVdyd*LD z1f;6Bj2dXH`HsInCIt<-M(PjuzXL3mz4i2QGAv#3gU%9L-2&4bICE3~V0Kyl5Y@o3 z??PYUL#-&d@t)%1L7t9MgsPd(o;*rO(@!)Fo^+@+lolmjUP!4m>;5xEL!^lCWrv@S zNYD7(Yde1<63v0J9(I9FX)vW39*i=n;ELu5)wQtEpS>x3ogjZC{wJ5!Vq$x8`3M!9 zAX~UfpP~{K(nD8TP|-P-o!CMT_LEJH3nA zL$`BNG1rMgawStZ5@Ohkxn&1guf4ee1~HbT6(;6~#}d-TaY<>oV@xxs>l|i?@7Of% zhqCkz&wBb0i+QU%b7vX6unZCy{_zZF%@aOMxA}v(nUD%&kb^xrl~BuxGy)unXsw=J z+FCJ(^+e#=sFjb^k}zRx_So4K{-+&y3uL}*fH=kX8+F{?@i7XtM{TKZ)CbudXPr~n zjMYluEIp;vr{GyKZU=`_yZP1CBM#K%Xauk9`uqKx%9_;;D)& ztwb~xpf_vQU{uz_+qA21s*s)5qR6e^=r)y7g%ZT@95SeLAc;w}sv*M?87B@CyH*+@ z(__0s)IPh-Jy+hKds+DnW7)M=e}oXsNbI`Gm*jS-^J@vVG9MZoPb_5p$hmtp(@xYzQWY zY3Us7t4tGpbJe*Zr>C1GLQvuaQy0wMVAlJ>bs*x2ik`nv31TJ?Cs zCtnJnLHu4x>aZ@vut}`x&>lBzB*q!Rb6gprNGd%;-S6Kn(G+|iV3{iSi`d9Em7rn+ z0?rE2#=ZP>?ph-lPJlU+JXG>_)crfoR=5381D|rd@8iZ>NQ1LmT5!*>lX18GAts=Q z&#eUp-JCDrMyI^c?v`0h{N{jAf$dBDB`wSfe+^^$XCvSE;CCeVdGYrRLW3)8+(+l< z@@u!PAt8s#?vKL2{ZL;oMFiRt`r2;qW9E!XyH%_Pre`g%uU`1pC%NiKreyUFzot5c>C(i6wvty05owc8Rva)T;!S0 z_Fc{umh>{${-DH;q4`Qz0z5WoAwN}8;(KxFO}bi#3@*C_e-xlblL4N&qUT}(tJ*)p z1L46QkO$yj_1tt!Rt z#7yzQ)rwb98>(*1l{S}mOS>|P=?3gjxA0esz>9*bHBfz9_0g2G5k1&;gsJ^??>qFe z9Q?g@Y2$)t{|*V-0=Gc@uW{c6S1+0lV<|hsf?WjWKs03sB#ZT+bX5iTT1BA`unt%KcXn`hEMF- zmU5~U-r2PMCnEV7P}&Dp)RPui03_jr+M5n~q#d_+ce0&Zn644`%&%`RrCR_HUPfmw zqf0VE?S#OymtO8@u0XU|A3){`1?Qr#8U{h7bI&3Fsn_F*v$Jo<3T)G#bNKm8ug2{w&VUIE?coVkQT8K#|?fvNaep`>G zJ@-59t;_&BO+SbL`s*2==rWX*z6E`{#ILY<#sqN@5ZYmlp>>ppPOL*J!*#7`6rV9- z6RS|7MtsB-RcXtUsMI6>Sm)h5tid)mJ2PN7e0v4qwoMA}6F0UZw)4Jqxvn&jk`Knx zx)=UzJ>(QVr&X;!-B}#E9`Aa5WjppA^V}Yi469eVAiy<7_(J_#)kijLwhL{t}4@kFJSWP1xghGfbg$V z#ruX`8*K{N?b#lH{0^VGzI2cD_@edmhqjXBUN`U@+UexDmdK&=uu2LCJ+c>f%?3r0 zS!$7Y1bKA*4F}Nf_|^$^E7V=#R`nP~-&HG;WlBH-^4*8(=)*M7_B&15N@mtkP)|Q0 z)%w%?D%Z&f=HHfnplV@myNU7GAoYT;-_|D1;d^>TB+V(NTeQVf! zU7OZAtfVjiz7FixJ|kLQ^$5)P;N`w@J>{`2YhApke0^N;@BXsB{^COf9LtOS>emdM zhIv_=&MT<(^SQfR%iAyn)xLszp3?n2FTT9KLhek~^Y-#~vF-o1@Bi|}@cHWPKD_6x z%>Sj+|0Uf2wG8qy_qY3aHhDC**Of1CJ8xGTZ-<7!$2CL$yEj+|eT?`5OAM(00SWrR A!~g&Q literal 0 HcmV?d00001 diff --git a/research/fresh-helper-boundary/PROOF.md b/research/fresh-helper-boundary/PROOF.md new file mode 100644 index 0000000000..4fe9fa7eec --- /dev/null +++ b/research/fresh-helper-boundary/PROOF.md @@ -0,0 +1,224 @@ +# Proof and conditional transfer + +## 1. Boundary contract + +Use the source full-identity native unit with 632 independent persistent +fields: 224 main fields and 408 helpers. Its two orientations give the source +main shears, while every helper is autonomous in its own logical reference. +The separately owned C0 field is cleared before each use and at return. No +arbitrary persistent input is overwritten or cleared. + +A field at frame f has physical value `C_f z`, where z denotes its logical +value and `C_f` is the source canonical Fourier frame. At entry this means +`z=C_start^-1 x` for an arbitrary physical input x. It does **not** require +precomputing a Fourier transform of x for free. The helper's actual final +operator is `C_end C_start^-1`, not merely `C_end`. + +For nested frame spaces S0` and `F(.0027212601276)<0`. To establish a fixed-profile +ceiling, arithmetic.py encloses `sum (T_r-P_r) r^(1-C) log r` on each of 16 +closed intervals covering `[0,1/20]`, and proves a strictly positive lower +bound throughout. Thus F is strictly decreasing there. On 128 further closed +intervals covering `[1/20,1]`, it bounds F directly strictly below zero. These +are interval implications for every real C in the covered intervals, not +extrapolation from point samples. The positive rank-one surplus at C=0 then +gives the unique relevant crossing and excludes any later positive region. + +A chronological tensor power multiplies both moments. Paid completion of a +rank-K target by D axes changes its moment by `(K+D)^t-K^t <= D^t`, which is +at most the added paid charge. Splitting a paid job on disjoint axes increases +or preserves its t-charge. Hence tensoring, this paid completion and paid +splitting cannot pass the raw fixed-profile ceiling. This is not a ceiling +on different native profiles or other algorithms. + +## 5. Pay both strictification tails + +Let `C=.00272125`, `t=1-C`, `u=3/10`, `v=150`, `J=10^v` and `L=15^v`. +Use the chronological native product of PR4416 and PR4433, restoring every +whole-job matcher and center before resuming a suspended caller. The product +has target and paid moments `T_t^v` and `P_t^v`, respectively; it is a +substitution of whole array programs, not the tensor power of a sum. + +Canonicalize each complete raw job with both recorded monomial factors; these +need not be an inverse pair. Subsequent placement on specified disjoint axes +is coordinate conjugation. No raw Clifford endpoint is assumed conjugate to +a canonical Fourier transform merely because its rank agrees. + +After the product finishes, complete every productive rank KJ, its split charge is at most +`2 R J^-C <= 2 R^(t+u) J^-u`, since `t+u>=1`. A completion has charge below +`2 L J^-C`. Therefore the complete normalized paid moment is bounded by + +``` +alpha^v + 2 gamma^v + 2 delta^v, +alpha=P_t/T_t, +gamma=P_(t+u)/(10^u T_t), +delta=7688*15/(10^C T_t). +``` + +The interval engine certifies `alpha<1-16/10^9`, `gamma<911/1000` and +`delta<173/200`. Bernoulli's inequality and an exact rational power test give + +``` +1/(1+150*16/10^9) + 2*(911/1000)^150 + 2*(173/200)^150 < 1. +``` + +Both original tails and every completion are paid. The product ambient rank +is `m=121^150`, with no need to materialize its immense word. + +## 6. Uniform compiler, BIT and outer bill + +Use the inherited finite integer mixed-target compiler only after strict +separation. Its fields, source complements, owned centers, integral batching, +matcher restoration and final exits are those of the specified new unit. +The new logarithmic majorant of PR4433 applies with `theta=6/7` and power 13: +`10^7<15^6`, `2*(10^150)^7 <= (121^150)^6`, and +`eta=t*121^(-150*C) > theta^13`. Its base-range condition is checked as well. +For declared `kappa=.00272124`, put `d=(C-kappa)/7=1/700000000` and uniform +saving `C-d`. The explicit integer comparison at `H=349300000000` is + +``` +(H+1)^13 < 2^499, d*H=499. +``` + +It specifies a finite uniform supplier at `N=2^H` with the required strict +saving. The instruction list and integer width B_N are generated by the +source finite algorithm rather than emitted here. + +The source BIT all-size parameter proof gives, before its last relaxation, +`(1-.003)*.00275 + .003*.0000384599 = .0027418653797`. Admit this unchanged +supplier at `.00273`; both the atom/adapter and borrowed-stock inequalities +remain strict. No BIT native word, cover or precision premise is weakened. +The old `.0027` relaxation fails the new outer bill and is a rejection control. + +Set `b=kappa+5d`, `a=kappa+4d`, `q=kappa+3d`, `epsilon=1-d`, `beta=1-3d`, +`r0=d/10`, `stop=d` and `layout=d`. The complete retained ledger recomputes all +nine cost rows, 54 current strict predicates and three functional guards. +Every one is strictly positive at this point. Closed uniform/epsilon gaps, +the insufficient old BIT relaxation and the unfunded tested endpoint fail. + +## 7. Costs and the precise conditional boundary + +Replace the old finite-unit constants by counts of the actual new word: +3363 paid local calls, the complete unchanged scalar lists and coefficients, +new serialized monomial/phase generators, 632 persistent fields and one owned +C0, all 408 helper normalizers, the unchanged p7 bridges and whole idles, the +150-fold chronological substitution, every completion and split, and finally +every integer-compiler unit, route, owned bank and rank-one leaf. A literal +finite recursive enumeration defines their counts and coefficient heights; +no p3 raw count is substituted for the compiled word. The new transport and +helper recipes are available explicitly in NATIVE-RESULT.json.gz. Internal +normalizers are restored before resuming a caller. + +Apply the source finite-template precision and stock argument with these new +constants. The native fixed coefficients and generators are finite, semantic +prefix bounds are rechecked, and all changed movement/scalar/normalizer work +enters the finite constants. The positive outer spare powers absorb those +constants after an effective threshold, under the inherited semantic, +all-column, physical primitive and fixed-tape hypotheses. This is the same +conditional transfer mechanism used by PR4416/4433, not a proof that local +savings are automatically a multiplication theorem. + +Analytic decomposition, permitted physical movement and whole-job frame +realization, source all-column correctness, finite-template closure, fine-prime +padding, fixed-tape execution and exact recovery remain stated source premises. +There is no formal verification or independent human mathematical review of +the complete theorem, no practical implementation claim, and no selected-result +change. Source files and contributor attribution are retained. diff --git a/research/fresh-helper-boundary/README.md b/research/fresh-helper-boundary/README.md new file mode 100644 index 0000000000..cbcfab9ccd --- /dev/null +++ b/research/fresh-helper-boundary/README.md @@ -0,0 +1,155 @@ +# Conditional κ = 0.00272124 from fresh-helper boundary retiming + +This changes the complete native p7 paid profile and proposes + +``` +T(n) = O(n (log n)^(1 - 0.00272124)). +``` + +The conditional saving exceeds [PR4416](https://github.com/CrocSwap/integer-mult-bounds/pull/4416)'s +`0.00268647` by **0.00003477 (about 1.2943%)**, and the pinned selected +`0.0023` by **18.31%**. This is a conditional construction submitted for review; +it does not change the selected record or establish an unconditional theorem. + +The new lever is to optimize helper entrances and exits for **fresh independent +helper inputs**, rather than retain frames selected for a hosted owner fill. +Changing those boundaries together with scalar contact frames saves recursive +calls without changing the scalar order, coefficients, main operator, warp +contacts or owned center program. The exact finite patch changes **117 helper +entrances, 42 helper exits and 395 scalar contact frames**. + +| Complete raw p7 invoice | PR4416 | This construction | +| --- | ---: | ---: | +| Independent productive fields | 7,688 | 7,688 | +| Paid calls | 55,998 | **53,133** | +| Productive rank mass | 131,723 | 133,718 | +| Paid rank mass | 131,115 | 133,110 | +| Rank-one surplus | 608 | 608 | +| Proposed conditional κ | 0.00268647 | **0.00272124** | + +The call reduction is **2,865 (about 5.12%)**. These are finite instruction +counts, not measured runtime speedups. The changed masses illustrate why +counting calls or rank-one mass alone does not establish the saving: the exact +concave moment and complete consumer are checked separately. + +## Native unit and exact evidence + +For each forward or backward local invocation, the new productive helper +profile and complete paid profile are + +``` +H = {4:26, 5:2, 7:29, 8:42, 9:309}, +P = {1:2253, 2:515, 3:445, 4:102, 5:40, 8:8}. +``` + +Every one of the 408 helpers has an independent arbitrary input. The center +remains separately owned, explicitly cleared, reused and uncredited. The +source p7 controller is unchanged: `pairs=7, keep_idle_mask=232127`. Its full +rational Laurent word is replayed; all 2,688 main idle calls are retained. +The complete new raw profiles are + +``` +T = {4:390, 5:30, 7:435, 8:630, 9:4635, + 25:448, 41:448, 57:448, 121:224}, +P = {1:33795, 2:7725, 3:6675, 4:1530, 5:600, + 8:1464, 16:448, 32:448, 48:448}. +``` + +[PROOF.md](PROOF.md) proves the retiming equivalence and explains the complete +transfer. [CHANGES.json](CHANGES.json) is the explicit circuit patch; +`native.py` resynthesizes every transport and replays both orientations on all +632 arbitrary inputs using two retained literal interpreters. All new transport +edges and every distinct helper boundary are independently lowered and decoded +as exact Clifford operations, including their absolute phase. Unchanged +transport phase evidence and the original all-column/native model remain +inherited source premises. + +`arithmetic.py` uses the unchanged interval engine of +[PR4433](https://github.com/CrocSwap/integer-mult-bounds/pull/4433). It certifies + +``` +0.0027212601275 < fixed-profile mixed root < 0.0027212601276. +``` + +An interval argument covers all real `0 0 and margin(ROOT_HIGH)[1] < 0, 'Certified changed-profile root bracket') + need(KAPPA < TESTED < ROOT_LOW, 'Strict supplier and outer headroom') + # An interval proof over real C, rather than signs only at a finite mesh. + signed = {r: targets[r]-paid[r] for r in targets.keys() | paid.keys()} + derivative_lower = None + for i in range(16): + left, right = Q(i, 320), Q(i+1, 320) + lower = Q(0) + for r, count in signed.items(): + power = E.power(r, 1-right if count > 0 else 1-left) + term = E.mul(power, E.log_bounds(r)) + lower += count*term[0 if count > 0 else 1] + derivative_lower = lower if derivative_lower is None else min(derivative_lower, lower) + need(derivative_lower > 0, 'Moment is strictly decreasing on [0,1/20]') + negative_upper = None + for i in range(128): + left, right = Q(1,20)+Q(19*i,2560), Q(1,20)+Q(19*(i+1),2560) + upper = sum(count*E.power(r, 1-left if count > 0 else 1-right)[1 if count > 0 else 0] + for r, count in signed.items()) + negative_upper = upper if negative_upper is None else max(negative_upper, upper) + need(negative_upper < 0, 'Every C in [1/20,1] has negative moment') + t, v, c, b, u = 1-TESTED, 150, 10, 15, Q(3,10) + target = E.moment(targets, t) + alpha = E.divide(E.moment(paid,t), target) + gamma = E.divide(E.moment(paid,t+u), E.mul(E.power(c,u),target)) + delta = E.divide((Q(sum(targets.values())*b),)*2, E.mul(E.power(c,TESTED),target)) + limits = (1-Q(16,10**9), Q(911,1000), Q(173,200)) + for bounds, limit in zip((alpha,gamma,delta),limits): + need(0 < bounds[0] <= bounds[1] < limit < 1, 'Certified complete tail limit') + a, g, d = limits + normalized_upper = 1/(1+v*(1-a))+2*g**v+2*d**v + need(normalized_upper < 1, 'All product, original paid tail and padding charges fit') + need(1 < c < b < 121 and t+u >= 1, 'Strictification hypotheses') + # PR4433's logarithmic majorant, rebound to this changed complete invoice. + theta, power = Q(6,7), 13 + eta = E.scale(E.exp_interval(E.scale(E.log_bounds(121),-v*TESTED)),t) + need(10**7 < 15**6 and 2*(10**v)**7 <= (121**v)**6, 'Actual exit cutoff and shifted logarithm') + need(eta[0] > theta**power, 'Strict exit versus complement contraction') + need(E.exp_interval(E.scale(E.log_bounds(121),v*TESTED))[1] < 2**power, 'Full initial rank range') + gap = (TESTED-KAPPA)/7 + need(gap.numerator == 1, 'Explicit integer grid for the uniform rank') + step = gap.denominator + def wins(j): + return (step*j+1)**power < 2**j + lo, hi = 1, 2 + while not wins(hi): + lo, hi = hi, 2*hi + while hi-lo > 1: + mid = (hi+lo)//2 + if wins(mid): hi = mid + else: lo = mid + H = step*hi + need(H > 7*v and wins(hi) and not wins(hi-1), 'Strict finite uniform-rank integer test') + # The original BIT proof already supplies the stronger, unrelaxed value. + bit = native.read(ROOT/'research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json') + bit_raw = (1-Q(bit['atom_power']))*Q(bit['C1_after_cover'])+Q(bit['atom_power'])*Q(bit['old_ordinary_saving']) + bit_admitted = Q('.00273') + need(bit_raw == Q(bit['ordinary_saving_before_final_relaxation']) > bit_admitted > KAPPA, 'Retain the existing stronger BIT conversion') + need(Q(bit['atom_power']) > bit_raw and 1-bit_raw-Q(bit['atom_power']) > 0, 'Both BIT adapter/stock gaps') + O = native.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py', 'fresh_boundary_outer') + params = {'kappa': KAPPA, 'tested_saving': TESTED, + 'complex_uniform_saving': KAPPA+6*gap, 'b': KAPPA+5*gap, + 'a': KAPPA+4*gap, 'q': KAPPA+3*gap, 'bit_saving': bit_admitted, + 'epsilon': 1-gap, 'beta': 1-3*gap, 'r0': gap/10, + 'stop': gap, 'layout': gap, 'd': gap} + outer = O.ledger(params) + need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 3, 'Complete consumer predicate inventory') + need(all(value > 0 for group in ('strict_checks','functional_checks') for value in outer[group].values()), 'Every inherited consumer predicate') + controls = {} + for label, patch in [('old_BIT_relaxation', {'bit_saving': Q('.0027')}), + ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('closed_epsilon', {'epsilon': Q(1)}), + ('unfunded_outer', {'kappa': TESTED})]: + bad = O.ledger(dict(params,**patch)) + failed = [key for key,value in bad['strict_checks'].items() if value <= 0] + need(failed, 'Reject '+label); controls[label] = failed + return encode({'status':'PASS_CHANGED_NATIVE_PROFILE_STRICTIFICATION_AND_COMPLETE_OUTER', + 'kappa':KAPPA, 'tested_saving':TESTED, 'gain_over_PR4416':KAPPA-PREVIOUS, + 'relative_gain_over_PR4416':(KAPPA-PREVIOUS)/PREVIOUS, + 'targets':dict(sorted(targets.items())), 'paid':dict(sorted(paid.items())), + 'productive_fields':sum(targets.values()), 'paid_calls':sum(paid.values()), + 'root_bracket':[ROOT_LOW,ROOT_HIGH], 'headroom_from_declared_to_root':[ROOT_LOW-KAPPA,ROOT_HIGH-KAPPA], + 'fixed_profile_ceiling':{'decreasing_C_interval':['0','1/20'], + 'negative_derivative_upper':E.display((-derivative_lower,)*2), + 'remaining_C_interval':['1/20','1'], 'negative_moment_upper':E.display((negative_upper,)*2)}, + 'strictification':{'tensor_power':v,'cutoff_base':c,'target_floor_base':b,'tail_offset':u, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta), + 'rational_upper_limits':limits, 'normalized_paid_upper':normalized_upper, + 'gap':E.display((1-normalized_upper,)*2)}, + 'compiler':{'theta_upper':theta,'logarithm_power':power,'eta':E.display(eta), + 'uniform_saving':params['complex_uniform_saving'],'gap':gap,'H':H, + 'N':'2^'+str(H), 'integer_test_exponent':hi, 'word_materialized':False}, + 'BIT':{'inherited_unrelaxed_saving':bit_raw,'admitted':bit_admitted,'gap':bit_raw-bit_admitted}, + 'outer':outer, 'negative_controls':controls}) + +if __name__ == '__main__': + result = run(native.read(HERE/'NATIVE-RESULT.json.gz')) + (HERE/'ARITHMETIC-RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({k:result[k] for k in ('status','kappa','gain_over_PR4416','root_bracket','compiler')},sort_keys=True)) diff --git a/research/fresh-helper-boundary/discover-cut.cpp b/research/fresh-helper-boundary/discover-cut.cpp new file mode 100644 index 0000000000..5caa077ea0 --- /dev/null +++ b/research/fresh-helper-boundary/discover-cut.cpp @@ -0,0 +1,35 @@ +// Optional floating-point discovery, never a proof checker. Apache-2.0. +// Prepared with substantial OpenAI Codex assistance. +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; +struct Arc{int v,rev;double cap;}; +struct Flow{vector> a;vector level,ptr;Flow(int n):a(n),level(n),ptr(n){};void edge(int u,int v,double c){Arc x{v,int(a[v].size()),c},y{u,int(a[u].size()),0};a[u].push_back(x);a[v].push_back(y);}double send(int u,int t,double f){if(u==t)return f;for(int&i=ptr[u];i1e-8&&level[e.v]==level[u]+1){double z=send(e.v,t,min(f,e.cap));if(z>1e-8){e.cap-=z;a[e.v][e.rev].cap+=z;return z;}}}return 0;}vectorcut(int s,int t){while(true){fill(level.begin(),level.end(),-1);queueq;level[s]=0;q.push(s);while(!q.empty()){int u=q.front();q.pop();for(auto e:a[u])if(e.cap>1e-8&&level[e.v]<0){level[e.v]=level[u]+1;q.push(e.v);}}if(level[t]<0){vectorv(level.size());for(int i=0;i=0;return v;}fill(ptr.begin(),ptr.end(),0);while(send(s,t,1e15)>1e-8){}}}}; +struct Node{bool mut;int oldf,newf;}; +int main(int argc,char**argv){if(argc!=3){cerr<<"usage: discover-cut entry|exit output-file"<>F>>N>>E;vectordim(F);vector>space(F);for(int f=0;f>dim[f];for(auto&x:space[f])cin>>x;}vector>sub(F,vector(F,true));for(int i=0;inodes(N);vectoridx(N,-1),rev;for(int i=0;i>m>>nodes[i].oldf>>nodes[i].newf;nodes[i].mut=m;if(m){idx[i]=rev.size();rev.push_back(i);}}vector>edges(E);for(auto&[a,b]:edges)cin>>a>>b; + int H;cin>>H;vector>helpers(H);for(auto&[i,f]:helpers)cin>>i>>f; + vectorcandidates;for(int f=0;funary(V,0);int s=V,t=V+1; + for(auto[a,b]:edges){int fa=nodes[a].newf,fb=nodes[b].oldf;double e0=powers[dim[fb]-dim[fa]];int i=idx[a],j=idx[b]; + double e10=sub[g][fb]?powers[dim[fb]-dim[g]]:INF;double e01=sub[fa][g]?powers[dim[g]-dim[fa]]:INF; + if(i>=0&&j>=0){double w=e10+e01-e0;if(w<-1e-7){cerr<<"nonsubmodular"<=0)unary[i]+=e10-e0;else if(j>=0)unary[j]+=e01-e0; + } + for(auto[i,f]:helpers){int old=nodes[i].newf;double delta=(entry?(sub[g][f] && dim[g]dim[f]))?(entry?powers[dim[f]-dim[old]]-powers[dim[f]-dim[g]]:powers[dim[old]-dim[f]]-powers[dim[g]-dim[f]]):INF;unary[idx[i]]+=delta;} + for(int i=0;i=0&&reach[idx[a]]?g:fa,gb=idx[b]>=0&&reach[idx[b]]?g:fb;if(!sub[ga][gb]){legal=false;break;}delta+=powers[dim[gb]-dim[ga]]-powers[dim[fb]-dim[fa]];} + for(auto[i,f]:helpers)if(reach[idx[i]]){int old=nodes[i].newf;if(entry?(!sub[g][f]||dim[g]>=dim[f]):(!sub[f][g]||dim[g]<=dim[f])){legal=false;break;}delta+=entry?powers[dim[f]-dim[old]]-powers[dim[f]-dim[g]]:powers[dim[old]-dim[f]]-powers[dim[g]-dim[f]];} + if(legal&&delta < -1e-8){int count=0;for(int i=0;i=-1e-8){cerr<<"NO_GAIN round "<= 224: + continue + out.append(e) + for r, f in enumerate(c['final']): + climb(r, f) + return out + +def run(changes=None, phase_check=True): + c = read(BASE/'THREE-base-FULL-IDENTITY-CANONICAL.json.gz') + original = read(BASE/'THREE-base-FULL-IDENTITY-NATIVE.json.gz') + changes = read(HERE/'CHANGES.json') if changes is None else changes + for key, frame_key in (('entrances', 'start'), ('exits', 'final')): + seen = set() + for role, old, new in changes[key]: + need(role not in seen and 224 <= role < 632 and c[frame_key][role] == old, 'Bound unique helper boundary') + seen.add(role); c[frame_key][role] = new + maps = {d: gates(p) for d, p in original.items()} + need(set(maps['forward']) == set(maps['backward']), 'Both scalar orientations have the same contact inventory') + for key in maps['forward']: + f = original['forward'][maps['forward'][key]] + b = original['backward'][maps['backward'][key]] + need(b[1] == dual(f[1]) and b[2] == f[2], 'Actual inverse-transpose scalar correspondence') + changed = deepcopy(original) + seen = set() + for phase, ordinal, old, new in changes['gates']: + key = (phase, ordinal) + need(key not in seen and key in maps['forward'], 'Bound unique retimed scalar contact') + seen.add(key) + for d in changed: + e = changed[d][maps[d][key]] + need(e[2] == old, 'Original scalar frame pin') + e[2] = new + programs = {d: synthesize(c, p) for d, p in changed.items()} + V = load(ROOT/'research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py', 'fresh_boundary_rows') + X = load(ROOT/'research/kappa-rebuild/complex/native_extensions.py', 'fresh_boundary_literal') + checks = {} + profiles = {} + for d, p in programs.items(): + rows, receipt = X.literal_replay(V, c, p, d == 'backward') + for r in range(632): + need(rows['L', r] == V.expected(('L', r), [], d == 'backward', False), 'Every actual arbitrary-input endpoint, role '+str(r)) + profiles[d] = Counter({int(k): v for k, v in receipt['paid_profile'].items()}) + rebound = deepcopy(c) + rebound['local_profile'] = dict(profiles[d]) + receipt['second_literal'] = V.replay(p, rebound, [], d == 'backward', False) + checks[d] = receipt + need(profiles['forward'] == profiles['backward'], 'Same complete native tariff in both orientations') + H = Counter() + for r in range(224, 632): + a, b = c['start'][r], c['final'][r] + need(span(c['frames'][a]) <= span(c['frames'][b]), 'Nested productive helper boundary') + width = len(c['frames'][b])-len(c['frames'][a]) + need(width > 0, 'Every declared helper is independently productive') + H[width] += 1 + physical = [] + if phase_check: + ce = load(ROOT/'research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py', 'fresh_boundary_clifford') + P = load(ROOT/'research/kappa-function-composition/complex/prune_native.py', 'fresh_boundary_lowering') + N = X.N + old_edges = {(e[3], e[4]) for e in original['forward'] if e[0] == 'climb'} + new_edges = {(e[3], e[4]) for e in programs['forward'] if e[0] == 'climb'} + helper_edges = {(c['start'][r], c['final'][r]) for r in range(224, 632)} + for a, b in sorted((new_edges-old_edges) | helper_edges): + op = ce.canonical_frame(9, c['frames'][a]).adjoint().then(ce.canonical_frame(9, c['frames'][b])) + want = len(c['frames'][b])-len(c['frames'][a]) + directions = {} + for d in ('forward', 'backward'): + actual = P.conjugate(ce, op) if d == 'backward' else op + rec = N.lower_exact(P, ce, actual) + need(rec['rank'] == want, 'New physical Fourier rank including phase') + directions[d] = rec + physical.append({'old': a, 'new': b, 'rank': want, 'recipes': directions}) + return {'status': 'PASS_RETIMED_BOTH_ORIENTATIONS_ALL_632_COLUMNS', + 'helpers': dict(sorted(H.items())), 'paid': dict(sorted(profiles['forward'].items())), + 'changed_entrances': len(changes['entrances']), 'changed_exits': len(changes['exits']), + 'changed_scalar_frames': len(changes['gates']), 'native': checks, + 'new_physical_edges_and_boundaries': physical}, c, programs + +if __name__ == '__main__': + import argparse + p = argparse.ArgumentParser(); p.add_argument('--skip-phase', action='store_true'); p.add_argument('--write-result', action='store_true'); args = p.parse_args() + result, _, _ = run(phase_check=not args.skip_phase) + if args.write_result: + need(not args.skip_phase, 'Do not replace a complete phase receipt with a diagnostic') + (HERE/'NATIVE-RESULT.json.gz').write_bytes(gzip.compress((json.dumps(result, indent=2, sort_keys=True)+'\n').encode(),mtime=0)) + print(json.dumps({k: v for k, v in result.items() if k not in ('native', 'new_physical_edges_and_boundaries')}, sort_keys=True)) diff --git a/research/fresh-helper-boundary/verify.py b/research/fresh-helper-boundary/verify.py new file mode 100644 index 0000000000..e434dbf7c6 --- /dev/null +++ b/research/fresh-helper-boundary/verify.py @@ -0,0 +1,99 @@ +"""Replay the changed native unit and its conditional multiplication endpoint. + +Standard library only. Apache-2.0; substantial OpenAI Codex assistance. +""" +import argparse +import gzip +from copy import deepcopy +from hashlib import sha256, sha1 +import json +from pathlib import Path +import native +import arithmetic + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + +def need(ok, why): + if not ok: + raise ValueError(why) + +def authenticate(): + manifest = native.read(HERE/'SOURCES.json') + seen = set() + for row in manifest['files']: + if row['usage'] != 'input': + continue + path = Path(row['path']) + need(not path.is_absolute() and '..' not in path.parts and str(path) not in seen, 'Canonical unique input') + seen.add(str(path)) + actual = ROOT + for part in path.parts: + actual /= part + need(not actual.is_symlink(), 'No source alias') + data = actual.read_bytes() + need(sha256(data).hexdigest() == row['sha256'], 'Changed source: '+str(path)) + need(sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest() == row['git_blob'], 'Changed source Git blob') + return len(seen) + +def controls(result, c, programs): + # This is a literal original-word control, not a second mathematical review. + baseline, _, _ = native.run({'entrances':[], 'exits':[], 'gates':[]}, phase_check=False) + need(baseline['helpers'] == {5:28,6:18,7:56,8:93,9:213}, 'Recover the actual predecessor helper profile') + need(baseline['paid'] == {1:2487,2:713,3:224,4:102,5:20,8:8}, 'Recover the actual predecessor paid profile') + V = native.load(ROOT/'research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py','boundary_control_rows') + rebound = deepcopy(c); rebound['local_profile'] = result['paid'] + bad = deepcopy(programs['forward']) + bad.pop(next(i for i, e in enumerate(bad) if e[0] == 'center')) + rejected = False + try: + V.replay(bad, rebound, [], False, False) + except (ValueError, AssertionError): + rejected = True + need(rejected, 'A missing paid center is rejected at the actual frame contact') + # A pure global-phase corruption has an unchanged Pauli tableau. + ce = native.load(ROOT/'research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py','boundary_control_phase') + P = native.load(ROOT/'research/kappa-function-composition/complex/prune_native.py','boundary_control_decode') + row = result['new_physical_edges_and_boundaries'][0] + rec = deepcopy(row['recipes']['forward']) + def decode(r): + left = P.monomial(ce, r['left'],9) + if r['rank']: + return P.monomial(ce,r['right'],9).then(ce.fourier(9,range(r['rank']))).then(left) + return left + original = decode(rec) + rec['left']['phase'] = (rec['left']['phase']+1)%4 + changed = decode(rec) + need(changed.tab == original.tab and changed.zero_state() != original.zero_state(), 'Absolute phase corruption is detected beyond tableau equality') + return {'predecessor_recovered':True,'omitted_center_rejected':True,'global_phase_only_corruption_rejected':True} + +def verify(write=False): + count = authenticate() + result, c, programs = native.run() + math = arithmetic.run(result) + checks = controls(result,c,programs) + artifacts = {'NATIVE-RESULT.json.gz': result, 'ARITHMETIC-RESULT.json': math} + for name, value in artifacts.items(): + normalized = json.loads(json.dumps(value)) + if write: + data = (json.dumps(normalized,indent=2,sort_keys=True)+'\n').encode() + (HERE/name).write_bytes(gzip.compress(data,mtime=0) if name.endswith('.gz') else data) + else: + need(normalized == native.read(HERE/name), 'Exact receipt replay: '+name) + receipt = {'status':'PASS_FRESH_HELPER_BOUNDARY_CONDITIONAL_KAPPA', + 'kappa_decimal':'0.00272124', 'source_inputs':count, + 'physical_edges_and_boundaries':len(result['new_physical_edges_and_boundaries']), + 'changed_entrances':result['changed_entrances'], 'changed_exits':result['changed_exits'], + 'changed_scalar_frames':result['changed_scalar_frames'], + 'controls':checks, 'scientific_receipts':{name:sha256(gzip.decompress((HERE/name).read_bytes()) if name.endswith('.gz') else (HERE/name).read_bytes()).hexdigest() for name in artifacts}} + if write: + (HERE/'RESULT.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n') + else: + need(receipt == native.read(HERE/'RESULT.json'), 'Final checked receipt') + return receipt + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--write-receipts', action='store_true', help='Author receipts explicitly; ordinary replay does not write.') + args = parser.parse_args() + print(json.dumps(verify(args.write_receipts),sort_keys=True)) From eb6195fe3acd45669f17d7dd957e5b0177957f57 Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 15:24:43 -0500 Subject: [PATCH 09/26] Combine query thinning and helper retiming for conditional kappa 0.00300105 --- .../FRONTIER-CHECKS.json | 9 +- research/fresh-helper-thinned/AUDIT-4440.md | 44 +++ research/fresh-helper-thinned/PROOF.md | 132 +++++++++ research/fresh-helper-thinned/README.md | 92 ++++++ research/fresh-helper-thinned/RESULT.json | 237 +++++++++++++++ research/fresh-helper-thinned/SOURCES.json | 278 ++++++++++++++++++ research/fresh-helper-thinned/TASK.json | 96 ++++++ research/fresh-helper-thinned/VALIDATION.md | 26 ++ research/fresh-helper-thinned/VERIFY.json | 60 ++++ research/fresh-helper-thinned/verify.py | 180 ++++++++++++ 10 files changed, 1153 insertions(+), 1 deletion(-) create mode 100644 research/fresh-helper-thinned/AUDIT-4440.md create mode 100644 research/fresh-helper-thinned/PROOF.md create mode 100644 research/fresh-helper-thinned/README.md create mode 100644 research/fresh-helper-thinned/RESULT.json create mode 100644 research/fresh-helper-thinned/SOURCES.json create mode 100644 research/fresh-helper-thinned/TASK.json create mode 100644 research/fresh-helper-thinned/VALIDATION.md create mode 100644 research/fresh-helper-thinned/VERIFY.json create mode 100644 research/fresh-helper-thinned/verify.py diff --git a/research/fresh-helper-boundary/FRONTIER-CHECKS.json b/research/fresh-helper-boundary/FRONTIER-CHECKS.json index 2bebc81a01..df86354352 100644 --- a/research/fresh-helper-boundary/FRONTIER-CHECKS.json +++ b/research/fresh-helper-boundary/FRONTIER-CHECKS.json @@ -9,6 +9,13 @@ "highest_conditional_claim_pr": 4416, "kappa": "0.00268647", "action": "No stronger new claim found. Continue from p7 and PR4433 tail theorem." + }, + { + "utc": "2026-10-21T20:12:23Z", + "latest_pr": 4442, + "highest_conditional_claim_pr": 4440, + "kappa": "0.00296", + "action": "Audited exact head 40e22a83; registered replay passed. Switched to the stronger query-thinned construction and combined the verified helper retiming. New result is in research/fresh-helper-thinned." } ] -} \ No newline at end of file +} diff --git a/research/fresh-helper-thinned/AUDIT-4440.md b/research/fresh-helper-thinned/AUDIT-4440.md new file mode 100644 index 0000000000..64c4a98675 --- /dev/null +++ b/research/fresh-helper-thinned/AUDIT-4440.md @@ -0,0 +1,44 @@ +# Audit of PR4440 at 40e22a83ed660d3d6074c4f2dbf14bfb621eee51 + +The 20:12 UTC frontier check found PR4440's conditional 0.00296 above the first +helper-retiming result. Work switched to that source. Its complete registered +Python 3.12.15 replay passed before this combination was developed. Normal +combined replay repeats its full verifier and compares its saved receipt. + +No blocking defect was found **under its stated native, arbitrary-column, +owned-erasure and transfer contracts**. This is an AI-assisted source/proof +and finite-replay audit, not independent human or formal theorem acceptance. + +- **Paid query primitive.** Clear an owned stream, copy the donor, pay one + rank-one Q or Q^-1 job, add/subtract into the target, and erase only the owned + stream. The donor is retained; copied data create no productive input. + The inverse complex Gaussian is normalized with its actual Pauli translation, + not an order-two assumption. Literal arbitrary X/Y/Z columns reject omitted + clear/erase steps. Arbitrary-column physical lowering and owned erasure remain + explicit retained contracts rather than consequences of the finite test. +- **Actual controller.** Rational Laurent and binary coefficient checks replay + every emitted LOCAL, QUERY_SHEAR, IDLE, bridge and boundary program. Replacing + even stages also removes exactly those stage factors from idle operators and + target monomials. Lost helper inventories are charged. A wrong query direction + or altered coefficient changes the checked operator. +- **Native geometry.** Complex forward/inverse contact phases use the same + old-nine/fresh-eight chart on all 112 ports; the central q is fixed. Removing + inactive spectator blocks does not remove an active transform. BIT separately + checks all 111 rational charts and the original native child/copy bills. +- **Chronology and owners.** Full calls return their center before the next + query call. The one sequential owned stream can be reused at raw level; + nested products allocate the distinct centers required by suspended callers. + All full-call helpers are fresh independent fields. No copy, center or inactive + stage receives productive credit. +- **Complete costs.** The literal and closed-form invoices agree. Paid products, + completion and splitting charge both tails; the strict compiler is used only + after separation. The stronger BIT conversion pays its delayed cover fallback + and changes its atom power to 0.004; retaining 0.003 fails the adapter comparison. + Nine outer rows, 54 predicates and four guards are recomputed, with controls. +- **Limits.** The huge winning words and widths are finite algorithmic + specifications. Source all-column, owned-erasure, legal matcher, tape, + precision, analytic and recovery obligations remain conditional. + +The combination below makes no edit to PR4440. Its full and query main operators +stay fixed. It replaces only each full unit by an all-input-equivalent native +unit, then independently rebuilds the complete paid/productive invoice. diff --git a/research/fresh-helper-thinned/PROOF.md b/research/fresh-helper-thinned/PROOF.md new file mode 100644 index 0000000000..bf68dc2b98 --- /dev/null +++ b/research/fresh-helper-thinned/PROOF.md @@ -0,0 +1,132 @@ +# Conditional combination proof + +## 1. Exact unit substitution + +Use the source full-identity main shears and autonomous helpers in both +orientations. The retiming lemma of `fresh-helper-boundary/PROOF.md` changes +helper entrance/exit gauges and scalar contact frames while preserving every +logical row, main boundary, warp contact, scalar order/coefficient and owned +center. Both actual native words are replayed on all 632 arbitrary input +columns; 320 distinct new transport edges/helper boundaries are lowered and +decoded with absolute phase. Every helper boundary is normalized with its +recorded input and output monomials around the complete local job. These +factors need not be an inverse pair. + +Consequently a full LOCAL call in PR4440's complex word can be replaced by +this unit without changing its physical main operator. Allocate its 408 fresh +helper fields on the same distinct owner slots. Their new target profile is +`{4:26,5:2,7:29,8:42,9:309}` and paid profile is +`{1:2253,2:515,3:445,4:102,5:40,8:8}`. Each center remains owned and uncredited. +The same formal gauge equivalence applies under the retained all-column block +lifts; no sum of operators is tensor-powered. + +The source p17 controller has 19 full calls and 16 copied query shears. Every +thin query, full-call phase contact, main boundary and whole idle is unchanged. +The copied-query primitive and its zero/erase and physical Q contracts are +those audited in AUDIT-4440.md. Substitution therefore preserves the entire +main word. The normal verifier freshly executes both source verifiers before +using this implication. + +## 2. Entire changed invoice + +Count the actual emitted source events. Each LOCAL contributes one new H and +P; each QUERY_SHEAR contributes 112 paid rank-one jobs and no productive field; +each nonzero IDLE contributes 224 jobs of rank eight times its listed active +stage count. Each actual main diagonal monomial contributes 112 independent +rank `1+8*number_of_active_stages` fields. This gives + +``` +T={4:494,5:38,7:551,8:798,9:5871,17:448,25:448,33:448, + 41:448,49:448,57:448,65:448,73:448,153:224}, +P={1:44599,2:9785,3:8455,4:1938,5:760,8:152,16:448, + 24:448,32:448,40:448,48:448,56:448,64:448,72:448}. +``` + +There are 11,560 independent productive fields, 69,273 paid calls and rank +masses 260,798 and 259,998. Surplus 800 is preserved. An independent subtraction +of nineteen old helper/paid inventories and addition of nineteen new ones to +the source invoice must agree exactly with these event counts. + +At C=.003001052 the strict raw moment is checked by two rational interval +engines. Root signs at .0030010541830 and .0030010541834 enclose the new root. +As in the source helper package, interval derivatives prove strict decrease +on [0,1/20], and 128 closed interval enclosures exclude any positive moment on +[1/20,1]. This is a fixed-profile ceiling, not a global optimum. Chronological +products multiply the moments; paid completion loses moment by concavity and +splitting increases paid charge. Those operations cannot beat this raw ceiling. + +## 3. Pay both tails and specify a finite uniform rank + +Use t=1-C, u=1/5, v=1024, cutoff J=20^v and floor L=21^v. Apply the source +chronological product and whole-job completion/splitting algorithm, preserving +all spectators, restored matchers, distinct productive fields and owned banks. +Exactly the same charged theorem bounds the normalized paid moment by + +``` +alpha^v + 2 gamma^v + 2 delta^v, +alpha=P_t/T_t, +gamma=P_(t+u)/(20^u*T_t), +delta=11560*21/(20^C*T_t). +``` + +The new exact limits are `alpha<1-10^-9`, `gamma<97/100`, `delta<19/20`. +The old gamma limit 31/32 fails on this changed invoice and is explicitly +rejected. Both new tail limits to power 128 are strictly below 1/16. Hence +both tails at v=1024 are below 2^-32, and the exact rational inequality is + +``` +1/(1+1024/10^9) + 4/2^32 < 1. +``` + +Every completion and original paid tail is included. Final paid ranks are +at most 20^v and every productive target is at least 21^v. The maximum target +and ambient rank is m=153^v. + +Use PR4433's general logarithmic majorant, not an uncharged direct compiler. +Put theta=63/64 and p=1000. Check `20^64<21^63`, +`2*(20^v)^64 <= (153^v)^63`, and `eta=t*153^(-v*C)>theta^1000`. +The complete base range satisfies `153^(v*C)<2^1000` as well. These are precisely +the shifted exit, complement and base-range hypotheses of that majorant. + +For declared kappa=.00300105, set d=(C-kappa)/7=1/3500000000 and uniform +saving C-d. Let H be the reported multiple of 3500000000 satisfying +`(H+1)^1000 < 2^(d*H)`, and reject the previous grid point. RESULT.json +records the exact integers, giving the explicit sufficient rank N=2^H. +The source integer mixed flow supplies its integral widths, complements, owned +centers and exit jobs. The massive word is algorithmically specified, not emitted. + +## 4. Nonrecursive work, BIT and outer bill + +The complete local scalar lists retain the checked maximum allowance 158,168. +Bound each paid-job and helper monomial pair by 1000 elementary fixed +nine-coordinate records: Gaussian elimination, swaps, quadratic/linear phases, +offsets and global phase fit this conservative bound. The resulting local +scalar plus route allowance is below 10^7. The remaining 240 fixed warp +events and 448 main boundary adapters contribute fewer than 688,000 further +elementary records, also within that 10^7 local budget. Nineteen such units, all source query +records, bridges, boundary words and fixed chart records fit the retained raw +10^9 record bound; the verifier checks that larger substituted allowance. + +Update every product/compiler count from this actual word. The source finite +record bound and precision/stock prescription include the new normalizers, +every paid query and copied stream, all completions/splits, source complements, +owned banks, routes and rank-one leaves. No small predecessor constant is +substituted for the final compiled word. Fixed constants are absorbed only +through the positive spare powers of the inherited conditional transfer. + +Retain PR4440's entire BIT construction: pre-cover saving .003459, covered +saving .00345 and atom power .004. Its ordinary saving is .0034363538396, +admitted at .0034, strictly above the new complex endpoint. Its adapter, stock, +cover, owned queries and effective compiler remain unchanged. Normal replay +freshly checks that complete source construction. + +Set b=kappa+5d, a=kappa+4d, q=kappa+3d, epsilon=1-d, beta=1-3d, +r0=d/10 and stop=layout=d. Recompute all nine outer rows, 54 strict predicates +and four functional guards, including the actual new BIT atom. Every check +passes. Old BIT admission, a closed uniform/epsilon gap and the unfunded tested +endpoint are rejected. + +The source arbitrary-column native, owned-erasure, permitted physical matching, +finite-template precision, analytic decomposition, fixed-tape, prime and exact +recovery contracts remain conditional premises. These finite exact checks are +not formal verification or independent human acceptance of the complete theorem. diff --git a/research/fresh-helper-thinned/README.md b/research/fresh-helper-thinned/README.md new file mode 100644 index 0000000000..344616d665 --- /dev/null +++ b/research/fresh-helper-thinned/README.md @@ -0,0 +1,92 @@ +# Conditional κ = 0.00300105: fresh helper retiming on query-thinned controllers + +This builds on the stronger [PR4440](https://github.com/CrocSwap/integer-mult-bounds/pull/4440) +found during the requested 20-minute frontier check. After auditing its exact +head, replace all 19 full complex native calls by the verified fresh-helper +unit of `research/fresh-helper-boundary`. The main controller, 16 paid query +shears and stronger ordinary BIT supplier stay those of PR4440. The proposed +conditional bound is + +``` +T(n) = O(n (log n)^(1 - 0.00300105)). +``` + +The gain is **0.00004105 (about 1.39%) over PR4440's 0.00296**, +**about 11.71% over PR4416's 0.00268647**, and **30.48% over the pinned +selected 0.0023**. The new result is author-checked and awaits review; it +retains the conditional source implementation and transfer contracts. + +| Complete complex raw invoice | PR4440 | Combined construction | +| --- | ---: | ---: | +| Full native calls / paid query shears | 19 / 16 | 19 / 16 | +| Independent productive fields | 11,560 | 11,560 | +| Paid calls | 72,902 | **69,273** | +| Productive / paid rank mass | 258,271 / 257,471 | 260,798 / 259,998 | +| Rank-one surplus | 800 | 800 | +| Proposed conditional κ | 0.00296 | **0.00300105** | + +The native retiming removes **3,629 paid calls**. It changes 117 helper +entrances, 42 exits and 395 scalar frames in each full invocation, with exactly +the same main operator and complete owned-center program. Thus substitution +is a native operator equivalence, not merely replacement of a histogram. +Every helper is still a distinct arbitrary original input; query copies and +centers receive no productive credit. [PROOF.md](PROOF.md) gives the join. + +The exact changed-profile root is enclosed by + +``` +0.0030010541830 < root < 0.0030010541834. +``` + +An interval proof covers every real `0 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "871499999253/875000000000", + "fixed_halo_explicit_metadata_branch": "67375000001/875000000", + "new_BIT_row_stock_sublinear_in_active_group": "3489499997009/3500000000000", + "new_semantic_group_guard": "3/3500000000" + }, + "margins": { + "boundary_algebraic_matrix": "18381438244748161/6125000000000000000", + "fused_gaussian": "18381438234244483/6125000000000000000", + "global_coordinate_router": "10503679/3500000000", + "group_bit_router": "36762879968488963/12250000000000000000", + "group_scans": "1749999999/1750000000", + "main_transform": "18381436494748161/6125000000000000000", + "microbox_face_corrections": "67375000001/875000000", + "polynomial_products": "3499999999/3500000000", + "sparse_union_movement": "2506662688244748161/6125000000000000000" + }, + "parameters": { + "a": "10503679/3500000000", + "b": "8206/2734375", + "beta": "3499999997/3500000000", + "bit_saving": "17/5000", + "cap_xi": "5569162686494748161/6125000000000000000", + "complex_uniform_saving": "10503681/3500000000", + "d": "1/3500000000", + "epsilon": "3499999999/3500000000", + "kappa": "60021/20000000", + "lambda_": "996998949/1000000000", + "lambda_prime": "1744748161/1750000000", + "layout": "1/3500000000", + "q": "5251839/1750000000", + "r0": "1/35000000000", + "stop": "1/3500000000", + "tested_saving": "750263/250000000" + }, + "strict_checks": { + "actual_bit_above_effective": "1396321/3500000000", + "actual_logarithmic_gamma_guard": "1/3500000000", + "actual_logarithmic_group_guard": "555837316130251839/3062500000000000000", + "alpha_logarithm_absorption": "1/35000000000", + "boundary_algebraic_matrix_above_kappa": "6994748161/6125000000000000000", + "cap_above_band": "2506662686494748161/6125000000000000000", + "cap_below_cell": "555837311755251839/6125000000000000000", + "cap_below_phase_cell_power": "6680837313505251839/6125000000000000000", + "complex_above_effective": "1/3500000000", + "complex_below_one_over_32": "2471783/87500000", + "complex_endpoint": "1/1750000000", + "epsilon_below_one": "1/3500000000", + "epsilon_positive": "3499999999/3500000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "6984244483/6125000000000000000", + "gaussian_above_main": "869748161/3062500000000000000", + "global_coordinate_router_above_kappa": "1/875000000", + "global_gamma_power_slack": "9/35000000000", + "group_below_dimension": "1/1750000000", + "group_bit_router_above_kappa": "17468488963/12250000000000000000", + "group_gauge_power_slack": "555837316042751839/3062500000000000000", + "group_key_fits_record": "1/1750000000", + "group_positive": "3499999997/3500000000", + "group_scans_above_kappa": "3489496323/3500000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "635039790400418148631/500000000000000000000000", + "lambda_above_internal": "1/7000000000", + "lambda_above_sigma": "3/7000000000", + "lambda_above_tau": "1/7000000000", + "lambda_prime_above_lambda": "1/7000000000", + "lambda_prime_above_leaf": "85321/149536132812500", + "leaf_saving_above_effective": "2726169/9570312500000000", + "main_transform_above_kappa": "5244748161/6125000000000000000", + "membership_arithmetic_fits_record": "1/3500000000", + "microbox_face_corrections_above_kappa": "269489496329/3500000000", + "microbox_halo_volume": "276500000003/3500000000", + "new_complex_uniform_saving_above_b": "1/3500000000", + "new_semantic_guard_with_C1_one": "1/3500000000", + "polynomial_products_above_kappa": "872374081/875000000", + "positive_layout_slack": "1/3500000000", + "q_below_effective": "1/3500000000", + "q_below_internal": "1/3500000000", + "q_below_leaf": "85321/149536132812500", + "q_positive": "5251839/1750000000", + "short_record_fallback": "2726169/2734375", + "source_axis_superpolynomial": "1/3500000000", + "sparse_union_movement_above_kappa": "2488281256994748161/6125000000000000000", + "stop_below_one": "3499999999/3500000000", + "stop_positive": "1/3500000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/3500000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/3500000000", + "union_tag_work_per_visit_fits_record": "3/3500000000" + } + }, + "paid": { + "1": 44599, + "16": 448, + "2": 9785, + "24": 448, + "3": 8455, + "32": 448, + "4": 1938, + "40": 448, + "48": 448, + "5": 760, + "56": 448, + "64": 448, + "72": 448, + "8": 152 + }, + "paid_calls": 69273, + "productive_fields": 11560, + "query_shears": 16, + "scope": "Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.", + "source_heads": { + "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", + "helper_retiming": "ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9" + }, + "source_inputs": 41, + "status": "PASS_CONDITIONAL_FRESH_HELPER_QUERY_THINNED_KAPPA", + "strictification": { + "alpha": { + "lower": "0.999999997758999184602267590366", + "upper": "0.999999997758999184602267590367" + }, + "cutoff": 20, + "delta": { + "lower": "0.932537400874663431699700098660", + "upper": "0.932537400874663431699700098661" + }, + "floor": 21, + "gamma": { + "lower": "0.969126930833863729265427869330", + "upper": "0.969126930833863729265427869331" + }, + "limits": [ + "999999999/1000000000", + "97/100", + "19/20" + ], + "normalized_paid_upper": "2097152001953127/2097154147483648", + "power": 1024, + "tail_offset": "1/5", + "tested": "750263/250000000" + }, + "targets": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 494, + "41": 448, + "49": 448, + "5": 38, + "57": 448, + "65": 448, + "7": 551, + "73": 448, + "8": 798, + "9": 5871 + } +} diff --git a/research/fresh-helper-thinned/SOURCES.json b/research/fresh-helper-thinned/SOURCES.json new file mode 100644 index 0000000000..4089ad3711 --- /dev/null +++ b/research/fresh-helper-thinned/SOURCES.json @@ -0,0 +1,278 @@ +{ + "schema_version": 1, + "base_commit": "3a23e9d9d2e67833515d1c60a17e966bcdcab43c", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "usage": "input", + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/ARITHMETIC-RESULT.json" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "usage": "input", + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/CHANGES.json" + }, + { + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "usage": "input", + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/NATIVE-RESULT.json.gz" + }, + { + "path": "research/fresh-helper-boundary/RESULT.json", + "usage": "input", + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/RESULT.json" + }, + { + "path": "research/fresh-helper-boundary/SOURCES.json", + "usage": "input", + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/SOURCES.json" + }, + { + "path": "research/fresh-helper-boundary/arithmetic.py", + "usage": "input", + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/arithmetic.py" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "usage": "input", + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/native.py" + }, + { + "path": "research/fresh-helper-boundary/verify.py", + "usage": "input", + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf", + "pin": "head:ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9:research/fresh-helper-boundary/verify.py" + }, + { + "path": "research/higher-moment-strictification/README.md", + "usage": "input", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "usage": "input", + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "usage": "input", + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7" + }, + { + "path": "research/kappa-function-composition/complex/prune_native.py", + "usage": "input", + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257" + }, + { + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "usage": "input", + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + { + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "usage": "input", + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef" + }, + { + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "usage": "input", + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0" + }, + { + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "usage": "input", + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "usage": "input", + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf" + }, + { + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "usage": "input", + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7" + }, + { + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "usage": "input", + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497" + }, + { + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "usage": "input", + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e" + }, + { + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "usage": "input", + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "usage": "input", + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/kappa-rebuild/complex/native_extensions.py", + "usage": "input", + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3" + }, + { + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "usage": "input", + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424" + }, + { + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "usage": "input", + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5" + }, + { + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "usage": "input", + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902" + }, + { + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "usage": "input", + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598" + }, + { + "path": "research/pr4359-p7-padding/TENSOR.md", + "usage": "input", + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/pr4359-p7-padding/native_inventory.py", + "usage": "input", + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32" + }, + { + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "usage": "input", + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "pin": "head:40e22a83ed660d3d6074c4f2dbf14bfb621eee51:research/query-thinned-controllers/BIT-CONTROLLER.json" + }, + { + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "usage": "input", + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088", + "pin": "head:40e22a83ed660d3d6074c4f2dbf14bfb621eee51:research/query-thinned-controllers/COMPLEX-CONTROLLER.json" + }, + { + "path": "research/query-thinned-controllers/RESULT.json", + "usage": "input", + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f", + "pin": "head:40e22a83ed660d3d6074c4f2dbf14bfb621eee51:research/query-thinned-controllers/RESULT.json" + }, + { + "path": "research/query-thinned-controllers/SOURCES.json", + "usage": "input", + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29", + "pin": "head:40e22a83ed660d3d6074c4f2dbf14bfb621eee51:research/query-thinned-controllers/SOURCES.json" + }, + { + "path": "research/query-thinned-controllers/controller.py", + "usage": "input", + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2", + "pin": "head:40e22a83ed660d3d6074c4f2dbf14bfb621eee51:research/query-thinned-controllers/controller.py" + }, + { + "path": "research/query-thinned-controllers/verify.py", + "usage": "input", + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950", + "pin": "head:40e22a83ed660d3d6074c4f2dbf14bfb621eee51:research/query-thinned-controllers/verify.py" + }, + { + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + ] +} diff --git a/research/fresh-helper-thinned/TASK.json b/research/fresh-helper-thinned/TASK.json new file mode 100644 index 0000000000..ee8b8e27d1 --- /dev/null +++ b/research/fresh-helper-thinned/TASK.json @@ -0,0 +1,96 @@ +{ + "schema_version": 1, + "task_id": "supplier-boundary-audit", + "priority_revision": 7, + "base_commit": "3a23e9d9d2e67833515d1c60a17e966bcdcab43c", + "original_card": { + "id": "supplier-boundary-audit", + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ], + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "existing_checks": [ + { + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3801: successor scatter-boundary decision package.", + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "status": "author-checked", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Combine the exact-head PR4440 query-thinned complex controller and stronger BIT supplier with the verified helper boundary retiming; certify a new complete conditional kappa beyond both predecessors.", + "scope_change_reason": "The explicit user task is to beat the strongest current kappa and switch to any stronger PR found in 20-minute checks. PR4440 at head 40e22a83 appeared during this run; its query-thinned native construction supersedes the first p7 result. This package audits and builds on that exact head, combining it with the independently replayed fresh helper retiming.", + "bottleneck_link": "Changing the complete nineteen-call native paid/productive profile improves the binding complex moment while retaining all copied-query charges and the stronger BIT consumer.", + "budget_minutes": 60, + "stop_rule": "Do not continue a superseded lesser kappa. Audit the stronger exact source, check actual unit substitution and the entire outer bill; no root digit-only or selected-frontier promotion.", + "outcome": "completed", + "evidence": "README.md; PROOF.md; AUDIT-4440.md; RESULT.json; SOURCES.json; VALIDATION.md", + "author": "1337isnot1337 with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance. No subagents or independent human mathematical review.", + "open_questions": [ + { + "question": "Can another simultaneous multi-frame or query/native topology change beat the new fixed-profile root?", + "why_it_matters": "Only about 4.18e-9 headroom remains in this invoice; another substantial improvement requires a changed profile.", + "first_step": "Start from the two pinned native units and emit a literal changed chronological word with all helper, owned-query and idle charges before a new root claim.", + "blocked_by": "No global optimum or complete multi-frame search is supplied." + }, + { + "question": "Can the owned-query and helper-retiming interfaces be independently proved at arbitrary column multiplicity?", + "why_it_matters": "The finite replays inherit source native, owned-erasure and whole-job contracts.", + "first_step": "Audit AUDIT-4440.md and the block-lift/whole-job clauses of both pinned source proofs.", + "blocked_by": "Finite phase/operator evidence is not formal or human acceptance of the entire source stack." + } + ] +} diff --git a/research/fresh-helper-thinned/VALIDATION.md b/research/fresh-helper-thinned/VALIDATION.md new file mode 100644 index 0000000000..ed9998e51a --- /dev/null +++ b/research/fresh-helper-thinned/VALIDATION.md @@ -0,0 +1,26 @@ +# Validation and limits + +- Source PR4440 head 40e22a83ed660d3d6074c4f2dbf14bfb621eee51: the unchanged + registered CPython 3.12.15 replay passed during the frontier audit. +- Helper retiming head ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9: complete + CPython 3.12.15 registered replay, 320 phase/boundary checks, all 632 arbitrary + columns in both native orientations, negative controls and separate Git-free + replay passed before composition. Its published optimizer reproduces its patch. +- New arithmetic authoring freshly authenticates all pinned inputs, counts the + actual combined event word, and checks the full changed moment, root ceiling, + both tail bounds, logarithmic rank, enlarged scalar/route budget and outer bill. + The authoring path uses previously checked source receipts. Normal registered + replay freshly executes both full source verifiers and compares the combined + receipt. That normal registered CPython 3.12.15 replay passed, freshly + executing both complete source verifiers before the new arithmetic checks. + +No source package was edited. Both exact predecessor commits are retained in +publication ancestry. The selected record is unchanged. No Lean, Docker, +all-history suite, formal theorem acceptance or independent human review is +claimed. Native all-column, owned-erasure, whole-job, physical/tape, analytic, +precision, prime and exact-recovery premises remain conditional. + +The first hosted plan run at predecessor ccdae89 failed four pre-existing +selected-status navigation tests before reaching research replay. The submission +repairs only the two navigation documents, retaining selected kappa 0.0023 and +all historical content. The six targeted navigation/locale tests pass. diff --git a/research/fresh-helper-thinned/VERIFY.json b/research/fresh-helper-thinned/VERIFY.json new file mode 100644 index 0000000000..5af213891f --- /dev/null +++ b/research/fresh-helper-thinned/VERIFY.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "research/fresh-helper-boundary/RESULT.json", + "research/fresh-helper-boundary/SOURCES.json", + "research/fresh-helper-boundary/arithmetic.py", + "research/fresh-helper-boundary/native.py", + "research/fresh-helper-boundary/verify.py", + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/verify.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-function-composition/complex/prune_native.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "research/kappa-rebuild/bit/bit_native_binding.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-rebuild/bit/mixed_productive_bit.py", + "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/kappa-rebuild/complex/native_extensions.py", + "research/kappa-rebuild/complex/power_two_balance.py", + "research/kappa-rebuild/complex/rebuild_native.py", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "research/pr4359-p7-padding/P7-FACTOR.json", + "research/pr4359-p7-padding/TENSOR.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/pr4359-p7-padding/native_inventory.py", + "research/query-thinned-controllers/BIT-CONTROLLER.json", + "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "research/query-thinned-controllers/RESULT.json", + "research/query-thinned-controllers/SOURCES.json", + "research/query-thinned-controllers/controller.py", + "research/query-thinned-controllers/verify.py", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Freshly replay both exact-head source constructions; independently count the combined native/query/idle invoice; certify changed root and all-C fixed-profile ceiling, both charged tails with repaired gamma limit, logarithmic compiler rank, complete stronger BIT and all 54 outer predicates plus four guards." + } + ] +} diff --git a/research/fresh-helper-thinned/verify.py b/research/fresh-helper-thinned/verify.py new file mode 100644 index 0000000000..9ba85a59aa --- /dev/null +++ b/research/fresh-helper-thinned/verify.py @@ -0,0 +1,180 @@ +"""Combine the exact helper retiming with audited PR4440 query thinning. + +Apache-2.0; substantial OpenAI Codex assistance. Source notices retained. +Normal replay freshly executes both source verifiers, then this new ledger. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha1, sha256 +import argparse +import gzip +import importlib.util +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +KAPPA, TESTED = Q('.00300105'), Q('.003001052') +ROOT_LOW, ROOT_HIGH = Q('.0030010541830'), Q('.0030010541834') + +def need(ok, why): + if not ok: raise ValueError(why) + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + +def load(path,name): + spec = importlib.util.spec_from_file_location(name,path) + module = importlib.util.module_from_spec(spec) + sys.modules[name]=module;spec.loader.exec_module(module) + return module + +def encode(x): + if isinstance(x,Q): return str(x) + if isinstance(x,dict): return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)): return [encode(v) for v in x] + return x + +def authenticate(): + seen=set() + for row in read(HERE/'SOURCES.json')['files']: + if row['usage']!='input': continue + p=Path(row['path']);need(not p.is_absolute() and '..' not in p.parts and str(p) not in seen,'Canonical input') + seen.add(str(p));actual=ROOT + for part in p.parts: + actual/=part;need(not actual.is_symlink(),'No source aliases') + b=actual.read_bytes() + need(sha256(b).hexdigest()==row['sha256'],'Changed source: '+str(p)) + need(sha1(b'blob '+str(len(b)).encode()+b'\0'+b).hexdigest()==row['git_blob'],'Changed Git source blob') + return len(seen) + +def ceiling(E,T,P): + signed={r:T[r]-P[r] for r in T.keys()|P.keys()} + def margin(c): + a,b=E.moment(T,1-c),E.moment(P,1-c) + return a[0]-b[1],a[1]-b[0] + need(margin(ROOT_LOW)[0]>0 and margin(ROOT_HIGH)[1]<0,'New complete profile root bracket') + derivative=None + for i in range(16): + l,r=Q(i,320),Q(i+1,320);low=Q(0) + for rank,n in signed.items(): + term=E.mul(E.power(rank,1-r if n>0 else 1-l),E.log_bounds(rank)) + low+=n*term[0 if n>0 else 1] + derivative=low if derivative is None else min(derivative,low) + upper=None + for i in range(128): + l,r=Q(1,20)+Q(19*i,2560),Q(1,20)+Q(19*(i+1),2560) + hi=sum(n*E.power(rank,1-l if n>0 else 1-r)[1 if n>0 else 0] for rank,n in signed.items()) + upper=hi if upper is None else max(hi,upper) + need(derivative>0 and upper<0,'Fixed-profile ceiling for every real 00,'No nonzero charge for erased idle stage') + P[rank]+=224;idle+=224 + for term in word['diagonal']: + need(term[0] in (-1,1) and all(x in (0,1) for x in term[1:]),'Actual normalized main target') + T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(19,16,3584),'Every full, copied-query and whole-idle event') + need(sum(T.values())==11560 and sum(P.values())==69273,'Complete new productive/call counts') + need((sum(r*n for r,n in T.items()),sum(r*n for r,n in P.items()))==(260798,259998),'Preserve the exact surplus 800') + # Independent substitution into the source invoice must give the same ledger. + oldH={5:28,6:18,7:56,8:93,9:213};oldP={1:2487,2:713,3:224,4:102,5:20,8:8} + ref=source_query['complex_invoice'] + for key,new,old_unit,new_unit in [('targets',T,oldH,H),('paid',P,oldP,N)]: + check=Counter({int(k):v for k,v in ref[key].items()}) + check.subtract({k:19*v for k,v in old_unit.items()});check.update({k:19*v for k,v in new_unit.items()}) + need(+check==new,'Literal event count equals whole-call substitution: '+key) + E=S.C.load(ROOT/'research/higher-moment-strictification/verify.py','combined_exact_intervals') + root=ceiling(E,T,P) + t,u,v,c,b=1-TESTED,Q(1,5),1024,20,21 + target=E.moment(T,t);alpha=E.divide(E.moment(P,t),target) + other=S.C.load(ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','combined_separate_intervals') + tl,th=other.moment(T,TESTED);pl,ph=other.moment(P,TESTED) + need(tl>ph and max(tl,target[0])<=min(th,target[1]),'Independent exact raw-moment engine') + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + alpha_gap=Q(1,1000000000);g,d=Q(97,100),Q(19,20) + need(alpha[1]<1-alpha_gap and gamma[1]Q(31,32),'The previous gamma limit fails and is explicitly replaced') + # Apply PR4433's general logarithmic majorant at the actual new ambient rank. + theta,power=Q(63,64),1000 + eta=E.scale(E.power(153,-v*TESTED),t) + need(2*(20**v)**64<=(153**v)**63 and eta[0]>theta**power,'Shifted exit and complement capacity') + need(E.power(153,v*TESTED)[1]<2**power,'Initial compiler range') + gap=(TESTED-KAPPA)/7;need(gap.numerator==1,'Integer compiler grid') + step=gap.denominator + def passes(j):return (step*j+1)**power<2**j + lo,hi=1,2 + while not passes(hi):lo,hi=hi,2*hi + while hi-lo>1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + height=step*hi + need(height>8*v and passes(hi) and not passes(hi-1),'Effective uniform rank integer inequality') + # The changed local list is charged under an explicit larger fixed bound. + local_scalar=max(x['real_scalar_allowance'] for x in local['native'].values()) + local_routes=(sum(N.values())+2*408)*1000 + need(local_scalar+local_routes<10**7,'Every new local scalar and monomial route fits') + scalar_upper=19*10**7+16*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program']) for k in ('left','right'))) + need(scalar_upper<10**9,'Retain the complete raw nonrecursive bound') + bit=source_query['ordinary_BIT'];atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']);need(atom==Q('.004') and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Complete stronger source BIT admission') + L=S.C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','combined_outer_ledger') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Complete outer predicate inventory') + need(all(x>0 for key in ('strict_checks','functional_checks') for x in outer[key].values()),'Every complete outer inequality') + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items() if x<=0] + need(failed,'Reject '+name);controls[name]=failed + return encode({'status':'PASS_CONDITIONAL_FRESH_HELPER_QUERY_THINNED_KAPPA', 'kappa':KAPPA,'kappa_decimal':'0.00300105', + 'source_inputs':count,'source_heads':{'PR4440':'40e22a83ed660d3d6074c4f2dbf14bfb621eee51','helper_retiming':'ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9'}, + 'gain_over_PR4440':KAPPA-Q('.00296'),'gain_over_PR4416':KAPPA-Q('.00268647'), + 'targets':dict(sorted(T.items())),'paid':dict(sorted(P.items())),'full_calls':full,'query_shears':thin, + 'paid_calls':sum(P.values()),'productive_fields':sum(T.values()),'fixed_profile_ceiling':root, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta), + 'limits':[1-alpha_gap,g,d],'normalized_paid_upper':bound}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'uniform_saving':params['complex_uniform_saving'], + 'gap':gap,'H':height,'N':'2^'+str(height),'integer_test_exponent':hi,'word_materialized':False}, + 'nonrecursive':{'local_scalar_allowance':local_scalar,'local_route_bound':local_routes,'raw_upper':scalar_upper,'raw_budget':10**9}, + 'ordinary_BIT':bit,'outer':outer,'negative_controls':controls, + 'scope':'Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.'}) + +if __name__=='__main__': + parser=argparse.ArgumentParser() + parser.add_argument('--write',action='store_true',help='Author the new arithmetic receipt from already-audited dependency receipts; normal replay freshly reruns both dependencies.') + args=parser.parse_args();result=run(execute_sources=not args.write) + if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:need(result==read(HERE/'RESULT.json'),'Exact combined receipt replay') + print(json.dumps({k:result[k] for k in ('status','kappa_decimal','gain_over_PR4440','compiler')},sort_keys=True)) From 5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39 Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 15:24:43 -0500 Subject: [PATCH 10/26] Repair selected checkpoint navigation blocking research CI --- docs/ci-verification.md | 12 ++++++++++++ docs/research/current-status.md | 6 ++++-- 2 files changed, 16 insertions(+), 2 deletions(-) diff --git a/docs/ci-verification.md b/docs/ci-verification.md index 582e416aaf..50e8120dc0 100644 --- a/docs/ci-verification.md +++ b/docs/ci-verification.md @@ -2,6 +2,18 @@ ## Current selected-family replay +Resolve the [selected record](../certificates/selected-result.json) before +running a historical checkpoint. The current cold replay is +`make frontier4359-verify`, using the +[proof review](research/pr-intake-evidence/pr4359/PROOF-REVIEW.md), +[validation](research/pr-intake-evidence/pr4359/VALIDATION.json) and +[source manifest](../certificates/frontier4359-source.json). +The [frontier4359 workflow](../.github/workflows/frontier4359.yml) provides +hosted replay evidence. Metadata and source-pin checks are separate from +operator replay and do not discharge the inherited theorem assumptions. + +## Historical frontier1094 replay + Start with the [selected record](../certificates/selected-result.json). Its `reproduce`, `review`, `source_manifest` and `validation` fields identify the replay command, scoped assessment, source bindings and integration evidence. diff --git a/docs/research/current-status.md b/docs/research/current-status.md index 62a8cbb097..532af84312 100644 --- a/docs/research/current-status.md +++ b/docs/research/current-status.md @@ -1,12 +1,14 @@ # Current reviewed status -Selected conditional κ: **0.0023 = 23/10000**, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. +Selected conditional κ: **0.0023** (= 23/10000), zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. [Selected record](../../certificates/selected-result.json) · [Proof review](pr-intake-evidence/pr4359/PROOF-REVIEW.md) · [Integration receipt](pr-intake-evidence/pr4359/INTEGRATION.json) · [Contributors](community-productive4359-contributors.md). Cold replay: `make frontier4359-verify`. The fresh 23-stage replay and 59 normalized artifacts pass; the changed interfaces have an AI-assisted proof review under retained analytic/native/fixed-tape hypotheses. Winning uniform templates are not materialized. This is not a complete formal or independent human verification. #4404 independently checks a narrower arithmetic/flow scope. -## Historical selected status through #1094 +All sections below are a historical snapshot; the selected-result.json record above is authoritative. + +## Historical checkpoint through #1094 Historical selected conditional κ: **0.001672660197076918**, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555. From 322e0ec764aa7ef7801383feb1f656e460dd8bed Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 16:14:44 -0500 Subject: [PATCH 11/26] research: adjoin missing contact span for conditional kappa 0.00300123 --- research/missing-join-frame/NATIVE.json.gz | Bin 0 -> 1462 bytes research/missing-join-frame/PATCH.json | 24 ++ research/missing-join-frame/PROOF.md | 121 +++++++++ research/missing-join-frame/README.md | 56 ++++ research/missing-join-frame/RESULT.json | 239 +++++++++++++++++ research/missing-join-frame/SOURCES.json | 294 +++++++++++++++++++++ research/missing-join-frame/TASK.json | 73 +++++ research/missing-join-frame/VALIDATION.md | 27 ++ research/missing-join-frame/VERIFY.json | 65 +++++ research/missing-join-frame/native_join.py | 99 +++++++ research/missing-join-frame/verify.py | 183 +++++++++++++ 11 files changed, 1181 insertions(+) create mode 100644 research/missing-join-frame/NATIVE.json.gz create mode 100644 research/missing-join-frame/PATCH.json create mode 100644 research/missing-join-frame/PROOF.md create mode 100644 research/missing-join-frame/README.md create mode 100644 research/missing-join-frame/RESULT.json create mode 100644 research/missing-join-frame/SOURCES.json create mode 100644 research/missing-join-frame/TASK.json create mode 100644 research/missing-join-frame/VALIDATION.md create mode 100644 research/missing-join-frame/VERIFY.json create mode 100644 research/missing-join-frame/native_join.py create mode 100644 research/missing-join-frame/verify.py diff --git a/research/missing-join-frame/NATIVE.json.gz b/research/missing-join-frame/NATIVE.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..2f41b11d02726a60da449aaa6c603716c0310ead GIT binary patch literal 1462 zcmV;n1xflJiwFP!00002|LvR4bE7sC$M5+oGMs%t5@5Txbf?p1C!2KY?WH>zjSM1D zgMkVhC$p3Py-(P|faDk)XYFjbc+lfX=*L%|CkyfYRPvJZE25YlSBGsmEr3Gvk)}WHa*ez4ntE;E-aWnQnp<>BQK>s9CJ;15m z3==tH5ltlz#RH8Hcv#3AmyfVgCIYyfgd*bgDl1=jx>Knx29t}b7NW+?san)nBb!t# zYQP=4Vo(D;(%MqgM6&pf&REfXE*_V;EXko6na?67DT|_H!D3%k7`Y?ljY_wbM=05h zXVkyt{+&Mh8TXSoppnSAWKq4<$WPpTCI61#Y_~| z&251EfsowKMG~vwDwSS!cw~X_L4!ODg)cx`8D-F@*z`kqhXH3Y^vreaoyUD^p<5s|4?#H zRlR8f<*6wMAPLe$KnKrQ4nvUX{a*#jG?6k{z=K4b&hyp7>P%5HS!6|Nls~Xp8Wn|p zyRJCI{AMXOP+ksDp+JOOwK!r~UiMDe_f5SfQrrMRA{wxqtt)|Xbz*NMg^?8|T9|lY zB8Gt(4QkYtVI;>hUrs9C7U1w51`RZ}$K#Gs!|4pvfSL8lBLUQ)MQuMx6Z&pT?JeqFk!w~v{CuA@A-;p=>5*a08a z0_2upw~|OHg?JTwLG@~31tz#ic_U01{t7L_3J>#!O<6?@qNM*gjR;bNjX}d;AIMNk zU)OI#gvup^C71$Pn>IL2!>DOMUeiKI)8c8xAUtlGu&b4XUTjJdh8fT6ZvwCn-X6d#m#L;>F!WPO)03mK`-JH; zFKSxL7wt>FJEMMkHfOsc`o(vT;vU5ZKrz~bM~~wD%J*HOxW$^=8{@{3yS55n%>w6O zYi_btW%$@YuS;4VVQ<`O%Vg9&X6WI-J~Zjk4*LxUK)v%?)Z^|eX4HK%eES4IuMn@} zY$vpV>xAg&bM$Td(RSDyAljPtWVlJhs59^NIZN>N!O`2S2QR&3Jao2}3{O9r)prl& z9?I_)%IGb&Lbgu;@?oJoB70kezf&l;ScebS?>AmphvOf$4kv>n*@1b@tl5sdR{uV| z9XD9I5n%twC*8?+3_C9P?TL@yVtX9zllX>rjRul&?MzD2~lb{%`St#Ohmx Qlc$sa0fn9AIsH2T0P2?3WB>pF literal 0 HcmV?d00001 diff --git a/research/missing-join-frame/PATCH.json b/research/missing-join-frame/PATCH.json new file mode 100644 index 0000000000..f96d295d40 --- /dev/null +++ b/research/missing-join-frame/PATCH.json @@ -0,0 +1,24 @@ +{ + "phase": "B", + "ordinal": 480, + "old_frame": 732, + "new_basis": [ + 168, + 336, + 45 + ], + "old_basis": [ + 258, + 133, + 82, + 45 + ], + "incoming_frames": [ + 364, + 360 + ], + "outgoing_frames": [ + 736, + 692 + ] +} diff --git a/research/missing-join-frame/PROOF.md b/research/missing-join-frame/PROOF.md new file mode 100644 index 0000000000..d240cd8e14 --- /dev/null +++ b/research/missing-join-frame/PROOF.md @@ -0,0 +1,121 @@ +# One missing contact span and its conditional endpoint + +This is an author-checked conditional construction with declared saving +**kappa = 0.00300123**. It retains every native, arbitrary-column, owned-erasure, +whole-job matching, finite compiler, tape, precision, analytic, prime and recovery +premise of PR4440 and PR4441. It does not change the selected record or establish +an unconditional multiplication theorem. The increment is small; the concrete +new search lever is closure of the frame catalog under spans and intersections. + +## The actual changed contact + +Start at PR4441 head `5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39` and retain its +117 helper entrances, 42 exits and 395 scalar retimings. At persistent scalar +contact B/480, the forward gate is ADD(L90,L253,+1); the inverse-transpose gate +is the source's corresponding backward ADD. Both currently use frame 732, +with basis [258,133,82,45] of dimension four. + +The two incoming frames have bases [336,45] and [133,45], each of dimension +two. Their span has basis [168,336,45], dimension three. The equality +168 XOR 45 = 133 verifies the non-obvious inclusion. This three-space is absent +from the frozen 1,159-label catalog. It is contained in both outgoing spaces, +whose dimensions are five and seven. PATCH.json pins all four neighboring +labels, the old basis, and the exact phase/ordinal of the changed gate. + +Adjoin the three-space as frame 1159 and retime that single common-frame scalar +gate in both orientations. Use the source synthesizer to regenerate every +chronological climb. Every source nesting predicate remains in force. No scalar +coefficient/order, warp, center, main boundary or helper boundary changes. + +For frame operators C_a,C_b the physical transport is C_b C_a^-1. A common-frame +scalar gate preserves its logical row for arbitrary inputs, independently of +which common C is used. Thus the source retiming lemma applies. native_join.py +replays both words with two source interpreters and compares every one of the +632 independent arbitrary persistent input columns, retaining the independently +owned C0 input and its zero return. All four new transport operators are freshly +lowered and independently decoded in both orientations, checking their Pauli +tableaux and absolute phases. Their monomial factors are charged as fixed +routes; no assumption that the two factors are inverses is made. + +## A strict improvement for every exponent + +The four incident paid ranks change from [2,2,1,3] to [1,1,2,4]. Rank mass, +number of paid calls and all independent helper outputs remain unchanged. +For 0 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "348599999253/350000000000", + "fixed_halo_explicit_metadata_branch": "26950000001/350000000", + "new_BIT_row_stock_sublinear_in_active_group": "1395799997009/1400000000000", + "new_semantic_group_guard": "3/1400000000" + }, + "margins": { + "boundary_algebraic_matrix": "235296655831931/78400000000000000", + "fused_gaussian": "235296655495793/78400000000000000", + "global_coordinate_router": "2100863/700000000", + "group_bit_router": "2941208893697411/980000000000000000", + "group_scans": "699999999/700000000", + "main_transform": "235296599831931/78400000000000000", + "microbox_face_corrections": "26950000001/350000000", + "polynomial_products": "1399999999/1400000000", + "sparse_union_movement": "32085296655831931/78400000000000000" + }, + "parameters": { + "a": "2100863/700000000", + "b": "4201727/1400000000", + "beta": "1399999997/1400000000", + "bit_saving": "17/5000", + "cap_xi": "71285296599831931/78400000000000000", + "complex_uniform_saving": "16413/5468750", + "d": "1/1400000000", + "epsilon": "1399999999/1400000000", + "kappa": "300123/100000000", + "lambda_": "398799507/400000000", + "lambda_prime": "55831931/56000000", + "layout": "1/1400000000", + "q": "168069/56000000", + "r0": "1/14000000000", + "stop": "1/1400000000", + "tested_saving": "600247/200000000" + }, + "strict_checks": { + "actual_bit_above_effective": "279137/700000000", + "actual_logarithmic_gamma_guard": "1/1400000000", + "actual_logarithmic_group_guard": "7114703484168069/39200000000000000", + "alpha_logarithm_absorption": "1/14000000000", + "boundary_algebraic_matrix_above_kappa": "223831931/78400000000000000", + "cap_above_band": "32085296599831931/78400000000000000", + "cap_below_cell": "7114703344168069/78400000000000000", + "cap_below_phase_cell_power": "85514703400168069/78400000000000000", + "complex_above_effective": "1/1400000000", + "complex_below_one_over_32": "39548273/1400000000", + "complex_endpoint": "1/700000000", + "epsilon_below_one": "1/1400000000", + "epsilon_positive": "1399999999/1400000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "223495793/78400000000000000", + "gaussian_above_main": "27831931/39200000000000000", + "global_coordinate_router_above_kappa": "1/350000000", + "global_gamma_power_slack": "9/14000000000", + "group_below_dimension": "1/700000000", + "group_bit_router_above_kappa": "3493697411/980000000000000000", + "group_gauge_power_slack": "7114703481368069/39200000000000000", + "group_key_fits_record": "1/700000000", + "group_positive": "1399999997/1400000000", + "group_scans_above_kappa": "348949569/350000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "635129790400418148631/500000000000000000000000", + "lambda_above_internal": "1/2800000000", + "lambda_above_sigma": "3/2800000000", + "lambda_above_tau": "1/2800000000", + "lambda_prime_above_lambda": "1/2800000000", + "lambda_prime_above_leaf": "2795798273/1960000000000000000", + "leaf_saving_above_effective": "1395798273/1960000000000000000", + "main_transform_above_kappa": "167831931/78400000000000000", + "membership_arithmetic_fits_record": "1/1400000000", + "microbox_face_corrections_above_kappa": "53897899141/700000000", + "microbox_halo_volume": "110600000003/1400000000", + "new_complex_uniform_saving_above_b": "1/1400000000", + "new_semantic_guard_with_C1_one": "1/1400000000", + "polynomial_products_above_kappa": "1395798277/1400000000", + "positive_layout_slack": "1/1400000000", + "q_below_effective": "1/1400000000", + "q_below_internal": "1/1400000000", + "q_below_leaf": "2795798273/1960000000000000000", + "q_positive": "168069/56000000", + "short_record_fallback": "1395798273/1400000000", + "source_axis_superpolynomial": "1/1400000000", + "sparse_union_movement_above_kappa": "31850000223831931/78400000000000000", + "stop_below_one": "1399999999/1400000000", + "stop_positive": "1/1400000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/1400000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/1400000000", + "union_tag_work_per_visit_fits_record": "3/1400000000" + } + }, + "paid": { + "1": 44618, + "16": 448, + "2": 9766, + "24": 448, + "3": 8436, + "32": 448, + "4": 1957, + "40": 448, + "48": 448, + "5": 760, + "56": 448, + "64": 448, + "72": 448, + "8": 152 + }, + "paid_calls": 69273, + "productive_fields": 11560, + "query_shears": 16, + "scope": "Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.", + "source_heads": { + "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", + "PR4441_combination": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", + "helper_retiming": "ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9" + }, + "source_inputs": 46, + "status": "PASS_CONDITIONAL_MISSING_JOIN_KAPPA_00300123", + "strictification": { + "alpha": { + "lower": "0.999999995876754782344502280335", + "upper": "0.999999995876754782344502280336" + }, + "cutoff": 20, + "delta": { + "lower": "0.932537504513523310068879094384", + "upper": "0.932537504513523310068879094385" + }, + "floor": 21, + "gamma": { + "lower": "0.969136675521053502676120887993", + "upper": "0.969136675521053502676120887994" + }, + "limits": [ + "999999999/1000000000", + "97/100", + "19/20" + ], + "normalized_paid_upper": "2097152001953127/2097154147483648", + "power": 1024, + "tail_offset": "1/5", + "tested": "600247/200000000" + }, + "targets": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 494, + "41": 448, + "49": 448, + "5": 38, + "57": 448, + "65": 448, + "7": 551, + "73": 448, + "8": 798, + "9": 5871 + } +} diff --git a/research/missing-join-frame/SOURCES.json b/research/missing-join-frame/SOURCES.json new file mode 100644 index 0000000000..27681f1015 --- /dev/null +++ b/research/missing-join-frame/SOURCES.json @@ -0,0 +1,294 @@ +{ + "schema_version": 1, + "base_commit": "40f307e835b9a61e1b998bb17bd99d8c6b879a96", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "usage": "input", + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "usage": "input", + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624" + }, + { + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "usage": "input", + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839" + }, + { + "path": "research/fresh-helper-boundary/RESULT.json", + "usage": "input", + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd" + }, + { + "path": "research/fresh-helper-boundary/SOURCES.json", + "usage": "input", + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0" + }, + { + "path": "research/fresh-helper-boundary/arithmetic.py", + "usage": "input", + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "usage": "input", + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29" + }, + { + "path": "research/fresh-helper-boundary/verify.py", + "usage": "input", + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf" + }, + { + "path": "research/fresh-helper-thinned/PROOF.md", + "usage": "input", + "git_blob": "bf68dc2b987cb7de6431ff5e3514b60af48720a5", + "sha256": "9883b3329fef7624d3471e27bb55258cd9dc18bb6d37779a3939de99add87347" + }, + { + "path": "research/fresh-helper-thinned/README.md", + "usage": "input", + "git_blob": "344616d6654a96085dd45cf2c3189ef283deeac1", + "sha256": "70c1c872c2327c3f71918e218d5f1ecb7a00037771a5dd1b8ae415b84cc90dc2" + }, + { + "path": "research/fresh-helper-thinned/RESULT.json", + "usage": "input", + "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55", + "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21" + }, + { + "path": "research/fresh-helper-thinned/SOURCES.json", + "usage": "input", + "git_blob": "4089ad37114540b23846596e2a641c4a4bd608e2", + "sha256": "5aec5df5096ee8a3e90618d311640b4bdfba42be5bc4bc5fab55e8be858ab2cb" + }, + { + "path": "research/fresh-helper-thinned/verify.py", + "usage": "input", + "git_blob": "9ba85a59aa5dcc5cdaec85ee18607cb050530c55", + "sha256": "c841265ccee9b6f79045ad818ce9d27cfd7ee1f60047525a75d491f0dd8b997a" + }, + { + "path": "research/higher-moment-strictification/README.md", + "usage": "input", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "usage": "input", + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "usage": "input", + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7" + }, + { + "path": "research/kappa-function-composition/complex/prune_native.py", + "usage": "input", + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257" + }, + { + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "usage": "input", + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + { + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "usage": "input", + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef" + }, + { + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "usage": "input", + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0" + }, + { + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "usage": "input", + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "usage": "input", + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf" + }, + { + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "usage": "input", + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7" + }, + { + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "usage": "input", + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497" + }, + { + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "usage": "input", + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e" + }, + { + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "usage": "input", + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "usage": "input", + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/kappa-rebuild/complex/native_extensions.py", + "usage": "input", + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3" + }, + { + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "usage": "input", + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424" + }, + { + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "usage": "input", + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5" + }, + { + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "usage": "input", + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902" + }, + { + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "usage": "input", + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598" + }, + { + "path": "research/pr4359-p7-padding/TENSOR.md", + "usage": "input", + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/pr4359-p7-padding/native_inventory.py", + "usage": "input", + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32" + }, + { + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "usage": "input", + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d" + }, + { + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "usage": "input", + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088" + }, + { + "path": "research/query-thinned-controllers/RESULT.json", + "usage": "input", + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f" + }, + { + "path": "research/query-thinned-controllers/SOURCES.json", + "usage": "input", + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29" + }, + { + "path": "research/query-thinned-controllers/controller.py", + "usage": "input", + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2" + }, + { + "path": "research/query-thinned-controllers/verify.py", + "usage": "input", + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950" + }, + { + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + ] +} diff --git a/research/missing-join-frame/TASK.json b/research/missing-join-frame/TASK.json new file mode 100644 index 0000000000..014ccd44af --- /dev/null +++ b/research/missing-join-frame/TASK.json @@ -0,0 +1,73 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "priority_revision": 7, + "base_commit": "40f307e835b9a61e1b998bb17bd99d8c6b879a96", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "changed", + "actual_scope": "Adjoin the missing incoming span at scalar B/480, replay both exact native words and carry the complete p17 invoice to conditional kappa 0.00300123.", + "scope_change_reason": "Explicit user assignment to push kappa. A new catalog label improves the audited #4441 supplier; no universal escape from older frame models is claimed.", + "bottleneck_link": "The finite catalog omits the three-dimensional span of two actual incoming frames, leaving a four-dimensional contact whose rank moment is strictly worse for every 00 and margin(ROOT_HIGH)[1]<0,'New complete profile root bracket') + derivative=None + for i in range(16): + l,r=Q(i,320),Q(i+1,320);low=Q(0) + for rank,n in signed.items(): + term=E.mul(E.power(rank,1-r if n>0 else 1-l),E.log_bounds(rank)) + low+=n*term[0 if n>0 else 1] + derivative=low if derivative is None else min(derivative,low) + upper=None + for i in range(128): + l,r=Q(1,20)+Q(19*i,2560),Q(1,20)+Q(19*(i+1),2560) + hi=sum(n*E.power(rank,1-l if n>0 else 1-r)[1 if n>0 else 0] for rank,n in signed.items()) + upper=hi if upper is None else max(hi,upper) + need(derivative>0 and upper<0,'Fixed-profile ceiling for every real 00,'No nonzero charge for erased idle stage') + P[rank]+=224;idle+=224 + for term in word['diagonal']: + need(term[0] in (-1,1) and all(x in (0,1) for x in term[1:]),'Actual normalized main target') + T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(19,16,3584),'Every full, copied-query and whole-idle event') + need(sum(T.values())==11560 and sum(P.values())==69273,'Complete new productive/call counts') + need((sum(r*n for r,n in T.items()),sum(r*n for r,n in P.items()))==(260798,259998),'Preserve the exact surplus 800') + # Independent substitution into the source invoice must give the same ledger. + oldH={5:28,6:18,7:56,8:93,9:213};oldP={1:2487,2:713,3:224,4:102,5:20,8:8} + ref=source_query['complex_invoice'] + for key,new,old_unit,new_unit in [('targets',T,oldH,H),('paid',P,oldP,N)]: + check=Counter({int(k):v for k,v in ref[key].items()}) + check.subtract({k:19*v for k,v in old_unit.items()});check.update({k:19*v for k,v in new_unit.items()}) + need(+check==new,'Literal event count equals whole-call substitution: '+key) + E=S.C.load(ROOT/'research/higher-moment-strictification/verify.py','combined_exact_intervals') + root=ceiling(E,T,P) + t,u,v,c,b=1-TESTED,Q(1,5),1024,20,21 + target=E.moment(T,t);alpha=E.divide(E.moment(P,t),target) + other=S.C.load(ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','combined_separate_intervals') + tl,th=other.moment(T,TESTED);pl,ph=other.moment(P,TESTED) + need(tl>ph and max(tl,target[0])<=min(th,target[1]),'Independent exact raw-moment engine') + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + alpha_gap=Q(1,1000000000);g,d=Q(97,100),Q(19,20) + need(alpha[1]<1-alpha_gap and gamma[1]Q(31,32),'The previous gamma limit fails and is explicitly replaced') + # Apply PR4433's general logarithmic majorant at the actual new ambient rank. + theta,power=Q(63,64),1000 + eta=E.scale(E.power(153,-v*TESTED),t) + need(2*(20**v)**64<=(153**v)**63 and eta[0]>theta**power,'Shifted exit and complement capacity') + need(E.power(153,v*TESTED)[1]<2**power,'Initial compiler range') + gap=(TESTED-KAPPA)/7;need(gap.numerator==1,'Integer compiler grid') + step=gap.denominator + def passes(j):return (step*j+1)**power<2**j + lo,hi=1,2 + while not passes(hi):lo,hi=hi,2*hi + while hi-lo>1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + height=step*hi + need(height>8*v and passes(hi) and not passes(hi-1),'Effective uniform rank integer inequality') + # The changed local list is charged under an explicit larger fixed bound. + local_scalar=max(x['real_scalar_allowance'] for x in local['native'].values()) + local_routes=(sum(N.values())+2*408+688)*1000 + need(local_scalar+local_routes<10**7,'Every new local scalar and monomial route fits') + scalar_upper=19*10**7+16*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program']) for k in ('left','right'))) + need(scalar_upper<10**9,'Retain the complete raw nonrecursive bound') + bit=source_query['ordinary_BIT'];atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']);need(atom==Q('.004') and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Complete stronger source BIT admission') + L=S.C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','combined_outer_ledger') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Complete outer predicate inventory') + need(all(x>0 for key in ('strict_checks','functional_checks') for x in outer[key].values()),'Every complete outer inequality') + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items() if x<=0] + need(failed,'Reject '+name);controls[name]=failed + return encode({'status':'PASS_CONDITIONAL_MISSING_JOIN_KAPPA_00300123', 'kappa':KAPPA,'kappa_decimal':'0.00300123', + 'source_inputs':count,'source_heads':{'PR4440':'40e22a83ed660d3d6074c4f2dbf14bfb621eee51','helper_retiming':'ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9','PR4441_combination':'5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39'}, + 'gain_over_PR4441':KAPPA-Q('.00300105'), 'gain_over_PR4440':KAPPA-Q('.00296'),'gain_over_PR4416':KAPPA-Q('.00268647'), + 'targets':dict(sorted(T.items())),'paid':dict(sorted(P.items())),'full_calls':full,'query_shears':thin, + 'paid_calls':sum(P.values()),'productive_fields':sum(T.values()),'fixed_profile_ceiling':root, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta), + 'limits':[1-alpha_gap,g,d],'normalized_paid_upper':bound}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'uniform_saving':params['complex_uniform_saving'], + 'gap':gap,'H':height,'N':'2^'+str(height),'integer_test_exponent':hi,'word_materialized':False}, + 'nonrecursive':{'local_scalar_allowance':local_scalar,'local_route_bound':local_routes,'raw_upper':scalar_upper,'raw_budget':10**9}, + 'ordinary_BIT':bit,'outer':outer,'negative_controls':controls, + 'scope':'Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.'}) + +if __name__=='__main__': + parser=argparse.ArgumentParser() + parser.add_argument('--write',action='store_true',help='Author the new arithmetic receipt from already-audited dependency receipts; normal replay freshly reruns both dependencies.') + args=parser.parse_args();result=run(execute_sources=not args.write) + if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:need(result==read(HERE/'RESULT.json'),'Exact combined receipt replay') + print(json.dumps({k:result[k] for k in ('status','kappa_decimal','gain_over_PR4441','compiler')},sort_keys=True)) From 53880d1ade4b1d50906ce5187577ae2ffb492067 Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 16:53:41 -0400 Subject: [PATCH 12/26] Improve native frame contact and conditional kappa to 0.00300120 --- .../native-lattice-retiming/LITERATURE.md | 42 + .../NATIVE-RESULT.json | 816 ++++++++++++++++++ research/native-lattice-retiming/NOTICE.md | 16 + research/native-lattice-retiming/PATCH.json | 8 + research/native-lattice-retiming/PROOF.md | 96 +++ research/native-lattice-retiming/README.md | 131 +++ research/native-lattice-retiming/RESULT.json | 396 +++++++++ research/native-lattice-retiming/SOURCES.json | 282 ++++++ research/native-lattice-retiming/TASK.json | 123 +++ .../native-lattice-retiming/VALIDATION.md | 26 + research/native-lattice-retiming/VERIFY.json | 69 ++ .../native-lattice-retiming/arithmetic.py | 136 +++ .../discover-lattice.cpp | 68 ++ research/native-lattice-retiming/discover.py | 59 ++ research/native-lattice-retiming/native.py | 94 ++ research/native-lattice-retiming/verify.py | 41 + 16 files changed, 2403 insertions(+) create mode 100644 research/native-lattice-retiming/LITERATURE.md create mode 100644 research/native-lattice-retiming/NATIVE-RESULT.json create mode 100644 research/native-lattice-retiming/NOTICE.md create mode 100644 research/native-lattice-retiming/PATCH.json create mode 100644 research/native-lattice-retiming/PROOF.md create mode 100644 research/native-lattice-retiming/README.md create mode 100644 research/native-lattice-retiming/RESULT.json create mode 100644 research/native-lattice-retiming/SOURCES.json create mode 100644 research/native-lattice-retiming/TASK.json create mode 100644 research/native-lattice-retiming/VALIDATION.md create mode 100644 research/native-lattice-retiming/VERIFY.json create mode 100644 research/native-lattice-retiming/arithmetic.py create mode 100644 research/native-lattice-retiming/discover-lattice.cpp create mode 100644 research/native-lattice-retiming/discover.py create mode 100644 research/native-lattice-retiming/native.py create mode 100644 research/native-lattice-retiming/verify.py diff --git a/research/native-lattice-retiming/LITERATURE.md b/research/native-lattice-retiming/LITERATURE.md new file mode 100644 index 0000000000..96469b6e48 --- /dev/null +++ b/research/native-lattice-retiming/LITERATURE.md @@ -0,0 +1,42 @@ +# Literature evaluated during this continuation + +Local research notes, 21 October 2026. This revisits zxv's +[0.0023 literature list](../kappa-0023-productive-jobs/LITERATURE.md). +The sources motivate experiments; their theorems are not imported as native +instructions or as a proof of the new multiplication bound. + +| Paper | Applicable idea | Missing transfer / outcome here | +| --- | --- | --- | +| [Dumas–Grenet, In-place accumulation, §3 and Theorem 5](https://arxiv.org/html/2307.12712v3) | Prepare output registers by subtraction, accumulate once, then distribute by restoring the changed register. Inputs must be restored; the computed function cannot use its output as scratch. | Native Fourier frame contacts still need payment. Our exact commuting-ADD folding removes 108 scalar records in each orientation but leaves the recursive profile unchanged, even after retiming. This is not the κ improvement. A multi-target native interface remains a useful larger direction. | +| [Brislawn, Causal Complementation, §§2.2–2.4](https://arxiv.org/html/2408.07970v1) | Couple elimination to divisibility and causal availability rather than use an arbitrary inverse. | The paper works with causal polynomial filter matrices; our controller has several independent Laurent variables and restricted dyadic/native contacts. No direct factorization theorem applies. It suggested checking the actual subspace lattice instead of the old finite frame menu. The accepted three-dimensional contact is proved separately by native replay and Clifford decoding. | +| [Urschel, block unitriangular representations, Lemma 5](https://arxiv.org/html/2305.00485v2) | Short alternating block shears can represent a general special-linear operator. | Its construction uses inverses over a field. Neither dyadic coefficients nor cheap native block operators follow from the six-factor count. Deferred until an explicit small legal block factorization replaces paid work. | +| [Buhrman–Cleve–Koucký–Loff–Speelman, catalytic space](https://eccc.weizmann.ac.il/report/2014/053/) | Arbitrary initial workspace must return exactly. | Tested a joint-boundary move allowing helpers to become zero-width catalysts and removing their productive credit. No improving move was found in the declared single-label experiment. The accepted move keeps all helpers productive. No catalytic-space upper bound is transferred. | +| [Robere–Zuiddam, amortized/catalytic circuits](https://eccc.weizmann.ac.il/report/2021/035/) | Optimize the cost against the complete resource ledger. | Repeated copies of one function on one input do not supply independent productive fields. Retained as a discipline for the objective, not a source of output credit. | + +The useful change of direction was to leave the exhausted p7 idle-mask model, +read the newly published #4440/#4441 constructions, and search new subspaces +of their actual native word. This produces a changed paid profile. No claim +is made that any cited author supplied this contact or the new κ. + +## Bounded discovery and limitations + +Before the new upstream sources appeared, bidirectional coordinate retiming, +75 commuting-ADD combinations (108 removed records), and 1,320 paired +same/complement rank-one idle-projector experiments found no paid improvement. +Those are local-only exploratory results; they are not global barriers. + +Starting from #4441's exact native patch, the optional lattice optimizer tries +joining frames with each binary line and intersecting them with each binary +hyperplane, with paired helper-boundary decisions and exact nesting checks. +At the discovery exponent 1−0.00300106 it finds one move: intersect frame 732 +with the hyperplane orthogonal to binary vector 2, at phase B scalar 480. +Its floating objective is only a ranking aid. `verify.py` does not run a +solver or trust the objective; it executes the explicit PATCH.json. + +Subsequent exploratory expansion over 111,887 distinct old/new candidate +spaces, and the same expansion after scalar folding, found no additional +improving single-label move in that particular program. Simultaneous +multiple-label moves, changed scalar graphs and other providers remain open. +No global or exact search-optimality claim is made. + +Apache-2.0 for these notes. Papers retain their own copyrights and licenses. diff --git a/research/native-lattice-retiming/NATIVE-RESULT.json b/research/native-lattice-retiming/NATIVE-RESULT.json new file mode 100644 index 0000000000..b5c0af78f1 --- /dev/null +++ b/research/native-lattice-retiming/NATIVE-RESULT.json @@ -0,0 +1,816 @@ +{ + "controls": { + "global_phase_only_corruption_rejected": true, + "wrong_scalar_frame_rejected": true + }, + "helpers": { + "4": 26, + "5": 2, + "7": 29, + "8": 42, + "9": 309 + }, + "native": { + "backward": { + "arbitrary_owned_C0_cleared": true, + "independent_interpreter": { + "all_scalar_frames_checked": true, + "clean_J": false, + "conservative_real_scalar_primitive_allowance": 158168, + "direction": "backward", + "dyadic_coefficients_and_unit_scales_checked": true, + "event_counts": { + "adapter": 448, + "center": 8, + "climb": 3355, + "phase": 10, + "scalar": 17453, + "warp": 240 + }, + "expected_restored_arbitrary_cleanup_buffers": 0, + "expected_restored_helpers": 408, + "explicitly_owned_C_fields_cleared": 1, + "free_warp_operator_endpoint_matches": true, + "independent_borrowed_input_fields": 632, + "mismatch_examples": [], + "negative_control_omitted_last_cleanup_scalar": false, + "original_data_fields": 224, + "paid_profile": { + "1": 2254, + "2": 514, + "3": 444, + "4": 103, + "5": 40, + "8": 8 + }, + "paid_rank_mass": 5290 + }, + "independent_owned_entry_columns": 1, + "independent_persistent_columns": 632, + "l1_witness": { + "event": 6396, + "role": [ + "L", + 225 + ] + }, + "max_denominator": 64, + "max_formal_prefix_l1": "169", + "paid_profile": { + "1": 2254, + "2": 514, + "3": 444, + "4": 103, + "5": 40, + "8": 8 + }, + "paid_rank_mass": 5290, + "real_scalar_allowance": 158168, + "scalar_frames_checked": true + }, + "forward": { + "arbitrary_owned_C0_cleared": true, + "independent_interpreter": { + "all_scalar_frames_checked": true, + "clean_J": false, + "conservative_real_scalar_primitive_allowance": 158120, + "direction": "forward", + "dyadic_coefficients_and_unit_scales_checked": true, + "event_counts": { + "adapter": 448, + "center": 8, + "climb": 3355, + "phase": 10, + "scalar": 17453, + "warp": 240 + }, + "expected_restored_arbitrary_cleanup_buffers": 0, + "expected_restored_helpers": 408, + "explicitly_owned_C_fields_cleared": 1, + "free_warp_operator_endpoint_matches": true, + "independent_borrowed_input_fields": 632, + "mismatch_examples": [], + "negative_control_omitted_last_cleanup_scalar": false, + "original_data_fields": 224, + "paid_profile": { + "1": 2254, + "2": 514, + "3": 444, + "4": 103, + "5": 40, + "8": 8 + }, + "paid_rank_mass": 5290 + }, + "independent_owned_entry_columns": 1, + "independent_persistent_columns": 632, + "l1_witness": { + "event": 19099, + "role": [ + "L", + 224 + ] + }, + "max_denominator": 32, + "max_formal_prefix_l1": "457", + "paid_profile": { + "1": 2254, + "2": 514, + "3": 444, + "4": 103, + "5": 40, + "8": 8 + }, + "paid_rank_mass": 5290, + "real_scalar_allowance": 158120, + "scalar_frames_checked": true + } + }, + "new_physical_edges": [ + { + "new_basis": [ + 45, + 133, + 336 + ], + "old_basis": [ + 133, + 45 + ], + "recipes": { + "backward": { + "left": { + "linear_Z4": [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 2, + 4, + 8, + 16, + 33, + 64, + 129, + 256, + 1 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 1, + "right": { + "linear_Z4": [ + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 2 + ], + "matrix_rows": [ + 336, + 1, + 2, + 4, + 8, + 272, + 32, + 320, + 128 + ], + "offset": 0, + "phase": 3, + "quadratic_rows": [ + 0, + 0, + 0, + 0, + 80, + 0, + 80, + 0, + 0 + ] + } + }, + "forward": { + "left": { + "linear_Z4": [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 2, + 4, + 8, + 16, + 33, + 64, + 129, + 256, + 1 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 1, + "right": { + "linear_Z4": [ + 0, + 0, + 0, + 0, + 3, + 0, + 3, + 0, + 2 + ], + "matrix_rows": [ + 336, + 1, + 2, + 4, + 8, + 272, + 32, + 320, + 128 + ], + "offset": 1, + "phase": 1, + "quadratic_rows": [ + 0, + 0, + 0, + 0, + 80, + 0, + 80, + 0, + 0 + ] + } + } + } + }, + { + "new_basis": [ + 45, + 133, + 336 + ], + "old_basis": [ + 336, + 45 + ], + "recipes": { + "backward": { + "left": { + "linear_Z4": [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 3, + 4, + 9, + 16, + 32, + 64, + 128, + 1, + 256 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 1, + "right": { + "linear_Z4": [ + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 2, + 0 + ], + "matrix_rows": [ + 133, + 129, + 2, + 132, + 8, + 16, + 32, + 64, + 256 + ], + "offset": 0, + "phase": 3, + "quadratic_rows": [ + 5, + 0, + 5, + 0, + 0, + 0, + 0, + 0, + 0 + ] + } + }, + "forward": { + "left": { + "linear_Z4": [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 3, + 4, + 9, + 16, + 32, + 64, + 128, + 1, + 256 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 1, + "right": { + "linear_Z4": [ + 3, + 0, + 3, + 0, + 0, + 0, + 0, + 2, + 0 + ], + "matrix_rows": [ + 133, + 129, + 2, + 132, + 8, + 16, + 32, + 64, + 256 + ], + "offset": 1, + "phase": 1, + "quadratic_rows": [ + 5, + 0, + 5, + 0, + 0, + 0, + 0, + 0, + 0 + ] + } + } + } + }, + { + "new_basis": [ + 258, + 128, + 64, + 33, + 18, + 9, + 5 + ], + "old_basis": [ + 45, + 133, + 336 + ], + "recipes": { + "backward": { + "left": { + "linear_Z4": [ + 2, + 3, + 2, + 2, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 16, + 40, + 69, + 129, + 258, + 4, + 8, + 5, + 10 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 0, + 10, + 0, + 2, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 4, + "right": { + "linear_Z4": [ + 2, + 3, + 0, + 3, + 2, + 0, + 2, + 2, + 1 + ], + "matrix_rows": [ + 172, + 16, + 36, + 338, + 13, + 18, + 128, + 160, + 256 + ], + "offset": 438, + "phase": 2, + "quadratic_rows": [ + 12, + 322, + 1, + 9, + 64, + 0, + 274, + 0, + 322 + ] + } + }, + "forward": { + "left": { + "linear_Z4": [ + 2, + 3, + 2, + 2, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 16, + 40, + 69, + 129, + 258, + 4, + 8, + 5, + 10 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 0, + 10, + 0, + 2, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 4, + "right": { + "linear_Z4": [ + 2, + 1, + 0, + 1, + 0, + 0, + 2, + 2, + 3 + ], + "matrix_rows": [ + 172, + 16, + 36, + 338, + 13, + 18, + 128, + 160, + 256 + ], + "offset": 443, + "phase": 3, + "quadratic_rows": [ + 12, + 322, + 1, + 9, + 64, + 0, + 274, + 0, + 322 + ] + } + } + } + }, + { + "new_basis": [ + 258, + 133, + 66, + 45, + 16 + ], + "old_basis": [ + 45, + 133, + 336 + ], + "recipes": { + "backward": { + "left": { + "linear_Z4": [ + 3, + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 4, + 10, + 16, + 32, + 66, + 128, + 1, + 256, + 3 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 3, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 2, + "right": { + "linear_Z4": [ + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 3 + ], + "matrix_rows": [ + 320, + 338, + 1, + 322, + 4, + 8, + 256, + 32, + 128 + ], + "offset": 64, + "phase": 3, + "quadratic_rows": [ + 0, + 18, + 0, + 0, + 66, + 0, + 272, + 0, + 320 + ] + } + }, + "forward": { + "left": { + "linear_Z4": [ + 3, + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 4, + 10, + 16, + 32, + 66, + 128, + 1, + 256, + 3 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 3, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 2, + "right": { + "linear_Z4": [ + 0, + 3, + 0, + 0, + 0, + 0, + 2, + 0, + 3 + ], + "matrix_rows": [ + 320, + 338, + 1, + 322, + 4, + 8, + 256, + 32, + 128 + ], + "offset": 66, + "phase": 0, + "quadratic_rows": [ + 0, + 18, + 0, + 0, + 66, + 0, + 272, + 0, + 320 + ] + } + } + } + } + ], + "paid": { + "1": 2254, + "2": 514, + "3": 444, + "4": 103, + "5": 40, + "8": 8 + }, + "status": "PASS_NEW_LATTICE_CONTACT_BOTH_ORIENTATIONS_ALL_COLUMNS" +} diff --git a/research/native-lattice-retiming/NOTICE.md b/research/native-lattice-retiming/NOTICE.md new file mode 100644 index 0000000000..e7add6c881 --- /dev/null +++ b/research/native-lattice-retiming/NOTICE.md @@ -0,0 +1,16 @@ +# Attribution + +New work prepared for zxv with substantial OpenAI Codex assistance; Apache-2.0. +No subagents were used. Source files remain unchanged in their existing paths. + +The native supplier, reconstruction, arbitrary-input interpreters, complex +controller, higher-moment strictification and logarithmic compiler retain zxv's +PR4359/PR4433 lineage. Fresh-helper boundary retiming is Cinna Davis's PR4441; +query thinning and the stronger BIT interface are Cinna Davis's PR4440. +Mixed-target integer flow is Jacob Alan Sussman's Theorem 1G. The retained +native/Clifford/BIT sources preserve their original contributor notices, +including DreamingOfClouds, eumemic and their predecessor contributions. + +The optional min-cut discovery code adapts PR4441's Apache-2.0 floating Dinic +implementation. Its new moves act on the subspace lattice. The mathematical +claim depends on the explicit exact contact, not the optimizer. diff --git a/research/native-lattice-retiming/PATCH.json b/research/native-lattice-retiming/PATCH.json new file mode 100644 index 0000000000..be818ab439 --- /dev/null +++ b/research/native-lattice-retiming/PATCH.json @@ -0,0 +1,8 @@ +{ + "phase": "B", + "scalar_ordinal": 480, + "old_frame": 732, + "old_basis": [258, 133, 82, 45], + "new_basis": [45, 133, 336], + "forward_gate": ["add", ["L", 90], ["L", 253], 1, 1] +} diff --git a/research/native-lattice-retiming/PROOF.md b/research/native-lattice-retiming/PROOF.md new file mode 100644 index 0000000000..c966d4df2c --- /dev/null +++ b/research/native-lattice-retiming/PROOF.md @@ -0,0 +1,96 @@ +# Native contact and conditional transfer + +## Scope and source boundary + +Source PR4441 is fixed at `5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39`, +including PR4440 at `40e22a83ed660d3d6074c4f2dbf14bfb621eee51`. +Their conditional contracts are retained. No selected result, independent +scientific acceptance or universal implementation hypothesis is promoted. +The exact byte closure is SOURCES.json. New work stays local for user review. + +## One legal contact outside the predecessor frame menu + +Use PR4441's chronological word and all its boundary changes. A field with +logical value z and frame S holds C_S z. A paid nested transport from S to T +implements C_T C_S^-1, retaining z. At a common frame T an ADD is +C_T z_i + a C_T z_j = C_T(z_i + a z_j). Thus changing common frames while +keeping every contact legal preserves the entire formal logical program. +This is an induction over the actual instruction sequence, not a tensor power +of an equality between sums of matrices. + +The source forward ADD at phase B, persistent ordinal 480, is +`L90 += L253`. Its old frame is span(258,133,82,45). Set +S=span(45,133,336), the intersection with the hyperplane perpendicular to 2. +The generator checks strict inclusion. Both previous contacts lie in S; +both following contacts contain S. Resynthesis therefore uses only ascending +nested transports. All warp and owned-center contacts keep their actual +original gauges. The backward ADD is matched to the literal source dual, +then receives the same common frame. + +Two source interpreters execute both new words on 632 arbitrary persistent +input columns, plus an arbitrary owned-center entry column. The main shears +and all autonomous helper rows match exactly; C0 is cleared only at its legal +owned operations. Main and helper boundaries are unchanged from PR4441. +Four newly used edge types receive complete forward and conjugate Clifford +recipes; serialized decoding checks tableau and exact zero-state phase. +The old edges and unchanged helper normalizers retain their pinned evidence. +Wrong-contact and phase-only corruptions are rejected. + +At every permitted positive column multiplicity the same formal gauge +induction applies to the allowed generator lifts. This uses the retained +all-column/native contract, including the new fixed Clifford monomial +recipes. The finite checks do not independently prove that universal +implementation or the physical tape model. + +## Why the invoice improves + +The complete local change is + + P_new = P_old + [1] + [4] - [2] - [3]. + +No target, field count, scalar coefficient/order, query or center is removed. +For 0theta^p and 153^(v*C)<2^p. These are the exit/contraction +and initial-range conditions of PR4433's generalized majorant. With +kappa=.00300120 and d=(C-kappa)/7=1/350000000, the verifier finds +H=2299850000000 with (H+1)^160<2^(d*H). The previous grid value fails. +The same construction at kappa=.00300105 gives H=249900000000. + +Every expanded program is finite. Its complete raw nonrecursive record bound +is below 10^9, and the source explicit product, adapter, precision and stock +prescriptions apply to these new finite ranks and lists. Suspended instances +retain distinct center storage; no materialized gigantic program is claimed. +The BIT supplier remains the source stronger ordinary admission .0034 with +atom .004. Exact outer arithmetic passes all nine rows, 54 current predicates, +four guards and 63 legacy predicates at the new point. The same-kappa rank +comparison separately checks the complete current outer ledger. + +The conclusion is conditional on the retained native/all-column, +whole-job/owned-erasure, finite-precision, analytic, physical tape, prime and +exact-recovery contracts: T(n)=O(n*(log n)^(1-.00300120)). It is not an +unconditional theorem, formal proof or practical runtime claim. diff --git a/research/native-lattice-retiming/README.md b/research/native-lattice-retiming/README.md new file mode 100644 index 0000000000..8d4e9ca201 --- /dev/null +++ b/research/native-lattice-retiming/README.md @@ -0,0 +1,131 @@ +# A new native contact: conditional κ = 0.00300120 + +**Local for user review. Do not push, publish a PR or post Discussions.** + +A changed native paid profile raises the conditional multiplication saving to +**κ = 0.00300120** and specifies sufficient uniform rank +**`2^2299850000000`**. The κ gain over +[PR4441](https://github.com/CrocSwap/integer-mult-bounds/pull/4441) is modest: +`0.00000015` (about 0.005%). The exponent of its sufficient uniform rank falls +by **71.88×**. At PR4441's unchanged κ=0.00300105, the rank can instead be +**`2^249900000000`**, a **661.53×** exponent reduction. +These are sufficient mathematical template sizes, not practical speedups. + +This builds on zxv's selected [0.0023 construction](../kappa-0023-productive-jobs/README.md), +its [higher-moment/logarithmic compiler](../higher-moment-strictification/README.md), +and Cinna Davis's new query-thinning and fresh-helper constructions +([PR4440](https://github.com/CrocSwap/integer-mult-bounds/pull/4440), +[PR4441](https://github.com/CrocSwap/integer-mult-bounds/pull/4441)). +Both pending source heads are pinned; they are author-checked conditional +claims, not independently accepted frontier updates. The selected record stays +0.0023. The new work retains their native/all-column, owned-erasure, whole-job, +precision, analytic, fixed-tape, prime and exact-recovery premises. + +## The actual construction change + +At phase B, persistent scalar ordinal 480, the forward ADD is +`L90 += L253`. Its old common frame has basis `[258,133,82,45]`. +Replace it by the three-dimensional subspace with basis `[45,133,336]`. +It is the old space intersected with the hyperplane orthogonal to binary +vector 2. Apply the same frame change at the literal inverse-transpose ADD in +the backward word. Scalar order, coefficients, warp contacts, main boundaries, +helper boundaries and all eight complete centers remain those of PR4441. + +Direct ascending transports before and after the changed contact give: + +| Local resource | PR4441 | New word | +| --- | ---: | ---: | +| Paid rank 1 | 2253 | 2254 | +| Paid rank 2 | 515 | 514 | +| Paid rank 3 | 445 | 444 | +| Paid rank 4 | 102 | 103 | +| Paid rank 5 / rank 8 | 40 / 8 | 40 / 8 | +| Productive helper widths | 26×4, 2×5, 29×7, 42×8, 309×9 | same | + +Thus the net paid change is `H2+H3 → H1+H4`. For every real `0 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "87149999253/87500000000", + "fixed_halo_explicit_metadata_branch": "6737500001/87500000", + "new_BIT_row_stock_sublinear_in_active_group": "348949997009/350000000000", + "new_semantic_group_guard": "3/350000000" + }, + "margins": { + "boundary_algebraic_matrix": "367648398949577/122500000000000000", + "fused_gaussian": "367648396848731/122500000000000000", + "global_coordinate_router": "131303/43750000", + "group_bit_router": "45956093356091/15312500000000000", + "group_scans": "174999999/175000000", + "main_transform": "367648048949577/122500000000000000", + "microbox_face_corrections": "6737500001/87500000", + "polynomial_products": "349999999/350000000", + "sparse_union_movement": "50133273398949577/122500000000000000" + }, + "parameters": { + "a": "131303/43750000", + "b": "42017/14000000", + "beta": "349999997/350000000", + "bit_saving": "17/5000", + "cap_xi": "111383273048949577/122500000000000000", + "complex_uniform_saving": "525213/175000000", + "d": "1/350000000", + "epsilon": "349999999/350000000", + "kappa": "7503/2500000", + "lambda_": "99699879/100000000", + "lambda_prime": "348949577/350000000", + "layout": "1/350000000", + "q": "1050423/350000000", + "r0": "1/3500000000", + "stop": "1/350000000", + "tested_saving": "150061/50000000" + }, + "strict_checks": { + "actual_bit_above_effective": "17447/43750000", + "actual_logarithmic_gamma_guard": "1/350000000", + "actual_logarithmic_group_guard": "11116727476050423/61250000000000000", + "alpha_logarithm_absorption": "1/3500000000", + "boundary_algebraic_matrix_above_kappa": "1398949577/122500000000000000", + "cap_above_band": "50133273048949577/122500000000000000", + "cap_below_cell": "11116726601050423/122500000000000000", + "cap_below_phase_cell_power": "133616726951050423/122500000000000000", + "complex_above_effective": "1/350000000", + "complex_below_one_over_32": "395483/14000000", + "complex_endpoint": "1/175000000", + "epsilon_below_one": "1/350000000", + "epsilon_positive": "349999999/350000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "1396848731/122500000000000000", + "gaussian_above_main": "173949577/61250000000000000", + "global_coordinate_router_above_kappa": "1/87500000", + "global_gamma_power_slack": "9/3500000000", + "group_below_dimension": "1/175000000", + "group_bit_router_above_kappa": "218356091/15312500000000000", + "group_gauge_power_slack": "11116727458550423/61250000000000000", + "group_key_fits_record": "1/175000000", + "group_positive": "349999997/350000000", + "group_scans_above_kappa": "174474789/175000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "635114790400418148631/500000000000000000000000", + "lambda_above_internal": "1/700000000", + "lambda_above_sigma": "3/700000000", + "lambda_above_tau": "1/700000000", + "lambda_prime_above_lambda": "1/700000000", + "lambda_prime_above_leaf": "27957983/4900000000000000", + "leaf_saving_above_effective": "13957983/4900000000000000", + "main_transform_above_kappa": "1048949577/122500000000000000", + "membership_arithmetic_fits_record": "1/350000000", + "microbox_face_corrections_above_kappa": "1684309349/21875000", + "microbox_halo_volume": "27650000003/350000000", + "new_complex_uniform_saving_above_b": "1/350000000", + "new_semantic_guard_with_C1_one": "1/350000000", + "polynomial_products_above_kappa": "348949579/350000000", + "positive_layout_slack": "1/350000000", + "q_below_effective": "1/350000000", + "q_below_internal": "1/350000000", + "q_below_leaf": "27957983/4900000000000000", + "q_positive": "1050423/350000000", + "short_record_fallback": "13957983/14000000", + "source_axis_superpolynomial": "1/350000000", + "sparse_union_movement_above_kappa": "49765626398949577/122500000000000000", + "stop_below_one": "349999999/350000000", + "stop_positive": "1/350000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/350000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/350000000", + "union_tag_work_per_visit_fits_record": "3/350000000" + } + }, + "paid": { + "1": 44618, + "16": 448, + "2": 9766, + "24": 448, + "3": 8436, + "32": 448, + "4": 1957, + "40": 448, + "48": 448, + "5": 760, + "56": 448, + "64": 448, + "72": 448, + "8": 152 + }, + "rank_exponent_reduction": "472330/6571", + "rank_surplus": 800, + "raw_moment_margin": { + "lower": "0.005035901012260126500228750242", + "upper": "0.005035901012260126500228750243" + }, + "raw_root": [ + "3001239017/1000000000000", + "30012390173/10000000000000" + ], + "raw_root_scope": "Unique crossing on [0,.01]; no universal or global mechanism ceiling.", + "same_kappa_rank_exponent_reduction": "236165/357", + "same_predecessor_kappa_compiler": { + "H": 249900000000, + "N": "2^249900000000", + "eta": { + "lower": "0.000037402048244786272108248731", + "upper": "0.000037402048244786272108248732" + }, + "gap": "17/700000000", + "integer_exponent": 6069, + "logarithm_power": 160, + "theta": "15/16", + "uniform_saving": "2100837/700000000", + "word_materialized": false + }, + "same_predecessor_kappa_outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "174299987301/175000000000", + "fixed_halo_explicit_metadata_branch": "13475000017/175000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899949153/700000000000", + "new_semantic_group_guard": "51/700000000" + }, + "margins": { + "boundary_algebraic_matrix": "735281032143319/245000000000000000", + "fused_gaussian": "735280996429957/245000000000000000", + "global_coordinate_router": "2100803/700000000", + "group_bit_router": "1470573892859047/490000000000000000", + "group_scans": "349999983/350000000", + "main_transform": "735275082143319/245000000000000000", + "microbox_face_corrections": "13475000017/175000000", + "polynomial_products": "699999983/700000000", + "sparse_union_movement": "100266531032143319/245000000000000000" + }, + "parameters": { + "a": "2100803/700000000", + "b": "105041/35000000", + "beta": "699999949/700000000", + "bit_saving": "17/5000", + "cap_xi": "222766525082143319/245000000000000000", + "complex_uniform_saving": "2100837/700000000", + "d": "17/700000000", + "epsilon": "699999983/700000000", + "kappa": "60021/20000000", + "lambda_": "199399773/200000000", + "lambda_prime": "348949607/350000000", + "layout": "17/700000000", + "q": "1050393/350000000", + "r0": "17/7000000000", + "stop": "17/700000000", + "tested_saving": "150061/50000000" + }, + "strict_checks": { + "actual_bit_above_effective": "279197/700000000", + "actual_logarithmic_gamma_guard": "17/700000000", + "actual_logarithmic_group_guard": "22233483842856681/122500000000000000", + "alpha_logarithm_absorption": "17/7000000000", + "boundary_algebraic_matrix_above_kappa": "23782143319/245000000000000000", + "cap_above_band": "100266525082143319/245000000000000000", + "cap_below_cell": "22233468967856681/245000000000000000", + "cap_below_phase_cell_power": "267233474917856681/245000000000000000", + "complex_above_effective": "17/700000000", + "complex_below_one_over_32": "988709/35000000", + "complex_endpoint": "17/350000000", + "epsilon_below_one": "17/700000000", + "epsilon_positive": "699999983/700000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "23746429957/245000000000000000", + "gaussian_above_main": "2957143319/122500000000000000", + "global_coordinate_router_above_kappa": "17/175000000", + "global_gamma_power_slack": "153/7000000000", + "group_below_dimension": "17/350000000", + "group_bit_router_above_kappa": "59392859047/490000000000000000", + "group_gauge_power_slack": "22233483545356681/122500000000000000", + "group_key_fits_record": "17/350000000", + "group_positive": "699999949/700000000", + "group_scans_above_kappa": "697899231/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "635039790400418148631/500000000000000000000000", + "lambda_above_internal": "17/1400000000", + "lambda_above_sigma": "51/1400000000", + "lambda_above_tau": "17/1400000000", + "lambda_prime_above_lambda": "17/1400000000", + "lambda_prime_above_leaf": "1188214303/24500000000000000", + "leaf_saving_above_effective": "593214303/24500000000000000", + "main_transform_above_kappa": "17832143319/245000000000000000", + "membership_arithmetic_fits_record": "17/700000000", + "microbox_face_corrections_above_kappa": "53897899333/700000000", + "microbox_halo_volume": "55300000051/700000000", + "new_complex_uniform_saving_above_b": "17/700000000", + "new_semantic_guard_with_C1_one": "17/700000000", + "polynomial_products_above_kappa": "43618703/43750000", + "positive_layout_slack": "17/700000000", + "q_below_effective": "17/700000000", + "q_below_internal": "17/700000000", + "q_below_leaf": "1188214303/24500000000000000", + "q_positive": "1050393/350000000", + "short_record_fallback": "34894959/35000000", + "source_axis_superpolynomial": "17/700000000", + "sparse_union_movement_above_kappa": "99531273782143319/245000000000000000", + "stop_below_one": "699999983/700000000", + "stop_positive": "17/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "51/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "51/700000000", + "union_tag_work_per_visit_fits_record": "51/700000000" + } + }, + "status": "PASS_CONDITIONAL_NEW_NATIVE_PROFILE_KAPPA", + "strictification": { + "alpha": { + "lower": "0.999999980480394484617151340349", + "upper": "0.999999980480394484617151340350" + }, + "cutoff": 18, + "delta": { + "lower": "0.977253011855658562221385892786", + "upper": "0.977253011855658562221385892787" + }, + "floor": 22, + "gamma": { + "lower": "0.981971726999571315878434078558", + "upper": "0.981971726999571315878434078559" + }, + "limits": [ + "999999981/1000000000", + "491/500", + "391/400" + ], + "normalized_paid_upper": "3135316342855047938216186285366284791836015552731567401908176734930110521667998541808860782674464246329116429895882753096247698522148271859666641784228677573912605332725923383934714825294597676931624212032514027646967981541336965729076185554268027233444327337403745878243356820959932112007771549864881590155015123496432209395021364448015796884438028569244657405717369951884743365972882095120039957983925379611291360772632665217708326491914268771819562848029846703500646180491671401882021101698766069617361586201262698776684351995258277190425359783195465694122176833672706484066530574724789787037479061017911116773108073612235843989560762616998581715509178001466468362876164703345435291409263816689904692103757941883488341058980494142712686923568812288022949192890478433946276536436589153790091599648369106702773634555281575360964032314712840386529515907102227717937795524446796747828703981436724132739380841411013441416769926025052267538328282156106210906013225055943965375562532068983730967116286827198591247798727678176171320478590738500846420117865786648859883120410371898612074031256962522241496076154923725770848767431043120528509433496714324101025959590085951574021714319434271053115042416232189788263853499205089931368330261666401396910361932147924932944049888383159214229752743917428741596819317242725132712760528603789131532630741472925548561970849762668570817110437699349242714467130025311116618881358860815044369352216933087978747203390374142945600672289781753394274808328461504479642084553107824308868694078844054600750174201186469373656303128692027810576278159672148330996943494335356428296005636709069876376626933852810296702680886721507369314046399539101605976615201231427346183584818214127701391923728250913847612146632050052126755457091296857078080483746571485029373221974027408859524785238239130664547070069062887791736006969711830300497542975648628304802085160737580120878371177685768802133093055833042983690068619665100866536539147891836775462897136439867703923989275080988185809322290236782727815805504224638071293970925407386829055785555936017618119880456302458931410718717523322804435169311032474465174265268263099422925367321268723174472263506975656429644591851528543559670335484908199131423006788263629803652987/3135325528854913035113346724853144051552102259356465975465195756269284493200158883437639560729811317502778741665335773348010541036368854326255535712764450586037113873286263239677927235348235120600546751065096192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "power": 675, + "tested": "150061/50000000", + "u": "3/25" + }, + "targets": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 494, + "41": 448, + "49": 448, + "5": 38, + "57": 448, + "65": 448, + "7": 551, + "73": 448, + "8": 798, + "9": 5871 + } +} diff --git a/research/native-lattice-retiming/SOURCES.json b/research/native-lattice-retiming/SOURCES.json new file mode 100644 index 0000000000..5378362135 --- /dev/null +++ b/research/native-lattice-retiming/SOURCES.json @@ -0,0 +1,282 @@ +{ + "base_commit": "28f58f6f9b72ddfe7aa5b986d1b678356c4e6350", + "files": [ + { + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7", + "usage": "input" + }, + { + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "path": "research/fresh-helper-boundary/CHANGES.json", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624", + "usage": "input" + }, + { + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839", + "usage": "input" + }, + { + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "path": "research/fresh-helper-boundary/RESULT.json", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd", + "usage": "input" + }, + { + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "path": "research/fresh-helper-boundary/SOURCES.json", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0", + "usage": "input" + }, + { + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "path": "research/fresh-helper-boundary/arithmetic.py", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07", + "usage": "input" + }, + { + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "path": "research/fresh-helper-boundary/native.py", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29", + "usage": "input" + }, + { + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "path": "research/fresh-helper-boundary/verify.py", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf", + "usage": "input" + }, + { + "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55", + "path": "research/fresh-helper-thinned/RESULT.json", + "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21", + "usage": "input" + }, + { + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "path": "research/higher-moment-strictification/README.md", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", + "usage": "input" + }, + { + "git_blob": "d3b6149c5c1cca84c7c305f6e2e32c814e30777e", + "path": "research/higher-moment-strictification/vendor/check_ledger.py", + "sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98", + "usage": "input" + }, + { + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "path": "research/higher-moment-strictification/verify.py", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", + "usage": "input" + }, + { + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85", + "usage": "input" + }, + { + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "usage": "input" + }, + { + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7", + "usage": "input" + }, + { + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "path": "research/kappa-function-composition/complex/prune_native.py", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257", + "usage": "input" + }, + { + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a", + "usage": "input" + }, + { + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef", + "usage": "input" + }, + { + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0", + "usage": "input" + }, + { + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443", + "usage": "input" + }, + { + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf", + "usage": "input" + }, + { + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7", + "usage": "input" + }, + { + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497", + "usage": "input" + }, + { + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e", + "usage": "input" + }, + { + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17", + "usage": "input" + }, + { + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6", + "usage": "input" + }, + { + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61", + "usage": "input" + }, + { + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39", + "usage": "input" + }, + { + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "path": "research/kappa-rebuild/complex/native_extensions.py", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3", + "usage": "input" + }, + { + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424", + "usage": "input" + }, + { + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5", + "usage": "input" + }, + { + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902", + "usage": "input" + }, + { + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "usage": "input" + }, + { + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "path": "research/pr4359-p7-padding/TENSOR.md", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3", + "usage": "input" + }, + { + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "usage": "input" + }, + { + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "path": "research/pr4359-p7-padding/native_inventory.py", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32", + "usage": "input" + }, + { + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "usage": "input" + }, + { + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088", + "usage": "input" + }, + { + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "path": "research/query-thinned-controllers/RESULT.json", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f", + "usage": "input" + }, + { + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "path": "research/query-thinned-controllers/SOURCES.json", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29", + "usage": "input" + }, + { + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "path": "research/query-thinned-controllers/controller.py", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2", + "usage": "input" + }, + { + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "path": "research/query-thinned-controllers/verify.py", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950", + "usage": "input" + }, + { + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "usage": "input" + }, + { + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "path": "docs/research/agent-task-catalog.json", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96", + "usage": "provenance" + }, + { + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "path": "certificates/selected-result.json", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9", + "usage": "provenance" + }, + { + "git_blob": "2fe84a7b30b1e26e60ce0ec4775894eb1831c5d6", + "path": "autoresearch.md", + "sha256": "d16f0d3bb4d4b213d06c128db6d6460b0fe9ec1ac5a6c1ea1febf1db40e7b60d", + "usage": "provenance" + } + ], + "schema_version": 1 +} diff --git a/research/native-lattice-retiming/TASK.json b/research/native-lattice-retiming/TASK.json new file mode 100644 index 0000000000..5c9dd61a4c --- /dev/null +++ b/research/native-lattice-retiming/TASK.json @@ -0,0 +1,123 @@ +{ + "actual_scope": "Build a changed native frame contact beyond PR4441, then completely pay tensor completion, finite uniform compilation and the integer-multiplication consumer.", + "ai_assistance": "Substantial OpenAI Codex assistance; no subagents.", + "author": "zxv, with substantial OpenAI Codex assistance", + "base_commit": "28f58f6f9b72ddfe7aa5b986d1b678356c4e6350", + "bottleneck_link": "New subspaces outside the predecessor frame menu can change the raw paid profile while exact native endpoints and all helper outputs stay fixed.", + "budget_minutes": 60, + "evidence": "Explicit one-contact native patch; two all-column replays in both orientations, new absolute-phase transports, complete changed invoice, two moment engines, both paid tails, finite ranks and all outer predicates.", + "open_questions": [ + { + "blocked_by": "No global optimization certificate; keep all fixed contacts and exact replay.", + "first_step": "Start from PATCH.json and test one fully charged coordinated new-label move.", + "question": "Can simultaneous moves to different frame labels improve the full invoice further?", + "why_it_matters": "A fixed-frame-menu optimum does not cover the subspace lattice." + }, + { + "blocked_by": "No complete restoration and frame-transfer invoice.", + "first_step": "Price the Dumas\u2013Grenet prepare/accumulate/distribute pattern through actual Fourier frames.", + "question": "Can a multi-target accumulating native interface share a paid query?", + "why_it_matters": "This could yield a larger change than local retiming." + }, + { + "blocked_by": "These universal contracts remain premises.", + "first_step": "Audit a named caller and retained hypothesis in PR4359/4440/4441.", + "question": "Do the inherited all-column, precision and tape contracts survive independent scientific review?", + "why_it_matters": "Exact finite arithmetic is not unconditional or formal acceptance." + } + ], + "original_card": { + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "existing_checks": [ + { + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "status": "author-checked" + }, + { + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "scope": "PR #3801: successor scatter-boundary decision package.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "status": "author-checked" + } + ], + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "id": "supplier-boundary-audit", + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ] + }, + "outcome": "completed", + "overlap": { + "checked_at_utc": "2026-10-21T20:51:25Z", + "discussion_records": 3289, + "limits": "Sparse local coverage; no arbitrary diffs or closed remote PR-body coverage; no novelty certificate. No public participation authorized for this successor.", + "local_HEAD_notes": 5739, + "local_notes_searched": 23, + "open_pr_bodies": 301, + "remote_pagination_complete": true + }, + "priority_revision": 7, + "publication_policy": "User explicitly requested no publication of this successor. No push, PR or Discussion post.", + "resource_budget": "Single-process bounded controller arithmetic, under a few minutes per screen; no Lean, Docker, concurrent artifact replay or native historical suites.", + "schema_version": 1, + "scope_change_reason": "The explicit user requests a genuine kappa improvement, keeps this successor local, and asks for a literature pivot if stuck. Newly published PR4440/4441 change the useful starting model.", + "scope_decision": "Stop this finite model screen. No new hill-climbing construction step found. Keep the root-retuning witness as a separately labelled diagnostic, and require changed words/interfaces/providers/stock for the next actual climb.", + "scope_status": "changed", + "stop_rule": "Freeze a strictly improving exact paid profile, retain all inherited native and consumer obligations, run complete relevant checks, and leave the result local for user review.", + "task_id": "supplier-boundary-audit", + "upstream_checkpoint": { + "checked_at_utc": "2026-10-21T20:31:00Z", + "commit": "2a13eb1827784206202db90e5dc8327cf8a250db", + "pending_sources": { + "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", + "PR4441": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39" + }, + "priority_revision": 7 + } +} diff --git a/research/native-lattice-retiming/VALIDATION.md b/research/native-lattice-retiming/VALIDATION.md new file mode 100644 index 0000000000..3e26da177c --- /dev/null +++ b/research/native-lattice-retiming/VALIDATION.md @@ -0,0 +1,26 @@ +# Validation + +Local only, CPython 3.12.8 on macOS arm64, 21 October 2026. + +- Explicit receipt generation: **PASS**. Two native interpreters replay both + orientations, 632 arbitrary persistent columns and owned-center erasure. +- Four new edge types: forward and conjugate serialized Clifford recipes + decode with the right rank, tableau and absolute zero-state phase. +- Complete p17 Laurent/source word and full changed invoice: **PASS**. +- Two exact interval engines, both paid tails, the two finite uniform ranks, + 54+4 current outer predicates, nine-row agreement and 63 legacy predicates: + **PASS**. Wrong contact, phase-only, short-product-bound and outer mutants + reject at their intended gates. +- Optional C++20 discovery: **PASS**, reproducing exactly phase B contact 480 + and the new span `[0,45,133,168,336,381,469,504]`. + +Registered replay, committed-byte preflight and Git-free optimized replay are +recorded after the first committed package is validated. No hosted CI, Lean, +Docker, complete historical suite or independent scientific review is claimed. + +Source ancestry includes PR4440 head +`40e22a83ed660d3d6074c4f2dbf14bfb621eee51` and PR4441 head +`5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39`. SOURCES.json binds the exact +43 consumed source files; unchanged historical native/owned-query/analytic +contracts remain explicit premises. Pending-source acceptance is not inherited +from the reviewed .0023 or .00268647 checkpoints. diff --git a/research/native-lattice-retiming/VERIFY.json b/research/native-lattice-retiming/VERIFY.json new file mode 100644 index 0000000000..a0eb02eb26 --- /dev/null +++ b/research/native-lattice-retiming/VERIFY.json @@ -0,0 +1,69 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "checks": "Authenticate exact source bytes; replay both orientations and 632 arbitrary inputs with two native interpreters; decode all new physical edges with absolute phase; rebuild the unchanged p17 Laurent controller and changed full invoice; certify two-engine moments, both paid tails, finite compiler ranks, stronger BIT and all 54+4 current and 63 legacy outer predicates, with mutation controls.", + "timeout_seconds": 600 + } + ], + "inputs": [ + "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "research/fresh-helper-boundary/RESULT.json", + "research/fresh-helper-boundary/SOURCES.json", + "research/fresh-helper-boundary/arithmetic.py", + "research/fresh-helper-boundary/native.py", + "research/fresh-helper-boundary/verify.py", + "research/fresh-helper-thinned/RESULT.json", + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/vendor/check_ledger.py", + "research/higher-moment-strictification/verify.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-function-composition/complex/prune_native.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "research/kappa-rebuild/bit/bit_native_binding.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-rebuild/bit/mixed_productive_bit.py", + "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/kappa-rebuild/complex/native_extensions.py", + "research/kappa-rebuild/complex/power_two_balance.py", + "research/kappa-rebuild/complex/rebuild_native.py", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "research/native-lattice-retiming/NATIVE-RESULT.json", + "research/native-lattice-retiming/PATCH.json", + "research/native-lattice-retiming/RESULT.json", + "research/native-lattice-retiming/SOURCES.json", + "research/native-lattice-retiming/arithmetic.py", + "research/native-lattice-retiming/native.py", + "research/native-lattice-retiming/verify.py", + "research/pr4359-p7-padding/P7-FACTOR.json", + "research/pr4359-p7-padding/TENSOR.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/pr4359-p7-padding/native_inventory.py", + "research/query-thinned-controllers/BIT-CONTROLLER.json", + "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "research/query-thinned-controllers/RESULT.json", + "research/query-thinned-controllers/SOURCES.json", + "research/query-thinned-controllers/controller.py", + "research/query-thinned-controllers/verify.py", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py" + ], + "python": "3.12", + "requirements": [], + "schema_version": 1, + "status": "ready" +} diff --git a/research/native-lattice-retiming/arithmetic.py b/research/native-lattice-retiming/arithmetic.py new file mode 100644 index 0000000000..ea5fb38dfb --- /dev/null +++ b/research/native-lattice-retiming/arithmetic.py @@ -0,0 +1,136 @@ +"""Complete changed invoice, paid tails, rank and outer consumer. +Apache-2.0. Substantial OpenAI Codex assistance. Credits: PR4359/4433, +Cinna Davis PR4440/4441, and Jacob Alan Sussman's mixed-target flow. +""" +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +import ast +import json +import native + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +KAPPA,TESTED=Q('.00300120'),Q('.00300122') +LOW,HIGH=Q('.0030012390170'),Q('.0030012390173') +need=native.need + +def encoded(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):encoded(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [encoded(v) for v in x] + return x + +def uniform(E,v,theta,power,kappa): + t=1-TESTED + eta=E.scale(E.power(153,-v*TESTED),t) + need(18**16<22**15 and 2*(18**v)**16<=(153**v)**15,'Strict shifted logarithm contraction') + need(eta[0]>theta**power and E.power(153,v*TESTED)[1]<2**power,'Both logarithmic induction conditions') + gap=(TESTED-kappa)/7 + step=gap.denominator + def passes(j):return (step*j+1)**power<2**(gap.numerator*j) + lo,hi=1,2 + while not passes(hi):lo,hi=hi,2*hi + while hi-lo>1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + H=step*hi + need(H>8*v and passes(hi) and not passes(hi-1),'Effective winning integer rank and prior-grid control') + return dict(theta=theta,logarithm_power=power,eta=E.display(eta),gap=gap, + uniform_saving=TESTED-gap,H=H,N='2^'+str(H),integer_exponent=gap.numerator*hi, + word_materialized=False) + +def legacy(params,outer): + source=ROOT/'research/higher-moment-strictification/vendor/check_ledger.py' + parsed=ast.parse(source.read_bytes()) + fn=next(n for n in parsed.body if isinstance(n,ast.FunctionDef) and n.name=='ledger') + constants=[n for n in parsed.body if isinstance(n,ast.Assign) and any(isinstance(t,ast.Name) and t.id.startswith('KAPPA_') for t in n.targets)] + d=params['d'];eps,beta,q,a=(params[k] for k in ('epsilon','beta','q','a')) + grid=10**10;backoff=Q((eps*q*grid).__floor__(),grid)-KAPPA + need(backoff>0,'Positive exact legacy grid backoff') + env={'Q':Q,'R0':params['r0'],'ZETA':Q(1,10**8),'SLACK':d,'STOP':d,'FLOOR':grid,'BACKOFF':backoff, + 'EPS':eps,'BETA':beta,'THETA_POWER':Q(2),'HALO_POWER':48,'CORE_POWER':128,'STRASSEN_TAU':Q(45,16), + 'b':params['b'],'q':q,'a':a,'bit':params['bit_saving'], + 'online':Q('0.001730970419199163702738'),'old':Q('0.001730970419199163702738')} + exec(compile(ast.fix_missing_locations(ast.Module(body=constants+[fn],type_ignores=[])),'pinned legacy outer','exec'),env) + result=env['ledger']('native_lattice') + need(result['kappa']==KAPPA and result['margins']==outer['margins'],'Nine outer rows agree independently') + need(len(result['strict_checks'])==63 and all(x>0 for x in result['strict_checks'].values()),'All 63 legacy predicates') + return dict(checks=result['strict_checks'],grid=grid,backoff=backoff) + +def run(local): + E=native.load(ROOT/'research/higher-moment-strictification/verify.py','lattice_exact_intervals') + C=native.load(ROOT/'research/query-thinned-controllers/controller.py','lattice_query_controller') + word=native.read(ROOT/'research/query-thinned-controllers/COMPLEX-CONTROLLER.json') + need(json.loads(json.dumps(C.run('complex',17,8)))==word,'Exact unchanged source physical word and Laurent boundaries') + H={int(k):v for k,v in local['helpers'].items()};N={int(k):v for k,v in local['paid'].items()} + T,P=Counter(),Counter();full=thin=idle=0 + for e in word['physical_events']: + if e[0]=='LOCAL':full+=1;T.update(H);P.update(N) + elif e[0]=='QUERY_SHEAR':thin+=1;P[1]+=112 + elif e[0]=='IDLE':P[8*len(e[2])]+=224;idle+=224 + for term in word['diagonal']:T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(19,16,3584),'Every native, query and whole idle') + predecessor=native.read(ROOT/'research/fresh-helper-thinned/RESULT.json') + oldT=Counter({int(k):v for k,v in predecessor['targets'].items()});oldP=Counter({int(k):v for k,v in predecessor['paid'].items()}) + need(T==oldT and P==oldP+Counter({1:19,4:19})-Counter({2:19,3:19}),'Independent complete profile substitution') + need(sum(T.values())==11560 and sum(P.values())==69273,'Complete field and call counts') + need((sum(r*n for r,n in T.items()),sum(r*n for r,n in P.items()))==(260798,259998),'Unchanged rank masses and surplus 800') + def margin(c): + a,b=E.moment(T,1-c),E.moment(P,1-c) + return a[0]-b[1],a[1]-b[0] + need(margin(LOW)[0]>0 and margin(HIGH)[1]<0,'Exact changed raw-root bracket') + # Positive decreasing on [0,.01], sufficient to isolate this first root. + derivative=sum(n*E.mul(E.power(r,Q('.99')),E.log_bounds(r))[0] for r,n in T.items())-sum(n*E.mul(E.power(r,1),E.log_bounds(r))[1] for r,n in P.items()) + need(derivative>0,'Strictly decreasing throughout C in [0,.01]') + other=native.load(ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','lattice_other_intervals') + tl,th=other.moment(T,TESTED);pl,ph=other.moment(P,TESTED) + t=1-TESTED;target=E.moment(T,t);paid=E.moment(P,t) + need(tl>ph and max(tl,target[0])<=min(th,target[1]),'Second exact raw moment engine') + alpha=E.divide(paid,target);u=Q(3,25);v=675;c=18;b=22 + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + ag,g,d=Q(19,10**9),Q(491,500),Q(391,400) + need(t+u>=1 and alpha[1]<1-ag and gamma[1]1,'Short-product bound negative control') + rank=uniform(E,v,Q(15,16),160,KAPPA) + same=uniform(E,v,Q(15,16),160,Q('.00300105')) + bit=native.read(ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599');admitted=Q(bit['admitted']) + need(atom==Q('.004') and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Retain the entire stronger ordinary BIT admission') + gap=(TESTED-KAPPA)/7 + params=dict(kappa=KAPPA,tested_saving=TESTED,complex_uniform_saving=rank['uniform_saving'], + b=KAPPA+5*gap,a=KAPPA+4*gap,q=KAPPA+3*gap,bit_saving=admitted, + epsilon=1-gap,beta=1-3*gap,r0=gap/10,stop=gap,layout=gap,d=gap) + L=native.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','lattice_outer') + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Full current consumer predicates') + need(all(x>0 for group in ('strict_checks','functional_checks') for x in outer[group].values()),'Every current outer predicate') + oldchecks=legacy(params,outer) + source_kappa=Q('.00300105');sg=(TESTED-source_kappa)/7 + sp=dict(kappa=source_kappa,tested_saving=TESTED,complex_uniform_saving=same['uniform_saving'], + b=source_kappa+5*sg,a=source_kappa+4*sg,q=source_kappa+3*sg,bit_saving=admitted, + epsilon=1-sg,beta=1-3*sg,r0=sg/10,stop=sg,layout=sg,d=sg) + same_outer=L.ledger(sp);same_outer['functional_checks']['actual_new_BIT_stock_sublinear']=sp['beta']*(1-atom) + need(all(x>0 for group in ('strict_checks','functional_checks') for x in same_outer[group].values()),'Same-kappa full outer comparison') + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_kappa',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items() if x<=0];need(failed,'Reject '+name);controls[name]=failed + local_scalar=max(x['real_scalar_allowance'] for x in local['native'].values()) + routes=(sum(N.values())+2*408)*1000 + need(local_scalar+routes<10**7,'All unchanged scalar and changed physical route costs fit') + raw=19*10**7+16*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program']) for k in ('left','right'))) + need(raw<10**9,'Complete nonrecursive raw budget') + return encoded(dict(status='PASS_CONDITIONAL_NEW_NATIVE_PROFILE_KAPPA',kappa=KAPPA,kappa_decimal='0.00300120', + gain_over_PR4441=KAPPA-Q('.00300105'),targets=dict(sorted(T.items())),paid=dict(sorted(P.items())), + rank_surplus=800,raw_root=[LOW,HIGH],raw_root_scope='Unique crossing on [0,.01]; no universal or global mechanism ceiling.', + derivative_negative_upper=-derivative,raw_moment_margin=E.display(margin(TESTED)), + strictification=dict(tested=TESTED,power=v,cutoff=c,floor=b,u=u,alpha=E.display(alpha),gamma=E.display(gamma),delta=E.display(delta),limits=[1-ag,g,d],normalized_paid_upper=bound), + compiler=rank,same_predecessor_kappa_compiler=same, + rank_exponent_reduction=Q(int(predecessor['compiler']['H']),rank['H']),same_kappa_rank_exponent_reduction=Q(int(predecessor['compiler']['H']),same['H']), + ordinary_BIT=bit,outer=outer,same_predecessor_kappa_outer=same_outer,legacy_outer=oldchecks,negative_controls=controls, + nonrecursive=dict(local_scalar=local_scalar,route_bound=routes,raw_upper=raw,budget=10**9))) diff --git a/research/native-lattice-retiming/discover-lattice.cpp b/research/native-lattice-retiming/discover-lattice.cpp new file mode 100644 index 0000000000..1798964ac4 --- /dev/null +++ b/research/native-lattice-retiming/discover-lattice.cpp @@ -0,0 +1,68 @@ +// Optional floating-point discovery, never a proof checker. Apache-2.0. +// Prepared with substantial OpenAI Codex assistance. +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std; +struct Arc{int v,rev;double cap;}; +struct Flow{vector> a;vector level,ptr;Flow(int n):a(n),level(n),ptr(n){};void edge(int u,int v,double c){Arc x{v,int(a[v].size()),c},y{u,int(a[u].size()),0};a[u].push_back(x);a[v].push_back(y);}double send(int u,int t,double f){if(u==t)return f;for(int&i=ptr[u];i1e-8&&level[e.v]==level[u]+1){double z=send(e.v,t,min(f,e.cap));if(z>1e-8){e.cap-=z;a[e.v][e.rev].cap+=z;return z;}}}return 0;}vectorcut(int s,int t){while(true){fill(level.begin(),level.end(),-1);queueq;level[s]=0;q.push(s);while(!q.empty()){int u=q.front();q.pop();for(auto e:a[u])if(e.cap>1e-8&&level[e.v]<0){level[e.v]=level[u]+1;q.push(e.v);}}if(level[t]<0){vectorv(level.size());for(int i=0;i=0;return v;}fill(ptr.begin(),ptr.end(),0);while(send(s,t,1e15)>1e-8){}}}}; + +struct Frame{int dim;array bits;}; +bool sub(const Frame&a,const Frame&b){for(int k=0;k<8;k++)if(a.bits[k]&~b.bits[k])return false;return true;} +bool contains(const Frame&f,int v){return(f.bits[v/64]>>(v%64))&1;} +Frame mapped(const Frame&f,int v,bool join){Frame g=f;if(join){if(contains(f,v))return g;g.dim++;for(int x=0;x<512;x++)if(contains(f,x))g.bits[(x^v)/64]|=1ULL<<((x^v)%64);}else{bool changed=false;for(int x=0;x<512;x++)if(contains(f,x)&&(__builtin_popcount(unsigned(x&v))&1)){g.bits[x/64]&=~(1ULL<<(x%64));changed=true;}if(changed)g.dim--;}return g;} +struct Node{bool mut;int oldf,newf;}; +int main(int argc,char**argv){ + if(argc!=2)return 2; + int F,N,E;cin>>F>>N>>E;vectorframes(F);map,int>lookup; + for(int f=0;f>frames[f].dim;for(auto&x:frames[f].bits)cin>>x;lookup[frames[f].bits]=f;} + vectornodes(N);vectoridx(N,-1),rev; + for(int i=0;i>m>>nodes[i].oldf>>nodes[i].newf;nodes[i].mut=m;} + vector>edges(E);for(auto&[a,b]:edges)cin>>a>>b; + int H;cin>>H;vector>helpers(H);for(auto&[a,b]:helpers)cin>>a>>b; + for(int i=0;iused;for(auto n:nodes){used.insert(n.oldf);used.insert(n.newf);}vectorproposal(frames.size()); + for(int f:used)proposal[f]=mapped(frames[f],v,join); + Flow flow(V+2);vectorunary(V,0);int s=V,t=V+1; + for(auto[a,b]:edges){int fa=nodes[a].newf,fb=nodes[b].oldf;auto A=frames[fa],B=frames[fb],GA=proposal[fa],GB=proposal[fb]; + if(!sub(A,B)){cerr<<"bad baseline edge"<=0&&i==j){unary[i]+=e11-e00;continue;} + if(i>=0&&j>=0){double w=e10+e01-e00-e11;if(w<-1e-7){cerr<<"nonsubmodular "<=0)unary[i]+=e10-e00;else if(j>=0)unary[j]+=e01-e00; + } + for(auto[a,b]:helpers){auto A=frames[nodes[a].newf],B=frames[nodes[b].oldf],GA=proposal[nodes[a].newf],GB=proposal[nodes[b].oldf]; + unary[idx[a]]+=powers[B.dim-A.dim]-powers[GB.dim-GA.dim]; + } + for(int i=0;i=0&&reach[idx[a]]?proposal[fa]:A,GB=idx[b]>=0&&reach[idx[b]]?proposal[fb]:B; + if(!sub(GA,GB)){legal=false;break;}delta+=powers[GB.dim-GA.dim]-powers[B.dim-A.dim]; + } + for(auto[a,b]:helpers)if(reach[idx[a]]){auto A=frames[nodes[a].newf],B=frames[nodes[b].oldf],GA=proposal[nodes[a].newf],GB=proposal[nodes[b].oldf];delta+=powers[B.dim-A.dim]-powers[GB.dim-GA.dim];} + if(legal&&delta < -1e-8){int count=0,h=0;for(auto[a,b]:helpers)if(reach[idx[a]])h++; + vectortranslated(frames.size(),-1); + for(int f:used){auto G=proposal[f];auto it=lookup.find(G.bits);if(it==lookup.end()){int k=frames.size();lookup[G.bits]=k;frames.push_back(G);translated[f]=k;}else translated[f]=it->second;} + for(int k=0;k=0&&reach[idx[k]]){nodes[k].oldf=translated[nodes[k].oldf];nodes[k].newf=translated[nodes[k].newf];count++;} + gain+=delta;cerr<<"ACCEPT round "<=-1e-8)break; + } +} diff --git a/research/native-lattice-retiming/discover.py b/research/native-lattice-retiming/discover.py new file mode 100644 index 0000000000..425a74925c --- /dev/null +++ b/research/native-lattice-retiming/discover.py @@ -0,0 +1,59 @@ +"""Optional floating discovery; never mathematical acceptance. +Apache-2.0, Codex assistance. Min-cut base credited to Cinna Davis PR4441. +""" +import argparse +import json +from pathlib import Path +import subprocess +import native + +def main(output): + output.mkdir(parents=True,exist_ok=False) + N,c,_,baseline=native.build() + c['frames'].pop() # The explicit candidate must not seed its own discovery. + program=baseline['forward'];nodes=[];paths=[[] for _ in range(632)] + def contact(old,new,roles,mutable=False,index=-1): + i=len(nodes);nodes.append(dict(old=old,new=new,roles=roles,mutable=mutable,index=index)) + for r in roles:paths[r].append(i) + for r,f in enumerate(c['start']):contact(f,f,[r],r>=224) + for i,e in enumerate(program): + if e[0]=='scalar': + g=e[1];rr=g[1:3] if g[0] in ('add','copy') else g[1:2];roles=[r[1] for r in rr if r[0]=='L'] + if roles:contact(e[2],e[2],roles,all(r[0]=='L' for r in rr),i) + elif e[0]=='warp':contact(e[3],e[4],[e[1][1]],False,i) + last=len(nodes) + for r,f in enumerate(c['final']):contact(f,f,[r],r>=224) + edges=[(a,b) for path in paths for a,b in zip(path,path[1:])] + graph=output/'input.graph' + with graph.open('w') as out: + print(len(c['frames']),len(nodes),len(edges),file=out) + for basis in c['frames']: + sp=N.span(basis) + print(len(basis),*[sum(1<<(v%64) for v in sp if v//64==b) for b in range(8)],file=out) + for n in nodes:print(int(n['mutable']),n['old'],n['new'],file=out) + for a,b in edges:print(a,b,file=out) + print(408,file=out) + for r in range(224,632):print(r,last+r,file=out) + executable=output/'discover-lattice';solution=output/'solution.txt' + subprocess.run(['c++','-O3','-std=c++20',str(native.HERE/'discover-lattice.cpp'),'-o',str(executable)],check=True,timeout=120) + with graph.open() as inp,(output/'discovery.log').open('w') as log: + subprocess.run([str(executable),str(solution)],stdin=inp,stdout=log,stderr=log,check=True,timeout=600) + native.need(solution.exists(),'No improved candidate found') + lines=solution.read_text().splitlines();F,M=map(int,lines[0].split());native.need(M==len(nodes),'Discovery dimensions') + spaces=[] + for line in lines[1:F+1]: + d,*chunks=map(int,line.split());sp=frozenset(x for x in range(512) if chunks[x//64]>>(x%64)&1) + native.need(len(sp)==1< Date: Wed, 21 Oct 2026 16:57:45 -0400 Subject: [PATCH 13/26] Record native lattice replay and isolated export validation --- research/native-lattice-retiming/README.md | 2 +- research/native-lattice-retiming/TASK.json | 16 +++- .../native-lattice-retiming/VALIDATION.md | 75 +++++++++++++------ 3 files changed, 70 insertions(+), 23 deletions(-) diff --git a/research/native-lattice-retiming/README.md b/research/native-lattice-retiming/README.md index 8d4e9ca201..2cc4f47bd9 100644 --- a/research/native-lattice-retiming/README.md +++ b/research/native-lattice-retiming/README.md @@ -1,4 +1,4 @@ -# A new native contact: conditional κ = 0.00300120 +# Conditional κ = 0.00300120 (71.9× smaller uniform-rank exponent) **Local for user review. Do not push, publish a PR or post Discussions.** diff --git a/research/native-lattice-retiming/TASK.json b/research/native-lattice-retiming/TASK.json index 5c9dd61a4c..6f6a1cc8bc 100644 --- a/research/native-lattice-retiming/TASK.json +++ b/research/native-lattice-retiming/TASK.json @@ -112,12 +112,26 @@ "stop_rule": "Freeze a strictly improving exact paid profile, retain all inherited native and consumer obligations, run complete relevant checks, and leave the result local for user review.", "task_id": "supplier-boundary-audit", "upstream_checkpoint": { - "checked_at_utc": "2026-10-21T20:31:00Z", + "checked_at_utc": "2026-10-21T20:56:24Z", "commit": "2a13eb1827784206202db90e5dc8327cf8a250db", "pending_sources": { "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", "PR4441": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39" }, "priority_revision": 7 + }, + "validation": { + "changed_receipt": "rejected", + "changed_source": "rejected", + "committed_bytes": "pass", + "export_integrity": "pass", + "git_free_optimized": "pass", + "metadata_pins": "pass", + "no_publication": true, + "optional_discovery": "reproduces exact patch", + "platform": "macOS arm64", + "python": "3.12.8", + "registered_replay": "pass", + "source_history": "unavailable: shallow checkout" } } diff --git a/research/native-lattice-retiming/VALIDATION.md b/research/native-lattice-retiming/VALIDATION.md index 3e26da177c..908ed71d94 100644 --- a/research/native-lattice-retiming/VALIDATION.md +++ b/research/native-lattice-retiming/VALIDATION.md @@ -1,26 +1,59 @@ # Validation -Local only, CPython 3.12.8 on macOS arm64, 21 October 2026. - -- Explicit receipt generation: **PASS**. Two native interpreters replay both - orientations, 632 arbitrary persistent columns and owned-center erasure. -- Four new edge types: forward and conjugate serialized Clifford recipes - decode with the right rank, tableau and absolute zero-state phase. -- Complete p17 Laurent/source word and full changed invoice: **PASS**. -- Two exact interval engines, both paid tails, the two finite uniform ranks, - 54+4 current outer predicates, nine-row agreement and 63 legacy predicates: - **PASS**. Wrong contact, phase-only, short-product-bound and outer mutants - reject at their intended gates. -- Optional C++20 discovery: **PASS**, reproducing exactly phase B contact 480 - and the new span `[0,45,133,168,336,381,469,504]`. - -Registered replay, committed-byte preflight and Git-free optimized replay are -recorded after the first committed package is validated. No hosted CI, Lean, -Docker, complete historical suite or independent scientific review is claimed. +All scientific checks below pass on CPython 3.12.8, macOS arm64, 21 October +2026. Scientific code/receipts were committed at +`71c54ffcfee4c77d77164f9b02bdf763a8f267d0`; the final follow-up only records +validation and changes documentation/task status. + +| Check | Result | +| --- | --- | +| Metadata and all source pins | PASS_PACKAGE_METADATA_AND_PINS | +| Registered full replay | PASS_REGISTERED_RESEARCH_PACKAGE | +| Both native orientations, two interpreters, 632 arbitrary persistent columns, arbitrary owned-center entry then legal erasure | PASS | +| Four new edge types, forward/conjugate Clifford decoding, exact rank and absolute phase | PASS | +| Complete p17 physical/Laurent word, changed full paid/productive invoice | PASS | +| Two interval engines, new root bracket, both paid strictification tails, both finite uniform ranks | PASS | +| Nine outer rows, 54 current predicates, four guards and 63 legacy predicates | PASS | +| Wrong contact, global-phase-only, short-product-bound and outer negative controls | REJECTED as intended | +| Committed-byte preflight, 59 exported files | PASS_RESEARCH_COMMIT_BYTES | +| Deterministic committed export and independent integrity check | PASS_RESEARCH_EXPORT | +| Isolated Git-free optimized replay (`-I -O -B`, explicit package import path) | PASS_CONDITIONAL_NEW_NATIVE_PROFILE_KAPPA | +| Changed pinned source comment in the Git-free export | Rejected by source authentication | +| Changed saved κ receipt in the Git-free export, full optimized replay | Rejected at exact RESULT.json comparison | +| Optional C++20 discovery | Reproduces exactly phase B contact 480 and the new span | + +Commands: + +```sh +python3.12 -B scripts/research_package.py --package research/native-lattice-retiming --check-only +python3.12 -B scripts/research_package.py --package research/native-lattice-retiming +python3.12 -B scripts/check_research_commit.py --package research/native-lattice-retiming +python3.12 -B scripts/export_research_package.py export --package research/native-lattice-retiming --ref 71c54ffcfee4c77d77164f9b02bdf763a8f267d0 --output /tmp/native-lattice-71c54ff.tar +python3.12 -B scripts/export_research_package.py check /tmp/native-lattice-71c54ff.tar +python3.12 -B research/native-lattice-retiming/discover.py --output /tmp/native-lattice-discovery-replay +``` + +The checked export was extracted without Git, then `verify.py` ran through +`runpy.run_path` under `python3.12 -I -O -B` with only the explicit package +folder inserted into `sys.path`. Its normal 43-input authentication, complete +native and arithmetic checks and receipt comparisons all ran. The two external +mutation controls used that export and restored the exact original bytes. +The optional compiler was Apple clang 21.0.0 with `-O3 -std=c++20`. + +`--check-source-history` is **unavailable**: its explicit precondition rejects +this shallow checkout with “source-history check requires full Git history.” +No unshallow fetch was attempted. Exact pending heads and consumed bytes are +present, pinned and retained in local merge ancestry; the unavailable check +is not presented as scientific or provenance acceptance. Source ancestry includes PR4440 head `40e22a83ed660d3d6074c4f2dbf14bfb621eee51` and PR4441 head -`5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39`. SOURCES.json binds the exact -43 consumed source files; unchanged historical native/owned-query/analytic -contracts remain explicit premises. Pending-source acceptance is not inherited -from the reviewed .0023 or .00268647 checkpoints. +`5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39`. SOURCES.json binds the 43 +consumed source files. The final upstream checkpoint at 20:56 UTC found +canonical main still `2a13eb1827784206202db90e5dc8327cf8a250db`, unchanged +priority guidance, unchanged pending heads and selected κ=.0023. + +No hosted CI, Lean, Docker, complete historical suite or independent +scientific review is claimed. Universal native/all-column, owned-query, +precision, physical tape, analytic and recovery contracts remain conditional +premises. No push, PR or Discussion post was made for this package. From de6869e2e4d9c6f630bac5de4a919d99a2cb884b Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 17:37:26 -0400 Subject: [PATCH 14/26] Prepare reviewed lattice contribution for publication --- .../native-lattice-retiming/LITERATURE.md | 6 ++++- research/native-lattice-retiming/PROOF.md | 2 +- research/native-lattice-retiming/README.md | 12 +++++++--- research/native-lattice-retiming/SOURCES.json | 2 +- research/native-lattice-retiming/TASK.json | 24 ++++++++++++------- .../native-lattice-retiming/VALIDATION.md | 18 +++++++++++++- 6 files changed, 48 insertions(+), 16 deletions(-) diff --git a/research/native-lattice-retiming/LITERATURE.md b/research/native-lattice-retiming/LITERATURE.md index 96469b6e48..2e3a5b7846 100644 --- a/research/native-lattice-retiming/LITERATURE.md +++ b/research/native-lattice-retiming/LITERATURE.md @@ -1,6 +1,6 @@ # Literature evaluated during this continuation -Local research notes, 21 October 2026. This revisits zxv's +Research notes, 21 October 2026. This revisits my [0.0023 literature list](../kappa-0023-productive-jobs/LITERATURE.md). The sources motivate experiments; their theorems are not imported as native instructions or as a proof of the new multiplication bound. @@ -40,3 +40,7 @@ multiple-label moves, changed scalar graphs and other providers remain open. No global or exact search-optimality claim is made. Apache-2.0 for these notes. Papers retain their own copyrights and licenses. + +Submission refresh: concurrent [PR4447](https://github.com/CrocSwap/integer-mult-bounds/pull/4447) +reports the same contact and profile. This separate discovery and replay is +retained with the smaller charged templates; no novelty claim is made. diff --git a/research/native-lattice-retiming/PROOF.md b/research/native-lattice-retiming/PROOF.md index c966d4df2c..5ed2cacea7 100644 --- a/research/native-lattice-retiming/PROOF.md +++ b/research/native-lattice-retiming/PROOF.md @@ -6,7 +6,7 @@ Source PR4441 is fixed at `5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39`, including PR4440 at `40e22a83ed660d3d6074c4f2dbf14bfb621eee51`. Their conditional contracts are retained. No selected result, independent scientific acceptance or universal implementation hypothesis is promoted. -The exact byte closure is SOURCES.json. New work stays local for user review. +The exact byte closure is SOURCES.json. The user authorized submission after review. ## One legal contact outside the predecessor frame menu diff --git a/research/native-lattice-retiming/README.md b/research/native-lattice-retiming/README.md index 2cc4f47bd9..22cb2378ee 100644 --- a/research/native-lattice-retiming/README.md +++ b/research/native-lattice-retiming/README.md @@ -1,6 +1,6 @@ # Conditional κ = 0.00300120 (71.9× smaller uniform-rank exponent) -**Local for user review. Do not push, publish a PR or post Discussions.** +**Submission authorized by the user after review on 21 October 2026.** A changed native paid profile raises the conditional multiplication saving to **κ = 0.00300120** and specifies sufficient uniform rank @@ -11,8 +11,14 @@ by **71.88×**. At PR4441's unchanged κ=0.00300105, the rank can instead be **`2^249900000000`**, a **661.53×** exponent reduction. These are sufficient mathematical template sizes, not practical speedups. -This builds on zxv's selected [0.0023 construction](../kappa-0023-productive-jobs/README.md), -its [higher-moment/logarithmic compiler](../higher-moment-strictification/README.md), +The submission refresh found concurrent [PR4447](https://github.com/CrocSwap/integer-mult-bounds/pull/4447), +which uses the same B/480 contact and paid profile and declares κ=0.00300123. +This contribution retains the reviewed κ=0.00300120 and supplies the smaller +paid-tail and uniform-template bounds above, with a separate discovery path. +No unique-discovery or strongest-κ claim is made. + +This builds on my selected [0.0023 construction](../kappa-0023-productive-jobs/README.md), +my [higher-moment/logarithmic compiler](../higher-moment-strictification/README.md), and Cinna Davis's new query-thinning and fresh-helper constructions ([PR4440](https://github.com/CrocSwap/integer-mult-bounds/pull/4440), [PR4441](https://github.com/CrocSwap/integer-mult-bounds/pull/4441)). diff --git a/research/native-lattice-retiming/SOURCES.json b/research/native-lattice-retiming/SOURCES.json index 5378362135..5dc627b3b2 100644 --- a/research/native-lattice-retiming/SOURCES.json +++ b/research/native-lattice-retiming/SOURCES.json @@ -1,5 +1,5 @@ { - "base_commit": "28f58f6f9b72ddfe7aa5b986d1b678356c4e6350", + "base_commit": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", "files": [ { "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", diff --git a/research/native-lattice-retiming/TASK.json b/research/native-lattice-retiming/TASK.json index 6f6a1cc8bc..544002777e 100644 --- a/research/native-lattice-retiming/TASK.json +++ b/research/native-lattice-retiming/TASK.json @@ -2,7 +2,7 @@ "actual_scope": "Build a changed native frame contact beyond PR4441, then completely pay tensor completion, finite uniform compilation and the integer-multiplication consumer.", "ai_assistance": "Substantial OpenAI Codex assistance; no subagents.", "author": "zxv, with substantial OpenAI Codex assistance", - "base_commit": "28f58f6f9b72ddfe7aa5b986d1b678356c4e6350", + "base_commit": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", "bottleneck_link": "New subspaces outside the predecessor frame menu can change the raw paid profile while exact native endpoints and all helper outputs stay fixed.", "budget_minutes": 60, "evidence": "Explicit one-contact native patch; two all-column replays in both orientations, new absolute-phase transports, complete changed invoice, two moment engines, both paid tails, finite ranks and all outer predicates.", @@ -100,19 +100,25 @@ "local_HEAD_notes": 5739, "local_notes_searched": 23, "open_pr_bodies": 301, - "remote_pagination_complete": true + "remote_pagination_complete": true, + "submission_refresh": { + "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "checked_at_utc": "2026-10-21T21:36:00Z", + "concurrent_PR4447": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "finding": "Same B/480 contact and paid profile, declared kappa .00300123. This contribution retains .00300120 and gives substantially smaller sufficient templates. No novelty or strongest-endpoint claim." + } }, "priority_revision": 7, - "publication_policy": "User explicitly requested no publication of this successor. No push, PR or Discussion post.", + "publication_policy": "User approved submission of this reviewed contribution on 2026-10-21. First-person prose refers to the author, zxv. No further Discussion participation is requested.", "resource_budget": "Single-process bounded controller arithmetic, under a few minutes per screen; no Lean, Docker, concurrent artifact replay or native historical suites.", "schema_version": 1, - "scope_change_reason": "The explicit user requests a genuine kappa improvement, keeps this successor local, and asks for a literature pivot if stuck. Newly published PR4440/4441 change the useful starting model.", - "scope_decision": "Stop this finite model screen. No new hill-climbing construction step found. Keep the root-retuning witness as a separately labelled diagnostic, and require changed words/interfaces/providers/stock for the next actual climb.", + "scope_change_reason": "The explicit user requested a changed native construction and literature evaluation when stuck, then approved submission after reviewing the local result. PR4440/4441 supplied the useful starting model.", + "scope_decision": "The new exact contact changes the paid profile and passes the fully charged conditional transfer. Publish the reviewed result and smaller finite ranks; acknowledge concurrent PR4447 without a novelty or strongest-kappa claim.", "scope_status": "changed", - "stop_rule": "Freeze a strictly improving exact paid profile, retain all inherited native and consumer obligations, run complete relevant checks, and leave the result local for user review.", + "stop_rule": "Publish the reviewed, strictly improving exact paid profile with all inherited native and consumer obligations retained; do not expand the mathematical scope during submission.", "task_id": "supplier-boundary-audit", "upstream_checkpoint": { - "checked_at_utc": "2026-10-21T20:56:24Z", + "checked_at_utc": "2026-10-21T21:36:00Z", "commit": "2a13eb1827784206202db90e5dc8327cf8a250db", "pending_sources": { "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", @@ -127,11 +133,11 @@ "export_integrity": "pass", "git_free_optimized": "pass", "metadata_pins": "pass", - "no_publication": true, "optional_discovery": "reproduces exact patch", "platform": "macOS arm64", "python": "3.12.8", "registered_replay": "pass", - "source_history": "unavailable: shallow checkout" + "source_history": "unavailable: shallow checkout", + "unpublished_at_initial_validation": true } } diff --git a/research/native-lattice-retiming/VALIDATION.md b/research/native-lattice-retiming/VALIDATION.md index 908ed71d94..d63d8cce0b 100644 --- a/research/native-lattice-retiming/VALIDATION.md +++ b/research/native-lattice-retiming/VALIDATION.md @@ -56,4 +56,20 @@ priority guidance, unchanged pending heads and selected κ=.0023. No hosted CI, Lean, Docker, complete historical suite or independent scientific review is claimed. Universal native/all-column, owned-query, precision, physical tape, analytic and recovery contracts remain conditional -premises. No push, PR or Discussion post was made for this package. +premises. At the initial validation checkpoint this package was unpublished. +The user subsequently approved submission after review. + +## Publication preparation + +The submission branch starts from public PR4441 head `5f9d871c` and carries +only this package beyond that dependency. The earlier unpublished p7 negative +screen remains on its local branch and is excluded. All 46 source/provenance +rows were checked byte-for-byte against this public base before updating the +base pin; no scientific program, patch or receipt changed. The original local +validation commit is retained locally, and its code/receipt bytes are identical +to this submission's scientific files. + +The 21:36 UTC refresh found unchanged canonical main and guidance, plus +concurrent PR4447 at `322e0ec764aa7ef7801383feb1f656e460dd8bed`. Its same +contact/profile and higher declared endpoint are acknowledged in README.md +and the PR description. No unique-discovery or strongest-kappa claim is made. From b990896676e7dd966c61950d6e979f7c383d1c22 Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 18:40:27 -0400 Subject: [PATCH 15/26] Add net-tax and log-moment rank compiler (18.28x smaller exponent) --- .../net-tax-rank-compiler/BENCHMARKS.json | 144 +++ research/net-tax-rank-compiler/LOG-MOMENTS.md | 284 +++++ research/net-tax-rank-compiler/PROOF.md | 343 +++++ research/net-tax-rank-compiler/README.md | 171 +++ research/net-tax-rank-compiler/RESULT.json | 1116 +++++++++++++++++ research/net-tax-rank-compiler/SHIFTED-LOG.md | 134 ++ research/net-tax-rank-compiler/SOURCES.json | 90 ++ research/net-tax-rank-compiler/TASK.json | 132 ++ research/net-tax-rank-compiler/VERIFY.json | 29 + .../net-tax-rank-compiler/WEIGHTED-EXITS.md | 268 ++++ research/net-tax-rank-compiler/compiler.py | 316 +++++ research/net-tax-rank-compiler/intervals.py | 150 +++ research/net-tax-rank-compiler/test_math.py | 186 +++ research/net-tax-rank-compiler/verify.py | 198 +++ 14 files changed, 3561 insertions(+) create mode 100644 research/net-tax-rank-compiler/BENCHMARKS.json create mode 100644 research/net-tax-rank-compiler/LOG-MOMENTS.md create mode 100644 research/net-tax-rank-compiler/PROOF.md create mode 100644 research/net-tax-rank-compiler/README.md create mode 100644 research/net-tax-rank-compiler/RESULT.json create mode 100644 research/net-tax-rank-compiler/SHIFTED-LOG.md create mode 100644 research/net-tax-rank-compiler/SOURCES.json create mode 100644 research/net-tax-rank-compiler/TASK.json create mode 100644 research/net-tax-rank-compiler/VERIFY.json create mode 100644 research/net-tax-rank-compiler/WEIGHTED-EXITS.md create mode 100644 research/net-tax-rank-compiler/compiler.py create mode 100644 research/net-tax-rank-compiler/intervals.py create mode 100644 research/net-tax-rank-compiler/test_math.py create mode 100644 research/net-tax-rank-compiler/verify.py diff --git a/research/net-tax-rank-compiler/BENCHMARKS.json b/research/net-tax-rank-compiler/BENCHMARKS.json new file mode 100644 index 0000000000..5c411a1916 --- /dev/null +++ b/research/net-tax-rank-compiler/BENCHMARKS.json @@ -0,0 +1,144 @@ +{ + "schema_version": 1, + "cases": [ + { + "name": "native-source-parameters", + "source": "research/native-lattice-retiming/RESULT.json", + "profile_key": null, + "witness": { + "saving": ".00300122", + "kappa": ".00300120", + "v": 675, + "cutoff": 18, + "floor": 22, + "u": "3/25", + "p": 160, + "log_shift": 1, + "uniform_method": "shifted", + "theta": "15/16" + } + }, + { + "name": "native-net-shift", + "source": "research/native-lattice-retiming/RESULT.json", + "profile_key": null, + "witness": { + "saving": ".00300122", + "kappa": ".00300120", + "v": 476, + "cutoff": 18, + "floor": 22, + "u": "3/25", + "p": 108, + "log_shift": 19040, + "uniform_method": "shifted", + "theta": "173/185" + } + }, + { + "name": "native-weighted-same-C", + "source": "research/native-lattice-retiming/RESULT.json", + "profile_key": null, + "witness": { + "saving": ".00300122", + "kappa": ".00300120", + "v": 227, + "cutoff": 20, + "floor": 21, + "u": "861/5000", + "p": 28, + "log_shift": 454, + "uniform_method": "weighted", + "weighted": { + "mean_upper": "431/500", + "A_lower": "231/500", + "A_upper": "463/1000", + "ambient_log_lower": "1679/1000", + "floor_log_lower": "127/125" + } + } + }, + { + "name": "native-concentrated-same-C", + "source": "research/native-lattice-retiming/RESULT.json", + "profile_key": null, + "witness": { + "saving": ".00300122", + "kappa": ".00300120", + "v": 227, + "cutoff": 20, + "floor": 21, + "u": "861/5000", + "p": 21, + "log_shift": 3405, + "uniform_method": "log-moments", + "weighted": { + "raw_mean_upper": "431/500", + "A_lower": "347/100", + "A_upper": "139/40", + "ambient_log_lower": "1679/1000", + "floor_log_lower": "127/125", + "raw_log_bound": "3/2", + "paid_excess_upper": "1/100000" + } + } + }, + { + "name": "native-concentrated-balanced", + "source": "research/native-lattice-retiming/RESULT.json", + "profile_key": null, + "witness": { + "saving": "90037/30000000", + "kappa": ".00300120", + "v": 260, + "cutoff": 20, + "floor": 21, + "u": "171/1000", + "p": 24, + "log_shift": 3900, + "uniform_method": "log-moments", + "weighted": { + "raw_mean_upper": "431/500", + "A_lower": "347/100", + "A_upper": "139/40", + "ambient_log_lower": "1679/1000", + "floor_log_lower": "127/125", + "raw_log_bound": "3/2", + "paid_excess_upper": "1/100000" + } + } + }, + { + "name": "p7-net-shift-same-C", + "source": "research/higher-moment-strictification/RESULT.json", + "profile_key": "invoice_oracle", + "witness": { + "saving": ".00268648", + "kappa": ".00268647", + "v": 113, + "cutoff": 9, + "floor": 15, + "u": "33/125", + "p": 7, + "log_shift": 1356, + "theta": "56/69" + } + }, + { + "name": "p7-net-shift-balanced", + "source": "research/higher-moment-strictification/RESULT.json", + "profile_key": "invoice_oracle", + "witness": { + "saving": "11551891/4300000000", + "kappa": ".00268647", + "v": 100, + "cutoff": 10, + "floor": 15, + "u": "31/100", + "p": 8, + "log_shift": 1700, + "theta": "57/67" + } + } + ] +} diff --git a/research/net-tax-rank-compiler/LOG-MOMENTS.md b/research/net-tax-rank-compiler/LOG-MOMENTS.md new file mode 100644 index 0000000000..b75cf923df --- /dev/null +++ b/research/net-tax-rank-compiler/LOG-MOMENTS.md @@ -0,0 +1,284 @@ +# Retaining concentration of the paid tensor's log ranks + +The mean-only certificate in [WEIGHTED-EXITS.md](WEIGHTED-EXITS.md) replaces +one completed unit's log rank by a Bernoulli random variable. A tensor unit +has substantially more structure: before splitting, its normalized log rank +is an average of independent raw log ranks. The following finite rational +certificate retains that concentration, bounds the effect of every paid +completion, and uses the same inherited integer compiler. + +This is a bound on normalized paid rank-one leaves, conditional on the +source native and finite compiler contracts. No new native operation, +unpaid completion, overlapping-rank compiler or selected-frontier change +is asserted. All probability laws below describe finite weighted +inventories; they do not replace whole integer jobs by fractional inputs. + +## Raw tensor moments + +Fix `01`, a positive integer `v`, a positive support bound `L`, +and a raw paid inventory with positive `t`-moment `P_t`. Under its +probability law `P_r*r^t/P_t`, put + +``` +Y = ln(r)/ln(c), +0<=Y<=L, E[Y]<=q0, 0<=q0<=L. +``` + +For a chronological `v`-fold product, let `J=c^v`. The normalized raw +tensor log rank is exactly + +``` +X_raw = ln(R)/ln(J) = (Y_1+...+Y_v)/v, +``` + +with independent copies of the raw law. The raw product's paid `t`-moment +is `A_raw=P_t^v`. + +The convex chord bound replaces each `Y_i` by `L` times a Bernoulli random +variable of mean `q0/L`. For every positive integer `i`, this gives + +``` +E[X_raw^i] <= M_i, +M_i = (L/v)^i * sum_(j=0..i) S(i,j)*(q0/L)^j*(v)_j. (1) +``` + +Here `S(i,j)` are Stirling numbers of the second kind, and `(v)_j` are +integer falling factorials, zero for `j>v`. Equation (1) follows either by +expanding the binomial moment or by applying convex order one variable at +a time to the nonnegative convex function `x^i`. When `L,q0` are rational, +all `M_i` are rational. + +## Splitting, full paid completion and normalization + +Split every original paid rank above `J`, and also split every paid +completion into positive ranks at most `J`. Let the final paid `t`-moment +be `Q_t`. Define its actual excess by + +``` +E_actual = Q_t-A_raw >= 0, +x = E_actual/A_raw. +``` + +The excess contains the increase in original-paid moment from splitting +**plus the full paid moment of completion calls**. It does not subtract +productive target-completion credit. Suppose a proved paid bound gives + +``` +0<=x<=epsilon. +``` + +For the final completed paid law, put `X=ln(r)/ln(J)`, so `0<=X<=1`. +Its `i`-th moment has the rational upper bound + +``` +E[X^i] <= mu_i := min(1, (M_i+epsilon)/(1+epsilon)), (2) +mu_0 := 1. +``` + +The denominator in (2) needs a capped reference law. It is not justified +merely by overcounting an unnormalized numerator. For an original tensor +call `R>J`, use the reference value +`min(ln(R)/ln(J),1)^i=1`. If its split paid moment is `Q_R`, the split +weighted `i`-moment is at most `Q_R`, so its increase over this capped +reference is at most `Q_R-R^t`. For `R<=J`, the original call is unchanged. +Each full completion contributes at most its full paid moment, because +its final log ranks also lie in `[0,1]`. Thus, with + +``` +m_i = E[min(X_raw,1)^i] <= min(1,M_i), +``` + +the final weighted numerator is at most `A_raw*m_i+E_actual`. +Dividing by the actual total `A_raw+E_actual` gives +`E[X^i]<=(m_i+x)/(1+x)`. For `m_i<=1`, this expression increases with +`x`, since its derivative is `(1-m_i)/(1+x)^2>=0`. Substitution of +`x<=epsilon` and `m_i<=min(1,M_i)` proves (2). The cap is an auxiliary +proof device, not a change to the native program. + +A convenient paid excess bound from this package is + +``` +epsilon >= (splitting_coefficient*gamma_u^v + 2*delta^v)/alpha^v. +``` + +The second term is the predecessor's full completion bound. A sharper +proved full completion bound may replace it. The net completion tax used +to prove a superpotential cannot replace it. + +## Bell-polynomial exit certificate + +The separated compiler's exact exit law is proved in WEIGHTED-EXITS.md: +at height `G`, it consists of `G+1` independent copies of the completed +paid log law. Take a positive integer `p`, positive scale `a=h*ln(2)`, +and rational bounds + +``` +a/ln(J) <= A_bar, +(a+ln(m))/ln(J) >= B_under, +ln(k_min)/ln(J) >= beta > 0. +``` + +Require `B_under>0` as well. + +The ambient `m` and productive minimum `k_min` in these displays belong +to the **completed tensor unit**, not the raw unit. + +For `0<=k<=n<=p`, construct partial exponential Bell polynomials from +the upper moments in (2): + +``` +Bell(0,0) = 1, +Bell(n,0) = 0 for n>0, +Bell(0,k) = 0 for k>0, +Bell(n,k) = sum_(i=1..n-k+1) + binom(n-1,i-1)*mu_i*Bell(n-i,k-1). +``` + +They have nonnegative coefficients in the `mu_i`. Also set + +``` +Shift(r) = sum_(i=0..r) binom(r,i)*A_bar^(r-i)*mu_i. +``` + +For `0<=j<=p`, form + +``` +C_j = sum_(i=j..p) binom(p,i)*Shift(p-i)*Bell(i,j), +D_j = sum_(i=j..p) binom(p,i)*S(i,j)*B_under^(p-i)*beta^i. +``` + +All `D_j` are positive. If `C_j<=lambda*D_j` for every `j`, then + +``` +E[(a+ln(exit))^p] <= lambda*(a+ln(n))^p (3) +``` + +at every integer compiler rank `n>=m`. + +To prove (3), write `u=G`, separate one completed paid variable `X_0`, +and expand the moments of the other `u` independent variables. For their +actual moments, the standard finite identity is + +``` +E[(X_1+...+X_u)^i] + = sum_(j=0..i) (u)_j*Bell_actual(i,j). +``` + +It follows directly by grouping the indices in the expanded power by +their equality partition; each occupied index contributes its corresponding +moment. Replacing actual moments by the upper bounds `mu_i` preserves the +inequality because all coefficients are nonnegative. Expanding +`(A_bar+X_0+...+X_u)^p` therefore gives at most +`sum_j C_j*(u)_j`. Expanding `(B_under+beta*u)^p` gives exactly +`sum_j D_j*(u)_j`. + +The falling factorials are nonnegative for every integer `u>=0`. +Coefficient domination proves the desired polynomial comparison. +Finally, `ln(n)>=ln(m)+G*ln(k_min)` implies +`(a+ln(n))/ln(J)>=B_under+beta*u`, completing the proof. + +This general coefficient test also accepts other rigorously proved upper +log moments; the raw chord bound (1) is one reusable source of them. + +## Uniform-rank consequence + +As in WEIGHTED-EXITS.md, it is enough that + +``` +lambda < eta := t*m^(t-1), +m^(1-t) <= (1+ln(m)/a)^p. +``` + +The first inequality pays exits by source complements. The second covers +the entire ordinary base range by the monotone endpoint argument in +SHIFTED-LOG.md. Strong induction gives + +``` +L(n) <= n^t*(1+ln(n)/a)^p. +``` + +For `N=2^H` and desired exponent `z>t`, the final exact guard is + +``` +(h+H)^p < h^p*2^((z-t)*H). +``` + +Neither the pointwise maximum-exit contraction nor the Bernoulli +mean-only certificate is needed when (3) is used instead. + +## Balanced native4453 diagnostic + +The package's balanced construction uses the unchanged raw paid profile +and the exact parameters + +``` +C=90037/30000000, t=1-C, +v=260, c=20, b=21, u=171/1000, +m=153^260, J=20^260, k_min>=21^260. +``` + +A rational log-moment witness is + +``` +q0=431/500, L=3/2, epsilon=1/100000, +p=24, h=3900=15*v, +A_bar=139/40, +B_under=347/100+1679/1000=5149/1000, +beta=127/125. +``` + +The raw maximum 72 satisfies `72^2<20^3`, proving `Y<=3/2`. The raw +mean and full paid excess need their separate profile-bound interval +checks. The full paid relative excess is below +`0.000001447491519=1`, paid ranks `r_j>=1`, +ambient rank `m=max_i k_i` containing every paid job, and `B` independent +productive fields. Write + +``` +T_s = sum_i k_i^s, P_s = sum_j r_j^s, +0=C, sigma=t+u>=1. +``` + +Choose integers `1=1`, and set `J=c^v`, `L=b^v`. +The chronological native product has productive ranks `K`, paid ranks `R`, +`B^v` productive fields and moments `T_s^v`, `P_s^v`. Its ambient rank is +`m^v`. These assertions use the native product contract in Section 6 below; +they are not consequences of histogram arithmetic alone. + +For an integer `D>=0`, define the exact disjoint splitting charge + +``` +S_t(D,J) = q J^t + r^t, D=qJ+r, 0<=r=0` has its unique maximum at +`x=t^(1/C)`, with value `h`. In particular `0J`, put `x=R/J>1` and `rho=frac(x)`. The exact charge gives + +``` +tau(R)/J^t = x-x^t+rho^t-rho <= x-x^t+h. (2) +``` + +For any `u>=C`, the right side is at most `A(C,u) x^(t+u)`. +Indeed, after dividing by `x^t`, the difference between this proposed upper +bound and (2) is + +``` +G(x) = A x^u-x^C+1-h x^(-t). +G(1) = A-h >= 0, +G'(x) = Au x^(u-1)-C x^(C-1)+ht x^(-t-1) >= 0. +``` + +The last inequality uses `Au>=C`, `u>=C` and `x>=1`. Hence + +``` +tau(R) <= A(C,u) R^(t+u) J^(-u). (3) +``` + +For the useful range `C<=u<=C/h`, this coefficient is simply `C/u`. +In particular this holds throughout `C<=u<=1`. + +A different bound can be stronger. Let `n=ceil(R/J)` be the number of +nonzero split pieces. Concavity gives + +``` +S_t(R,J) <= n^C R^t, +tau(R) <= (n^C-1) R^t. (4) +``` + +For `u>C`, the function `(y^C-1)y^(-u)` on `y>=1` has derivative + +``` +y^(-u-1) [u-(u-C)y^C]. +``` + +It increases up to the unique point `y^C=u/(u-C)` and decreases afterwards. +Its maximum is + +``` +M(C,u) = (C/u)(1-C/u)^((u-C)/C). +``` + +Since `n<2R/J`, (4) therefore implies + +``` +tau(R) <= K(C,u) R^(t+u) J^(-u), +K(C,u) = 2^u (C/u)(1-C/u)^((u-C)/C), u>C. (5) +``` + +At `u=C`, the supremum of `(y^C-1)y^(-C)=1-y^(-C)` is one, +so the valid endpoint definition is `K(C,C)=2^C`. The strict inequalities +in intermediate estimates are not needed: the final certificate will be +strict. Define + +``` +Q(C,u) = min(A(C,u),K(C,u)). +``` + +Then `0=1`, +`y^C-1 <= (C/u)(y^u-1) <= (C/u)y^u`, followed by `n<2R/J`. +For `u>C`, (5) improves its coefficient by the factor +`(1-C/u)^((u-C)/C)<1`; at `u=C`, (3) improves it from `2^C` to one. + +When `C,u` are rational, `K` can be certified without floating point. +Choose a positive integer `d` clearing the denominators of `u` and +`(u-C)/C`. Then + +``` +K(C,u)^d = 2^(du) (C/u)^d (1-C/u)^(d(u-C)/C) +``` + +is rational. A rational upper bound `q` for `K` is equivalent to the exact +rational comparison `q^d >= K^d`. Directed rational log/exp enclosures are +another option, particularly when the clearing exponent is large. + +## 3. Stronger completion net tax + +For `D=L-K>0`, the exact division formula and the definition of `h` imply + +``` +S_t(D,J) <= D J^(-C)+hJ^t. +``` + +Consequently + +``` +E(K) <= LJ^(-C)-L^t + (K^t-KJ^(-C)) + hJ^t + <= LJ^(-C)+2hJ^t-L^t =: H(L,J). (7) +``` + +The second step applies `x^t-x<=h` to `x=K/J`. It does not replace a +restricted sum over `K1`, + +``` +H(L,J)/J^t = L/J-(L/J)^t+2h > 0. +``` + +There are at most `B^v` completed owners, so multiplying the nonnegative +upper bound in (7) by `B^v` is legal even when fewer owners are completed: + +``` +sum_(K= 1-alpha^v-Q(C,u)gamma^v-delta^v-2h epsilon^v+delta0^v. +``` + +Therefore the exact strict inequality + +``` +alpha^v+Q(C,u)gamma^v+delta^v+2h epsilon^v-delta0^v < 1 (9) +``` + +certifies a strict final `t`-moment advantage. The negative term in (9) +belongs to the nonnegative per-owner bound (7), so it is not legitimate to +reuse it after independently discarding other parts of that bound. + +If the h-bound is inconvenient, the valid weaker certificate is + +``` +alpha^v+Q(C,u)gamma^v+3^C delta^v-delta0^v < 1. (10) +``` + +Both improve on charging the entire split/completion invoice on top of the +old moment. Equation (9) is uniformly stronger than (10). Neither requires +the ratios individually to be less than one if the displayed finite +inequality is certified directly. + +For a certificate with interval bounds, all positive terms use upper +bounds and the subtracted `delta0^v` uses a lower bound. Any upper bounds +on `Q` and `h` suffice. Displayed decimals are not substitutes for this +directed exact comparison. + +## 5. What the finite compiler receives + +The transformed unit has all paid ranks at most `J`, all productive ranks +at least `L`, and ambient rank `m^v`; hence strict separation holds. +If (9) or (10) holds, it has `P'_t 9.4810102643e-8, +raw normalized paid log mean < .860094 < 431/500, +full relative paid excess < 1.448e-6 < 1/100000, +largest polynomial coefficient ratio < .019353, +source complement capacity > .0196759. +``` + +The final check is the exact integer inequality + +``` +(3900+125790000000)^24 < 3900^24 * 2^599. +``` + +The previous specified grid point fails. Degree 23 fails this particular +moment-envelope certificate, and dropping tensor concentration makes the +degree-24 certificate fail. These are discriminating checks of the new +argument, not lower bounds on every possible compiler. + +## Reproduction and future use + +From the repository root, with Python 3.12 and no third-party dependencies: + +```sh +python3.12 -B research/net-tax-rank-compiler/verify.py +python3.12 -B scripts/research_package.py --package research/net-tax-rank-compiler +``` + +The first command authenticates the pinned sources, reproduces all seven +certificates, compares the committed receipt, checks the exact exit law +against six literal pinned compiler flows, and runs the mathematical and +rejection controls. It does not rerun the native or outer producer suites. +Use `--write` only after inspecting intentional changes to the exact receipt. + +The generic checker accepts a profile with positive integer `targets` and +`paid` histograms, and a rational witness. See [BENCHMARKS.json](BENCHMARKS.json) +for complete examples of the three compiler methods: + +```sh +python3.12 -B research/net-tax-rank-compiler/compiler.py --example native-concentrated-balanced +python3.12 -B research/net-tax-rank-compiler/compiler.py profile.json witness.json +``` + +The supported profile contract takes the ambient rank as the largest +productive rank and requires all paid ranks to fit. The witness specifies +`saving`, `kappa`, `v`, integer `cutoff` and `floor`, rational `u`, integer +`p` and `log_shift`. `uniform_method` selects `shifted`, `weighted`, or +`log-moments`. The latter two additionally give rational log bounds under +`weighted`; `log-moments` names its raw bound `raw_mean_upper` and requires +`raw_log_bound` and `paid_excess_upper`. The checker verifies every proposed +inequality; numerical search results are never accepted as evidence. + +For a new submission, bind its actual complete native histogram and native +hypotheses, propose a witness, run the checker, then bind the resulting +uniform saving to that submission's complete consumer. A generic profile +file is a conditional mathematical input, not a native admission. + +## Proof and verification boundaries + +Read [PROOF.md](PROOF.md), [SHIFTED-LOG.md](SHIFTED-LOG.md), +[WEIGHTED-EXITS.md](WEIGHTED-EXITS.md), and [LOG-MOMENTS.md](LOG-MOMENTS.md). +[RESULT.json](RESULT.json) records directed interval bounds, the complete +rational coefficient lists, source hashes, exact rank witnesses and rejected +mutations. Interval arithmetic is adapted from my PR4433 code, using exact +fractions, explicit series tails and outward rounding at 192 fractional bits. + +The package verifies the changed finite moment and leaf-count arguments. +The exact raw invoices, native operator receipts and outer parameter points +are inherited from the source-pinned predecessors. Every retained endpoint +has the same κ and a supplied uniform saving at least as strong as its +original consumer requires. This monotone comparison reuses its outer point +and recorded positive margins; checking receipt consistency is explicitly +different from replaying the producer's native or outer proof engines. + +All-column arbitrary-input correctness, whole-job adapters, spectators, +owned-center restoration, native tensor closure, analytic decomposition, +precision, fixed-tape costs, fine-prime exclusions and exact recovery remain +inherited hypotheses. The transformed words are finite algorithmic +prescriptions. Their numerical productive widths, denominator growth, +scalar counts and precision/storage constants are not materialized here; +their complete finite-word counting prescriptions remain required. +No Lean, Docker or all-history replay was run. + +## Open next questions + +- **Tighter raw log moments.** Replace the raw bounded-support chord bound + with exact raw moment enclosures, then check whether the positive + coefficient test reduces the integer degree. This needs a complete, + directed moment list; numerical precision alone is insufficient. +- **A changed paid profile for κ.** Replay one actual native transition + change with its complete invoice, then apply this compiler. The current + profile's raw moment ceiling is unchanged by smaller rank bounds. +- **Width and physical constants.** Start with one small separated unit's + exact batch-width recurrence. Ambient rank does not control the full + materialized word or its owned-bank requirement. + +Structured questions and blockers are in [TASK.json](TASK.json). + +## Attribution and review state + +zxv, with substantial OpenAI Codex assistance, including user-requested +Sol 6.1 xhigh subagents for divergent probes and independent mathematical +audits. These are author-side AI checks, not formal verification or an +independent human review. This contribution remains local for user review. + +The finite integer compiler is Jacob Alan Sussman's Theorem 1G, retained +through PR4268/PR4359. Chronological product/completion and logarithmic +predecessors are retained through PR4414/PR4416, PR4411 and my PR4433. +Native4453 retains Cinna Davis's PR4440/PR4441 contributions and the complete +predecessor attribution, including my κ=.0023 construction. +[SOURCES.json](SOURCES.json) pins exact bytes. New work is Apache-2.0; +existing source notices and frozen evidence are unchanged. diff --git a/research/net-tax-rank-compiler/RESULT.json b/research/net-tax-rank-compiler/RESULT.json new file mode 100644 index 0000000000..602eb0bf1a --- /dev/null +++ b/research/net-tax-rank-compiler/RESULT.json @@ -0,0 +1,1116 @@ +{ + "exact_math_tests": 9, + "examples": { + "native-concentrated-balanced": { + "consumer_binding": { + "available_uniform_saving": "105043/35000000", + "functional_checks_in_receipt": 4, + "legacy_checks_in_receipt": 63, + "producer_replayed": false, + "rank_exponent_reduction": "32855/1797", + "required_uniform_saving": "525213/175000000", + "retained_kappa": "7503/2500000", + "source_H": 2299850000000, + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING", + "strict_checks_in_receipt": 54 + }, + "net_tax": { + "alpha": { + "lower": "0.999999994166048050341243139078", + "upper": "0.999999994166048050341243139079" + }, + "ambient_base": 153, + "completion_net_tax_upper": { + "lower": "0.000000000484846449554332706462", + "upper": "0.000000000484846449554332706463" + }, + "concavity_remainder": { + "lower": "0.001105751766643808364288097960", + "upper": "0.001105751766643808364288097961" + }, + "cutoff": 20, + "delta": { + "lower": "0.932537503569635779748487117641", + "upper": "0.932537503569635779748487117642" + }, + "delta0": { + "lower": "0.932400961478163177802374052850", + "upper": "0.932400961478163177802374052851" + }, + "epsilon": { + "lower": "0.888130955780605504522368683467", + "upper": "0.888130955780605504522368683468" + }, + "floor": 21, + "gamma": { + "lower": "0.967655820956269741530571022394", + "upper": "0.967655820956269741530571022395" + }, + "normalized_net_charge": { + "lower": "0.999999905189897356748650974084", + "upper": "0.999999905189897356748650974085" + }, + "original_splitting_tax_upper": { + "lower": "0.000001421531411860752586215832", + "upper": "0.000001421531411860752586215833" + }, + "predecessor_full_charge_bound": { + "lower": "1.000386183864934564285670631313", + "upper": "1.000386183864934564285670631314" + }, + "productive_fields_base": 11560, + "rank_one_masses": { + "paid": 259998, + "target": 260798 + }, + "saving": "90037/30000000", + "splitting_coefficient": { + "lower": "0.007333629403448838634819398532", + "upper": "0.007333629403448838634819398533" + }, + "strict_gap_lower": { + "lower": "0.000000094810102643251349025915", + "upper": "0.000000094810102643251349025916" + }, + "u": "171/1000", + "v": 260, + "word_materialized": false + }, + "uniform": { + "H": 125790000000, + "N": "2^125790000000", + "eta": { + "lower": "0.019675906372710418424472814349", + "upper": "0.019675906372710418424472814350" + }, + "gap": "1/210000000", + "grid_index": 599, + "grid_step": 210000000, + "kappa": "7503/2500000", + "log_shift": 3900, + "method": "log-moments", + "ordinary_base_cost": { + "lower": "50.671046496209105952155578480793", + "upper": "50.671046496209105952155578480794" + }, + "ordinary_base_factor": { + "lower": "12977.481816126499548590581723378131", + "upper": "12977.481816126499548590581723378132" + }, + "p": 24, + "previous_grid_point_fails": true, + "uniform_saving": "105043/35000000", + "weighted_exit": { + "A": { + "lower": "3.470673197396387613955465516464", + "upper": "3.470673197396387613955465516465" + }, + "A_lower": "347/100", + "A_upper": "139/40", + "ambient_log_lower": "1679/1000", + "coefficient_ratio_max": { + "lower": "0.019352722774694608575957993948", + "upper": "0.019352722774694608575957993949" + }, + "completed_normalized_log_mean_upper": { + "lower": "0.860095297195434298601204332725", + "upper": "0.860095297195434298601204332726" + }, + "denominator_coefficients": [ + "120600582057083966985222497866594951562051162933266588135349751311636709249689784301586401/1000000000000000000000000000000000000000000000000000000000000000000000000", + "140091299482203946756650799580570647332698796754031453781251909453468271285657544206621941/15625000000000000000000000000000000000000000000000000000000000000000000", + "655248936980435441963651431543824354311388626622339266886848277826949833975871377568964781/3906250000000000000000000000000000000000000000000000000000000000000000", + "302461863406778525621616725778094576895003976282892177613212545734324785668427029821523667/244140625000000000000000000000000000000000000000000000000000000000000", + "549601453365507866728523085031541062277865255939602218486768740801809808451603739488169233/122070312500000000000000000000000000000000000000000000000000000000000", + "7018030724405521320644067028610555214072970513641971461952603152061319875773116798498411/762939453125000000000000000000000000000000000000000000000000000000", + "2202539648018547692552392282816507112851605359623520733933438362242896972839646619091861/190734863281250000000000000000000000000000000000000000000000000000", + "22614709664767393843908654306437583570301686102998584988567812305895124346906581490729/2384185791015625000000000000000000000000000000000000000000000000", + "63646779283742386541657826017972511124697053772971386260418865424680502396373952911651/11920928955078125000000000000000000000000000000000000000000000000", + "39718197745742295807975064220703857647589516793638380769608476858467810014025211177/18626451492309570312500000000000000000000000000000000000000000", + "14448463648231360253271738926770844451256648236319634315895460378468276152897444681/23283064365386962890625000000000000000000000000000000000000000", + "195437270953074588473926732591358053586298917788447818419207517679209780806376219/1455191522836685180664062500000000000000000000000000000000000", + "15972972743184864122149691293341898669389176713405382113474534590753212275290603/727595761418342590332031250000000000000000000000000000000000", + "12465767560288403438211369210554882155539108664577624154299418103562373603687/4547473508864641189575195312500000000000000000000000000000", + "299596170689031874670968977337863792243382454365625204799116192753738336613/1136868377216160297393798828125000000000000000000000000000", + "6959854394963275353657998049679728436854264673684062195421014156243068949/355271367880050092935562133789062500000000000000000000000", + "160192859372107830632618649204969087020287884205489133769079068858740391/142108547152020037174224853515625000000000000000000000000", + "555900940266730676576844743378860891716992913118238885299392685379973/11102230246251565404236316680908203125000000000000000000", + "4731086043186802110697666662074216161081320707685227908371157424229/2775557561562891351059079170227050781250000000000000000", + "7615098643688231931225760775463745710009428445930985813582756867/173472347597680709441192448139190673828125000000000000", + "72613357407572932794668738103941459221571496827460576279594589/86736173798840354720596224069595336914062500000000000", + "154766957201134167926961493349175327843874307419565315109691/13552527156068805425093160010874271392822265625000000", + "355885570479664803993430174414139167342974081519342512861/3388131789017201356273290002718567848205566406250000", + "123244730684073180978444312760214049298336249252019517/211758236813575084767080625169910490512847900390625", + "309948331588294698593287544714691068355585331491841/211758236813575084767080625169910490512847900390625" + ], + "floor_log_lower": "127/125", + "full_paid_relative_excess": { + "lower": "0.000001447491518642763738467577", + "upper": "0.000001447491518642763738467578" + }, + "log_moment_upper_bounds": [ + "1", + "86201/100001", + "48435999/65000650", + "1364637086213/2112521125000", + "308437753109728117/549255492500000000", + "8738323063568447445703/17850803506250000000000", + "15276519456561691021157261/35701607012500000000000000", + "5657124004159348095702170048633/15083928962781250000000000000000", + "646325327250368320781291962965505469/1960910765161562500000000000000000000", + "18509884718635517770440520334746758086507/63729599867750781250000000000000000000000", + "193272601234461939882122357000912878734192547/753167998437054687500000000000000000000000000", + "489653453045298997698617462666573749753636393441/2154060475529976406250000000000000000000000000000", + "56534203769260346846596762115671946690950029465178969/280027861818896932812500000000000000000000000000000000", + "125848253784652816744433115961284421475054270570227396711/700069654547242332031250000000000000000000000000000000000", + "189861520217562160166048117042858420738966317198847102965848301/1183117716184839541132812500000000000000000000000000000000000000", + "5522313133523833113105753159096271783476341265885053594220445709269/38451325776007285086816406250000000000000000000000000000000000000000", + "128820034436151998538908175152441730589489220243311975772263089453965261/999734470176189412257226562500000000000000000000000000000000000000000000", + "3765606512661548537729359320139249851014818193796331238611948117708132810451/32491370280726155898359863281250000000000000000000000000000000000000000000000", + "33952611745165148693846530554138937289138145428838509005606094775142693203917141/324913702807261558983598632812500000000000000000000000000000000000000000000000000", + "12965800498009573765694993402630921113129488988429663458714310211873434453251883213829/137276039436068008670570422363281250000000000000000000000000000000000000000000000000000", + "138835924039826542192378423992885974157598495859836021509299974721107744556253641914628119/1622353193335349193379468627929687500000000000000000000000000000000000000000000000000000000", + "9015784823538256024342420190188286899867781001498830043861225970739521266652564087106363589523/115998253323477467326632006896972656250000000000000000000000000000000000000000000000000000000000", + "1067032923049220883421510364391225726154853473925375742460456592920289616904717060784502927082930957/15079772932052070752462160896606445312500000000000000000000000000000000000000000000000000000000000000", + "31646014742217428903938522201673206398808544713244709059014745645953445021079904033320111884857219434349/490092620291692299455020229139709472656250000000000000000000000000000000000000000000000000000000000000000", + "3763040494571451223735210621765413527744330373580634770827370320687624568045294881480282169009424691387675553/63712040637919998929152629788162231445312500000000000000000000000000000000000000000000000000000000000000000000" + ], + "maximizing_coefficient": 24, + "numerator_coefficients": [ + "2062137846059713494507368073051105971137001507529951614375316476793406991831448800118608137727043162139987463750992207655239973/1019392650206719982866442076610595703125000000000000000000000000000000000000000000000000000000000000000000000000", + "998645066361285161627339654256620189054061734415995266943881655271432028638103889765373700759811042704870535832144700113319770812303/6371267775832637812914192131446011306762695312500000000000000000000000000000000000000000000000000000000000000000000", + "3687073783777443016806295578599553689023910256819687389462499594976640157086962703776418803878473322696702719334746882932014925912769/1225256055482768488325446398724485724399185180664062500000000000000000000000000000000000000000000000000000000000000", + "85259257644934138518886546090127573374000833900288452571283935337216982202992852110014268815976262080295090363843901719093508357909153/3770056332440994818493322009810686059250551300048828125000000000000000000000000000000000000000000000000000000000000", + "175501874131644173490068948240975293772588461131032540778498309453582493873698454562636147247747667736422550386486052596862991594794459/2109143514967451316610633254842396736285954576538085937500000000000000000000000000000000000000000000000000000000000", + "1391815381786752223607212512150693233400544705019643989809483995893622005213770919392799412949450858775553523522512907713675398784218697/8112171563086926888937689850672866000974297831091735839843750000000000000000000000000000000000000000000000000000000", + "13534818067294628777880937492676678841931469553802407457748106000603090048027593683551511346795921777232812650012990316804205978668855227/62401943729250444293896763289010559458725442877461898132324218750000000000000000000000000000000000000000000000000000", + "661464334440591504627379444957431232052795713625355484611342529418890606986728038023817739079476496721392417986694061173094004508254761/3692459630099866082741994216369434885462723676443235074041748046875000000000000000000000000000000000000000000000000", + "59833228372260507457038342385171225774360241487527864338052563759573439702832578039996688046845117185208146315847401233239376299908364181/590799448751386733024451461809855772769852528588799921022798154296875000000000000000000000000000000000000000000000000", + "18447208012639530755195219732113285524520866402300509474583436659631641884537169722662814726293461411695445094551799842970574140038653283/454465659035287882224447466403441439482754020856989083863083370983398437500000000000000000000000000000000000000000000", + "4141616158180736459267946670527868222057814695393935577935665344893198889490134994743819003672873835863186733197763541819841317753581479/349592464378367873156361316060081133767037575690152041349170770628544824218750000000000000000000000000000000000000000", + "9503368031066509144185583405005067209446093380548827840527934114699094868658354818810824542970233608678715709453513183461578438207124733/3697649580128007908832713150390056808040507410312498434197525851633425198400878906250000000000000000000000000000000000", + "670746325064630784190875748207355134092213170467221849651289246680686446957581824984615231384955855339610576679705636935875762522607/1593431196009107282458565705260938701719057591879879904735879352163145131269531250000000000000000000000000000000000", + "141783998806490618476815445539181933887541120506143708390702596029705213353183096977263332540411567319347475651198182211535593045311393/2692925650242603861268049591651405315769266382350299808974026141516766828998226267578125000000000000000000000000000000", + "24817380092039490002912449776223635279947543177884629418472735030515189698467701834573054239229000162962180910828572155081071737718799/4896277417271102340557567767540585145131680136389315112676574330505785448484574999710546875000000000000000000000000000", + "35521036558995230491762462063447675901718013400871266771611815589883458846116217187818292276959926099866384408390181982529537921627229/94160122693178366376557179677274241365060220253666903958225021081713278968058843181933538085937500000000000000000000000", + "50363397192899147716195724129790833326142836631091412916640695219605226104581214732617607244503695531676497051620618489051541488979937/2317810813400745800866977113823286501107049128759863153901897928170439288636271354347454951909375000000000000000000000000", + "1722299519112699594388784041319566006414294394645130511728634493990178089261168130159540495955741072212204783955179432520053481044039/1782949224237599852557681371995711333824661691731654425025720728576708456176275166969998789583764687500000000000000000000", + "2051549341206425683650881171293253935401175511292977714949613712628265674654332042784583629388048327451956409164795558131529225351/62341505375169308690776466741588506676153843998201809145803181321118679134994298242016380754253864515625000000000000000", + "894670599903329731333088305299118104687528130458762964844859633367014533094125501409205254923281393443423255939905215829367171167/1055020641065313329573072491644330997189887170620091850465909281357308913137910969284595092459500734764571875000000000000", + "47751099705639321960581406340104898373903033001042249216677859451247183539676215482185186404478525949899559161362322901395532169/2951136199361465685891939083550342490908696697879155388487871162098244716718999575928078149399791132229145512500000000000", + "5513957143090635009474491103568599383970734081827376798147452737467259726084609876736464649950718897120290090902964453766350261/24971402167660040235412906178733044567438202794851904600353320345314248223713718788586316716918566485803958341158750000000", + "858602638581411384438408126497023955077818051768616593566536689766306681690812426065157885321643734754710746113087468706092949/422597185689998284913796712901143309041111767608735975866757788713376484658700792590024966739912449824856892597175042250000", + "3660636248367252138453725003480071163537027573855914516003487487983726427088452404165847197619612148132903757951849713692567/325078008970657834535881423744824861903232445174163125558858812531741244941190291998423743838138345345657800897000780000325", + "28333178412079463821055346771782989625688214347123956821468603656941748560781642533001682048003322509856414874675508801/1000240027602024106264250534599461113548407523612809617104180961636126907511354744610534596425041062602024002760002400001" + ], + "paid_excess_upper": "1/100000", + "raw_log_bound": "3/2", + "raw_mean_upper": "431/500", + "raw_normalized_log_mean": { + "lower": "0.860093849703915655837465865147", + "upper": "0.860093849703915655837465865148" + } + }, + "word_materialized": false + } + }, + "native-concentrated-same-C": { + "consumer_binding": { + "available_uniform_saving": "525213/175000000", + "functional_checks_in_receipt": 4, + "legacy_checks_in_receipt": 63, + "producer_replayed": false, + "rank_exponent_reduction": "6571/541", + "required_uniform_saving": "525213/175000000", + "retained_kappa": "7503/2500000", + "source_H": 2299850000000, + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING", + "strict_checks_in_receipt": 54 + }, + "net_tax": { + "alpha": { + "lower": "0.999999980480394484617151340349", + "upper": "0.999999980480394484617151340350" + }, + "ambient_base": 153, + "completion_net_tax_upper": { + "lower": "0.000000004253136810652179152787", + "upper": "0.000000004253136810652179152788" + }, + "concavity_remainder": { + "lower": "0.001105746846824639582517605973", + "upper": "0.001105746846824639582517605974" + }, + "cutoff": 20, + "delta": { + "lower": "0.932537496018535482645863756363", + "upper": "0.932537496018535482645863756364" + }, + "delta0": { + "lower": "0.932400954534728454117835318138", + "upper": "0.932400954534728454117835318139" + }, + "epsilon": { + "lower": "0.888130948589081412043679767964", + "upper": "0.888130948589081412043679767965" + }, + "floor": 21, + "gamma": { + "lower": "0.967680583560301995122679333354", + "upper": "0.967680583560301995122679333355" + }, + "normalized_net_charge": { + "lower": "0.999999778491395888838568958850", + "upper": "0.999999778491395888838568958851" + }, + "original_splitting_tax_upper": { + "lower": "0.000004205178937668649448311045", + "upper": "0.000004205178937668649448311046" + }, + "predecessor_full_charge_bound": { + "lower": "1.001149814170285771597867700095", + "upper": "1.001149814170285771597867700096" + }, + "productive_fields_base": 11560, + "rank_one_masses": { + "paid": 259998, + "target": 260798 + }, + "saving": "150061/50000000", + "splitting_coefficient": { + "lower": "0.007288100286103697517156721620", + "upper": "0.007288100286103697517156721621" + }, + "strict_gap_lower": { + "lower": "0.000000221508604111161431041149", + "upper": "0.000000221508604111161431041150" + }, + "u": "861/5000", + "v": 227, + "word_materialized": false + }, + "uniform": { + "H": 189350000000, + "N": "2^189350000000", + "eta": { + "lower": "0.032382825087010588608864248290", + "upper": "0.032382825087010588608864248291" + }, + "gap": "1/350000000", + "grid_index": 541, + "grid_step": 350000000, + "kappa": "7503/2500000", + "log_shift": 3405, + "method": "log-moments", + "ordinary_base_cost": { + "lower": "30.787887632444907912678916220096", + "upper": "30.787887632444907912678916220097" + }, + "ordinary_base_factor": { + "lower": "3972.296205213899032456444751275063", + "upper": "3972.296205213899032456444751275064" + }, + "p": 21, + "previous_grid_point_fails": true, + "uniform_saving": "525213/175000000", + "weighted_exit": { + "A": { + "lower": "3.470673197396387613955465516464", + "upper": "3.470673197396387613955465516465" + }, + "A_lower": "347/100", + "A_upper": "139/40", + "ambient_log_lower": "1679/1000", + "coefficient_ratio_max": { + "lower": "0.031688327364701261637953429177", + "upper": "0.031688327364701261637953429178" + }, + "completed_normalized_log_mean_upper": { + "lower": "0.860098327562930756011096334931", + "upper": "0.860098327562930756011096334932" + }, + "denominator_coefficients": [ + "883447463930444712235886675793371162533624351604016247554458027902301325383149/1000000000000000000000000000000000000000000000000000000000000000", + "4736922792108896916920118845350561645062647971111512672710671858243264733008747/125000000000000000000000000000000000000000000000000000000000000", + "685986050958760330418874010205278493789133236347393500688662376913879397729681/1562500000000000000000000000000000000000000000000000000000000", + "410939691529848673085988144563459134011552753297015602059378146861090936560779/195312500000000000000000000000000000000000000000000000000000", + "250051940225663362974521842179967629476919865299878626109129945509223367992073/48828125000000000000000000000000000000000000000000000000000", + "43693086661540304562219323053776651430303887526925683508087765521331352396903/6103515625000000000000000000000000000000000000000000000000", + "2973138028164414059051315733179597358890913947959139067554711978130909760083/476837158203125000000000000000000000000000000000000000000", + "213549492208733116115809213207270830389228298858379262749835817406556455209/59604644775390625000000000000000000000000000000000000000", + "42190984073309767181608727890265100630200952526693674867322525751779756509/29802322387695312500000000000000000000000000000000000000", + "1477612761788935944075649692556149878686377339073610835993675050659948779/3725290298461914062500000000000000000000000000000000000", + "18766168667076263531312917086174234297818346837784431762474359936109719/232830643653869628906250000000000000000000000000000000", + "351413547210732218848565268575079250094714387231950728374782925815037/29103830456733703613281250000000000000000000000000000", + "1962096074333656049165470282821503815436166605661467862082042201117/1455191522836685180664062500000000000000000000000000", + "102718952069906422426013846244798293922236911355160896707663277711/909494701772928237915039062500000000000000000000000", + "40397214484292387855561452294472608858259673674300193148621119/5684341886080801486968994140625000000000000000000", + "1189053543217003945042796092160905592033642336630654964676849/3552713678800500929355621337890625000000000000000", + "41486939458809279963242847610606296920283256145338574698041/3552713678800500929355621337890625000000000000000", + "131531635562873761007130691922492769794110829783403245343/444089209850062616169452667236328125000000000000", + "29339533982776349978593873360100241309580097717396161/5551115123125782702118158340454101562500000000", + "43481068681037372165253559014731618761674235805179/693889390390722837764769792556762695312500000", + "383036832090610985740265237532920452797521870289/867361737988403547205962240695953369140625000", + "151313661355466579537756144585602921111718527/108420217248550443400745280086994171142578125" + ], + "floor_log_lower": "127/125", + "full_paid_relative_excess": { + "lower": "0.000004465382864981825236973860", + "upper": "0.000004465382864981825236973861" + }, + "log_moment_upper_bounds": [ + "1", + "86201/100001", + "84611607/113501135", + "83319388192/128823788225", + "2057717209191442/3655374990884375", + "203917302397906572571/414885061465376562500", + "5067769452592213974801793/11772363619080059960937500", + "505335576544482506157628273543/1336163270765586805566406250000", + "2527198359404298466844060991607763/7582726561594705121589355468750000", + "253537174835430108721286068278374798207/860639464740999031300391845703125000000", + "579816871688752527505465199460607379288899/2220058619275077046649874420166015625000000", + "643682834929594720314562692977099080978940743253/2771743186164933692742368213577270507812500000000", + "16288235790016960879594418964502655356601810715178697/78648212907429993531564698060255050659179687500000000", + "330694757951279319907753132044773600870430067041632886901/1785314432998660853166518645967789649963378906250000000000", + "8416652864165622802095012671923276086148821483375772148730871/50658297036337001708599966579336031317710876464843750000000000", + "859306779404414493066904198675830099095590393586477172856156976413/5749716713624249693926096206754639554560184478759765625000000000000", + "21994895977446900099119971700793338255228922845591512579633423074070909/163148211749088085065152979866662897360645234584808349609375000000000000", + "2258233002313888284634699510175129865561300723116002185321664292767173823369/18517322033521497654894863214866238850433234125375747680664062500000000000000", + "11624848440041454510750927033470474838670444029569190945458695513120441305889547/105085802540234499191528348744365905476208603661507368087768554687500000000000000", + "600062231005838148325831831199031506487558585169136766176450833516490992369936088269/5963619294158307829119233791242765135774838257790543138980865478515625000000000000000", + "1411763595138825175732800785871780963602941700531805009840069177053936490002344687234223/15383427042885634968296205347864860066146457778618787415325641632080078125000000000000000", + "1611912714294816976087265352133708549968081181020242962517706741224708631348238262266248826051/19206208663042715257917812376809277792583852536605556088034063577651977539062500000000000000000" + ], + "maximizing_coefficient": 21, + "numerator_coefficients": [ + "33381325498576173946633352804456890625347204719556265988143242909030365314803195967818835311208780966985056698139759277939/1351516784032486946960133475766433823924661747423764582400000000000000000000000000000000000000000000000000000", + "1687657483901809701629373517272210660993601251167070938170728986362160454615027748458425997821080805165105362459430167036859603/1535829885454917354351821678524081236662387493228680477324800000000000000000000000000000000000000000000000000000", + "4406593638937689563155101885793996865691384197785873611865315452068664128812407862985885031853321586324625547762548209748306591/338291903910522445710432862718252528078139673370839815887571200000000000000000000000000000000000000000000000000", + "171796575138269319852688129104574782123090621239169039813094331738800254466136423555633096325299419447919315042093854094976497/2709613831233973175289467096891307253531601560012603318267761920000000000000000000000000000000000000000000000", + "4097682450003474265264940469071148375391075348514905041841054688705731186640492450379211657441741426947929563213099990169135459/26260837181581621731483189345537478266648022587057478314810916805120000000000000000000000000000000000000000000", + "1156465497032203623118985666917982067375443181611533257029193760889866257731167372793146342865328857154369979681406219051146897/5258530194223756016760213091195621474055003818038315756827005389324800000000000000000000000000000000000000000", + "3069848655704013772843402376510826026051344774506609233878311500360893192243465347398165109397288783097971338752822866403879469/15926324497462191849538597914810536270090084815209652406340944452964104000000000000000000000000000000000000000", + "780891960415226343270737147660758230777636075166573618183156606924050434639369160803154891301818223512358387959044900900209261/7016072141280690075531759163343473293151006923373482159852426371105124952000000000000000000000000000000000000", + "109167664490247631052297897729546546216680239616286658864980592043783196560192658185602110032379248805355219484674895986507471/2472649269428053879271370742179773296170550989759547451867497760482409164140800000000000000000000000000000000", + "13516268373492040599479785197044124946166466583465414333917056033358330582476250713655481711306074519569633019789306108790131/1089283698643501391986856147967927354142516605845570505437011645577098673230150400000000000000000000000000000", + "3032559551281794370645717550291599598291762570722240454504728853300699827086744224714106568299476115919439166793959832139801/1199663647004942540749753322168950477330460386576683877909764334464267009049430288000000000000000000000000000", + "1002744213025635549809294715175676971729125034967947569316709212898368534925934859239692827903501634732069546539483500593093/2642457364848926410077446739432097283778047777930726089754500951778880290131103044720000000000000000000000000", + "98825858485747314083351078810278361105918420103230921345659868844105713519687768592107886013797183110444544334336590034659/2328179550152048369463918514448891281718841901681502552436474446509601831659915731938720000000000000000000000", + "8034028057713130517454255948556380409966035979534204391762584666724837970336424307737783078396991935599326503639015823169/2256408030962383153253193364755453169775176210670106875954360081391606714049388162295720992000000000000000000", + "55741462426227847804543958666028475488928955192242787003785729298226217176649736902543494719836726432895185187896275351/248505572141265724348538094349019903558025766787688719936466919052028703757326944512923342424000000000000000", + "526165548759686098145073009269941590216904519816164471108870583646478647322868429294028141111308575740866366381256969/49761325029432746697192947482972245445947406296627272091242748041894117750173111290021720395960000000000000", + "323754693913279674541697492748769629763247655608418803384278571682631350686415192977757868386761052385388549787373719/876860310884282661227487566739155509575363273492339002008170228535234126719834590680786266311259200000000000", + "39818021316703088552305685858194027957327695715459198895192357665115262571737721047355798763002111696664829098854521/4249145319101897156209294386679758551733501893557626951268763617891063554921638625239481857230460545600000000", + "31318609622707673862111854306531183690049100399501107986032389442515431170807287866188529147789108448979847369469/187188890332823267629112620247736799529472212712623899891554022269922575575206512846948645464715103533280000", + "163645697748391089490273719224813591793836555495936580117762260491499209945949472661324835360985826060156950293/82462890846575592890655908094246377487871148649670055564120236920768843524652980137478905264832489288244640", + "127057886584561407085334329857200202932771964618779781689388944613485511204459573606188523421645832603607529053/9081906990692076943456477384727678408771588916426933068796902876997582732718967694634392076419068019068009080", + "44234221092026053757821239229324760531561751071429280695515994821806815750175243229402504974160634210201/1000210021001330059852034954265162820349293933527195271893932034911628054264203490598501330002100002100001" + ], + "paid_excess_upper": "1/100000", + "raw_log_bound": "3/2", + "raw_mean_upper": "431/500", + "raw_normalized_log_mean": { + "lower": "0.860093862180065774185859361071", + "upper": "0.860093862180065774185859361072" + } + }, + "word_materialized": false + } + }, + "native-net-shift": { + "consumer_binding": { + "available_uniform_saving": "525213/175000000", + "functional_checks_in_receipt": 4, + "legacy_checks_in_receipt": 63, + "producer_replayed": false, + "rank_exponent_reduction": "6571/2765", + "required_uniform_saving": "525213/175000000", + "retained_kappa": "7503/2500000", + "source_H": 2299850000000, + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING", + "strict_checks_in_receipt": 54 + }, + "net_tax": { + "alpha": { + "lower": "0.999999980480394484617151340349", + "upper": "0.999999980480394484617151340350" + }, + "ambient_base": 153, + "completion_net_tax_upper": { + "lower": "0.000004364803520178245236237837", + "upper": "0.000004364803520178245236237838" + }, + "concavity_remainder": { + "lower": "0.001105746846824639582517605973", + "upper": "0.001105746846824639582517605974" + }, + "cutoff": 18, + "delta": { + "lower": "0.977253011855658562221385892786", + "upper": "0.977253011855658562221385892787" + }, + "delta0": { + "lower": "0.976664631677490096071204495515", + "upper": "0.976664631677490096071204495516" + }, + "epsilon": { + "lower": "0.799570646063720641817497548643", + "upper": "0.799570646063720641817497548644" + }, + "floor": 22, + "gamma": { + "lower": "0.981971726999571315878434078558", + "upper": "0.981971726999571315878434078559" + }, + "normalized_net_charge": { + "lower": "0.999996829571729106399397178801", + "upper": "0.999996829571729106399397178802" + }, + "original_splitting_tax_upper": { + "lower": "0.000001756057360637542674691433", + "upper": "0.000001756057360637542674691434" + }, + "predecessor_full_charge_bound": { + "lower": "1.000372586718960987074603543263", + "upper": "1.000372586718960987074603543264" + }, + "productive_fields_base": 11560, + "rank_one_masses": { + "paid": 259998, + "target": 260798 + }, + "saving": "150061/50000000", + "splitting_coefficient": { + "lower": "0.010125639068149840285647268152", + "upper": "0.010125639068149840285647268153" + }, + "strict_gap_lower": { + "lower": "0.000003170428270893600602821198", + "upper": "0.000003170428270893600602821199" + }, + "u": "3/25", + "v": 476, + "word_materialized": false + }, + "uniform": { + "H": 967750000000, + "N": "2^967750000000", + "eta": { + "lower": "0.000754547474185486933219190219", + "upper": "0.000754547474185486933219190220" + }, + "gap": "1/350000000", + "grid_index": 2765, + "grid_step": 350000000, + "kappa": "7503/2500000", + "log_shift": 19040, + "method": "shifted", + "ordinary_base_cost": { + "lower": "1321.320147650394729187842555665094", + "upper": "1321.320147650394729187842555665095" + }, + "ordinary_base_factor": { + "lower": "66107367.515365596532016231725406878240", + "upper": "66107367.515365596532016231725406878241" + }, + "p": 108, + "previous_grid_point_fails": true, + "theta": "173/185", + "uniform_saving": "525213/175000000", + "word_materialized": false + } + }, + "native-source-parameters": { + "consumer_binding": { + "available_uniform_saving": "525213/175000000", + "functional_checks_in_receipt": 4, + "legacy_checks_in_receipt": 63, + "producer_replayed": false, + "rank_exponent_reduction": "1", + "required_uniform_saving": "525213/175000000", + "retained_kappa": "7503/2500000", + "source_H": 2299850000000, + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING", + "strict_checks_in_receipt": 54 + }, + "net_tax": { + "alpha": { + "lower": "0.999999980480394484617151340349", + "upper": "0.999999980480394484617151340350" + }, + "ambient_base": 153, + "completion_net_tax_upper": { + "lower": "0.000000060052817548701191872008", + "upper": "0.000000060052817548701191872009" + }, + "concavity_remainder": { + "lower": "0.001105746846824639582517605973", + "upper": "0.001105746846824639582517605974" + }, + "cutoff": 18, + "delta": { + "lower": "0.977253011855658562221385892786", + "upper": "0.977253011855658562221385892787" + }, + "delta0": { + "lower": "0.976664631677490096071204495515", + "upper": "0.976664631677490096071204495516" + }, + "epsilon": { + "lower": "0.799570646063720641817497548643", + "upper": "0.799570646063720641817497548644" + }, + "floor": 22, + "gamma": { + "lower": "0.981971726999571315878434078558", + "upper": "0.981971726999571315878434078559" + }, + "normalized_net_charge": { + "lower": "0.999986931420767776182585713057", + "upper": "0.999986931420767776182585713058" + }, + "original_splitting_tax_upper": { + "lower": "0.000000047015002103422332013161", + "upper": "0.000000047015002103422332013162" + }, + "predecessor_full_charge_bound": { + "lower": "0.999996470237080130167576831940", + "upper": "0.999996470237080130167576831941" + }, + "productive_fields_base": 11560, + "rank_one_masses": { + "paid": 259998, + "target": 260798 + }, + "saving": "150061/50000000", + "splitting_coefficient": { + "lower": "0.010125639068149840285647268152", + "upper": "0.010125639068149840285647268153" + }, + "strict_gap_lower": { + "lower": "0.000013068579232223817414286942", + "upper": "0.000013068579232223817414286943" + }, + "u": "3/25", + "v": 675, + "word_materialized": false + }, + "uniform": { + "H": 2299850000000, + "N": "2^2299850000000", + "eta": { + "lower": "0.000037402048244786272108248731", + "upper": "0.000037402048244786272108248732" + }, + "gap": "1/350000000", + "grid_index": 6571, + "grid_step": 350000000, + "kappa": "7503/2500000", + "log_shift": 1, + "method": "shifted", + "ordinary_base_cost": { + "lower": "26656.261536130671513711578407307682", + "upper": "26656.261536130671513711578407307683" + }, + "ordinary_base_factor": { + "lower": "267694942215561885759272880041880831892636834258631116311698250860802331654876074069894046033948125898443838918385195838082756425482317467039027699496433289330162974770067221610815524231296755934942652439677452910274860327315054710197958597952276785268229395338649775171563335829726820284119487089139881578668883657403257100441406263810921146057022571941605637346753723029657962947464901656427325368793817171764556048306294277058705951831353196206205621302314471472108355845663696487989144051287492238048307523402007707250360523850416125492683304294723707595137781290596861589731634843546442.995990766841384415868643409334", + "upper": "267694942215561885759272880041880831892636834258631116328618412640433566922146474715544713703370486436685783850953258256132778811833634663445420922749256369730460192128259516546170257040632035940317955776131178509576423452919410542836245428284906882046738880198963044939075874360151165452299798895689155230192551789456907271664942891756059061883883996833204282454363378864997122212545323122097510012024912589198313992567964515852176373195933618819224772702439799687563690509734115252271624229131037507175306660844179682064676718225404685711489106338671938818492975872517936528993887850276327.513876789723636475978575589811" + }, + "p": 160, + "previous_grid_point_fails": true, + "theta": "15/16", + "uniform_saving": "525213/175000000", + "word_materialized": false + } + }, + "native-weighted-same-C": { + "consumer_binding": { + "available_uniform_saving": "525213/175000000", + "functional_checks_in_receipt": 4, + "legacy_checks_in_receipt": 63, + "producer_replayed": false, + "rank_exponent_reduction": "6571/819", + "required_uniform_saving": "525213/175000000", + "retained_kappa": "7503/2500000", + "source_H": 2299850000000, + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING", + "strict_checks_in_receipt": 54 + }, + "net_tax": { + "alpha": { + "lower": "0.999999980480394484617151340349", + "upper": "0.999999980480394484617151340350" + }, + "ambient_base": 153, + "completion_net_tax_upper": { + "lower": "0.000000004253136810652179152787", + "upper": "0.000000004253136810652179152788" + }, + "concavity_remainder": { + "lower": "0.001105746846824639582517605973", + "upper": "0.001105746846824639582517605974" + }, + "cutoff": 20, + "delta": { + "lower": "0.932537496018535482645863756363", + "upper": "0.932537496018535482645863756364" + }, + "delta0": { + "lower": "0.932400954534728454117835318138", + "upper": "0.932400954534728454117835318139" + }, + "epsilon": { + "lower": "0.888130948589081412043679767964", + "upper": "0.888130948589081412043679767965" + }, + "floor": 21, + "gamma": { + "lower": "0.967680583560301995122679333354", + "upper": "0.967680583560301995122679333355" + }, + "normalized_net_charge": { + "lower": "0.999999778491395888838568958850", + "upper": "0.999999778491395888838568958851" + }, + "original_splitting_tax_upper": { + "lower": "0.000004205178937668649448311045", + "upper": "0.000004205178937668649448311046" + }, + "predecessor_full_charge_bound": { + "lower": "1.001149814170285771597867700095", + "upper": "1.001149814170285771597867700096" + }, + "productive_fields_base": 11560, + "rank_one_masses": { + "paid": 259998, + "target": 260798 + }, + "saving": "150061/50000000", + "splitting_coefficient": { + "lower": "0.007288100286103697517156721620", + "upper": "0.007288100286103697517156721621" + }, + "strict_gap_lower": { + "lower": "0.000000221508604111161431041149", + "upper": "0.000000221508604111161431041150" + }, + "u": "861/5000", + "v": 227, + "word_materialized": false + }, + "uniform": { + "H": 286650000000, + "N": "2^286650000000", + "eta": { + "lower": "0.032382825087010588608864248290", + "upper": "0.032382825087010588608864248291" + }, + "gap": "1/350000000", + "grid_index": 819, + "grid_step": 350000000, + "kappa": "7503/2500000", + "log_shift": 454, + "method": "weighted", + "ordinary_base_cost": { + "lower": "30.787887632444907912678916220096", + "upper": "30.787887632444907912678916220097" + }, + "ordinary_base_factor": { + "lower": "4293752188920541966.342259029754834491198963559165", + "upper": "4293752188920541966.342259029754834491198963559166" + }, + "p": 28, + "previous_grid_point_fails": true, + "uniform_saving": "525213/175000000", + "weighted_exit": { + "A": { + "lower": "0.462756426319518348527395402195", + "upper": "0.462756426319518348527395402196" + }, + "A_lower": "231/500", + "A_upper": "463/1000", + "ambient_log_lower": "1679/1000", + "coefficient_ratio_max": { + "lower": "0.032042961827364629932195365523", + "upper": "0.032042961827364629932195365524" + }, + "completed_normalized_log_mean_upper": { + "lower": "0.860098327562930756011096334931", + "upper": "0.860098327562930756011096334932" + }, + "denominator_coefficients": [ + "1808284185863726540702967547173055928078210174894892077356143934264567521633136942977046092721/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "596430825264474838099419057796928332073220241846930949550486678119805589488440141343621955308573/6250000000000000000000000000000000000000000000000000000000000000000000000000000000", + "36814858936591661397439705900337861057490360254679372361904581491315017695126152917587948864550237/312500000000000000000000000000000000000000000000000000000000000000000000000000000", + "1702020144942068007690595151280795411494056539635594558489033291572678041630953171333099894688743353/97656250000000000000000000000000000000000000000000000000000000000000000000000000", + "155759610013868990297525291740043135581525417536393232783266374717874541263464109376710763944986823451/244140625000000000000000000000000000000000000000000000000000000000000000000000000", + "32447331258461605316561558139573243866109743303354278949456073215706263518909547861290102791010585659/3814697265625000000000000000000000000000000000000000000000000000000000000000000", + "49604342396965407024930669082730368729079537720155849133418229409922164698099810122528711054193952337/953674316406250000000000000000000000000000000000000000000000000000000000000000", + "10091061224481847895875862023553770424945582142670970339294260831140901228060857425346367662124856571/59604644775390625000000000000000000000000000000000000000000000000000000000000", + "19357498166982316201834041477341196067419741603194494180580964052155793347019513198947341239790855961/59604644775390625000000000000000000000000000000000000000000000000000000000000", + "5884654865390220331503506952872155480245177709010815093815417195587265231334563157630161474777631/14901161193847656250000000000000000000000000000000000000000000000000000000", + "29919614329112170704485547105165448255200190310349974815988821374999465504643162228766350008557791/93132257461547851562500000000000000000000000000000000000000000000000000000", + "1060127679176428711746506735006953521754479883685679731918691323719842752679736625408345387123043/5820766091346740722656250000000000000000000000000000000000000000000000000", + "216125580244242635668151945015815061296739050618009947114774482884592427374440180463348841889983/2910383045673370361328125000000000000000000000000000000000000000000000000", + "20298268091092026318690926701134192340427656902396698101547054061921561240718108914284334069/909494701772928237915039062500000000000000000000000000000000000000000", + "5729704299983446598819461137892779929055195988103196054191716600715417077949878717072043583/1136868377216160297393798828125000000000000000000000000000000000000000", + "308367698233694482019668061121678529365783918555807726223970976647101965711498627262994757/355271367880050092935562133789062500000000000000000000000000000000000", + "81923057474567640087855505570860221671452859034359822585843064656120937009216981555789199/710542735760100185871124267578125000000000000000000000000000000000000", + "52885879973424031037713709914014007144018395070972427949937853756370693733549834597023/4440892098500626161694526672363281250000000000000000000000000000000", + "1067425712900408453035868242800415435795678278163116896148518415091298544666983085747/1110223024625156540423631668090820312500000000000000000000000000000", + "4219799779395377069763444461383231455107080688179300893204784383156643109732883747/69388939039072283776476979255676269531250000000000000000000000000", + "522421612470664508690257290008392101231562533085205555996614374849142875481079253/173472347597680709441192448139190673828125000000000000000000000000", + "63035179665958625170909560046714094313045366841199848922280151397820868163211/542101086242752217003726400434970855712890625000000000000000000", + "470469775915280509688092723628659337017869568616004126052832604989165425593/135525271560688054250931600108742713928222656250000000000000000", + "133867708907810158479164162469900782694154942053669806162638857582719199/1694065894508600678136645001359283924102783203125000000000000", + "56812131922264485408762385838504623097134955491068173796404267595493551/42351647362715016953416125033982098102569580078125000000000000", + "108468789314613320716388072170928346884774378073025702396314703216293/6617444900424221398971269536559702828526496887207031250000000", + "224709887453168148200390874928821342844930490414960246531762022069/1654361225106055349742817384139925707131624221801757812500000", + "70472476263831366588476578784169041535492831817626866232689897/103397576569128459358926086508745356695726513862609863281250", + "80631397449585884167753993329574755403270206405810971374081/51698788284564229679463043254372678347863256931304931640625" + ], + "floor_log_lower": "127/125", + "full_paid_relative_excess": { + "lower": "0.000004465382864981825236973860", + "upper": "0.000004465382864981825236973861" + }, + "maximizing_coefficient": 11, + "mean_upper": "431/500", + "numerator_coefficients": [ + "36504667523283372496164164310126922643795971902886487561026481282417087361175540943462233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "8490395228733322650483300259141175607316365102358679963954315706974764573971189220440100101661/125000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "407477995555848662796537500893382325387626915967585828608764191883455509667469007039369250955477/1000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "4438795666907729592969887787705671130789502273945603945080975930783518186733412521714281263674664597/31250000000000000000000000000000000000000000000000000000000000000000000000000000000", + "21752254091255382585831342199127672961081727032258746723466840851913462275685625161103075070245547203/2500000000000000000000000000000000000000000000000000000000000000000000000000000000", + "125753951469783300683479146429288732572135973744985545388458271222253922170892875832718457400513706587/781250000000000000000000000000000000000000000000000000000000000000000000000000000", + "952767403719305706726862329877803235487276565987032659916069671826025297190156513128610120954278597297/781250000000000000000000000000000000000000000000000000000000000000000000000000000", + "178444467875094853441374499896529272580602166973123591680824782868002598313025943011995439147293453443/39062500000000000000000000000000000000000000000000000000000000000000000000000000", + "7487565274032247573953368268457898416468002008150068181096495776525281267186637125150541001642465154141/781250000000000000000000000000000000000000000000000000000000000000000000000000000", + "239966740470880845534895070665052469156336696413113542867463761209306867151436430145614811205305246511/19531250000000000000000000000000000000000000000000000000000000000000000000000000", + "1001103934745868077423803915457030699027716905336389037424461302029833313576111364928093841908989539027/97656250000000000000000000000000000000000000000000000000000000000000000000000000", + "142478958158342362675100026568217710834639673115150116274114501315462626434459066865117980775670227963/24414062500000000000000000000000000000000000000000000000000000000000000000000000", + "22947850305226636163931933325017117205807568283078272429580196091955452187081763091111166996013990227/9765625000000000000000000000000000000000000000000000000000000000000000000000000", + "1049960782085096330491894401099186735869327983221218601796261981449216569523774166543932160418027889/1525878906250000000000000000000000000000000000000000000000000000000000000000000", + "45696564441130397378362149426590246923339436196633227260515360099073690390651919170021645044287499/305175781250000000000000000000000000000000000000000000000000000000000000000000", + "9393148882756589682089309957722249497815154757276945181616271844463362641271941509744691142590053/381469726562500000000000000000000000000000000000000000000000000000000000000000", + "9457563298287887205336902367019816963077606700412721100639268005569735518537976930498098281662279/3051757812500000000000000000000000000000000000000000000000000000000000000000000", + "22986802093084164527522949501567762662079586796558145100597914721112482681530395658575480849139/76293945312500000000000000000000000000000000000000000000000000000000000000000", + "8684492896362163823924088878384387139972844237144664636466715255613525856226103113361546007459/381469726562500000000000000000000000000000000000000000000000000000000000000000", + "25578897294343604861419942008140876774183602625215688971853536962205449447447134213471222859/19073486328125000000000000000000000000000000000000000000000000000000000000000", + "11745864071704310248921218243711703155774858081750363737839717694658117728381710949856145413/190734863281250000000000000000000000000000000000000000000000000000000000000000", + "26183753687717393583599155970874935357359980659962522087878524308680530252489381727527763/11920928955078125000000000000000000000000000000000000000000000000000000000000", + "143930152998042142521993361024312390761588217033305802398911014216380268106731487266077/2384185791015625000000000000000000000000000000000000000000000000000000000000", + "3758888255263971542589302524160539041242136499717586830726839466403052815488357057911/2980232238769531250000000000000000000000000000000000000000000000000000000000", + "46725470301106159509243654086702340617733956065901720885762479340573570352374507883/2384185791015625000000000000000000000000000000000000000000000000000000000000", + "1629131485032213594525805334953466679869465625333466122169664599757215904452879089/7450580596923828125000000000000000000000000000000000000000000000000000000000", + "12299022910438634571675263256698452977216855489477754441620561843906409134622929/7450580596923828125000000000000000000000000000000000000000000000000000000000", + "561098396673636890118142489521264961349902196520296156037167276905281407161/74505805969238281250000000000000000000000000000000000000000000000000000000", + "58259072263632257200896028182044133544159924524270692183093012851403586241/3725290298461914062500000000000000000000000000000000000000000000000000000000" + ], + "raw_normalized_log_mean": { + "lower": "0.860093862180065774185859361071", + "upper": "0.860093862180065774185859361072" + } + }, + "word_materialized": false + } + }, + "p7-net-shift-balanced": { + "consumer_binding": { + "available_uniform_saving": "11551881/4300000000", + "functional_checks_in_receipt": 3, + "legacy_checks_in_receipt": 63, + "producer_replayed": false, + "rank_exponent_reduction": "17465/4429", + "required_uniform_saving": "376107/140000000", + "retained_kappa": "268647/100000000", + "source_H": 349300000000, + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING", + "strict_checks_in_receipt": 54 + }, + "net_tax": { + "alpha": { + "lower": "0.999999995226160367448558520784", + "upper": "0.999999995226160367448558520785" + }, + "ambient_base": 121, + "completion_net_tax_upper": { + "lower": "0.000000229256243311259605573976", + "upper": "0.000000229256243311259605573977" + }, + "concavity_remainder": { + "lower": "0.000989632686375363818713799788", + "upper": "0.000989632686375363818713799789" + }, + "cutoff": 10, + "delta": { + "lower": "0.877942790977848064391977059295", + "upper": "0.877942790977848064391977059296" + }, + "delta0": { + "lower": "0.876986989232235238455954259827", + "upper": "0.876986989232235238455954259828" + }, + "epsilon": { + "lower": "0.585295193985232042927984706197", + "upper": "0.585295193985232042927984706198" + }, + "floor": 15, + "gamma": { + "lower": "0.904120626501763030210363841895", + "upper": "0.904120626501763030210363841896" + }, + "normalized_net_charge": { + "lower": "0.999999918356490204683584275239", + "upper": "0.999999918356490204683584275240" + }, + "original_splitting_tax_upper": { + "lower": "0.000000166484097340338773822667", + "upper": "0.000000166484097340338773822668" + }, + "predecessor_full_charge_bound": { + "lower": "1.000087847161358855383372140894", + "upper": "1.000087847161358855383372140895" + }, + "productive_fields_base": 7688, + "rank_one_masses": { + "paid": 131115, + "target": 131723 + }, + "saving": "11551891/4300000000", + "splitting_coefficient": { + "lower": "0.003969492866208143004795927169", + "upper": "0.003969492866208143004795927170" + }, + "strict_gap_lower": { + "lower": "0.000000081643509795316415724760", + "upper": "0.000000081643509795316415724761" + }, + "u": "31/100", + "v": 100, + "word_materialized": false + }, + "uniform": { + "H": 88580000000, + "N": "2^88580000000", + "eta": { + "lower": "0.274975671868075902247454481374", + "upper": "0.274975671868075902247454481375" + }, + "gap": "1/430000000", + "grid_index": 206, + "grid_step": 430000000, + "kappa": "268647/100000000", + "log_shift": 1700, + "method": "shifted", + "ordinary_base_cost": { + "lower": "3.626915453812975067216784358696", + "upper": "3.626915453812975067216784358697" + }, + "ordinary_base_factor": { + "lower": "15.357938139093674718917526192385", + "upper": "15.357938139093674718917526192386" + }, + "p": 8, + "previous_grid_point_fails": true, + "theta": "57/67", + "uniform_saving": "11551881/4300000000", + "word_materialized": false + } + }, + "p7-net-shift-same-C": { + "consumer_binding": { + "available_uniform_saving": "376107/140000000", + "functional_checks_in_receipt": 3, + "legacy_checks_in_receipt": 63, + "producer_replayed": false, + "rank_exponent_reduction": "499/186", + "required_uniform_saving": "376107/140000000", + "retained_kappa": "268647/100000000", + "source_H": 349300000000, + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING", + "strict_checks_in_receipt": 54 + }, + "net_tax": { + "alpha": { + "lower": "0.999999984403907977028692329024", + "upper": "0.999999984403907977028692329025" + }, + "ambient_base": 121, + "completion_net_tax_upper": { + "lower": "0.000000060655354547465695101486", + "upper": "0.000000060655354547465695101487" + }, + "concavity_remainder": { + "lower": "0.000989630370214448971145589376", + "upper": "0.000989630370214448971145589377" + }, + "cutoff": 9, + "delta": { + "lower": "0.878191321134544702177728120307", + "upper": "0.878191321134544702177728120308" + }, + "delta0": { + "lower": "0.876986985700210447011163521179", + "upper": "0.876986985700210447011163521180" + }, + "epsilon": { + "lower": "0.526914792680726821306636872184", + "upper": "0.526914792680726821306636872185" + }, + "floor": 15, + "gamma": { + "lower": "0.930676354460701007214399379978", + "upper": "0.930676354460701007214399379979" + }, + "normalized_net_charge": { + "lower": "0.999999644856914397431457677392", + "upper": "0.999999644856914397431457677393" + }, + "original_splitting_tax_upper": { + "lower": "0.000001346558419236001069293288", + "upper": "0.000001346558419236001069293289" + }, + "predecessor_full_charge_bound": { + "lower": "1.000595129602136722680533740393", + "upper": "1.000595129602136722680533740394" + }, + "productive_fields_base": 7688, + "rank_one_masses": { + "paid": 131115, + "target": 131723 + }, + "saving": "33581/12500000", + "splitting_coefficient": { + "lower": "0.004518292673517239417487878298", + "upper": "0.004518292673517239417487878299" + }, + "strict_gap_lower": { + "lower": "0.000000355143085602568542322607", + "upper": "0.000000355143085602568542322608" + }, + "u": "33/125", + "v": 113, + "word_materialized": false + }, + "uniform": { + "H": 130200000000, + "N": "2^130200000000", + "eta": { + "lower": "0.232571174583557478852309977539", + "upper": "0.232571174583557478852309977540" + }, + "gap": "1/700000000", + "grid_index": 186, + "grid_step": 700000000, + "kappa": "268647/100000000", + "log_shift": 1356, + "method": "shifted", + "ordinary_base_cost": { + "lower": "4.288207778912378366129882553496", + "upper": "4.288207778912378366129882553497" + }, + "ordinary_base_factor": { + "lower": "24.210097689715686829319529444643", + "upper": "24.210097689715686829319529444644" + }, + "p": 7, + "previous_grid_point_fails": true, + "theta": "56/69", + "uniform_saving": "376107/140000000", + "word_materialized": false + } + } + }, + "literal_pinned_flow_checks": [ + { + "G": 0, + "exits": { + "1": 4, + "2": 1 + }, + "literal_classes": 1, + "top_rank": 5 + }, + { + "G": 0, + "exits": { + "1": 4, + "2": 1 + }, + "literal_classes": 1, + "top_rank": 14 + }, + { + "G": 1, + "exits": { + "1": 16, + "2": 8, + "4": 1 + }, + "literal_classes": 6, + "top_rank": 15 + }, + { + "G": 1, + "exits": { + "1": 16, + "2": 8, + "4": 1 + }, + "literal_classes": 6, + "top_rank": 44 + }, + { + "G": 2, + "exits": { + "1": 64, + "2": 48, + "4": 12, + "8": 1 + }, + "literal_classes": 31, + "top_rank": 45 + }, + { + "G": 3, + "exits": { + "1": 256, + "2": 256, + "4": 96, + "8": 16, + "16": 1 + }, + "literal_classes": 156, + "top_rank": 135 + } + ], + "rejected_mutations": { + "closed_uniform_saving": "uniform exponent domain", + "degree23": "all weighted exit polynomial coefficients below capacity", + "drop_tensor_concentration": "all weighted exit polynomial coefficients below capacity", + "invalid_tail_exponent": "net tax exponent domain", + "too_small_tensor": "strict net moment certificate", + "understated_full_paid_excess": "full paid mass perturbation", + "understated_log_support": "raw paid log support", + "understated_raw_mean": "raw paid log mean", + "wrong_log_shift_enclosure": "normalized log shift enclosure" + }, + "schema_version": 1, + "scope": "Conditional finite rank/leaf bounds; inherited native and outer producer receipts; no new kappa, selected frontier, materialized word or physical runtime claim.", + "source_mutation_rejected": true, + "source_sha256": { + "research/higher-moment-strictification/README.md": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", + "research/higher-moment-strictification/RESULT.json": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156", + "research/higher-moment-strictification/vendor/FINITE-PRECOMPILATION.md": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "research/higher-moment-strictification/vendor/p7-TENSOR.md": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3", + "research/higher-moment-strictification/verify.py": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", + "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/research/record-track/programs/theorem-1g/tree_flow.py": "750782f6d1cc0a9fff8a768899f3f4c62a7efdf0696d8b5a5d640b1836f5ab72", + "research/native-lattice-retiming/NATIVE-RESULT.json": "a2e7a8f9eba6712dc92c47e6d86aaf18b8400f1ae5fe13ca19bbb65e76a25018", + "research/native-lattice-retiming/PROOF.md": "d137119bd238304295498d85186e6c0d36915002f7fcca4d75605f76a339edfc", + "research/native-lattice-retiming/README.md": "c2ef9c38cfd1d9ea8b2a3de3910471001a0592ea334d1e364e6ca41a8e322ee2", + "research/native-lattice-retiming/RESULT.json": "1ac2e581ea51e6448503a68caf4bf44aeb32470c2e2674c91f007af4a3abd2e3" + }, + "status": "PASS_NET_TAX_AND_LOG_MOMENT_RANK_COMPILER" +} diff --git a/research/net-tax-rank-compiler/SHIFTED-LOG.md b/research/net-tax-rank-compiler/SHIFTED-LOG.md new file mode 100644 index 0000000000..48a70bceba --- /dev/null +++ b/research/net-tax-rank-compiler/SHIFTED-LOG.md @@ -0,0 +1,134 @@ +# A normalized logarithmic majorant + +This extends the logarithmic majorant in PR4411 and PR4433 without changing +their finite integer compiler, its source complements, or its native +hypotheses. The new parameter normalizes the logarithm by a scale adapted to +the fixed mixed unit. All logarithms in the theorem are base two. + +Assume the separated finite compiler has ordinary base `L(n)=n` for +`0<=n=m`, + +``` +L(n) = sum_s w_s L(n-s) + sum_e x_e L(e), +sum_s w_s = 1, +n/m < s <= n, +sum_e x_e e^t <= sum_s w_s s^t, +1 <= e <= r_max*(n/m)^theta < n, +theta = log(r_max)/log(k_min) < 1. +``` + +Here the normalized nonnegative weights arise from whole integer batches; +the moment inequality follows from the strict mixed-unit superpotential. +These are the inherited compiler premises, not a replacement native proof. + +Choose `0=1, +F(0) := 0. +``` + +The scale and power may be real. Integer `h` and `p`, and rational +`theta_bar`, make the shift guard and final-rank checks particularly simple +exact arithmetic. The separate check `r_max^b<=k_min^a` implies the required +`theta<=theta_bar`. + +## Base range + +Put `x=log(n)` and `M=log(m)`. For positive `x`, the function +`log(1+x/h)/x` decreases: its derivative has the sign of +`x/(h+x)-ln(1+x/h)`, which is nonpositive because +`ln(1+u)>=u/(1+u)` for `u>=0`. Therefore the base guard implies + +``` +p*log(1+x/h) >= (1-t)*x for 0<=x<=M. +``` + +Exponentiation proves `F(n)>=n` throughout the ordinary base range. At +`n=1`, both sides are one. This single endpoint guard covers every integer +base rank; checking a sample of them is unnecessary. + +## Exit contraction + +Because `n/m>=1` and `theta<=theta_bar`, + +``` +log(e) <= log(r_max) + theta_bar*(log(n)-log(m)). +``` + +The shift guard is exactly + +``` +(1-theta_bar)*h + log(r_max)-theta_bar*log(m) <= 0. +``` + +Consequently `h+log(e)<=theta_bar*(h+log(n))`. Writing +`A(n)=(1+log(n)/h)^p` gives + +``` +A(e) <= theta_bar^p*A(n), +sum_e x_e F(e) <= theta_bar^p*A(n)*sum_s w_s s^t. +``` + +The factor `h` cancels in this ratio. Increasing it is therefore available +up to the explicit shift guard, rather than forcing the original value one. + +## Complements and induction + +The factor `A` increases on positive ranks. For `y=s/n>1/m`, concavity gives + +``` +1-(1-y)^t >= t*y >= t*m^(t-1)*y^t = eta*y^t. +``` + +Treating a zero-rank complement as zero, this implies + +``` +F(n)-sum_s w_s F(n-s) >= eta*A(n)*sum_s w_s s^t. +``` + +The strict capacity guard pays the exit bound. All recursive ranks are +smaller than `n`, so strong induction proves the assertion. The argument +uses monotonicity of `A`; it does not require that `A` be concave or that +`p<=1`. + +## Specified uniform rank + +For a desired exponent `z>t` and `N=2^H`, the sufficient final condition is + +``` +(1+H/h)^p < 2^((z-t)*H). +``` + +For positive integers `h,p,H`, and an integer `J=(z-t)*H`, this is exactly + +``` +(h+H)^p < h^p*2^J. +``` + +Thus normalized logarithms preserve a finite exact integer final-rank +certificate. This bounds normalized paid rank-one leaves. Actual productive +width, scalar records, owned banks, precision constants, physical costs and +recovery thresholds still come from the newly compiled finite word and the +inherited native and outer arguments. + +As a diagnostic using PR4453's unchanged `v=675`, `p=160` and +`theta_bar=15/16`, one may take `h=40*v=27000`: the shift condition reduces +to `2^40*18^16<=153^15`. The endpoint base condition also remains strict. +This changes the final sufficient-rank inequality itself. A standalone +numerical diagnostic is not a new certified rank or an independent native +admission; the package's exact verifier supplies its instantiated values. + +Prepared with substantial OpenAI Codex assistance. The finite integer +lockstep compiler is Jacob Alan Sussman's construction, retained through +PR4359; the logarithmic-majorant predecessors are zxv's PR4411 and PR4433. +New material is Apache-2.0. diff --git a/research/net-tax-rank-compiler/SOURCES.json b/research/net-tax-rank-compiler/SOURCES.json new file mode 100644 index 0000000000..81684a2e2c --- /dev/null +++ b/research/net-tax-rank-compiler/SOURCES.json @@ -0,0 +1,90 @@ +{ + "schema_version": 1, + "base_commit": "de6869e2e4d9c6f630bac5de4a919d99a2cb884b", + "files": [ + { + "path": "research/native-lattice-retiming/RESULT.json", + "usage": "input", + "sha256": "1ac2e581ea51e6448503a68caf4bf44aeb32470c2e2674c91f007af4a3abd2e3", + "git_blob": "93defc5ececebd542332fc42d6a78f0af222cd1c" + }, + { + "path": "research/native-lattice-retiming/NATIVE-RESULT.json", + "usage": "input", + "sha256": "a2e7a8f9eba6712dc92c47e6d86aaf18b8400f1ae5fe13ca19bbb65e76a25018", + "git_blob": "b5c0af78f1c2aa07e921898b48862bb6e8d9569c" + }, + { + "path": "research/native-lattice-retiming/README.md", + "usage": "input", + "sha256": "c2ef9c38cfd1d9ea8b2a3de3910471001a0592ea334d1e364e6ca41a8e322ee2", + "git_blob": "22cb2378eedf42895126b19ad22aa609774876ce" + }, + { + "path": "research/native-lattice-retiming/PROOF.md", + "usage": "input", + "sha256": "d137119bd238304295498d85186e6c0d36915002f7fcca4d75605f76a339edfc", + "git_blob": "5ed2cacea7e8e4ceeace5bc21745bfae6d41c4a1" + }, + { + "path": "research/higher-moment-strictification/RESULT.json", + "usage": "input", + "sha256": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156", + "git_blob": "e66b39c674028adfd22f0de3170555dccda52f6a" + }, + { + "path": "research/higher-moment-strictification/README.md", + "usage": "input", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699" + }, + { + "path": "research/higher-moment-strictification/vendor/p7-TENSOR.md", + "usage": "input", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3", + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656" + }, + { + "path": "research/higher-moment-strictification/vendor/FINITE-PRECOMPILATION.md", + "usage": "input", + "sha256": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "git_blob": "4badb40f0919c515823cb07e44c6470d4d6469ca" + }, + { + "path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/research/record-track/programs/theorem-1g/tree_flow.py", + "usage": "input", + "sha256": "750782f6d1cc0a9fff8a768899f3f4c62a7efdf0696d8b5a5d640b1836f5ab72", + "git_blob": "31a9c1ae4d116b12e8db7d8e06f723f10425068d" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40" + }, + { + "path": "autoresearch.md", + "usage": "provenance", + "sha256": "d16f0d3bb4d4b213d06c128db6d6460b0fe9ec1ac5a6c1ea1febf1db40e7b60d", + "git_blob": "2fe84a7b30b1e26e60ce0ec4775894eb1831c5d6" + }, + { + "path": "CONTRIBUTING.md", + "usage": "provenance", + "sha256": "8a49fe97e2ad088a2b2e0c5b222aaab08752783b1f9c1260790d7dd13011d215", + "git_blob": "fe54f23f19b082a9f8df3da9b2e205f7e230acf3" + } + ] +} diff --git a/research/net-tax-rank-compiler/TASK.json b/research/net-tax-rank-compiler/TASK.json new file mode 100644 index 0000000000..b91c112d79 --- /dev/null +++ b/research/net-tax-rank-compiler/TASK.json @@ -0,0 +1,132 @@ +{ + "schema_version": 1, + "task_id": "supplier-boundary-audit", + "priority_revision": 7, + "base_commit": "de6869e2e4d9c6f630bac5de4a919d99a2cb884b", + "original_card": { + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "existing_checks": [ + { + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "status": "author-checked" + }, + { + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "scope": "PR #3801: successor scatter-boundary decision package.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "status": "author-checked" + } + ], + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "id": "supplier-boundary-audit", + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ] + }, + "scope_status": "changed", + "actual_scope": "Develop reusable structural rank reductions for the chronological-product and finite uniform compiler, with exact reusable witnesses on native4453 and p7 profiles.", + "scope_change_reason": "The user explicitly assigned systematic structural rank reduction for future submissions; this overrides the catalogue default supplier audit. No new native profile or kappa hill step is claimed.", + "bottleneck_link": "Net concavity taxes and paid logarithmic moments reduce the tensor power and the sufficient uniform rank without changing native jobs.", + "stop_rule": "Finish a source-bound theorem and exact reusable certificate with discriminating controls; keep local for user review and leave further supplier changes open.", + "evidence": "Net gap identity, sharp concavity coefficients, normalized-log induction, exact iid exit law, convex-order and Bell-polynomial certificates, literal pinned-flow probes and independent agent audit.", + "author": "zxv, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance, including three user-requested Sol 6.1 xhigh subagents for divergent probes and independent audits.", + "budget_minutes": 60, + "outcome": "completed", + "open_questions": [ + { + "question": "Can exact raw logarithmic moments tighten the bounded-support concentration certificate?", + "why_it_matters": "The current Bernoulli bound keeps the tensor concentration but still overestimates the raw log law.", + "first_step": "Replace concentrated_moments with raw-moment Bell coefficients, retaining the capped-reference excess proof and the same positive coefficient test.", + "blocked_by": "Need directed enclosures for the complete moment list and explicit coefficient controls." + }, + { + "question": "Can a native word change improve kappa while using this smaller-rank compiler?", + "why_it_matters": "Compiler improvements preserve the raw moment ceiling; a kappa hill step needs a changed fully paid profile.", + "first_step": "Pin the recent native frame/contact proposals, alter one actual paid transition, replay its complete operator and invoice, then run this generic certificate tool.", + "blocked_by": "No new paid-profile improvement is proved in this package." + }, + { + "question": "Can productive width and batch denominators be bounded usefully as well?", + "why_it_matters": "A smaller ambient rank alone does not control materialized word size or owned-bank requirements.", + "first_step": "Record exact batch-width and source/exit recurrences for a small separated unit before extrapolating.", + "blocked_by": "The winning words remain algorithm-defined and their full widths are not emitted." + } + ], + "publication_policy": "Keep this contribution local for user review. No PR or Discussion publication is authorized for this contribution yet.", + "upstream_checkpoint": { + "checked_at_utc": "2026-10-21T22:13:49Z", + "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "priority_revision": 7, + "refresh_checked_at_utc": "2026-10-21T22:39:21Z", + "refresh_result": "Canonical main and relevant guidance unchanged." + }, + "overlap": { + "checked_at_utc": "2026-10-21T22:18:00Z", + "open_prs": 310, + "discussion_records": 3301, + "remote_pagination_complete": true, + "local_notes_searched": 23, + "local_HEAD_notes": 5739, + "limits": "Sparse local note coverage (5716 unsearched); no arbitrary diffs or closed remote PR-body search. This is not a novelty certificate. Start-here, recent handoffs and active discussions were read." + }, + "validation": { + "registered_replay": "pass", + "metadata_and_source_pins": "pass", + "isolated_optimized_direct_replay": "pass", + "exact_math_tests": 9, + "rejected_certificate_mutations": 9, + "literal_pinned_flow_checks": 6, + "source_mutation_control": "rejected", + "native_and_outer_producer_suites": "inherited source receipts, not rerun", + "platform": "macOS arm64", + "python": "3.12.8", + "independent_mathematical_checks": "Separate Sol 6.1 xhigh audit; Bell coefficients independently recovered through iid moment convolution and Newton differences." + } +} diff --git a/research/net-tax-rank-compiler/VERIFY.json b/research/net-tax-rank-compiler/VERIFY.json new file mode 100644 index 0000000000..0527cd3652 --- /dev/null +++ b/research/net-tax-rank-compiler/VERIFY.json @@ -0,0 +1,29 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/native-lattice-retiming/RESULT.json", + "research/native-lattice-retiming/NATIVE-RESULT.json", + "research/native-lattice-retiming/README.md", + "research/native-lattice-retiming/PROOF.md", + "research/higher-moment-strictification/RESULT.json", + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/verify.py", + "research/higher-moment-strictification/vendor/p7-TENSOR.md", + "research/higher-moment-strictification/vendor/FINITE-PRECOMPILATION.md", + "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/research/record-track/programs/theorem-1g/tree_flow.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "Authenticate source receipts; certify seven net-tax, shifted-log, weighted-exit and concentrated-log-moment witnesses with rational intervals and polynomial coefficients; compare literal pinned lockstep exits, exact mathematical controls, and deliberate rejection cases. Native and outer producers are inherited receipts, not rerun." + } + ] +} diff --git a/research/net-tax-rank-compiler/WEIGHTED-EXITS.md b/research/net-tax-rank-compiler/WEIGHTED-EXITS.md new file mode 100644 index 0000000000..c0f6469d31 --- /dev/null +++ b/research/net-tax-rank-compiler/WEIGHTED-EXITS.md @@ -0,0 +1,268 @@ +# A paid-log-moment compiler bound + +The largest paid rank need not determine the logarithmic power. The +separated integer compiler has an exact exit distribution: its exits are +the chronological paid word raised to the power `G+1`. This permits an +average logarithmic contraction, certified by a finite list of rational +polynomial coefficients. + +The construction, native premises, source complement recurrence and moment +cancellation are inherited from Jacob Alan Sussman's separated lockstep +compiler as retained in PR4359 and the logarithmic compiler of PR4411 and +PR4433. Only the bound on its normalized leaves changes here. There is no +new routing operation, fractional job, or independent productive credit. + +## Exact exits of the separated compiler + +Let the fixed mixed unit have ambient rank `m`, productive minimum `k_min`, +and a chronological paid inventory `P_r`, with + +``` +1 <= r_max < k_min <= m. +``` + +At top rank `n>=m`, put + +``` +G = floor(log_(k_min)(n/m)). +``` + +The inherited construction has one class for every paid-round path of +length `d<=G`, and degree `G-d` in that class. Separation consumes all +parent paid jobs, so there are no premature exits. At depth `G`, a path +has column multiplier `rho<=r_max^G0`; for `G=0`, +the single root has multiplier one and `m<=n`. Consequently the degree-zero +point is present in every depth-`G` class, with its exact integer weight +`u(0)=1`. + +Each such leaf unit issues its complete chronological paid word. Therefore +the complete exit multiset is exactly + +``` +{ r_1*...*r_(G+1) : each position chooses one actual paid call }, +``` + +including all multiplicities. The statement uses the compiler's complete +class construction, including child classes whose missing inputs are top +sources. A missing parent point does not omit the corresponding child +class. Chronological paths are not matched across different paid positions. + +For `0=r_max`, with `J>1`, and let + +``` +X = ln(r)/ln(J) in [0,1], +E[X] <= q, 0<=q<=1. +``` + +Take an integer power `p>=1` and a positive natural-log shift `a`. Choose +positive rational bounds `A_bar`, `B_under`, `beta` satisfying + +``` +a/ln(J) <= A_bar, +(a+ln(m))/ln(J) >= B_under, +ln(k_min)/ln(J) >= beta. +``` + +Let `S(i,j)` be the Stirling numbers of the second kind, with +`S(0,0)=1`, zero outside `0<=j<=i`, and + +``` +S(i+1,j) = j*S(i,j)+S(i,j-1). +``` + +For `0<=j<=p`, form the nonnegative numerator coefficients and positive +denominator coefficients + +``` +C_j = q^j * sum_(i=j..p) binom(p,i)*S(i,j) + * [q*(A_bar+1)^(p-i)+(1-q)*A_bar^(p-i)], +D_j = sum_(i=j..p) binom(p,i)*S(i,j) + * B_under^(p-i)*beta^i. +``` + +If every `C_j<=lambda*D_j`, then for every integer top rank `n>=m`, + +``` +E[(a+ln(exit))^p] <= lambda*(a+ln(n))^p. (1) +``` + +Here the expectation uses the exact `t`-weighted exit inventory above. +The certificate has only `p+1` rational comparisons; it does not enumerate +the product paid histogram or the compiler flow at unbounded ranks. + +### Proof by convex order + +For a convex function `f` on `[0,1]`, the chord inequality gives +`f(x)<=(1-x)f(0)+x*f(1)`. For an increasing convex function, taking the +expectation and using `E[X]<=q` bounds it by the Bernoulli-`q` expectation. +Applying this one variable at a time to +`(A_bar+x_1+...+x_(G+1))^p` proves + +``` +E[(a/ln(J)+sum X_i)^p] + <= E[(A_bar+Binomial(G+1,q))^p]. +``` + +Write `u=G` and split the binomial as `Binomial(u,q)+Z`, with `Z` an +independent Bernoulli-`q` variable. The identity + +``` +E[Binomial(u,q)^i] = sum_(j=0..i) S(i,j)*q^j*(u)_j +``` + +uses the falling factorial `(u)_j=u*(u-1)*...*(u-j+1)`, with `(u)_0=1`. +Expanding the previous display gives exactly `sum_j C_j*(u)_j`. +The same power-to-falling-factorial identity expands +`(B_under+beta*u)^p` as `sum_j D_j*(u)_j`. + +For every integer `u>=0`, all `(u)_j` are nonnegative (and vanish when +`j>u`). Coefficient domination therefore proves + +``` +E[(A_bar+Binomial(u+1,q))^p] + <= lambda*(B_under+beta*u)^p. +``` + +Finally `ln(n)>=ln(m)+G*ln(k_min)`, so +`(a+ln(n))/ln(J)>=B_under+beta*u`. Multiplication by `ln(J)^p` proves (1). +The coefficient condition is sufficient; its failure is not a theorem +about the compiler's true optimum. + +## Closing the source-complement induction + +Retain the exact compiler recurrence and moment inequality from +[SHIFTED-LOG.md](SHIFTED-LOG.md). Set + +``` +A(n) = (1+ln(n)/a)^p, +eta = t*m^(t-1). +``` + +If the finite coefficient certificate has `lambda= eta*A(n)*sum_s w_s*s^t. +``` + +It is enough to check the same endpoint base guard + +``` +m^(1-t) <= (1+ln(m)/a)^p. +``` + +The monotonicity argument in SHIFTED-LOG.md then covers every ordinary base +rank, and strong induction proves `L(n)<=n^t*A(n)`. The earlier pointwise +shift guard is not required when it is replaced by this averaged exit +certificate. The final sufficient-rank check remains + +``` +(h+H)^p < h^p*2^((z-t)*H), where a=h*ln(2), N=2^H. +``` + +This still requires the stated native compiler and strict mixed-unit +superpotential. It does not establish a compiler for overlapping ranks. + +## Bounding the paid log mean after splitting and completion + +The mean premise can be checked without emitting the completed histogram. +For a raw paid inventory with moment `P_t`, put + +``` +mu_raw = sum_r P_r*r^t*ln(r) / P_t, +A_raw = P_t^v, +J = c^v. +``` + +Suppose `E_split` bounds the **increase** in original-paid `t`-moment from +splitting, and `F_completion` bounds the **full paid `t`-moment** of all +split completion calls. Define `E=E_split+F_completion`. In particular, +`F_completion` must not subtract productive target-completion credit. A net +completion tax suitable for proving a superpotential cannot replace this +full paid charge in the mean bound. + +An original call `R>J` has split paid moment `Q_R>=R^t`, and every split +rank is at most `J`. Thus + +``` +sum_(split r) r^t*ln(r)-R^t*ln(R) + <= (Q_R-R^t)*ln(J). +``` + +Calls `R<=J` are unchanged. Every completion call also has split ranks at +most `J`, so its weighted log sum is at most its full paid moment times +`ln(J)`. The completed paid moment is at least `A_raw`, because splitting +increases a sublinear positive moment and completion adds nonnegative paid +calls. Consequently its normalized log mean obeys + +``` +E[X] <= mu_raw/ln(c) + E/A_raw. (2) +``` + +For example, certifying `mu_raw/ln(c)<=179/200` and +`E/A_raw<=1/200` gives `q=9/10`. Equation (2) is deliberately conservative; +the actual completed paid moment can give a sharper denominator. + +## A small rational specialization + +For a completed native4453 unit with + +``` +m=153^v, J=18^v, k_min>=22^v, h=4*v, +``` + +the integer comparisons + +``` +18^19 < 2^80, 2^4 < 18, +18^26 < 153^15, 18^16 < 22^15 +``` + +give `19/20<=a/ln(J)<=1`, +`(a+ln(m))/ln(J)>=19/20+26/15=161/60`, and +`ln(k_min)/ln(J)>=16/15`. Hence one may use + +``` +A_bar=1, B_under=161/60, beta=16/15, q=9/10. +``` + +At `p=60`, all 61 rational coefficient ratios are strictly below +`17/25000=0.00068`; the largest is at `j=16`, approximately +`0.0006795228122899847`. Thus any instance with `eta>3/4000=0.00075` passes +the exit guard, provided the paid-mean and base obligations also pass. +With the same bounds, `p=58` fails this coefficient guard. Setting `q=1` +also fails at `p=60`, so the certificate uses distribution information that +the largest-rank estimate omits. + +These are exact finite polynomial comparisons; displayed decimal values +are explanatory. The package verifier must bind the actual raw profile, +full completion bill, exponent, power, scale, all inequalities and final +rank before treating a concrete specialization as certified. This note +does not select a new frontier or independently admit a native supplier. + +Prepared with substantial OpenAI Codex assistance. New material is +Apache-2.0. The source compiler and prior logarithmic arguments retain the +attribution stated above and in the package provenance. diff --git a/research/net-tax-rank-compiler/compiler.py b/research/net-tax-rank-compiler/compiler.py new file mode 100644 index 0000000000..f5b5e5bb93 --- /dev/null +++ b/research/net-tax-rank-compiler/compiler.py @@ -0,0 +1,316 @@ +#!/usr/bin/env python3 +"""Reusable exact sufficient certificates; no search result is trusted. + +The mathematical contracts are in PROOF.md. This checker certifies finite +moment and compiler inequalities, conditional on the supplied native unit. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import json +from fractions import Fraction as Q +from math import comb +from pathlib import Path +import sys +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import intervals as E + + +def histogram(value): + E.need(isinstance(value, dict) and value, 'nonempty rank histogram') + result = {} + for key, count in value.items(): + rank = int(key) + E.need(str(rank) == str(key) and rank > 0, 'canonical positive rank') + E.need(type(count) is int and count > 0, 'positive integer multiplicity') + result[rank] = count + return result + + +def tax_data(profile, witness): + T, P = histogram(profile['targets']), histogram(profile['paid']) + m = max(T) + C, u = Q(witness['saving']), Q(witness['u']) + t = 1-C + v, c, b = (witness[k] for k in ('v', 'cutoff', 'floor')) + E.need(all(type(x) is int for x in (v, c, b)), 'integer construction') + E.need(0 < C < 1 and C <= u and v >= 1, 'net tax exponent domain') + E.need(1 < c < b < m and max(P) <= m, 'strict finite rank separation') + T1, P1 = (sum(k*n for k, n in h.items()) for h in (T, P)) + E.need(T1 > P1, 'positive rank-one surplus') + target = E.moment(T, t) + paid = E.moment(P, t) + alpha = E.divide(paid, target) + gamma = E.divide(E.moment(P, t+u), E.mul(E.power(c, u), target)) + B = sum(T.values()) + delta = E.divide((Q(B*b),)*2, E.mul(E.power(c, C), target)) + delta0 = E.divide(E.scale(E.power(b, t), B), target) + concavity_remainder = E.scale(E.qpower(t, t/C), C) + monotone_coefficient = (max(C/u, concavity_remainder[0]), + max(C/u, concavity_remainder[1])) + if u == C: + jensen_coefficient = E.power(2, C) + else: + jensen_coefficient = E.scale( + E.mul(E.power(2, u), E.qpower(1-C/u, u/C-1)), C/u) + coefficient = (min(monotone_coefficient[0], jensen_coefficient[0]), + min(monotone_coefficient[1], jensen_coefficient[1])) + epsilon = E.divide(E.scale(E.power(c, t), B), target) + original_tax = E.mul(coefficient, E.ipow(gamma, v)) + completion_tax = E.sub( + E.add(E.ipow(delta, v), + E.scale(E.mul(concavity_remainder, E.ipow(epsilon, v)), 2)), + E.ipow(delta0, v)) + bound = E.add(E.add(E.ipow(alpha, v), original_tax), completion_tax) + E.need(bound[1] < 1, 'strict net moment certificate') + old_bound = E.add(E.ipow(alpha, v), + E.scale(E.add(E.ipow(gamma, v), E.ipow(delta, v)), 2)) + return locals() + + +def net_tax(profile, witness): + data = tax_data(profile, witness) + C, u, v, c, b, m, B, T1, P1 = (data[k] for k in + ('C', 'u', 'v', 'c', 'b', 'm', 'B', 'T1', 'P1')) + alpha, gamma, delta, delta0, epsilon = (data[k] for k in + ('alpha', 'gamma', 'delta', 'delta0', 'epsilon')) + concavity_remainder, coefficient, original_tax, completion_tax, bound, old_bound = ( + data[k] for k in ('concavity_remainder', 'coefficient', 'original_tax', + 'completion_tax', 'bound', 'old_bound')) + return {'saving': str(C), 'v': v, 'cutoff': c, 'floor': b, + 'u': str(u), 'ambient_base': m, 'productive_fields_base': B, + 'rank_one_masses': {'target': T1, 'paid': P1}, + 'alpha': E.display(alpha), 'gamma': E.display(gamma), + 'delta': E.display(delta), 'delta0': E.display(delta0), + 'epsilon': E.display(epsilon), + 'concavity_remainder': E.display(concavity_remainder), + 'splitting_coefficient': E.display(coefficient), + 'original_splitting_tax_upper': E.display(original_tax), + 'completion_net_tax_upper': E.display(completion_tax), + 'normalized_net_charge': E.display(bound), + 'strict_gap_lower': E.display(E.sub((Q(1),)*2, bound)), + 'predecessor_full_charge_bound': E.display(old_bound), + 'word_materialized': False} + + +def weighted_coefficients(p, q, A, B0, beta): + """Coefficient comparison in the nonnegative integer falling-factorial basis.""" + E.need(type(p) is int and 1 <= p <= 200, 'bounded positive polynomial degree') + E.need(0 < q <= 1 and A > 0 and B0 > 0 and beta > 0, + 'positive weighted-exit constants') + S = [[0]*(p+1) for _ in range(p+1)] + S[0][0] = 1 + for i in range(1, p+1): + for j in range(1, i+1): + S[i][j] = S[i-1][j-1]+j*S[i-1][j] + numerator, denominator = [], [] + for j in range(p+1): + numerator.append(q**j*sum( + comb(p, i)*S[i][j]*(q*(A+1)**(p-i)+(1-q)*A**(p-i)) + for i in range(j, p+1))) + denominator.append(sum( + comb(p, i)*S[i][j]*B0**(p-i)*beta**i + for i in range(j, p+1))) + ratios = [x/y for x, y in zip(numerator, denominator)] + return max(ratios), ratios.index(max(ratios)), numerator, denominator + + +def moment_coefficients(p, moments, A, B0, beta): + """Arbitrary upper log moments, using partial exponential Bell polynomials.""" + E.need(type(p) is int and 1 <= p <= 200 and len(moments) == p+1, + 'bounded complete moment list') + E.need(moments[0] == 1 and all(0 <= x <= 1 for x in moments), + 'unit-interval moment upper bounds') + bell = [[Q(0)]*(p+1) for _ in range(p+1)] + bell[0][0] = Q(1) + for n in range(1, p+1): + for k in range(1, n+1): + bell[n][k] = sum(comb(n-1, j-1)*moments[j]*bell[n-j][k-1] + for j in range(1, n-k+2)) + shifted = [sum(comb(n, i)*A**(n-i)*moments[i] for i in range(n+1)) + for n in range(p+1)] + numerator = [sum(comb(p, l)*shifted[p-l]*bell[l][j] + for l in range(j, p+1)) for j in range(p+1)] + # The denominator's conversion to falling factorials is unchanged. + _, _, _, denominator = weighted_coefficients(p, Q(1), A, B0, beta) + ratios = [x/y for x, y in zip(numerator, denominator)] + return max(ratios), ratios.index(max(ratios)), numerator, denominator + + +def concentrated_moments(p, v, raw_mean_upper, raw_bound, excess_upper): + """Raw tensor concentration, then capped-reference mass perturbation.""" + E.need(type(v) is int and v >= 1 and 0 < raw_mean_upper <= raw_bound, + 'bounded raw log law') + E.need(excess_upper >= 0, 'nonnegative paid mass perturbation') + q = raw_mean_upper/raw_bound + S = [[0]*(p+1) for _ in range(p+1)] + S[0][0] = 1 + for n in range(1, p+1): + for k in range(1, n+1): + S[n][k] = S[n-1][k-1]+k*S[n-1][k] + falling = [1] + for k in range(1, p+1): + falling.append(falling[-1]*(v-k+1) if k <= v else 0) + moments = [Q(1)] + for i in range(1, p+1): + raw = (raw_bound/v)**i*sum(S[i][k]*falling[k]*q**k for k in range(i+1)) + moments.append(min(Q(1), (raw+excess_upper)/(1+excess_upper))) + return moments + + +def weighted_exit(profile, witness, eta): + data = tax_data(profile, witness) + p, h, v, c, b, m = (witness['p'], witness['log_shift'], data['v'], + data['c'], data['b'], data['m']) + options = witness['weighted'] + mean_key = ('raw_mean_upper' if witness['uniform_method'] == 'log-moments' + else 'mean_upper') + q, amin, amax, D, K = (Q(options[k]) for k in + (mean_key, 'A_lower', 'A_upper', 'ambient_log_lower', 'floor_log_lower')) + E.need(0 < q <= 1 and 0 < amin <= amax and D > 0 and K > 0, + 'weighted guard domain') + logc = E.log_bounds(c) + A = E.scale(E.divide(E.log_bounds(2), logc), Q(h, v)) + E.need(amin <= A[0] and A[1] <= amax, 'normalized log shift enclosure') + E.need(D <= E.divide(E.log_bounds(m), logc)[0], 'ambient log ratio') + E.need(K <= E.divide(E.log_bounds(b), logc)[0], 'target log ratio') + P, t = data['P'], data['t'] + log_moment = (Q(0), Q(0)) + for rank, count in P.items(): + log_moment = E.add(log_moment, + E.scale(E.mul(E.power(rank, t), E.log_bounds(rank)), count)) + raw_mean = E.divide(log_moment, E.mul(data['paid'], logc)) + # Full completion paid charge is needed here; the net completion tax + # subtracts new target credit and cannot bound paid log moments. + full_excess = E.add(data['original_tax'], E.scale(E.ipow(data['delta'], v), 2)) + relative_excess = E.divide(full_excess, E.ipow(data['alpha'], v)) + mean = E.add(raw_mean, relative_excess) + if witness['uniform_method'] == 'log-moments': + raw_bound = Q(options['raw_log_bound']) + excess_upper = Q(options['paid_excess_upper']) + E.need(raw_bound > 0 and excess_upper > 0, 'concentration guard domain') + E.need(raw_mean[1] < q, 'raw paid log mean') + E.need(max(P)**raw_bound.denominator <= c**raw_bound.numerator, + 'raw paid log support') + E.need(relative_excess[1] < excess_upper, 'full paid mass perturbation') + moments = concentrated_moments(p, v, q, raw_bound, excess_upper) + ratio, degree, num, den = moment_coefficients(p, moments, amax, amin+D, K) + moment_details = {'raw_log_bound': str(raw_bound), + 'paid_excess_upper': str(excess_upper), + 'log_moment_upper_bounds': [str(x) for x in moments]} + else: + E.need(mean[1] < q, 'completed paid log mean') + ratio, degree, num, den = weighted_coefficients(p, q, amax, amin+D, K) + moment_details = {} + E.need(ratio < eta[0], 'all weighted exit polynomial coefficients below capacity') + return {mean_key: str(q), **moment_details, + 'raw_normalized_log_mean': E.display(raw_mean), + 'full_paid_relative_excess': E.display(relative_excess), + 'completed_normalized_log_mean_upper': E.display(mean), + 'A': E.display(A), 'A_lower': str(amin), 'A_upper': str(amax), + 'ambient_log_lower': str(D), 'floor_log_lower': str(K), + 'coefficient_ratio_max': E.display((ratio, ratio)), + 'maximizing_coefficient': degree, + 'numerator_coefficients': [str(x) for x in num], + 'denominator_coefficients': [str(x) for x in den]} + + +def uniform(profile, witness): + """Shifted-log induction, with exact integer-grid final-rank search.""" + T = histogram(profile['targets']) + m = max(T) + C, kappa = Q(witness['saving']), Q(witness['kappa']) + t = 1-C + v, c, b = (witness[k] for k in ('v', 'cutoff', 'floor')) + p, h = witness['p'], witness.get('log_shift', 1) + E.need(type(p) is int and p > 0 and type(h) is int and h > 0, + 'positive integer logarithm power and shift') + E.need(0 < kappa < C < 1, 'uniform exponent domain') + eta = E.scale(E.ipow(E.power(m, -C), v), t) + method = witness.get('uniform_method', 'shifted') + details = {} + if method == 'shifted': + theta = Q(witness['theta']) + E.need(0 < theta < 1, 'theta domain') + a, d = theta.numerator, theta.denominator + E.need(c**d < b**a, 'theta above actual separation exponent') + E.need(2**(h*(d-a))*c**(v*d) <= m**(v*a), 'shifted logarithm guard') + E.need(theta**p < eta[0], 'exit contraction below complement capacity') + details['theta'] = str(theta) + elif method in ('weighted', 'log-moments'): + details['weighted_exit'] = weighted_exit(profile, witness, eta) + else: + raise ValueError('unknown uniform certificate method') + log_m = E.scale(E.divide(E.log_bounds(m), E.log_bounds(2)), v) + base_factor = E.ipow(E.add((Q(1),)*2, E.scale(log_m, Q(1, h))), p) + base_cost = E.ipow(E.power(m, C), v) + E.need(base_cost[1] < base_factor[0], 'entire ordinary base range fits') + gap = (C-kappa)/7 + step, gain = gap.denominator, gap.numerator + + def passes(j): + H = step*j + # (1+H/h)^p < 2^(gap*H), with no transcendental evaluation. + return (h+H)**p < h**p * 2**(gain*j) + + low, high = 0, 1 + while not passes(high): + low, high = high, 2*high + E.need(high.bit_length() < 40, 'bounded final-rank grid search') + while high-low > 1: + mid = (low+high)//2 + if passes(mid): + high = mid + else: + low = mid + H = step*high + E.need(passes(high) and (high == 1 or not passes(high-1)), + 'passing grid point and preceding failure') + # Above p/gap/ln(2), p*ln(1+H/h)-gap*H*ln(2) decreases. + # ln(2)>1/2 is enough for this conservative check. + E.need(H+h > 2*p/gap, 'decreasing final rank comparison') + E.need(Q(H) > log_m[1], 'uniform rank beyond ordinary base') + return {'kappa': str(kappa), 'gap': str(gap), 'method': method, **details, + 'uniform_saving': str(C-gap), + 'p': p, 'log_shift': h, 'eta': E.display(eta), + 'ordinary_base_cost': E.display(base_cost), + 'ordinary_base_factor': E.display(base_factor), + 'H': H, 'N': '2^'+str(H), 'grid_step': step, + 'grid_index': high, 'previous_grid_point_fails': high > 1, + 'word_materialized': False} + + +def certify(profile, witness): + return {'net_tax': net_tax(profile, witness), + 'uniform': uniform(profile, witness)} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('profile', type=Path, nargs='?') + parser.add_argument('witness', type=Path, nargs='?') + parser.add_argument('--example', help='replay one source-bound BENCHMARKS.json example') + args = parser.parse_args() + if args.example: + if args.profile or args.witness: + parser.error('choose --example or two input files') + here = Path(__file__).resolve().parent + cases = json.loads((here/'BENCHMARKS.json').read_text())['cases'] + matches = [case for case in cases if case['name'] == args.example] + if len(matches) != 1: + parser.error('unknown example') + case = matches[0] + profile = json.loads((here.parents[1]/case['source']).read_text()) + if case['profile_key']: + profile = profile[case['profile_key']] + witness = case['witness'] + else: + if not args.profile or not args.witness: + parser.error('provide profile.json witness.json, or --example NAME') + profile, witness = (json.loads(path.read_text()) + for path in (args.profile, args.witness)) + result = certify(profile, witness) + print(json.dumps(result, sort_keys=True, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/net-tax-rank-compiler/intervals.py b/research/net-tax-rank-compiler/intervals.py new file mode 100644 index 0000000000..f3d990ab63 --- /dev/null +++ b/research/net-tax-rank-compiler/intervals.py @@ -0,0 +1,150 @@ +#!/usr/bin/env python3 +"""Outward rational intervals, adapted from my PR4433 arithmetic. + +All endpoints are fractions; series tails and every rounding are outward. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +from fractions import Fraction as Q +from functools import lru_cache +GRID = 2**192 + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + + +def encoded(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encoded(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encoded(v) for v in x] + return x + + + +def add(a, b): + return rounded(a[0]+b[0], a[1]+b[1]) + + +def sub(a, b): + return rounded(a[0]-b[1], a[1]-b[0]) + + +def ipow(a, n): + """Integer powers of a nonnegative interval, bounded-size endpoints.""" + need(type(n) is int and n >= 0 and a[0] >= 0, 'nonnegative integer power') + out = (Q(1), Q(1)) + while n: + if n & 1: + out = mul(out, a) + a = mul(a, a) + n //= 2 + return out + + +def qpower(x, exponent): + """Positive rational base, rational exponent, with an enclosed logarithm.""" + x = Q(x) + need(x > 0, 'positive rational power base') + return exp_interval(scale(sub(log_bounds(x.numerator), + log_bounds(x.denominator)), exponent)) diff --git a/research/net-tax-rank-compiler/test_math.py b/research/net-tax-rank-compiler/test_math.py new file mode 100644 index 0000000000..25344d6eec --- /dev/null +++ b/research/net-tax-rank-compiler/test_math.py @@ -0,0 +1,186 @@ +"""Discriminating exact checks of the two structural proof steps. + +These finite cases check identities and failure modes; the general proofs +remain PROOF.md and SHIFTED-LOG.md. +""" +from collections import Counter +from fractions import Fraction as Q +from itertools import product +from math import comb, prod, factorial +import unittest +import intervals as E +import compiler + + +def exact_splits(rank, cutoff): + q, r = divmod(rank, cutoff) + return [cutoff]*q + ([r] if r else []) + + +def polynomial(ranks): + """Formal coefficients of symbols X_rank, before evaluating X_rank=rank^t.""" + return Counter(ranks) + + +def linear(*terms): + out = Counter() + for multiplier, values in terms: + for key, count in values.items(): + out[key] += multiplier*count + return {key: count for key, count in out.items() if count} + + +class NetTaxMath(unittest.TestCase): + def test_literal_gap_identity_and_target_credit_control(self): + targets, paid = [1, 4, 4, 9], [1, 1, 8] + for v in (1, 2, 3): + T = [prod(word) for word in product(targets, repeat=v)] + P = [prod(word) for word in product(paid, repeat=v)] + J, L = 2**v, 5**v + split_paid = [part for rank in P for part in exact_splits(rank, J)] + completions = [K for K in T if K < L] + split_completion = [part for K in completions + for part in exact_splits(L-K, J)] + final_targets = polynomial([max(K, L) for K in T]) + final_paid = polynomial(split_paid+split_completion) + raw_gap = linear((1, polynomial(T)), (-1, polynomial(P))) + original_tax = linear((1, polynomial(split_paid)), (-1, polynomial(P))) + completion_tax = linear((1, polynomial(split_completion)), + (-1, polynomial([L]*len(completions))), + (1, polynomial(completions))) + direct = linear((1, final_targets), (-1, final_paid)) + decomposed = linear((1, raw_gap), (-1, original_tax), (-1, completion_tax)) + self.assertEqual(direct, decomposed) + # Omitting the new target moment is a genuine incorrect identity. + missing_credit = linear((1, raw_gap), (-1, original_tax), + (-1, polynomial(split_completion))) + self.assertNotEqual(direct, missing_credit) + self.assertEqual(sum(T)-sum(P), + sum(max(K, L) for K in T)-sum(split_paid+split_completion)) + + def test_paid_tax_against_literal_splits(self): + C, t = Q(1, 2), Q(1, 2) + for u in (C, Q(3, 4), Q(3, 2), Q(3)): + h = E.scale(E.qpower(t, t/C), C) + monotone = (max(C/u, h[0]), max(C/u, h[1])) + jensen = (E.power(2, C) if u == C else E.scale( + E.mul(E.power(2, u), E.qpower(1-C/u, u/C-1)), C/u)) + for J in range(1, 13): + for R in range(J+1, 65): + charge = E.moment(Counter(exact_splits(R, J)), t) + tax = E.sub(charge, E.power(R, t)) + scale = E.mul(E.power(R, t+u), E.power(J, -u)) + # Each coefficient is valid independently, including u=C + # and u large enough that h dominates C/u. + for coefficient in (monotone, jensen): + bound = E.mul(coefficient, scale) + self.assertLess(tax[1], bound[0]) + + def test_completion_net_tax_against_literal_splits(self): + C, t = Q(1, 2), Q(1, 2) + h = E.scale(E.qpower(t, t/C), C) + for J in range(1, 9): + for L in range(J+1, 25): + universal = E.sub(E.add(E.mul((Q(L),)*2, E.power(J, -C)), + E.scale(E.mul(h, E.power(J, t)), 2)), + E.power(L, t)) + for K in range(1, L): + literal = E.sub(E.add(E.power(K, t), + E.moment(Counter(exact_splits(L-K, J)), t)), + E.power(L, t)) + if 4*K == J and 4*((L-K) % J) == J: + # Both maxima rho^t-rho are attained at rho=1/4; + # this is exact equality, independently of rounding. + self.assertLessEqual(literal[0], universal[1]) + self.assertLessEqual(universal[0], literal[1]) + else: + self.assertLess(literal[1], universal[0]) + # Including target credit matters: completion can cost + # far less than its entire paid charge. + if K == L-1: + paid = E.moment(Counter(exact_splits(L-K, J)), t) + self.assertLess(literal[1], paid[0]) + + def test_rational_interval_reference_points(self): + self.assertLess(E.log_bounds(2)[0], Q('0.693147180559945309417232121459')) + self.assertGreater(E.log_bounds(2)[1], Q('0.693147180559945309417232121458')) + for base, exponent, exact in ((4, Q(1, 2), 2), (9, Q(1, 2), 3), + (Q(1, 4), Q(-1, 2), 2)): + lo, hi = E.qpower(base, exponent) + self.assertLessEqual(lo, exact) + self.assertGreaterEqual(hi, exact) + + def test_convex_order_against_nonbernoulli_inventory(self): + # A genuine three-point law with mean1/2. Iterated chord domination + # bounds it by Binomial(n,1/2), including its actual variance. + law = [(Q(0), Q(1, 4)), (Q(1, 2), Q(1, 2)), (Q(1), Q(1, 4))] + for n in range(1, 5): + for p in (1, 2, 5, 8): + actual = sum(prod(w for _, w in word)*(1+sum(x for x, _ in word))**p + for word in product(law, repeat=n)) + chord = sum(Q(comb(n, k), 2**n)*(1+k)**p for k in range(n+1)) + self.assertLessEqual(actual, chord) + + def test_weighted_polynomial_identity_and_shift_control(self): + p, q, A, B0, beta = 7, Q(3, 5), Q(4, 5), Q(5, 2), Q(6, 5) + _, _, numerator, denominator = compiler.weighted_coefficients(p, q, A, B0, beta) + for G in range(0, 10): + falling = [prod(range(G-j+1, G+1)) for j in range(p+1)] + lhs = sum(comb(G+1, k)*q**k*(1-q)**(G+1-k)*(A+k)**p + for k in range(G+2)) + self.assertEqual(lhs, sum(x*y for x, y in zip(numerator, falling))) + self.assertEqual((B0+beta*G)**p, + sum(x*y for x, y in zip(denominator, falling))) + # Dropping the final paid round (G rather thanG+1) is false atG0. + self.assertNotEqual(numerator[0], A**p) + + def test_target_credit_is_invalid_for_paid_log_mean(self): + J, L, K, t = 4, 25, 1, Q(1, 2) + paid = E.moment(Counter(exact_splits(L-K, J)), t) + net = E.sub(E.add(E.power(K, t), paid), E.power(L, t)) + self.assertGreater(paid[0], net[1]) + # Every completion piece here has rankJ. Its full paid moment, + # rather than the smaller net tax, multiplies lnJ exactly. + literal_log = E.scale(E.log_bounds(J), 12) + wrong_log = E.mul(net, E.log_bounds(J)) + self.assertGreater(literal_log[0], wrong_log[1]) + + def test_bell_coefficients_against_independent_newton_differences(self): + p, A, B0, beta = 7, Q(4, 5), Q(5, 2), Q(6, 5) + law = {Q(0): Q(1, 4), Q(1, 2): Q(1, 2), Q(1): Q(1, 4)} + moments = [sum(weight*x**i for x, weight in law.items()) for i in range(p+1)] + _, _, numerator, _ = compiler.moment_coefficients(p, moments, A, B0, beta) + distribution = {Q(0): Q(1)} + values = [] + for G in range(p+1): + changed = Counter() + for x, a in distribution.items(): + for y, b in law.items(): + changed[x+y] += a*b + distribution = changed + values.append(sum(weight*(A+x)**p for x, weight in distribution.items())) + newton = [] + while values: + newton.append(values[0]/factorial(len(newton))) + values = [b-a for a, b in zip(values, values[1:])] + self.assertEqual(numerator, newton) + # Bernoulli moments reduce exactly to the earlier weighted theorem. + q = Q(3, 5) + self.assertEqual(compiler.moment_coefficients(p, [Q(1)]+[q]*p, A, B0, beta), + compiler.weighted_coefficients(p, q, A, B0, beta)) + + def test_concentration_and_capped_mass_perturbation(self): + v, rho, raw_mean, epsilon = 3, Q(3, 2), Q(3, 4), Q(1, 10) + p = 9 + bounds = compiler.concentrated_moments(p, v, raw_mean, rho, epsilon) + for i in range(1, p+1): + capped = sum(Q(comb(v, k), 2**v)*min(Q(1), rho*k/v)**i + for k in range(v+1)) + for actual_excess in (Q(0), epsilon/2, epsilon): + final = (capped+actual_excess)/(1+actual_excess) + self.assertLessEqual(final, bounds[i]) + self.assertLessEqual(bounds[i], 1) + + +if __name__ == '__main__': + unittest.main() diff --git a/research/net-tax-rank-compiler/verify.py b/research/net-tax-rank-compiler/verify.py new file mode 100644 index 0000000000..62f81b2a38 --- /dev/null +++ b/research/net-tax-rank-compiler/verify.py @@ -0,0 +1,198 @@ +#!/usr/bin/env python3 +"""Source-bound replay of the scoped rank certificates. + +Native and outer producer receipts are inherited, not recomputed here. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha1, sha256 +import io +import json +from pathlib import Path +import sys +import unittest +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import compiler +import intervals as E +import test_math + +ROOT = HERE.parents[1] +FLOW = ('research/kappa-rebuild/architecture/sources/Sussman-563b4e6/' + 'research/record-track/programs/theorem-1g/tree_flow.py') + + +def authenticate_bytes(raw, row): + E.need(sha256(raw).hexdigest() == row['sha256'], 'source SHA256: '+row['path']) + E.need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'source Git blob: '+row['path']) + + +def authenticate(): + manifest = json.loads((HERE/'SOURCES.json').read_text()) + receipts = {} + for row in manifest['files']: + if row['usage'] == 'input': + raw = (ROOT/row['path']).read_bytes() + authenticate_bytes(raw, row) + receipts[row['path']] = row['sha256'] + first = next(row for row in manifest['files'] if row['usage'] == 'input') + try: + authenticate_bytes((ROOT/first['path']).read_bytes()+b' ', first) + except ValueError: + pass + else: + raise ValueError('source mutation control accepted') + return receipts + + +def literal_flow_checks(): + # Execute authenticated source bytes directly, bypassing bytecode caches. + path = ROOT/FLOW + env = {'__file__': str(path), '__name__': 'pinned_tree_flow_oracle'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + receipt = [] + for n in (5, 14, 15, 44, 45, 135): + paid = [1, 1, 1, 1, 2] + actual, tree = env['lockstep_literal']({3: 2, 5: 1}, paid, n) + expected = Counter({1: 1}) + for _ in range(tree.G+1): + changed = Counter() + for rank, count in expected.items(): + for r in paid: + changed[rank*r] += count + expected = changed + E.need(actual['issued_before_start'] and actual['exits'] == dict(expected), + 'literal chronological exit law') + receipt.append({'top_rank': n, 'G': tree.G, + 'exits': dict(sorted(expected.items())), + 'literal_classes': actual['classes']}) + return receipt + + +def inherited_consumer(source, result, kind): + if kind == 'native': + outer, original = source['outer'], source['compiler'] + legacy = source['legacy_outer']['checks'] + else: + outer, original = source['outer']['ledger'], source['uniform_rank'] + legacy = source['outer']['legacy_63_checks'] + point = outer['parameters'] + E.need(Q(result['uniform']['kappa']) == Q(source['kappa']) == Q(point['kappa']), + 'unchanged inherited kappa point') + required = Q(point['complex_uniform_saving']) + available = Q(result['uniform']['uniform_saving']) + E.need(available >= required, 'new uniform bound supplies retained outer point') + E.need(Q(original['uniform_saving']) == required, 'source compiler/consumer binding') + for name in ('strict_checks', 'functional_checks'): + E.need(outer[name] and all(Q(x) > 0 for x in outer[name].values()), + 'positive inherited consumer receipt: '+name) + E.need(len(outer['margins']) == 9 + and all(Q(x) > Q(source['kappa']) for x in outer['margins'].values()), + 'nine inherited outer margins') + E.need(len(legacy) == 63 and all(Q(x) > 0 for x in legacy.values()), + 'legacy inherited receipt') + return {'status': 'INHERITED_RECEIPT_AND_MONOTONE_BOUND_BINDING', + 'producer_replayed': False, 'source_H': original['H'], + 'retained_kappa': str(Q(source['kappa'])), + 'required_uniform_saving': str(required), + 'available_uniform_saving': str(available), + 'strict_checks_in_receipt': len(outer['strict_checks']), + 'functional_checks_in_receipt': len(outer['functional_checks']), + 'legacy_checks_in_receipt': len(legacy), + 'rank_exponent_reduction': str(Q(original['H'], result['uniform']['H']))} + + +def expect_rejected(profile, witness, fragment, mutate): + changed = deepcopy(witness) + mutate(changed) + try: + compiler.certify(profile, changed) + except ValueError as exc: + E.need(fragment in str(exc), 'unexpected rejection: '+str(exc)) + return str(exc) + raise ValueError('invalid certificate accepted: '+fragment) + + +def run(): + sources = authenticate() + tests = unittest.defaultTestLoader.loadTestsFromModule(test_math) + stream = io.StringIO() + tested = unittest.TextTestRunner(stream=stream, verbosity=1).run(tests) + E.need(tested.wasSuccessful(), stream.getvalue()) + examples, profiles, witnesses = {}, {}, {} + for case in json.loads((HERE/'BENCHMARKS.json').read_text())['cases']: + source = json.loads((ROOT/case['source']).read_text()) + kind = 'p7' if case['profile_key'] else 'native' + if kind == 'native': + E.need(source['status'] == 'PASS_CONDITIONAL_NEW_NATIVE_PROFILE_KAPPA', + 'native source receipt status') + else: + E.need(source['status'] == 'PASS_HIGHER_MOMENT_STRICTIFICATION', + 'p7 source receipt status') + profile = source if case['profile_key'] is None else source[case['profile_key']] + result = compiler.certify(profile, case['witness']) + result['consumer_binding'] = inherited_consumer(source, result, kind) + examples[case['name']] = result + profiles[case['name']], witnesses[case['name']] = profile, case['witness'] + baseline = examples['native-source-parameters']['uniform']['H'] + native = json.loads((ROOT/'research/native-lattice-retiming/RESULT.json').read_text()) + E.need(baseline == native['compiler']['H'], 'source rank reproduced by old parameters') + final_name = 'native-concentrated-balanced' + profile, witness = profiles[final_name], witnesses[final_name] + negatives = {} + for name, fragment, mutation in ( + ('too_small_tensor', 'strict net moment', lambda w: w.update(v=20)), + ('invalid_tail_exponent', 'net tax exponent', lambda w: w.update(u='1/100000')), + ('closed_uniform_saving', 'uniform exponent', lambda w: w.update(kappa=w['saving'])), + ('degree23', 'polynomial coefficients', lambda w: w.update(p=23)), + ('understated_raw_mean', 'raw paid log mean', + lambda w: w['weighted'].update(raw_mean_upper='4/5')), + ('understated_log_support', 'raw paid log support', + lambda w: w['weighted'].update(raw_log_bound='1')), + ('understated_full_paid_excess', 'full paid mass perturbation', + lambda w: w['weighted'].update(paid_excess_upper='1/100000000')), + ('wrong_log_shift_enclosure', 'normalized log shift', + lambda w: w['weighted'].update(A_upper='347/100')), + ('drop_tensor_concentration', 'polynomial coefficients', + lambda w: (w.update(uniform_method='weighted'), + w['weighted'].update(mean_upper=w['weighted']['raw_mean_upper']))), + ): + negatives[name] = expect_rejected(profile, witness, fragment, mutation) + # The earlier full-charge proof fails on the new small tensor, so the + # improvement cannot be obtained merely by retaining its estimate. + old = examples[final_name]['net_tax']['predecessor_full_charge_bound'] + E.need(Q(old['lower']) > 1, 'old full-charge comparison fails') + return {'schema_version': 1, 'status': 'PASS_NET_TAX_AND_LOG_MOMENT_RANK_COMPILER', + 'scope': 'Conditional finite rank/leaf bounds; inherited native and outer producer receipts; no new kappa, selected frontier, materialized word or physical runtime claim.', + 'source_sha256': sources, 'examples': examples, + 'literal_pinned_flow_checks': literal_flow_checks(), + 'exact_math_tests': tested.testsRun, + 'rejected_mutations': negatives, + 'source_mutation_rejected': True} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true', help='replace the local exact receipt') + args = parser.parse_args() + result = run() + payload = json.dumps(result, indent=2, sort_keys=True)+'\n' + target = HERE/'RESULT.json' + if args.write: + target.write_text(payload) + else: + E.need(target.read_text() == payload, 'receipt differs; inspect then run --write') + print(json.dumps({'status': result['status'], 'examples': { + name: {'H': item['uniform']['H'], 'v': item['net_tax']['v'], + 'method': item['uniform']['method']} + for name, item in result['examples'].items()}, + 'exact_math_tests': result['exact_math_tests'], + 'rejected_mutations': len(result['rejected_mutations'])}, sort_keys=True)) + + +if __name__ == '__main__': + main() From 638f4fb6035abb2562f25d9fb7b570d9f2354108 Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 18:40:50 -0400 Subject: [PATCH 16/26] Enforce authenticated benchmark and compiler-oracle coverage --- research/net-tax-rank-compiler/README.md | 3 ++- research/net-tax-rank-compiler/compiler.py | 2 +- research/net-tax-rank-compiler/verify.py | 2 ++ 3 files changed, 5 insertions(+), 2 deletions(-) diff --git a/research/net-tax-rank-compiler/README.md b/research/net-tax-rank-compiler/README.md index ccf5fe17a5..fca02f443e 100644 --- a/research/net-tax-rank-compiler/README.md +++ b/research/net-tax-rank-compiler/README.md @@ -13,7 +13,8 @@ The contribution is four connected proof steps and a generic exact checker: 1. **Net splitting and completion taxes.** Charge the increase in paid moment and retain the productive moment added by same-owner completion. - The splitting coefficient scales as `O(C/u)` rather than a fixed two. + For `C<=u<=1`, the splitting coefficient scales as `O(C/u)` rather + than a fixed two. 2. **Normalized logarithmic majorants.** Use `(1+log2(n)/h)^p`, checking the entire ordinary base range at one endpoint. The scale is a certified parameter adapted to the finite unit. diff --git a/research/net-tax-rank-compiler/compiler.py b/research/net-tax-rank-compiler/compiler.py index f5b5e5bb93..bc58fbd7a7 100644 --- a/research/net-tax-rank-compiler/compiler.py +++ b/research/net-tax-rank-compiler/compiler.py @@ -288,7 +288,7 @@ def main(): parser = argparse.ArgumentParser(description=__doc__) parser.add_argument('profile', type=Path, nargs='?') parser.add_argument('witness', type=Path, nargs='?') - parser.add_argument('--example', help='replay one source-bound BENCHMARKS.json example') + parser.add_argument('--example', help='replay a BENCHMARKS.json example; verify.py authenticates sources') args = parser.parse_args() if args.example: if args.profile or args.witness: diff --git a/research/net-tax-rank-compiler/verify.py b/research/net-tax-rank-compiler/verify.py index 62f81b2a38..048fd977e2 100644 --- a/research/net-tax-rank-compiler/verify.py +++ b/research/net-tax-rank-compiler/verify.py @@ -119,12 +119,14 @@ def expect_rejected(profile, witness, fragment, mutate): def run(): sources = authenticate() + E.need(FLOW in sources, 'literal oracle must be an authenticated live input') tests = unittest.defaultTestLoader.loadTestsFromModule(test_math) stream = io.StringIO() tested = unittest.TextTestRunner(stream=stream, verbosity=1).run(tests) E.need(tested.wasSuccessful(), stream.getvalue()) examples, profiles, witnesses = {}, {}, {} for case in json.loads((HERE/'BENCHMARKS.json').read_text())['cases']: + E.need(case['source'] in sources, 'benchmark source must be an authenticated live input') source = json.loads((ROOT/case['source']).read_text()) kind = 'p7' if case['profile_key'] else 'native' if kind == 'native': From 393cdcf0a2dd33c3d05487d8251b84b284bbc57d Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 18:42:32 -0400 Subject: [PATCH 17/26] Record portable replay and independent audit evidence --- research/net-tax-rank-compiler/TASK.json | 8 ++- research/net-tax-rank-compiler/VALIDATION.md | 53 ++++++++++++++++++++ 2 files changed, 60 insertions(+), 1 deletion(-) create mode 100644 research/net-tax-rank-compiler/VALIDATION.md diff --git a/research/net-tax-rank-compiler/TASK.json b/research/net-tax-rank-compiler/TASK.json index b91c112d79..343ea8f7f4 100644 --- a/research/net-tax-rank-compiler/TASK.json +++ b/research/net-tax-rank-compiler/TASK.json @@ -127,6 +127,12 @@ "native_and_outer_producer_suites": "inherited source receipts, not rerun", "platform": "macOS arm64", "python": "3.12.8", - "independent_mathematical_checks": "Separate Sol 6.1 xhigh audit; Bell coefficients independently recovered through iid moment convolution and Newton differences." + "independent_mathematical_checks": "Separate Sol 6.1 xhigh audit; Bell coefficients independently recovered through iid moment convolution and Newton differences.", + "committed_bytes": "pass at 638f4fb6035abb2562f25d9fb7b570d9f2354108", + "export_integrity": "pass", + "git_free_isolated_optimized_export": "pass; PATH=/nonexistent", + "exported_source_and_receipt_mutations": "rejected", + "optional_source_history": "unavailable: shallow checkout; not a passing ancestry check", + "publication": "local only" } } diff --git a/research/net-tax-rank-compiler/VALIDATION.md b/research/net-tax-rank-compiler/VALIDATION.md new file mode 100644 index 0000000000..185a4bcb95 --- /dev/null +++ b/research/net-tax-rank-compiler/VALIDATION.md @@ -0,0 +1,53 @@ +# Validation of the structural rank compiler + +Validated on 2026-10-21, macOS arm64, Python 3.12.8. Scientific code at +`638f4fb6035abb2562f25d9fb7b570d9f2354108`; later validation metadata does +not change the certificate machinery or mathematical receipt. + +- Registered metadata/source pins and the bounded package replay pass. +- Seven exact benchmark certificates pass, including the original native + rank parameters and two separate source profiles. +- Nine mathematical tests pass: formal net-gap accounting, literal split + taxes, completion bounds including equality, rational interval reference + points, convex order, coefficient identities, independent Newton-difference + reconstruction of Bell coefficients, and capped mass perturbations. +- Nine invalid witnesses are rejected, including degree 23, removal of + tensor concentration, understated full paid costs and invalid log bounds. +- Six literal flows from the unchanged authenticated Sussman oracle agree + exactly with independent `(G+1)`-fold paid-histogram convolution. +- Committed-byte preflight passes for all 24 package/input files. +- The committed export passes transport/inventory integrity. Its direct + verifier passes under `python3.12 -I -O -B` with no Git checkout and + `PATH=/nonexistent`. Mutating a pinned source or its output receipt is + rejected in that export. +- Separate user-requested Sol 6.1 xhigh agents audited the mathematical + bounds and source/consumer binding. One audit recovered Bell coefficients + through ordinary iid moment convolution and Newton differences, avoiding + the implementation's Bell recurrence. + +Reproduction: + +```sh +python3.12 -B scripts/research_package.py --package research/net-tax-rank-compiler +python3.12 -I -O -B research/net-tax-rank-compiler/verify.py +python3.12 -B scripts/check_research_commit.py --package research/net-tax-rank-compiler +``` + +The optional `--check-source-history` preflight is **unavailable** because +this checkout is shallow; it requests full Git history. This is not a +passing ancestry check. Exact committed input bytes and Git-free direct +replay were checked separately; no full-history fetch was attempted. + +Canonical main was refreshed at 22:39 UTC and remains +`2a13eb1827784206202db90e5dc8327cf8a250db`; relevant guidance is unchanged. +Overlap checking covers 310 open PR bodies and 3,301 discussion records, +with complete remote pagination. Local coverage is sparse: 23 of 5,739 +HEAD note paths were searched. This is not a novelty certificate. + +Native and outer producer suites were not rerun. Their authenticated source +receipts and conditional obligations are explicitly inherited. The new +uniform saving supplies the retained outer point by monotonicity. No +winning word, full productive width, physical count, precision constant, +new κ or selected-frontier update is certified by this replay. + +No PR, Discussion post or remote branch was published for this contribution. From 843f753a97681c010ba7d13561fc25da28619389 Mon Sep 17 00:00:00 2001 From: Cinna Davis <164028474+1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 23:06:03 +0000 Subject: [PATCH 18/26] Construct conditional kappa 0.00302015 with joint helper boundaries --- research/joint-helper-lattice/CONTROLLER.json | 5224 ++++++++ research/joint-helper-lattice/DISCOVERY.json | 10886 ++++++++++++++++ research/joint-helper-lattice/FRONTIER.json | 187 + research/joint-helper-lattice/NATIVE.json.gz | Bin 0 -> 35042 bytes research/joint-helper-lattice/PATCH.json | 8991 +++++++++++++ research/joint-helper-lattice/PROOF.md | 102 + research/joint-helper-lattice/README.md | 46 + research/joint-helper-lattice/RESULT.json | 274 + research/joint-helper-lattice/SOURCES.json | 330 + research/joint-helper-lattice/TASK.json | 73 + research/joint-helper-lattice/VALIDATION.md | 7 + research/joint-helper-lattice/VERIFY.json | 70 + research/joint-helper-lattice/native_joint.py | 118 + research/joint-helper-lattice/verify.py | 233 + 14 files changed, 26541 insertions(+) create mode 100644 research/joint-helper-lattice/CONTROLLER.json create mode 100644 research/joint-helper-lattice/DISCOVERY.json create mode 100644 research/joint-helper-lattice/FRONTIER.json create mode 100644 research/joint-helper-lattice/NATIVE.json.gz create mode 100644 research/joint-helper-lattice/PATCH.json create mode 100644 research/joint-helper-lattice/PROOF.md create mode 100644 research/joint-helper-lattice/README.md create mode 100644 research/joint-helper-lattice/RESULT.json create mode 100644 research/joint-helper-lattice/SOURCES.json create mode 100644 research/joint-helper-lattice/TASK.json create mode 100644 research/joint-helper-lattice/VALIDATION.md create mode 100644 research/joint-helper-lattice/VERIFY.json create mode 100644 research/joint-helper-lattice/native_joint.py create mode 100644 research/joint-helper-lattice/verify.py diff --git a/research/joint-helper-lattice/CONTROLLER.json b/research/joint-helper-lattice/CONTROLLER.json new file mode 100644 index 0000000000..49a2f06758 --- /dev/null +++ b/research/joint-helper-lattice/CONTROLLER.json @@ -0,0 +1,5224 @@ +{ + "ambient_rank": 145, + "boundaries": { + "left": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "left_program": [ + [ + "SWAP", + 30, + 31 + ], + [ + "SWAP", + 29, + 30 + ], + [ + "SWAP", + 28, + 30 + ], + [ + "SWAP", + 27, + 29 + ], + [ + "SWAP", + 26, + 28 + ], + [ + "SWAP", + 25, + 30 + ], + [ + "SWAP", + 24, + 25 + ], + [ + "SWAP", + 23, + 26 + ], + [ + "SWAP", + 22, + 30 + ], + [ + "SWAP", + 20, + 26 + ], + [ + "SWAP", + 19, + 22 + ], + [ + "SWAP", + 18, + 29 + ], + [ + "SWAP", + 17, + 23 + ], + [ + "SWAP", + 16, + 27 + ], + [ + "SCALE", + 15, + "-1" + ], + [ + "SWAP", + 15, + 31 + ], + [ + "ADD", + 12, + 14, + "1" + ], + [ + "ADD", + 10, + 14, + "-1" + ], + [ + "ADD", + 8, + 14, + "1" + ], + [ + "ADD", + 6, + 14, + "-1" + ], + [ + "ADD", + 4, + 14, + "1" + ], + [ + "ADD", + 2, + 14, + "-1" + ], + [ + "ADD", + 0, + 14, + "1" + ], + [ + "SWAP", + 14, + 15 + ], + [ + "ADD", + 31, + 13, + "1" + ], + [ + "SWAP", + 13, + 30 + ], + [ + "ADD", + 10, + 12, + "1" + ], + [ + "ADD", + 8, + 12, + "-1" + ], + [ + "ADD", + 6, + 12, + "1" + ], + [ + "ADD", + 4, + 12, + "-1" + ], + [ + "ADD", + 2, + 12, + "1" + ], + [ + "ADD", + 0, + 12, + "-1" + ], + [ + "SWAP", + 12, + 14 + ], + [ + "ADD", + 31, + 11, + "-1" + ], + [ + "ADD", + 30, + 11, + "-1" + ], + [ + "SCALE", + 11, + "-1" + ], + [ + "SWAP", + 11, + 29 + ], + [ + "ADD", + 8, + 10, + "1" + ], + [ + "ADD", + 6, + 10, + "-1" + ], + [ + "ADD", + 4, + 10, + "1" + ], + [ + "ADD", + 2, + 10, + "-1" + ], + [ + "ADD", + 0, + 10, + "1" + ], + [ + "SWAP", + 10, + 13 + ], + [ + "ADD", + 31, + 9, + "1" + ], + [ + "ADD", + 30, + 9, + "1" + ], + [ + "ADD", + 29, + 9, + "1" + ], + [ + "SWAP", + 9, + 28 + ], + [ + "ADD", + 6, + 8, + "1" + ], + [ + "ADD", + 4, + 8, + "-1" + ], + [ + "ADD", + 2, + 8, + "1" + ], + [ + "ADD", + 0, + 8, + "-1" + ], + [ + "SWAP", + 8, + 12 + ], + [ + "ADD", + 31, + 7, + "-1" + ], + [ + "ADD", + 30, + 7, + "-1" + ], + [ + "ADD", + 29, + 7, + "-1" + ], + [ + "ADD", + 28, + 7, + "-1" + ], + [ + "SCALE", + 7, + "-1" + ], + [ + "SWAP", + 7, + 27 + ], + [ + "ADD", + 4, + 6, + "1" + ], + [ + "ADD", + 2, + 6, + "-1" + ], + [ + "ADD", + 0, + 6, + "1" + ], + [ + "SWAP", + 6, + 11 + ], + [ + "ADD", + 31, + 5, + "1" + ], + [ + "ADD", + 30, + 5, + "1" + ], + [ + "ADD", + 29, + 5, + "1" + ], + [ + "ADD", + 28, + 5, + "1" + ], + [ + "ADD", + 27, + 5, + "1" + ], + [ + "SWAP", + 5, + 26 + ], + [ + "ADD", + 2, + 4, + "1" + ], + [ + "ADD", + 0, + 4, + "-1" + ], + [ + "SWAP", + 4, + 10 + ], + [ + "ADD", + 31, + 3, + "-1" + ], + [ + "ADD", + 30, + 3, + "-1" + ], + [ + "ADD", + 29, + 3, + "-1" + ], + [ + "ADD", + 28, + 3, + "-1" + ], + [ + "ADD", + 27, + 3, + "-1" + ], + [ + "ADD", + 26, + 3, + "-1" + ], + [ + "SCALE", + 3, + "-1" + ], + [ + "SWAP", + 3, + 25 + ], + [ + "ADD", + 0, + 2, + "1" + ], + [ + "SWAP", + 2, + 9 + ], + [ + "ADD", + 31, + 1, + "1" + ], + [ + "ADD", + 30, + 1, + "1" + ], + [ + "ADD", + 29, + 1, + "1" + ], + [ + "ADD", + 28, + 1, + "1" + ], + [ + "ADD", + 27, + 1, + "1" + ], + [ + "ADD", + 26, + 1, + "1" + ], + [ + "ADD", + 25, + 1, + "1" + ], + [ + "SWAP", + 1, + 24 + ], + [ + "SWAP", + 0, + 8 + ] + ], + "right": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "right_program": [ + [ + "ADD", + 30, + 31, + "-1" + ], + [ + "ADD", + 29, + 31, + "-1" + ], + [ + "ADD", + 28, + 31, + "-1" + ], + [ + "ADD", + 27, + 31, + "-1" + ], + [ + "SCALE", + 31, + "-1" + ], + [ + "ADD", + 31, + 30, + "-1" + ], + [ + "ADD", + 29, + 30, + "-1" + ], + [ + "ADD", + 28, + 30, + "-1" + ], + [ + "ADD", + 27, + 30, + "-1" + ], + [ + "ADD", + 31, + 29, + "-1" + ], + [ + "ADD", + 28, + 29, + "-1" + ], + [ + "ADD", + 27, + 29, + "-1" + ], + [ + "SCALE", + 29, + "-1" + ], + [ + "ADD", + 31, + 28, + "-1" + ], + [ + "ADD", + 27, + 28, + "-1" + ], + [ + "SWAP", + 28, + 29 + ], + [ + "ADD", + 31, + 27, + "-1" + ], + [ + "SCALE", + 27, + "-1" + ], + [ + "SWAP", + 27, + 29 + ], + [ + "ADD", + 31, + 26, + "1" + ], + [ + "SWAP", + 26, + 29 + ], + [ + "ADD", + 29, + 25, + "-1" + ], + [ + "ADD", + 24, + 25, + "-1" + ], + [ + "SWAP", + 25, + 28 + ], + [ + "ADD", + 28, + 24, + "1" + ], + [ + "SWAP", + 23, + 29 + ], + [ + "SWAP", + 22, + 25 + ], + [ + "SWAP", + 20, + 23 + ], + [ + "SWAP", + 19, + 25 + ], + [ + "SWAP", + 18, + 27 + ], + [ + "SWAP", + 17, + 29 + ], + [ + "SWAP", + 16, + 31 + ], + [ + "ADD", + 14, + 15, + "-1" + ], + [ + "SWAP", + 15, + 30 + ], + [ + "ADD", + 13, + 14, + "-1" + ], + [ + "SWAP", + 14, + 30 + ], + [ + "ADD", + 12, + 13, + "-1" + ], + [ + "SWAP", + 13, + 22 + ], + [ + "ADD", + 11, + 12, + "-1" + ], + [ + "SWAP", + 12, + 30 + ], + [ + "ADD", + 10, + 11, + "-1" + ], + [ + "SWAP", + 11, + 18 + ], + [ + "ADD", + 9, + 10, + "-1" + ], + [ + "SWAP", + 10, + 22 + ], + [ + "ADD", + 8, + 9, + "-1" + ], + [ + "SWAP", + 9, + 26 + ], + [ + "SWAP", + 8, + 30 + ], + [ + "SWAP", + 7, + 16 + ], + [ + "SWAP", + 6, + 18 + ], + [ + "SWAP", + 5, + 20 + ], + [ + "SWAP", + 4, + 22 + ], + [ + "SWAP", + 3, + 24 + ], + [ + "SWAP", + 2, + 26 + ], + [ + "SWAP", + 1, + 28 + ], + [ + "SWAP", + 0, + 30 + ] + ] + }, + "diagonal": [ + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ] + ], + "invoice": { + "main": { + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 46446, + "2": 12834, + "3": 4032, + "4": 1836, + "5": 360, + "8": 144, + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + }, + "paid_calls": 69012, + "productive_fields": 10928, + "rank_surplus": 752, + "raw_scalar_record_bound": 1000000000, + "targets": { + "5": 504, + "6": 324, + "7": 1008, + "8": 1674, + "9": 3834, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "thick_calls": 18, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ], + "thin_queries": 1680, + "whole_idle": { + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + } + }, + "keep_mask": 35047648968703, + "kind": "complex", + "pairs": 16, + "physical_events": [ + [ + "LOCAL", + 0, + 0, + false + ], + [ + "LOCAL", + 1, + 0, + true + ], + [ + "IDLE", + 1, + [ + 0, + 1 + ] + ], + [ + "ADD", + 0, + 2, + 1 + ], + [ + "ADD", + 3, + 1, + -1 + ], + [ + "QUERY_SHEAR", + 2, + 0, + false + ], + [ + "ADD", + 0, + 2, + -1 + ], + [ + "ADD", + 3, + 1, + 1 + ], + [ + "LOCAL", + 3, + 1, + true + ], + [ + "IDLE", + 2, + [ + 0, + 1, + 3 + ] + ], + [ + "ADD", + 2, + 4, + 1 + ], + [ + "ADD", + 5, + 3, + -1 + ], + [ + "QUERY_SHEAR", + 4, + 1, + false + ], + [ + "ADD", + 2, + 4, + -1 + ], + [ + "ADD", + 5, + 3, + 1 + ], + [ + "LOCAL", + 5, + 2, + true + ], + [ + "IDLE", + 3, + [ + 0, + 1, + 3, + 5 + ] + ], + [ + "ADD", + 4, + 6, + 1 + ], + [ + "ADD", + 7, + 5, + -1 + ], + [ + "QUERY_SHEAR", + 6, + 2, + false + ], + [ + "ADD", + 4, + 6, + -1 + ], + [ + "ADD", + 7, + 5, + 1 + ], + [ + "LOCAL", + 7, + 3, + true + ], + [ + "IDLE", + 4, + [ + 0, + 1, + 3, + 5, + 7 + ] + ], + [ + "ADD", + 6, + 8, + 1 + ], + [ + "ADD", + 9, + 7, + -1 + ], + [ + "QUERY_SHEAR", + 8, + 3, + false + ], + [ + "ADD", + 6, + 8, + -1 + ], + [ + "ADD", + 9, + 7, + 1 + ], + [ + "LOCAL", + 9, + 4, + true + ], + [ + "IDLE", + 5, + [ + 0, + 1, + 3, + 5, + 7, + 9 + ] + ], + [ + "ADD", + 8, + 10, + 1 + ], + [ + "ADD", + 11, + 9, + -1 + ], + [ + "QUERY_SHEAR", + 10, + 4, + false + ], + [ + "ADD", + 8, + 10, + -1 + ], + [ + "ADD", + 11, + 9, + 1 + ], + [ + "LOCAL", + 11, + 5, + true + ], + [ + "IDLE", + 6, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11 + ] + ], + [ + "ADD", + 10, + 12, + 1 + ], + [ + "ADD", + 13, + 11, + -1 + ], + [ + "QUERY_SHEAR", + 12, + 5, + false + ], + [ + "ADD", + 10, + 12, + -1 + ], + [ + "ADD", + 13, + 11, + 1 + ], + [ + "LOCAL", + 13, + 6, + true + ], + [ + "IDLE", + 7, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13 + ] + ], + [ + "ADD", + 12, + 14, + 1 + ], + [ + "ADD", + 15, + 13, + -1 + ], + [ + "QUERY_SHEAR", + 14, + 6, + false + ], + [ + "ADD", + 12, + 14, + -1 + ], + [ + "ADD", + 15, + 13, + 1 + ], + [ + "LOCAL", + 15, + 7, + true + ], + [ + "ADD", + 14, + 16, + 1 + ], + [ + "ADD", + 17, + 15, + -1 + ], + [ + "QUERY_SHEAR", + 16, + 7, + false + ], + [ + "ADD", + 14, + 16, + -1 + ], + [ + "ADD", + 17, + 15, + 1 + ], + [ + "LOCAL", + 17, + 8, + true + ], + [ + "ADD", + 16, + 18, + 1 + ], + [ + "ADD", + 19, + 17, + -1 + ], + [ + "QUERY_SHEAR", + 18, + 8, + false + ], + [ + "ADD", + 16, + 18, + -1 + ], + [ + "ADD", + 19, + 17, + 1 + ], + [ + "LOCAL", + 19, + 9, + true + ], + [ + "ADD", + 18, + 20, + 1 + ], + [ + "ADD", + 21, + 19, + -1 + ], + [ + "QUERY_SHEAR", + 20, + 9, + false + ], + [ + "ADD", + 18, + 20, + -1 + ], + [ + "ADD", + 21, + 19, + 1 + ], + [ + "LOCAL", + 21, + 10, + true + ], + [ + "ADD", + 20, + 22, + 1 + ], + [ + "ADD", + 23, + 21, + -1 + ], + [ + "QUERY_SHEAR", + 22, + 10, + false + ], + [ + "ADD", + 20, + 22, + -1 + ], + [ + "ADD", + 23, + 21, + 1 + ], + [ + "LOCAL", + 23, + 11, + true + ], + [ + "ADD", + 22, + 24, + 1 + ], + [ + "ADD", + 25, + 23, + -1 + ], + [ + "QUERY_SHEAR", + 24, + 11, + false + ], + [ + "ADD", + 22, + 24, + -1 + ], + [ + "ADD", + 25, + 23, + 1 + ], + [ + "LOCAL", + 25, + 12, + true + ], + [ + "ADD", + 24, + 26, + 1 + ], + [ + "ADD", + 27, + 25, + -1 + ], + [ + "QUERY_SHEAR", + 26, + 12, + false + ], + [ + "ADD", + 24, + 26, + -1 + ], + [ + "ADD", + 27, + 25, + 1 + ], + [ + "LOCAL", + 27, + 13, + true + ], + [ + "ADD", + 26, + 28, + 1 + ], + [ + "ADD", + 29, + 27, + -1 + ], + [ + "QUERY_SHEAR", + 28, + 13, + false + ], + [ + "ADD", + 26, + 28, + -1 + ], + [ + "ADD", + 29, + 27, + 1 + ], + [ + "LOCAL", + 29, + 14, + true + ], + [ + "ADD", + 28, + 30, + 1 + ], + [ + "ADD", + 31, + 29, + -1 + ], + [ + "QUERY_SHEAR", + 30, + 14, + false + ], + [ + "ADD", + 28, + 30, + -1 + ], + [ + "ADD", + 31, + 29, + 1 + ], + [ + "LOCAL", + 31, + 15, + true + ], + [ + "LOCAL", + 32, + 15, + false + ], + [ + "IDLE", + 7, + [ + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 8, + [ + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 9, + [ + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 10, + [ + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 11, + [ + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 12, + [ + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 13, + [ + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 14, + [ + 31, + 32 + ] + ], + [ + "ADD", + 30, + 28, + 1 + ], + [ + "ADD", + 29, + 31, + -1 + ], + [ + "ADD", + 28, + 26, + 1 + ], + [ + "ADD", + 27, + 29, + -1 + ], + [ + "ADD", + 26, + 24, + 1 + ], + [ + "ADD", + 25, + 27, + -1 + ], + [ + "ADD", + 24, + 22, + 1 + ], + [ + "ADD", + 23, + 25, + -1 + ], + [ + "ADD", + 22, + 20, + 1 + ], + [ + "ADD", + 21, + 23, + -1 + ], + [ + "ADD", + 20, + 18, + 1 + ], + [ + "ADD", + 19, + 21, + -1 + ], + [ + "ADD", + 18, + 16, + 1 + ], + [ + "ADD", + 17, + 19, + -1 + ], + [ + "ADD", + 16, + 14, + 1 + ], + [ + "ADD", + 15, + 17, + -1 + ], + [ + "ADD", + 14, + 12, + 1 + ], + [ + "ADD", + 13, + 15, + -1 + ], + [ + "ADD", + 12, + 10, + 1 + ], + [ + "ADD", + 11, + 13, + -1 + ], + [ + "ADD", + 10, + 8, + 1 + ], + [ + "ADD", + 9, + 11, + -1 + ], + [ + "ADD", + 8, + 6, + 1 + ], + [ + "ADD", + 7, + 9, + -1 + ], + [ + "ADD", + 6, + 4, + 1 + ], + [ + "ADD", + 5, + 7, + -1 + ], + [ + "ADD", + 4, + 2, + 1 + ], + [ + "ADD", + 3, + 5, + -1 + ], + [ + "ADD", + 2, + 0, + 1 + ], + [ + "ADD", + 1, + 3, + -1 + ], + [ + "SIGNED_SWAP", + 0, + 1 + ], + [ + "SIGNED_SWAP", + 2, + 3 + ], + [ + "SIGNED_SWAP", + 4, + 5 + ], + [ + "SIGNED_SWAP", + 6, + 7 + ], + [ + "SIGNED_SWAP", + 8, + 9 + ], + [ + "SIGNED_SWAP", + 10, + 11 + ], + [ + "SIGNED_SWAP", + 12, + 13 + ], + [ + "SIGNED_SWAP", + 14, + 15 + ], + [ + "SIGNED_SWAP", + 16, + 17 + ], + [ + "SIGNED_SWAP", + 18, + 19 + ], + [ + "SIGNED_SWAP", + 20, + 21 + ], + [ + "SIGNED_SWAP", + 22, + 23 + ], + [ + "SIGNED_SWAP", + 24, + 25 + ], + [ + "SIGNED_SWAP", + 26, + 27 + ], + [ + "SIGNED_SWAP", + 28, + 29 + ], + [ + "SIGNED_SWAP", + 30, + 31 + ] + ], + "prefix_pairs": 7 +} diff --git a/research/joint-helper-lattice/DISCOVERY.json b/research/joint-helper-lattice/DISCOVERY.json new file mode 100644 index 0000000000..53f7d1028f --- /dev/null +++ b/research/joint-helper-lattice/DISCOVERY.json @@ -0,0 +1,10886 @@ +{ + "changes": [ + { + "new": [ + 51 + ], + "old": [], + "ordinal": 449, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 451, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 453, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 455, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 482, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 483, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 502, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 503, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 504, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 525, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 526, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 527, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 548, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 549, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 550, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 551, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 578, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 580, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 594, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 595, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 598, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 599, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 600, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 601, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 606, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 607, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 608, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 609, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 614, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 615, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 616, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 617, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 622, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 623, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 624, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 625, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 626, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 627, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 627, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 628, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 629, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 630, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 631, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 632, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 633, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 1997, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2002, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2151, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2156, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2305, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2310, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4007, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4008, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4013, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4014, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 9, + 17, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 4019, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 4025, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 8, + 16, + 33, + 65, + 128, + 256 + ], + "old": [ + 4, + 10, + 16, + 35, + 65, + 128, + 256 + ], + "ordinal": 4043, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "old": [ + 1, + 14, + 16, + 34, + 68, + 128, + 256 + ], + "ordinal": 4049, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 5, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 6, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 7, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 8, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 9, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 10, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 17, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 18, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 21, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 22, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 25, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 26, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 29, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 30, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 33, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 34, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 37, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 38, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 41, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 42, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 44, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 45, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 47, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 49, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 50, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 97, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 98, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 99, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 100, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 101, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 102, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 103, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 104, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 105, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 106, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 107, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 108, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 109, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 110, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 111, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 112, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 113, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 114, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 135, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 136, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 137, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 138, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 139, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 140, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 141, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 142, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 143, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 144, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 145, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 146, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 147, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 148, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 149, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 150, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 151, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 152, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 153, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 154, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 171, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 172, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 173, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 174, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 175, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 176, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 177, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 178, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 179, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 180, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 181, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 182, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 183, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 184, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 185, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 186, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 199, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 200, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 201, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 202, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 203, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 204, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 205, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 206, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 207, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 208, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 209, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 210, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 211, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 212, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 213, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 214, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 234, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 235, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 236, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 237, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 238, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 239, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 240, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 241, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 242, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 243, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 244, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 245, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 246, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 247, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 248, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 249, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 80, + 144, + 256 + ], + "old": [ + 45, + 80, + 144, + 256 + ], + "ordinal": 332, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 208, + 336 + ], + "old": [ + 5, + 11, + 35, + 208, + 336 + ], + "ordinal": 335, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 400 + ], + "old": [ + 5, + 11, + 35, + 80, + 400 + ], + "ordinal": 336, + "phase": "B" + }, + { + "new": [ + 7, + 16, + 42, + 64, + 128, + 256 + ], + "old": [ + 16, + 45, + 64, + 128, + 256 + ], + "ordinal": 337, + "phase": "B" + }, + { + "new": [ + 7, + 9, + 16, + 35, + 64, + 128, + 256 + ], + "old": [ + 14, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 338, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 16, + 33, + 192, + 320 + ], + "old": [ + 5, + 11, + 16, + 35, + 192, + 320 + ], + "ordinal": 339, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 128, + 272 + ], + "old": [ + 5, + 11, + 35, + 80, + 128, + 272 + ], + "ordinal": 340, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 144, + 256 + ], + "old": [ + 5, + 11, + 35, + 80, + 144, + 256 + ], + "ordinal": 341, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 137, + 286 + ], + "old": [ + 25, + 45, + 73, + 137, + 263 + ], + "ordinal": 353, + "phase": "B" + }, + { + "new": [ + 45, + 87, + 137, + 265 + ], + "old": [ + 25, + 45, + 78, + 137, + 265 + ], + "ordinal": 355, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 146, + 261 + ], + "old": [ + 2, + 45, + 80, + 144, + 261 + ], + "ordinal": 374, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 194, + 265 + ], + "old": [ + 5, + 40, + 82, + 144, + 265 + ], + "ordinal": 376, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 388, + "phase": "B" + }, + { + "new": [ + 45, + 400 + ], + "old": [ + 45, + 76, + 400 + ], + "ordinal": 389, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 400 + ], + "old": [ + 9, + 36, + 69, + 400 + ], + "ordinal": 394, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 146, + 272 + ], + "old": [ + 9, + 36, + 69, + 146, + 272 + ], + "ordinal": 397, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 130, + 274 + ], + "old": [ + 9, + 36, + 69, + 130, + 274 + ], + "ordinal": 398, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 144, + 274 + ], + "old": [ + 5, + 40, + 73, + 144, + 274 + ], + "ordinal": 399, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 410, + "phase": "B" + }, + { + "new": [ + 45, + 475 + ], + "old": [ + 45, + 76, + 407 + ], + "ordinal": 411, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 469 + ], + "old": [ + 14, + 35, + 66, + 407 + ], + "ordinal": 416, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 130, + 341 + ], + "old": [ + 14, + 35, + 66, + 130, + 279 + ], + "ordinal": 419, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 215, + 258 + ], + "old": [ + 14, + 35, + 66, + 149, + 258 + ], + "ordinal": 420, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 199, + 268 + ], + "old": [ + 28, + 45, + 76, + 139, + 268 + ], + "ordinal": 421, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 217, + 256 + ], + "old": [ + 5, + 40, + 219, + 256 + ], + "ordinal": 440, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 393 + ], + "old": [ + 21, + 45, + 69, + 398 + ], + "ordinal": 441, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 66, + 130, + 258 + ], + "old": [ + 45, + 69, + 133, + 261 + ], + "ordinal": 442, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 130, + 258 + ], + "old": [ + 21, + 45, + 69, + 133, + 261 + ], + "ordinal": 443, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 393 + ], + "old": [ + 5, + 16, + 40, + 64, + 395 + ], + "ordinal": 444, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 89, + 128, + 256 + ], + "old": [ + 5, + 40, + 91, + 128, + 256 + ], + "ordinal": 445, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 25, + 40, + 64, + 128, + 256 + ], + "old": [ + 5, + 27, + 40, + 64, + 128, + 256 + ], + "ordinal": 446, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 33, + 66, + 130, + 258 + ], + "old": [ + 11, + 21, + 38, + 69, + 133, + 261 + ], + "ordinal": 447, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 128, + 265 + ], + "old": [ + 5, + 16, + 40, + 64, + 128, + 267 + ], + "ordinal": 448, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 137, + 256 + ], + "old": [ + 5, + 16, + 40, + 64, + 139, + 256 + ], + "ordinal": 449, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 194, + 258 + ], + "old": [ + 5, + 25, + 40, + 194, + 258 + ], + "ordinal": 461, + "phase": "B" + }, + { + "new": [ + 21, + 45, + 66, + 386 + ], + "old": [ + 12, + 21, + 33, + 66, + 386 + ], + "ordinal": 462, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 137, + 336 + ], + "old": [ + 5, + 40, + 82, + 137, + 258 + ], + "ordinal": 483, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 137, + 274 + ], + "old": [ + 2, + 45, + 80, + 137, + 272 + ], + "ordinal": 485, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 387 + ], + "old": [ + 4, + 17, + 34, + 64, + 395 + ], + "ordinal": 530, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 388 + ], + "old": [ + 11, + 17, + 34, + 68, + 388 + ], + "ordinal": 532, + "phase": "B" + }, + { + "new": [ + 12, + 21, + 38, + 71, + 132, + 260 + ], + "old": [ + 21, + 38, + 75, + 132, + 260 + ], + "ordinal": 556, + "phase": "B" + }, + { + "new": [ + 11, + 18, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 51, + 64, + 132, + 260 + ], + "ordinal": 558, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 385 + ], + "old": [ + 10, + 20, + 38, + 65, + 385 + ], + "ordinal": 583, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 390 + ], + "old": [ + 1, + 10, + 20, + 64, + 422 + ], + "ordinal": 585, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 38, + 64, + 129, + 257 + ], + "old": [ + 30, + 38, + 64, + 129, + 257 + ], + "ordinal": 608, + "phase": "B" + }, + { + "new": [ + 11, + 21, + 33, + 71, + 129, + 257 + ], + "old": [ + 11, + 21, + 102, + 129, + 257 + ], + "ordinal": 610, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 394 + ], + "old": [ + 6, + 24, + 32, + 64, + 395 + ], + "ordinal": 632, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 416 + ], + "old": [ + 6, + 11, + 19, + 96, + 416 + ], + "ordinal": 634, + "phase": "B" + }, + { + "new": [ + 7, + 25, + 33, + 75, + 129, + 257 + ], + "old": [ + 30, + 38, + 75, + 134, + 262 + ], + "ordinal": 658, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 64, + 160, + 288 + ], + "old": [ + 11, + 21, + 64, + 160, + 288 + ], + "ordinal": 660, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [ + 3, + 48, + 72, + 413 + ], + "ordinal": 685, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 392 + ], + "old": [ + 3, + 21, + 37, + 72, + 392 + ], + "ordinal": 687, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 401 + ], + "old": [ + 3, + 8, + 48, + 64, + 405 + ], + "ordinal": 689, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 33, + 64, + 136, + 264 + ], + "old": [ + 21, + 38, + 64, + 136, + 264 + ], + "ordinal": 711, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 51, + 82, + 131, + 259 + ], + "old": [ + 11, + 51, + 85, + 131, + 259 + ], + "ordinal": 713, + "phase": "B" + }, + { + "new": [ + 4, + 51, + 82, + 136, + 264 + ], + "old": [ + 4, + 51, + 136, + 264 + ], + "ordinal": 759, + "phase": "B" + }, + { + "new": [ + 30, + 32, + 76, + 129, + 257 + ], + "old": [ + 30, + 32, + 129, + 257 + ], + "ordinal": 769, + "phase": "B" + }, + { + "new": [ + 13, + 19, + 33, + 455 + ], + "old": [ + 13, + 19, + 33, + 65, + 390 + ], + "ordinal": 770, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 70, + 129, + 257 + ], + "old": [ + 30, + 32, + 70, + 129, + 257 + ], + "ordinal": 779, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 129, + 262 + ], + "old": [ + 10, + 20, + 65, + 161, + 262 + ], + "ordinal": 784, + "phase": "B" + }, + { + "new": [ + 15, + 17, + 37, + 67, + 129, + 257 + ], + "old": [ + 30, + 37, + 67, + 129, + 257 + ], + "ordinal": 840, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 34, + 68, + 129, + 257 + ], + "old": [ + 8, + 22, + 102, + 129, + 257 + ], + "ordinal": 841, + "phase": "B" + }, + { + "new": [ + 2, + 28, + 40, + 76, + 129, + 257 + ], + "old": [ + 2, + 28, + 100, + 129, + 257 + ], + "ordinal": 842, + "phase": "B" + }, + { + "new": [ + 5, + 27, + 42, + 73, + 129, + 257 + ], + "old": [ + 30, + 47, + 73, + 129, + 257 + ], + "ordinal": 843, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 848, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 849, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 850, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 851, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 872, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 873, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 874, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 875, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 880, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 881, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 882, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 883, + "phase": "B" + }, + { + "new": [], + "old": [ + 2, + 5, + 40, + 80, + 409 + ], + "ordinal": 928, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 949, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 951, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 1052, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 1053, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 1054, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 1055, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 1101, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 1102, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 1103, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 1104, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 1121, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 1122, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 1123, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 1124, + "phase": "B" + }, + { + "new": [ + 3, + 12, + 21, + 37, + 68, + 132, + 260 + ], + "old": [ + 15, + 21, + 38, + 68, + 132, + 260 + ], + "ordinal": 1185, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 67, + 128, + 256 + ], + "old": [ + 4, + 17, + 34, + 75, + 128, + 256 + ], + "ordinal": 1186, + "phase": "B" + }, + { + "new": [ + 4, + 11, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 51, + 64, + 128, + 256 + ], + "ordinal": 1187, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 17, + 34, + 64, + 132, + 260 + ], + "ordinal": 1188, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 128, + 259 + ], + "old": [ + 4, + 17, + 34, + 64, + 128, + 267 + ], + "ordinal": 1194, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 132, + 256 + ], + "old": [ + 11, + 17, + 34, + 68, + 132, + 256 + ], + "ordinal": 1196, + "phase": "B" + }, + { + "new": [ + 1, + 12, + 18, + 38, + 64, + 128, + 256 + ], + "old": [ + 1, + 30, + 38, + 64, + 128, + 256 + ], + "ordinal": 1201, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 64, + 129, + 257 + ], + "old": [ + 10, + 20, + 38, + 64, + 129, + 257 + ], + "ordinal": 1202, + "phase": "B" + }, + { + "new": [ + 6, + 11, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 11, + 21, + 39, + 65, + 129, + 257 + ], + "ordinal": 1203, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 102, + 128, + 256 + ], + "ordinal": 1204, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 30, + 32, + 70, + 128, + 256 + ], + "ordinal": 1205, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 129, + 256 + ], + "old": [ + 10, + 20, + 38, + 65, + 129, + 256 + ], + "ordinal": 1210, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 1, + 10, + 20, + 64, + 128, + 294 + ], + "ordinal": 1212, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 10, + 20, + 33, + 65, + 128, + 262 + ], + "ordinal": 1213, + "phase": "B" + }, + { + "new": [ + 7, + 10, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 13, + 19, + 38, + 70, + 134, + 262 + ], + "ordinal": 1217, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 74, + 128, + 256 + ], + "old": [ + 6, + 24, + 32, + 75, + 128, + 256 + ], + "ordinal": 1218, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 11, + 21, + 32, + 64, + 128, + 256 + ], + "ordinal": 1219, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 6, + 11, + 19, + 64, + 160, + 288 + ], + "ordinal": 1220, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 1, + 12, + 18, + 70, + 160, + 288 + ], + "ordinal": 1221, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 128, + 266 + ], + "old": [ + 6, + 24, + 32, + 64, + 128, + 267 + ], + "ordinal": 1226, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 11, + 19, + 96, + 160, + 256 + ], + "ordinal": 1228, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 10, + 18, + 96, + 161, + 256 + ], + "ordinal": 1229, + "phase": "B" + }, + { + "new": [ + 7, + 8, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 8, + 21, + 38, + 64, + 128, + 256 + ], + "ordinal": 1233, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 64, + 136, + 264 + ], + "old": [ + 3, + 21, + 37, + 64, + 136, + 264 + ], + "ordinal": 1234, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 17, + 34, + 67, + 131, + 259 + ], + "old": [ + 11, + 22, + 37, + 67, + 131, + 259 + ], + "ordinal": 1235, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 81, + 128, + 256 + ], + "old": [ + 3, + 8, + 48, + 85, + 128, + 256 + ], + "ordinal": 1236, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 136, + 256 + ], + "old": [ + 3, + 21, + 37, + 72, + 136, + 256 + ], + "ordinal": 1242, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 128, + 273 + ], + "old": [ + 3, + 8, + 48, + 64, + 128, + 277 + ], + "ordinal": 1244, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1417, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1418, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1433, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1434, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1437, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1438, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1445, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1446, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 0, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 1, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 2, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 3, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 4, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 5, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 6, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 7, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 8, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 9, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 10, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 11, + "phase": "cleanup_tail" + }, + { + "new": [ + 2, + 5, + 24, + 40, + 72, + 385 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 12, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 20, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 21, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 22, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 23, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 24, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 25, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 26, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 27, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 28, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 29, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 30, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 31, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 32, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 33, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 34, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 35, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 36, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 37, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 38, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 39, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 47, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 48, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 49, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 50, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 51, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 52, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 55, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 56, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 60, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 61, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 62, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 63, + "phase": "cleanup_tail" + }, + { + "new": [ + 3, + 12, + 17, + 33, + 64, + 388 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 67, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 73, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 74, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 75, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 76, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 85, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 88, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 94, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 95, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 96, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 97, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 98, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 99, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 100, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 101, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 102, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 103, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 104, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 105, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 106, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 107, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 108, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 109, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 110, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 111, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 116, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 117, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 121, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 122, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 123, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 124, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 125, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 126, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 127, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 128, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 129, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 130, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 131, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 132, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 133, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 134, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 135, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 136, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 137, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 138, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 139, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 140, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 141, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 142, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 143, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 144, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 145, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 146, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 147, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 148, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 149, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 150, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 151, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 152, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 153, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 154, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 155, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 156, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 157, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 158, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 159, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 160, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 161, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 162, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 163, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 164, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 165, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 166, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 167, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 168, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 169, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 170, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 171, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 172, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 173, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 174, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 175, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 176, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 177, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 178, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 179, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 180, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 181, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 182, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 183, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 188, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 189, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 191, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 192, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 193, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 194, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 195, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 196, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 197, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 198, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 199, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 200, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 201, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 202, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 204, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 205, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 206, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 207, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 208, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 209, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 226, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 228, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 230, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 249, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 251, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 265, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 267, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 299, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 304, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 320, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 331, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 363, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 395, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 408, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 412, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 424, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 428, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 448, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 449, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 450, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 451, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 452, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 453, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 454, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 455, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 482, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 483, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 496, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 497, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 503, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 504, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 507, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 508, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 526, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 527, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 550, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 551, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 566, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 567, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 568, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 569, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 574, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 575, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 576, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 577, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 580, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 582, + "phase": "exit" + } + ], + "log": [ + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.001075597945600748, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006404789164662361, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006386309396475554, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005889208987355232, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000636169919744134, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006324949208647013, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.01074653910472989, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006191260181367397, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005904210265725851, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005857199430465698, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005849860608577728, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006328618619590998, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006294939666986465, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006302008405327797, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005877329967916012, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000590289942920208, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006303780246526003, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006298108492046595, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006195418536663055, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006841688882559538, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006465218029916286, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006277388893067837, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005882920231670141, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006315950304269791, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006366858724504709, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005855481140315533, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005937719251960516, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006369180046021938, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006377371028065681, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586268026381731, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006332618650048971, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006257679779082537, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005849250592291355, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005888910964131355, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005945321172475815, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005879260133951902, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005923090502619743, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006292159669101238, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005877669900655746, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000592509051784873, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005896689835935831, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005870978347957134, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006910338997840881, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005820540245622396, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006245570257306099, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005984250456094742, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006365531589835882, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006284690462052822, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005876009818166494, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006361349951475859, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005852370522916317, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006305361166596413, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005846978165209293, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006745990831404924, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005877090152353048, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006306229624897242, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006269770674407482, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000637667952105403, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006279710214585066, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005855760537087917, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006291440222412348, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005854519549757242, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006271519232541323, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005840531084686518, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006309140007942915, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005870680324733257, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006304038688540459, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005886279977858067, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000638019060716033, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006365550216287374, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005845869891345501, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006315300706773996, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586286187171936, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005884871352463961, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006310341414064169, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005902270786464214, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.002707120031118393, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006361750420182943, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005890568718314171, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005862549878656864, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006373829673975706, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005868400912731886, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586383044719696, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005930899642407894, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005855520721524954, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006308129522949457, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006310890894383192, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005876431241631508, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006608550902456045, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006281349342316389, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005921840202063322, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005838889628648758, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007187989540398121, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005906580481678247, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005960490088909864, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005959039553999901, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005850319284945726, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005865979474037886, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006297028157860041, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005901618860661983, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005843169055879116, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005854018963873386, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005893418565392494, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005946510937064886, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006296269129961729, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005865739658474922, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586255919188261, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005932447966188192, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005939060356467962, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005937861278653145, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000588906928896904, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005843418184667826, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005870410241186619, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006217740010470152, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006238999776542187, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006359750404953957, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006392451468855143, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000669943168759346, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006323710549622774, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006138479802757502, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006138591561466455, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006473229732364416, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007065420504659414, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007806401699781418, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007903361693024635, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007443451322615147, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007032470311969519, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000755043001845479, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000780660891905427, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007481130305677652, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0008334990125149488, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007098079659044743, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006818929687142372, + "status": 0, + "variables": 2 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0021314399782568216, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.001980497967451811, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019613991025835276, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.001956850988790393, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019325779285281897, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019336049444973469, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019299481064081192, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.001986332004889846, + "status": 0, + "variables": 374 + }, + { + "best": 13.129143554949362, + "bound": 13.129143554949362, + "constraints": 6, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 13.129143554949362, + "seconds": 0.0007041699718683958, + "status": 0, + "variables": 7 + }, + { + "best": 13.129143554949362, + "bound": 13.129143554949362, + "constraints": 6, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 13.129143554949362, + "seconds": 0.0006857099942862988, + "status": 0, + "variables": 7 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.6408980239648372, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.518841665936634, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5807887772098184, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5805281768552959, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5855261508841068, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.6540732628200203, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5800754020456225, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 378, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.007595666917040944, + "status": 0, + "variables": 817 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5755825641099364, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 378, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.00785870710387826, + "status": 0, + "variables": 817 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5494221800472587, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5762166669592261, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5391419599764049, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5634573090355843, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5678934010211378, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5686389121692628, + "status": 0, + "variables": 6517 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 6, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 0.0, + "seconds": 0.0007262879516929388, + "status": 0, + "variables": 7 + }, + { + "best": 15.034699473516357, + "bound": 15.034699473516358, + "constraints": 11, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 15.034699473516357, + "seconds": 0.0009872689843177795, + "status": 0, + "variables": 13 + }, + { + "best": 15.034699473516357, + "bound": 15.034699473516358, + "constraints": 11, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 15.034699473516357, + "seconds": 0.0009186109527945518, + "status": 0, + "variables": 13 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1127, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 5.53365780699012, + "seconds": 0.5781218349002302, + "status": 0, + "variables": 6960 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1127, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 5.53365780699012, + "seconds": 0.5941225439310074, + "status": 0, + "variables": 6960 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008034992963075638, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008022414986044168, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.007987846154719591, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008007899858057499, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.06002827896736562, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008030876982957125, + "status": 0, + "variables": 312 + }, + { + "best": -13.848534080955442, + "bound": -13.848534080955442, + "constraints": 104, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 16, + "previous": -13.848534080955442, + "seconds": 0.0012454588431864977, + "status": 0, + "variables": 98 + }, + { + "best": 72.27751861391584, + "bound": 72.27751861391584, + "constraints": 21559, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1631, + "previous": 159.47331231171188, + "seconds": 1.9969544738996774, + "status": 0, + "variables": 34903 + } + ], + "saving": 0.003001235, + "source": "322e0ec764aa7ef7801383feb1f656e460dd8bed" +} diff --git a/research/joint-helper-lattice/FRONTIER.json b/research/joint-helper-lattice/FRONTIER.json new file mode 100644 index 0000000000..7496ef6926 --- /dev/null +++ b/research/joint-helper-lattice/FRONTIER.json @@ -0,0 +1,187 @@ +{ + "checked_at": "2026-10-21T23:05:41.906476+00:00", + "purpose": "Refresh before publishing the 0.00302015 candidate; no higher kappa found among these recent open PRs.", + "coverage": "Latest 30 open PRs sorted by update; earlier research checkpoints separately covered the active kappa chain.", + "pull_requests": [ + { + "number": 4459, + "title": "research: #4436 boundary exits \u2014 exact mirror identity, rigorous share bound 0.321, and a correction (leaf exits dominate)", + "head": "488a75a9e95e14448b6301719249f876f3999931", + "updated_at": "2026-10-21T23:05:07Z" + }, + { + "number": 4463, + "title": "Add a source-bound baseline for the selected productive-helper schema", + "head": "108509ac7a441617e3783fbd991bdf249fd23e64", + "updated_at": "2026-10-21T22:58:53Z" + }, + { + "number": 4462, + "title": "Transfer the \u03b4 halo exponents 11, 24, 26, 26, 6 across cells; robust to the 'rounded' reading (no new \u03ba)", + "head": "c8fd7f81696d5b8b838c996cc384e76ab378dae3", + "updated_at": "2026-10-21T22:57:39Z" + }, + { + "number": 4460, + "title": "Independently check #4451/#4452: within-cell halo exponents 11, 24, 26, 26, 6 under delta (no new \u03ba)", + "head": "6aaf48105c2100d0dcf47b5b1ff5a85c37ddef52", + "updated_at": "2026-10-21T22:52:22Z" + }, + { + "number": 4457, + "title": "Independently execute #4440's controllers and #4447's native word on lifted operators and physical frames; check #4359's delayed cover (no new \u03ba)", + "head": "dd40f88a4d45a0ae2487eb24f935516f749cefef", + "updated_at": "2026-10-21T22:44:27Z" + }, + { + "number": 4456, + "title": "Independently check #4436's direct overlapping flow: all 9 recorded flows reproduced, exact potential identity to rank 1000, L(1000) matches (no new \u03ba)", + "head": "bbef80cd12c66afa31cb347c7393fafc873a0c88", + "updated_at": "2026-10-21T22:42:02Z" + }, + { + "number": 4455, + "title": "Independently check the p17 chain #4440, #4441, #4446, #4447, #4453 (kappa 0.00296..0.0030012): invoices, strictification, roots and compiler ranks hold (no new \u03ba)", + "head": "e02ca27f9a30b9aeb5e2eb701bf2eb0a27d4e193", + "updated_at": "2026-10-21T22:28:06Z" + }, + { + "number": 4454, + "title": "Extend the rank dual to four planes: COPY floor 16 over every field on 361,706 of 367,290 plane quadruples; 5,584 open (no new \u03ba)", + "head": "6eea96234209fcf9cb3901d9c298d81ae3b3d808", + "updated_at": "2026-10-21T22:19:14Z" + }, + { + "number": 4453, + "title": "Conditional \u03ba = 0.00300120 (71.9\u00d7 smaller uniform-rank exponent)", + "head": "de6869e2e4d9c6f630bac5de4a919d99a2cb884b", + "updated_at": "2026-10-21T21:38:35Z" + }, + { + "number": 4452, + "title": "Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new \u03ba)", + "head": "af68f5973a572305af174b3c49c440592172134d", + "updated_at": "2026-10-21T21:36:09Z" + }, + { + "number": 4451, + "title": "The published 4\u03b7 weight error meets the 1/(16p^2) ratio budget (no new \u03ba)", + "head": "be243a2818f0de3421c118dd21601aafe8e839dd", + "updated_at": "2026-10-21T21:21:26Z" + }, + { + "number": 4448, + "title": "Independently reconstruct PR4441 helper tariffs and complete p17 invoice", + "head": "6d535abed7b60d4a99dc54903011a72ec367e901", + "updated_at": "2026-10-21T21:21:23Z" + }, + { + "number": 4450, + "title": "Audit THREE-base supplier billing from native events (no new kappa)", + "head": "e8305f07db188d6fa0be1c91ae77cc2414ea029d", + "updated_at": "2026-10-21T21:19:46Z" + }, + { + "number": 4449, + "title": "Prove the downward rounding contract for across-cell Gaussian entries", + "head": "1fb77b377f570ca84a89a465b2ee4ce8674b7159", + "updated_at": "2026-10-21T21:18:04Z" + }, + { + "number": 4447, + "title": "Conditional kappa = 0.00300123 via a missing three-dimensional contact span", + "head": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "updated_at": "2026-10-21T21:14:57Z" + }, + { + "number": 4446, + "title": "Independent retimed p17 certificate: conditional kappa = 0.003001053", + "head": "7d05d73f96c27a9d360011e04af69b23fa903757", + "updated_at": "2026-10-21T21:07:29Z" + }, + { + "number": 4441, + "title": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", + "head": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", + "updated_at": "2026-10-21T20:42:39Z" + }, + { + "number": 4440, + "title": "Conditional \u03ba = 0.00296 via query-thinned productive controllers (+10.18%)", + "head": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", + "updated_at": "2026-10-21T20:14:35Z" + }, + { + "number": 4442, + "title": "Apply the smaller halo exponents across a cell, under the downward reading (no new \u03ba)", + "head": "d079c2b058ebd3d7a9ff424113b095bf61175427", + "updated_at": "2026-10-21T20:11:41Z" + }, + { + "number": 4439, + "title": "Apply the smaller halo exponents inside one cell, with normalizer 6 (no new \u03ba)", + "head": "26af8afbadd7f8feb737d98b47ac9f4b45d35c7a", + "updated_at": "2026-10-21T20:02:46Z" + }, + { + "number": 4438, + "title": "Bound the within-cell column gap by a relative weight error of 1/(16p^2) (no new \u03ba)", + "head": "6157a47bfe169cd9c5f666f85ab8caa929e1174f", + "updated_at": "2026-10-21T19:56:30Z" + }, + { + "number": 4436, + "title": "Bound compiler width by exp(O(N log N)) and route overlapping ranks", + "head": "56003680aee2871773de408e5f01cc5dd46b144c", + "updated_at": "2026-10-21T19:54:23Z" + }, + { + "number": 4437, + "title": "Extend the ideal column majorant across every legal g=2 step (no new \u03ba)", + "head": "7ca94e9762ee33edbfb2e527e7313bc579e463ee", + "updated_at": "2026-10-21T19:49:34Z" + }, + { + "number": 4079, + "title": "Research: seven-source weight-at-most-four connector boundary (L<=18 excluded, 216-call floor) (no new kappa)", + "head": "39a1fd620d1c702b72ab080ec11b090ea9ce98b7", + "updated_at": "2026-10-21T19:46:06Z" + }, + { + "number": 2411, + "title": "[Lean] Link an end-to-end proof of multiplication below n log n", + "head": "ab708c78a6e50b1ba469262c23acffa5f508d6fd", + "updated_at": "2026-10-21T16:05:33Z" + }, + { + "number": 4338, + "title": "Extract optional ordinary B2 bootstrap with canonical-source replay", + "head": "0ac8192bdf6b5217787ffe44c4b1d91732ef6b23", + "updated_at": "2026-10-21T11:03:05Z" + }, + { + "number": 4192, + "title": "Audit uniform Bene\u0161 compiler with charged sequential arena scans", + "head": "519d811cc48693ad9969d6d7994bef3940167005", + "updated_at": "2026-10-20T21:04:42Z" + }, + { + "number": 4187, + "title": "Audit conditional CRT last-K two-slice streaming tariff", + "head": "45fc0750436ae5cc14b95fba81c030a3d7df3412", + "updated_at": "2026-10-20T21:03:38Z" + }, + { + "number": 4110, + "title": "fix(research): repin central-factor-packed sources to the integrated tree (batch952 red streak)", + "head": "2d5da0e018082b8fa140cb5e4a9553bb9b9de283", + "updated_at": "2026-10-20T19:30:44Z" + }, + { + "number": 3143, + "title": "Certify precision-40 \u03ba above PR #3133", + "head": "dcfaf1d1a7cfebaab22b95776a36a543bc684d50", + "updated_at": "2026-10-20T18:53:54Z" + } + ] +} diff --git a/research/joint-helper-lattice/NATIVE.json.gz b/research/joint-helper-lattice/NATIVE.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..0910f74138decf498e7fc445cc2daff4390169d6 GIT binary patch literal 35042 zcmX6@Wk8eP+a{Ed2I=l@BqSA;4gu-z?uOAJIXVPEq@)|9M#tz-Lb^qIFa~U}cfbF; zZ~O3^^E~I==Q>y1j7d0X|NSs9PkW~`=#?^RJNvZItNa8If-*Ap0S^AG*Ux;)pGR>F z2q?EG6ORA;m&5ybp2=i{mS?ZByl2I*!%$L?b67Pse1CQK7WgIq5Auo8V-s;u&nXG4(jY40(&57KY}x`&1L!0*nEl!_QbU{@CMGVB=mMH z9C7)y)`83ofggjzLy^aoVfS}1m=+QNCXx?@KUKnJkw@_sVaQc2!Nb1Iu&vwjeosRVZ0>i??5O>Fn%Hem6 zeekQjtxW*(wi0;J2fr-#=!4D5Ur`o!%p!*^!h&HtYe&fYu?x9Sh27mf6j0?W<9oK z`^x%|mpi!@$U6Cu&Ay_Mqpe5ywa4SmNOz{+Xs?_#m9$-u*%7TD%hWP!h^%o=f9AtWdwEflh^w@n77M%iL+(KZK?@us>L*PfS>)Z=@*8Q^p#?5f# z*{nt6a5(gO3xL{xS^NGdMC7)=>;XLV-^W;rIWr!vc{Wee~@|nXpMw zy-hi?om{PkJ9vOR5^}$BkJ#*!X^;;?TzbqtyMH?CxCje^9jL@yLSr9!xb^fMTjv5x zNEEF`@thG?wm3)7Dy|MD$Kc^T0OXm6MP9~aF(drA0SUd1KY|@~Ag`8_jxCBC z(mb{Rh|9IL$CIu5(3+s9Z25JzFvQbZ1JQaEH4S5UX_+70buZvA1_@_S(0xCL=Iw)C_e6zNcX8%fnBbZjl(kl#SW~V`?ssvE zjP)*ej4!<(eE~zd$G-ZDf|nezDpopyg%|Oqx>RYaC1qcx1S+LguCB28K=H2^FG_0e zPKTG(FREv&?z@jymp_NH_p@>ef%3Y!o~{;8;sQQKNyam;pqmYnNrOrXl2|;P#_tJo zy_*xPtn;Wi;!dbEud*@e>Itotodt)K-SDEuGN~Dt${(^Kz60}nz1wqH8qywC-S59H zl3aw)nFomMF5cd)rX-Q?Py)Z2w|Ltn15z7`SLZllaIN0v5!ZuHe;R{NSA~+tPu*(3 zr(&L3{&aP=-14SDj?FS?B#j2Pb-H2K)4LrD1Ia`{#&eN~%#2%7kbqWCV1>T)l+ns{DW`?Sdr20>{>SlkQiA2g^ zrO|r2%sY_c?pw@yG(+U?-AcVPDy^B(HIwn--u8 zCpQ11&Pu(>CXyf%f9uZF+;Im9(qf@(>Dudg7q=f!26J<2`)tExmQ_en!;Ze8*8ITU zw{_n_i>nLO?WtH^*p9T8OJy(gXM?1E`W_;79Hup55iU!8coeWPF$tj&%-Yt|X} zb+?KKkVyOJ@it$(z2iOK=^2*6W4*Tc$x{L4L>i9PO+SB-U_tXRdn*t2kO6jB>qqQu zEYDz|6(-VQ7@*kVGURlA5;ghHgpU@jiR*KAxfk=N)MvKF*#qCAwLB*vQhd$#IzbH- zTSBr#prdqg$r5$0f>{HsXs%4qhr20lai2lXI1#qN+=O?5R7J3fz@|X*nuaAoR?A5) zfT{P3J=gVk?x>oKAkXX(qua6Dh@;?7W~sG7?{j~h<$QX|Ikl4kVVZV^MIg|agjknn z;~}EDM5d&}&#uzUKVJyT(BbY{6Z&9n@SDj_&bR1Cr;_K5-WUZgVM=P&6U9}D5 zZ3B3&1!SN%EYN?RSgi{$OKi)q%`8E{I4kIi@K`(#|7CdN8ok6l ze&}MvW0Yjf*xJS>^RXB0c7(Y4U#IZcFbN}d3KL*IoZ(QJEy<1kg4+t;={zMTV7W8c zsgY~o%Y4TjcRJSOkGzYP#E_hG^bmu9%TrCn6dfqm@(zo8I3sgxjZiFHx}mcF-yn>_AwR~*|1hjnVj({aSl zo0Bb<8Y>d=j!6u=a&$YedMzHRzISgB1-s$BZ>g!SqTh-;(Cz1=vh9}9-VWPUzTeMCChiowB@+(tMV7LJeD?dB) zZ@b%Z4R+C5RZP`a#<)I4j2`ltPR)C-h=RA%UG#-%b(9HHt9X>-bl$cX-5V0+{cf+% zUQBUg%)0C#cZBgb710tO8Jnx1Rs+W2&6cjRpSs4|CpOMTr zZ$nq5_rdO?qLeiIk}L|~ZEA^FZ-_BIZPrI;sVWwTVYkOoSq|eTOSg+j)<{j*{3@w|TdtRLvP;2MC&WiUJ!0Q)^Z@aY}3s~eZEee+&%4ySS=Ea9pTf2GA z=7x^2ZV*LI^qpL64?0>Hf@Dlwt;1_#JzID;tcqfwX`qh+_Ao+YH zAi~?7ZLENmI(>UhKX>~{4EOwS573&o80iUYb0dM_ocDHO1Yl{lOShBh6LzXKONdcX z*w&X1t)>tyiy0&ld7Xs>6X~zB3E|3MNAly(D`RvNnsxi1cjDmVobDqOFr>{%E|PFJ z0Vk%zt98)`q#K6FtRvr)?A%@4yu# zNe7P-Pmh`K!Kd#S*ZhY(p`8loBHo05iF9B$*b_c{Wr!gIQ zPB)yKX=Q%THD6knb7jf9@jzAv)dlFaB#cjf4< zd@sT_z{-9X!5ZY3nuiBovPJzd9b7HhT$@-sNIxP#JuYYpZ zdTyy;?r?#f_>@FBo{vE&-RN5qH1coNUp17*_TABT9(Pjc>9xu8gDSQ2tLBOY?;qJp zL@R@orz0xk&jWuPl$|AN4|pyF|( zxxGq~UE^S8w5o_(UwzXuEdzClZ<+dy*oyUgvc=7A3QHll4!S;wf4MPpTv~dSXS7jh z;><{9wa_ygNk%L zAqtN0A6ycuemg}Jb)QL!-i>$8U(iY>?({Wl!ZT$vHIMfaeSobGuit!@Gex;_f^|#?zs$ zXXbyi53I-Iol7axX{sN}6%VIv&%9g*;N@>pvwv*LkPcJB^>hKVn^{-nCtU-}EqO1PoFVT5q*<@w{PUgdU*8!vcET~dBtv*`mQ(sAMkW~08 z70TJmqkBoX-9=i%UH`MC(l6rZ?+{w8*5OlPc<8>caZJ&vWN!_2d-O|NDy4M-ee6Ji z_gBn>_5fTCOzG!TU(71M6tX4b?m1cFC%+;c-LP~Omyu#kCfVSB2ZQMN=H|Z(5DK)U zJc{gMz5FejA0*=7V;;nfB4ZJtylBwDU!y{Y#XY=X&GIn+5_v$<=UEM483;QtbU=fc zY`8Sy=OhMQl;JCRoxbUd(o(9lwUV-~ZF6jjb+dP=+(&KKh0z0rS0rusk9o7du|IG* z)IW~2OCNd`h=A&~@e_)SsTn1ffmi(|MJE!Vq#8G!JQQ=h(AXJ)ck57*{4uG*JM%Rr zgC&zsk>?E?MMl}Z!w?&*v3yw57dkl@kBcgoZ;v`YaceL}*VPYfy<24jG`y! zotSh0B~bF!Z%s2l4nmlT5Ob2HnZv?fq0DqjyLpo5(KZUfV?UGmdKHIM)Gz?+3G^fHsu;jGke6vq(7%isMidckYy)tbF<0QFKS(4qJc* zZNLR^?D;H5)R9cC(nGHMWWg$c@WPE!J5iqEMB<3)$ZYV1ByZyT7Kgn{7xtOE%e&Oj z?~u-h1qz-fW3X0Y!86&H);kP=EcwdkDYi;%Fs0@`k_=|tBBh+|9gd!c4j!)GGg5&U z<8T9pOIdfciXN@1UqQtutnzc;cbK6a-YK!ctIeAqPO|UT`PKIUWGII7NnxG64W7f) zJ}I0}JRGsE=~Xl77XHVwyZ{JkT6QHA<7z50+wt|$*#tIXZ(1+TfTqr$OMcw>fk~*i zX;kG_*BUrACaGP3%dC#0^(9pWhM_zg|LAa(5-zvUI}q8c&4XeJt1tR4$y- z@l`J0;krvt>K*{lUle`@N7+3~hs9rltk$|E##3I&cDXzzA3XePX>;211P;-{lnl@< zGE?P1S?lkFNY;PpSU2Gm;hgidb1Dk4G#Q9z(oMsrf268_wAh>Y|7g6v-gtFsmfDkh zqI`Nan8MwNYl(69!%79?&Nfn3B!VQ!?1M8)f_?9fk}!oycMlKRMl-#u4_&P{O$?K%x0H?)2$+S&xR6uAq<8nZcK=Ct#arwsAM!eo&SzbEWZ z>yxv1Uk9>x{;1RGp38uL7mfI{(_D^_Vp$8^HZyYGj!ePj_+{WO7_w|BU&v3cnwt=? zKl{%^PWMUKI^zzZqpoHGqgQclH}zH}WsQ=?|5^=*<$p0zKUc>-o$c~6?l3f0yzhFM z3(cv%rrAK!%&}#fCAX%WU!v~giq4wix~n2bCOA5W2E4xqS2?sovF(n?cY!}6mYaVa z*^sxexA_?~)l1c%0o0$VTr|4H9zv4+XcM6x~DL0Zt3udZUP?Ag-L9iY-u+A!!pXeAl0K7M6m{W(ayfq1}EYy6aMtaf}v9oxg_As*4rSyAaE=N4Y0lsLK6$ z{P%;%oh25$MwCi>)hehnRV0+$83I4n+B4kR6LiaFG&ijo`=Ayv{kw%-;wu()Wgnf! zUHMZ_?gOtBIt09K?4*3y?m4knw0EK(^rMV3gSqt01Lj0el9%DB!MhNzEXLH!)MhVj z2EBv$g+yQ8&#(c^#kXOmM+J@?U*g~UC|)(r@)6F5x`?r6gqE{O9ESDcX?y9t=zlC{ zCO~gR_N?e806uHPIfY9P+1~G(Mrj<6G!&aC}mHBl7w?F{p5n()8faJ}w z%6h5(clD%C-c?zzuqRfh>aCuXq~`y&_68cCIRw^8f9~Ab(;$!^@OzCaF+%vBw`7P)8`Hg+yAQ@cX*8!Z=k(U*H{J=9vi2c5B8R-2!)9((y zc30Z7lcefjSD#Z_D<9ltyS*|m(|>n7kLZm$!}#_7_nXkxE+@YzGV531ZYEL&yyWG{ z@RNJiZwQVw-2JZ(%U^9`wkXCot1m)ym~0-_h|2mJ(!{#k^`s)_A5>;?F=GnS2FN&Z~3XZDJ`OEEz0y!`!S85-14|W9UEKjo6}^7*UPU zn%o~%$ckOeZP$h2iP!>tU4F-_*qU({YJ?tWehS|wRfL@rudTKIqpraw>e4L%mpX(ZsQ7V&9sl7?)Xw4)#*js8T{c3fbtbnYEo8LGiV zHok|kO8xWiGYEfV^7zFrcV9>de^pqZa!Bx2il;>OR#M9H_gVy|y(89@an`WZ(LYkc z5`lC00w6!`h=WIt@=WOTa=ArUro~ zPv!*J9+IWUk)2Yt{wt2O?*{MV=Z+Nt<=>*1++W|U{xGilJ{|%d7~iUfh?-^GnJvvS zx<*aXs#g~Yj`)1ct4o1pz1B?{(!3y@X3?hD&*vFcuU9fYcv!31Jg4CCL=i3VbA{t5 z8znlju^%_)<=91Bz0xgV{7_XpzE8@*<*Lib%cD1N~F{u|; z5eu1+^(klL%vU+Id96nWRu?JA=;UUV32T$ij9MQ~cq8HzNimFO8eE7+vl@p>IgVq{ zA&zqi_Q83nkh?CIjr1Px1Mq~WdvrGNN;!yNlxaLKe@m{3`eK`US5Ho*7_u?N-Jjgd zg$wXPg+FnUy3Ju+OJkLUPm`XwJH#h@Sab3P&0&B8wD|arH+<0NiB&S2!OF)Pr~wRy znxv%|3ndvy$J}~%vNkJY<};wVEk+#4oTjd>6zn2uUwCrFldPz6bR4qR>$gS=+Uq|C zlZ_2u^}iqAX&y+}WA<97&`>@Gd?0pPVbE%3JrNuWmIxJ*v~L+6a-(Q@Q7PiX3CCI< zbIbYv8IN`X2is(ZugWB`$~uTFHX*ZrOopT4OIri}dUev_!^>y3FxCmn$jDxJirF&$ z8mJA>ik7*gI*twkEV6{R9~?F+Rq~N4yJQN?YuXRTh3rp1r#mw`V`=;c(|x|^U0+!; z%#XZuqUMSbwvypaHW82+Tp=Aj7!?}zg}qKYPo-3NG*$xatrJB(c#8kqV^*Lgf>M-E zI&KdP%l?ROm*8T(86VL5UaBL)_GoX{{A}ASw|4;2k+H_7jSOv}AHC*CP1uw2biFF% z&%k{&^Kw0kQcti^5219vxV9o<8^`|qL~9k!d`3^Ww3%TAZkso+H^3uaEm*8=clC?P zeduPuYb1KDQt&=V!mRf|r0ebf&VBFifWKGz_uUw)wW}feD9j5feL6Qetfh?2Dth;= z!9{%?UXUZD#C<`NEA<$aQuean6usul^st2PHu!ht;p6w@KSA5f!xJAf@>$s>^VK^5YzLGI8_M2lH&;G+A` z-A^z*t*M6^tqk{&q<5Z7Il)^{D8!qH+LtmS9x&LRM*wG&s$vT;4859&JqP!-l=+29>B_ve&r@!g^h zqk?lYb?@5BihPCH^4O0z=S?ngXKlSyr=Tw`JzdZDbFEX=(!!p~xtG^sL zSrPZpe>AOje)mOX*N3~_cu~(#el3w^hXOmNTd^`6K{od#CXG_tJP=R*t|6caB17iNs+K`2`Ck{BH*MAaps zrDANZ4yE13|iJ9N{~BCh6a5|$Oi_Se<8HWfZ|unHmV^+&t?*d zeEqcdKZVh8pA57%NN5SB|CkN0HUV(t1XiYmg#cP+Un)veA(1|Hzcb2ewQp)qxxFvXz1q^Hzy+5wo;K7?d@ zG>X7Q=RKujU;}6uP3RXDy15F}=1JA>2_=R0OOL64x#1=mwJk2=^>oVR92$IE$&Y;C zJo6aL6Ov;XrC`kui1iYwc|U_=qa5Jj&a?rTzGsk1EGP)ZktJ;k_bD`nm0xiLkbaPur~wkw1UxeHicLm{CiYA;PrmyJlxJSI^$iD4i5)~CozCc-5m*Va3q z2aQ`Qen=Tl_aXwzQo0u6THndw*EZ%tLOw+QVDi945{N@xrq!?5e2}&zk)Y0UA=5Q> zQShFo+_;M5Z8UsT;i?qwNX${ zN1IwY3eGH_^RVLlKH*;5OgO!IjPTC}O>W+za& zC^{EFv{Yc(gp#O|zS#E)?a3^V*&MMEC6HqW3PXDd%Rqu8{N2CeS+k-X&_RB65Roj{PYOze-xg(eZq4?oJ9+5`>M=G`Yl(_E5<5@i6E zL(ved5A1XLMz}3=*#FUzb6tG4>yNg#0W6{w<1O0zL3Hv6(kg?_^S)nr1*);W<3CqD z7rq8dBFhJ!(=#5`-GwC#uACRqM)%TA)od?ORSn`x z9`an>x*l9{rSQ>2)kwE?0Ap(Kvwb&PMi0nQy;Dnx(zfLm(@S>BPA0R!l1*10L5xnA zmC~A3tIJ!X>K_)2NWH9B!qt?oQEyRhriTEjDtYie!7ag?{QMD@j+e!_hRId#oo-?D zmB@Y4k1f2!0om#zyVyd8yDG=}dz{}4Ye6!hi*{J}IfjCIs-GJM#BZfgm&>~$*;dEdt2Up2BLi-sx+(<(vtFN5Kz>Z&KH>+@9Z<@0H|RU zI+*`3)c^Uky<_i}GDE1S!E3w@%M~N4-h4=XuDH!3DAv~8?qS1L*hmH|iQirT(+EME z)bi=f>jQ;NwTXM4pt`j1*ME_GInVR{UE$}^Q$jble>`N4ogDm&D^tG=ycd%os&h^Y zH#^r*o)%XVD+Q1UzE<1F{zpF3jJ5~mZ4}P;;zT98u4eUKSl8muAjN1wP0hWP&qONv zh7=y)q`FYTMq_bX^D$=bw@{UDJGV9b5+l9grr{Fr%1+lBuznq7XVOHn6Hn}9m%dT$ zp!W}Lkw{X?fyp$8VNEaz;f8#xE#Z$euly7EU;flWDn&!w=`jO-o^X1hX!~PNdUAN+ ztQ>=APjcHmaC35Uprh9R6CIV^p5h}d{O!>5UBF*?-3$CcA_Q-UcU_rbdJ@eSe=;ULqHNnxadt1e2K_INIeCkUW85kwHeU{=&6sy|%~UKtes0)}d{3w* zOK#5Em7Fv!-RH1qAmyINN#{+rlFi6Fnb)kzD1m)Sq=MI6A;}f?9Z{k)r=Mw=bK3iC zTeCv!iKj)gzp`44Sa5=9{(>VHe1QI86KqE-0Ec^0>+HS1`5H=1dw)cpj&%+vEd3~t zrc33r7z6ZnyXW~hIWVUsTf6Zzr^U%;e9v$n-OX{LyRmTX_1y94_d~tBuCRA=4=V7G z4s5#W!uYKsb;vrcNu=(`eU_x#0mvNNzrvAmcYK{7D}v)OwP*V(PLwmPsUnkYze8Rl zOd?NUXvaMNI5IIm%BuL*21Q@vmD4C&ktdY)GJe; zgi00X6jMoG|pZe&RJL zb};dH$aN$`z_?y{RZWKJ(2AT;PYXsz`8HzE+0=}mW$L}8(eH2S@Mfu`GiQ3JeA6b-*E}1WqHOGeRf2jI*NkCB zH`Ag#fA^nBOm=UV9BX^B5>Jt*b+!>elsiB?2(G63@~dfL#i4Hyn}>pz>9Ut}_kY6D zP+Wpdt#iJs`^dhnJ|N(BR-nEE>U47sos2{CRq#*nRk}pq)lMCf$&)OUw;M z$gr~XExC*Jhsmo#Oc>Eh!s>$`AUF7pfw1nsiNIvlrJt+M1*@D9LTxp>57i)3}yWWV}KIvm| zR}!bZ?A+^AeyBH2yuq@YkfdWb;u?R|Jh}I;zEGB6|D=>1ybd zA8{i)?>au0+9Nzp`0hex&Y^PHvXh>~V8-?9mjDyMu#$Q5M4gAm?+y=4_taU&p?4|V zwj%j59GSFCZcUWe?dpVU-T@po_t9QVvXV(hSDA|r+I&1d9Ox23HZ&|Gtd5T) z8S+m=6~BZ%K&@`N_5!;;E4aP`inUR>=}runnkhvBv~XGc?2T9 z-Hb5gL(r6%KSq18AA%X~jZr`@r zSlyXS8PUgMKmZ_IE^1TPPVTe@n`6F7%y9o3j>Hgnk+G*b$^cOvHj#F_w#6*Ksg{|2{Z>9+{H zl`3Q942qiUSNsSr%=Upztkoj;ks|muW#zfUqE|AaMZE)FXFXvK-ZGrL9=7f>tP4Fo zr!Y-{X}0Mh&r>C9E7r@wtPL%K6tj@C;m1=L6rSmFmwq*V!I-;2L7S=}su?8))oCkg zaMk0jl7lxZ;Pni|ZtQ0KnfLvBl4RU^w;o)q__(*U8JR0B5Vy4ZpIM0mqy17y4URJ#Ul+$vyZh{RZS4!l;PD4 zR=cXq5-ewz8M9>k^X&Jzu=H>hTmXg@|t{ea`$_wKah;U284=T0h|GUUfTEc?`vUkgsU!M*#ym|aT&Icfr8f-!{%l$ z@3^M~;7Sk1{3-&}gcHnbw%oqD#vjZ8^_=+vuWkoiUy9mM7d7!|jcc{7FXTS3T0w_C zds^okf&_Btn?i|mHryJMrFOn!vzO-=UhY(ci(HQU8hf@K9MlsHE@p^ePiljd*F(`u z8qG=$gs5b;fnTTfMuTnrbf}|MASGPatr@4%SwkO2+Gd`Ht&id-$^K@;-hdaizi=F| zGa?c4Q$aP`|B=aYIfZgYLq3`Qy5+iv7@dOl`$`& zY~uG7Uoru;T0QgnmZ}M@)sI~YxnVI@ziG9#JEO+XafW;bH0#Ox*qsfrcqA?0yiLF8 zn4Y3-;LX+O1h8B78CMl2ynIO-V--B~p9~q5xg{6|aRb#lFi|$QFqB{BN)Ttq)P9IP zx;9jK{2Rz6GK41ecJHj|b=)n%p}$O!fT;T}b=K&IA$(sxV@(YH5xz?8)cdkv!Cm`w z){>YfZ@x?+j^r~dI!3Jw*`M5Y_EZI(Te^c(iyQC%o@>Ti6C4&J2S7dB1M>wWV@#U8ET5zlZxq zop=j-nBWJ9^Ye7hOD!C0b&sT*3&EWE2)Tef;_Gr%5En=XO#b7`GK&&yL|8WX?^CVW z7@7Vneul;~epB`XaU;7$7OQj>#J8!=gV*n`f{JY`KG}jlbrNvPw^7}FHn(5v^6GU* z*~J`bNcHM1%JH?jpk(j`LMN;NZ%v($sPO%l7i7&zw@o$0kuCbIM6$sjXjH$3@D!M@ zg=3%bkIG~^+ne}8Ua!oJujXEvN`DBcZV=3_xLk=VMIzi=W@E%SQc|uh&47{`3wL-a z)1>{JWx^Fb1|>bK+p>ZuL#xqH+sBfLHUAzR0Xf|d+FA42pIzD0?+gUUrw8+OgIsD} zo+w!a`Os%epv;HaZ#^n|AG2XiVxw6dhCMCydYd7jYK)VdtVDZ^nZyPP?bf>Sp=`-T zb}Pp2;ViLG{w>j&%t*}g;R-3Xy*CVAy3#VK!RPyob{-j@VoQ$g-?FkFFY%EJLX{rFeVqQK!NB9xe+XW51H#i$+ z=s;ilBt6leGNq;~Zq)tU>bozEtoDtdWt}LWeVe8Qf^56&gKfcgY=*aCZWXO$-ub3Q zd6Pw^;s@ShHR>}HcIqif43`=9I(t@P|7`eUpRSTjsF~1~l)h=0Jhs!rmfYpqs8K3PtTo6O8rmOtE#>qI}uJOddtXCL;r1MdOb}q_{KSYFHJEE*q85ExaLOZR)u8#alV|ah^H-W_XF-qnBFwNq-t9@I8{KMo}lm$Fq z7$Uh;GgnzozT!21BQUGwsQ>2wM-a3rL`R%!>oh*{aWm4b0`UftC&LgkMv=s~v3d?` zmC>{(;PQb`>25uhKM;Bqo@Y90C(CyoX`kCBLe1Y0g$gTT6+Ygs1YEFwAuOf+?$auL z#-I9KK8Q=y9kQ1>NtqQAwV=iYC(SH$N+RSgk7_coPuWf+(3{wc7q11g;2-te{g==b zQI4DW7j)WiiX34z_q|F-M+emj8dwN;QCGs)%$a@sYr=yjPjq{?aGlH`4j#tWzmMUe zi|<~-d}GYF+RonKcB%F^WA`b)1@8jJ=aj=lPp2W;S>(^#t-Mi)M?$^AJ zvYe?++MZRtO6DV?R%mr1XDuv?a%+3}t-7w^p1HOFp}aPaH1P_T<(}oP4K!zX@LlH8 zM_$Z!?+}D5j{YvKV^fx(B!-I!aWT7AYf?N4T^lfLl2DD+R7k?T+|!mR3`U00ymN}W zttRb&3m$TGcxng7QsqOe-1cF7LE|Q)wE%kkWNHg93^=UOPRtYSLVBBMLYy{Gv;ex_ zIgtHf7E~F$7>OVOCLdwSXVR7b=QJ`FKWZ?nK~~g5XUA>$d@m13i|mY6yqfnCSJ76E z9@s#@di2|g>eZcKd`#X#`nKtMX2yQjtgn8M(}|rNG*^Xro}!Y7$JkZZzdG&k`ex@o z^hhREAvgED?kx;jO=X*fp8>lnRP~P@)-(;U3KaT{j2{e|Ul zbP&JkZ4T!DZGwAH?)4C66QKJ`qD{4ZHT7zdqyc+^~-gz)Lv-{WK ziLL@9Sxy&aS?ap*f5D^IGzw+>yu-|k99E5~%<5ar2wI&l`0?xWf?`b`7xmuOmnH4) zOYhOnAg|@c=fBg7gdPVhULb2r5D%^Y&Oh3 zeq+Ec>nZm6B9~WL;A`|{Dd3B_k#i1<$m`unIXSw zlOTfs%HdmPqu$A?&W~Z&&%q9{!3KT$k-(-K***t}JYrPmsUI^P?oKB3)|S|PjiC>9 z66z@ie>HQu)e(()C_LGYS6--?)G)4k1F4JRydGNY+7}M6#fT@`KiO$`Wo61Q(Z@J7 zK|1X&y}3{##6$0Joae#CN$Su2Unap%%rg@VV_vzpR z{TI!BULVLex4nwZjcG$G4%t=mVTx`snsQ@fXUCU+JxdFL9n=(J3~zr1PdeqTGBXaZV?$ zg`b>4bSIaZfG^u})oPc#&<=aJR8@Bb-6d$CwT(ZbUR7yklG9lA@f9oR#U+V@`!q8U zym!7u2>=#WNnZyZw@W%;FxY4YFen4Y7)qd+?wp!m+sRzse{WH&Iq&+uLj`sFv(<}k zX&}Ujxg??kGCdeM^N$(%P;;zmN9{$w=TaL@ud?em0he`;V?t3Ji=0u4Ein%@8_^wE z_7veQlMe+iQBvT6FJUdg;~+$7jhz5j(hu|#t9XQST<@budNl1E>~_@;Vw4q72>M@g zvJ-+*5qFz=S5()%%aOk%zUBZlla_AYR~}4&0!~AG$s5(Cm^G84ypCJ%+8)ugwnKR7 zwjw%~=VAZZrqrPx3xNz<-JB^U(^55`U-Ds|eJ=KN8o~%Yn(8kS+xLD0xyGyv-YjhH zXtuHiS!sRg5Hr?ikLAHEVrp!A!yKa8uWyqFWi}iL!}K-iHLfzPj{s+gNc<%pjcICw zxZ`9vM|iO%hsQUqQtaSbCA-zCv!0v>YW!;GFXH-Ufk&GqNekVn=;~&EH)kz>Rn$WJ zZ|m9qYPJc@+g>>;BB>rCi7$LmN{6NZHuWrrx6jB1azC!6dK?5##ad3SQ7mR1 z^weEmVMJIIP>^DBs`X;D2iFV^M4;MYWWt!6q}c$|t!dN;!3|Whqn^7mEOp| zmKC&i3dq_kUyhb#+lqI?G<|tLb7!}HOZuNmBFUkZJWH^%zTYAAXcBdx4f3-q^ej>e zTQsdP2*IK$h`TZVmow)L3}WyQ+Foon3DZi=ZXmMY{%FuIHk$+Q;s+<+qUS9pK)?82 zK_%*c=DT@h7NNp0O3CeypNR8-5EDhj?=KkhLJrNZx+zs-X zcnOrYjoK9JRpsvX_yZETN?=j?v>MtT`}%>!xv5saH|Bl*k4b`j^zyLET#ug%x!mIV zp4AyL9Kf?6x_C86QT|xLr%7;`%;>KU%6|pYya9kuDGGwjb0x9(^OGH%N#TG4uGs?J z_Hz2`h+{4-CODq7@$K|0LG=*7R>+lVFX=w{$w#X3yHrSgRyP`@ zVFuV1Ql@@u>%BqViI*u%4oa>a6#RJNN>{vV1v4%+y}k7UZtX+ z^^!Y90DC69F0*&B{%aoQ_7q`?G+3@v95$UDeFNoh*eefm)Z$p%GUUhEkJ;EkE|Q;C2^K76gy_74#7W;v<& z?$P-jv8oZbbA>@wfNynt?q8AriS8}fxcu}7elMHlPmQV+EXyQJ)BVg# z{Y2n4Z(Jj@!h`IK7b6m={1SF9-K5a$v<0407RQ4ZQGxTIy&B~ML*({n*;O_JPFyRx z3{9T5wU1`l0KNq)jirmzd7j-E_Hs|4A-A({ZH81jx*)c{X<_~j%fT{fMEuK?CGDeG zx*j%ETf~spy3j8LI!2N(5!TeEI%z@LzLq`vN%W=aR|3L^#%&+|5H+nX*y=crt$xC& ziP*L=`kD#-I2_d~-vgI0;SsD?lk?8w+AF~4h#s@`lwtdmjeq{nUu)D--A?eWoli$O z_fAIz))2X*%Q#`1=PjQW+qMPV5kIkLw1$7ASWQ($m+;)Nq=i;Yv%!@pvs^1Q$yj)C zZGyCgm<5t%fS(`SrnqUML-!#lb8;U-d!EIaJKcHeK4kY}Yj`Br8Bv3{Sd_gGVuUU( z?vc-a4y}8CN+Fd)Yq%ZiGx5R3V=ltmH&PVMiV(z*Si9ZJWJ34HM5Fe#MuZ{$whbR( z_F`3o!&Zn|20Oa+%`z@^XycJAbu>x#S;k+!tE=(}P0Y%m_#KSeh>Qc{KHv23_W4$E za$3TpnNzrohc2vosaii^{ckm55_i)0NiMAA$1$g;JLO8m+7>wC!B*aRboJgV-QC_) z*R8r{Zi|bXdzDNi`c2$}iD47{VTmX6%Nw~6mk$$(P;td8>1MirBxLqzTC|oRBJ5&| z;6JDrTfgb*uKmmz4G;cfBZ?X(T6=Y}zv%W&i_B37w>hU8N^&W8?8r zt4S!5oxrTMiDE!8}k_{4N5ujh;1Z&2mV!OykSN5|$#1@{JRhU)MlmHL9Ar<-d| z(J2LXRFg|43Q8C_#^6HKx;sWcE+fUq#_kuav#XWSKOFjG(qh)S7!rPXvTlstCN0=Q zrO=}xiR{3aJ|9ak2Iee8;iL!_Pe0gXNN5R$ z#xcas<{THxPB$N4rHk5aL;7kFDN&#;-`SAWZ!~ zWy$1(^N!D2^)6gp@D4j%z;382Dasn6s0d(-_ajuQxt6AnC-E^MG#T}?^pRHoTgBx! zS^jh;WzQs7`OASQmEj~oE7}t2syk99dU<7aYqm!14X7-}c-sFrO8xe!>>T46Ha}&} zt$ROVdi}=+=Ng6WRGYQ*oz5DR<|te-&1+Fil}ignhs0?!cY{qfSi;^_e8i;6I@iX?=e2K7!k zP}!i&c5UGLJ{@#L6BZ?1$s#$MSVP+02kLTowc4QAueB@>Jxwzk`{WIT>5k%uxag$X2$}K=DDi;P=)^pb4!m( zMzt$}1ljU2-5UepvG84(%(cH3>H6)D$R8eN?`6P4mMSBv$SpIwf zYx@;7u|H7}vy}_G>-pyVf^oEMcsS}sdYZa@Md!tyWx=08(3P}j`;rNW6>nsjzReN6<<5Ehw-s^Tq?ZmTd8#YkQsg+ zES&FEzv)Wtd9wUp$l4( zGClIf>oIseJH1V;q(-fkRFc%6xt=VjV%RNukogat6 z0I*V;$YXS;3J}Y|rSt$Un@}LtO2&#NWf^GC<6OLg%Y^>Of(S{Y_lQT>Un1!EBiwMe zUg!R5^O7H@Ia$;n>%UXq4^a5Pcb@m(7pR!1X=x25aFT^JwWS< zjwXTIKeM9jh%Q>r)C`w0r5u{{p9cWul8DsT+5gCDW(=<|5g&qugKjY{)lS|`r=9|1 zy2SjlbaF%f6#n~O%y-!r%vfe{@QuHtd<3^Bw?Fz_;ueWHzJ16YYSH!gdPG8TTk{(zt83|F~%*t^t392jIeT?UObhVfdJV1cZ|C#K&I*$4+|2Tav&^0zp+cdZf zxSbect-4MUNe<3TCcZC;P7RhqwJ86W{W8B#ibs0`CZt1Sr-HIjOhzG~#^;5aKSC*O z+B&;)$;1sqOYPKUJb!z_Y1Zn=W~?$#*kV_$S{I}~7-YKXXBz+3b+xzFNT#`RN#d)i zXOu=YEgOOIgz$?@0@sddMOlVJ-Q^`NZxw{Xw6z2u);jE;5|y}e(;B6pC2g2vq)MiIWrOInGDdUn8m=cc|=4J#zi2gl!E%&}U3>EWsjMHxFMiwgSC+`3xY zw@d%L_6*j;QN+B&x5M;{%B$jEYRCWeJSjlRIucwqLlv>j!1%uP(UtwNL);Z!F7%cY z{+Z-1u?wL>PO+*%D?9%aNLn3h-70(YjsAhLC;p)T-aPQ#2Z<+8M=Yg&cTW^21FMnd zGsG!8;v&m?LEi6qpn}b6<)QhH@Hrr(D``@tP3%fx2Fgek zeUOe0duldg4%IpTQhvz%+(?bZYS(YY)TzSf_yHA~Ivc$o-3;30ldcB|By(c0EoxYL zWg{ifBP!{@b#q&ErrU;6)khZQI@PmafI8Sl{bJ5iSeTdY9A)ejJSw`umyUWQ$ zvVuDcsiU~2sgb1Zld-g>Q&dAKoMgEt1LyxkW!O_Uhecab%n$`{Exz` zi1GqmKfjwEAEP4L90FCi-7w!~T3_bu9ebLm&WeWVnD_pXrjcf~5$)Fz*V39NrX31- zkcmt|_@DZ5JbWvq9|G{N)i5(@k}Kq8UYtT*y7z1|2>So@)ofb_8>+&f@i$HYGP2`H zrgXp0QQ91;vKHReOuHY7+>A0lx_d<7M7cLHWs~Y9GJn@=mMTY4u)QbNM$M~`ddMe# z_-P6<^1T#1%+Oivd41c#-wpR#*n`o_+@$Qg4)v;7&l%~G`LP`r4RKU5R}7Ac<1?~x zWx5<@Co%UgD+wdknalll-!-i0zm;v7EHqAryT&A+?JBsrurW*}sIYhH!OBR~Lpr*M z3$+Y6kKb9QVf{w5nBdgG8o^n`>e=R$`-40Fr>nSyY{c3?yKc&>;kc&F!-djg(^C>_ zvH!8I2&;eg1TOSLqfrRs@? zx$5?#vT7tKd{ui#-}-CH2*A~e`kBH?AbBM6CU-*o?T=%mt%)0K;rX(S*ei>8&9$IE z$8xNx|3ks^Nyy(1wesWbVMV_M=LHM=u@_u5YbM8#_0$kvs1lU!hF#l1Iv03*cgIba zy;M)U25MLGw;wrTZO$@sm}1tJ-AqaFNrTWL&08}}1U#B}gW7PN2;FyoUDYkF z;2nPDy6|vv48zn4&sRv8DcwsV4gauOy7#W|L>y+aL{=I9;%Q00P0ay}pX^#|#>ujz zh4)M&{yuw;P07;vrVqr$eU|WTliOXgcWUVD{aD4h6S z07Rm$d@sgC(v5do(TN33ym$x>^hY>jG02*u2>TVx!(Kxr{t7Q!qwr})7GwdUnHBZU zTAaGnTopz53Lj@&y!ymTxTA}G<(RKk#;tzEJ~)3*mZeJuy>og8kfClHmfTO39pY|% zPvT#QbkUL3`WKj*6HO29(xK2QV9St}IM!Pbb{F&i8Ho1ozW>eiAt+!Y zAOBo>$6E`{OkN13ByVNB^YGN>Cp`#$9$8Z^oXRd+A>kJOqrAhCS@tlczh{gv=vpYe z@lPTO)7r06f;}yluj8663aNZ0hV}aI?_8lWbr-L;Ghb)kTKioZwzB>a2LflG6J zV&nQlwIriHQwi3O?BcBIS+ePasYR#a3-nn|Ck}er5dmfUX0Jz%W0r>Hx^NsWr4CjM zB^z3DmT_THY@$hI>~(*mYQVNtMi@yuv`}5OeVkd$BJS>k2^mOl8wxv63vm$oZsZMn z1zlU@Hs<>*nfSyAItsVtm&aa+cLv>}X3V$c9#>U58h;&LFgjN|aRNvvM46a+OQP$s z%(T%)V38M*z3Y#fCuDY!M{{qZuhZauUsB(l+B`PT##eh?SW|^t?30)(yBs3f$F!ip zuJLWF@3&}+5wEd1{fKSxbz%acnReUE3A7B|!>MxQdPHgP)1;H2_Q#G z4MMPI!W`oh=EcV}Z48sp#dL@xWJTlUA!2R2e~CB3YScB)Yo4?l4bSIORm8`NGIipJ zbko9TM<%3{k>KP~KHd|y&@FERe%h)}G+E7h1QGIWfMxjZTItVW1Cr6FVV(j4C_{yR zm1mxtMQN%FSBuscX%~C2(DG&__U~Q7ka_Moi(x)HMrRbc5vi@ILhT#E9q7_gHRPq- zDkKazfocoB#J@FBm9a?Kml`!l{L`H)`&lcluC>Q*zskeef1%qeJkBHci{xXD(ZhU^ zq2E7jo^Q&jutK%ByUpMtRfGao-USDDBCE}E;7A*Y<0r7@erH_DOaS8I_&N#gH?&&y zM#Db+Zc4I=C&|SknWa8v^fao|;d&Dbr(c#nA7-X*#WfOQC#@21Hg!;)kXZ<-*Sat; z8lt-0O%>nP1aB}w*jWqz*^y`XN)_G4k)2na&BS;zATHaooHF$Z!pT45c1PGKJRsxU zv9?jtQtT$?1tafLKT$rBO>Q_JyJ^ppNQORi1S~rU{$=StGZLq7N><|W130Nb(x?8%@+a2V zu9F3sXbpx3aNh}j^`|}LBa{NZ2m7ojy9ZAKw4`;dfK!I>WEJ&9bCXyS@^9&v^`Lqm zf(VNiT7rbZ?^moBzifX|tJsDYHfo6W1f@7tn>G9=6P~gEOsKr(U^-%I|FL5^y@7>Y z!;2s25lJ;vL)orBAQPJ^Oryf{O_oNDsJidCH1j*w!D$q0JCMZuAs@|3<(uCMd~!cc z{0A;j(F~R&3wp1-*Z6o{KI^_gMrE@JH=mp$?)0bKhy~Pq055G_)=7TsfOcSuc6Ng^ zkN-t`X)D^^FZHSE>HRA1uz{zmIYmHcE$mYe#473={YPMKbfrmz!|6xy3-V{h5wq*% z*6HGLCWY&VV)2w6?^us4@4~KkWz0b4oHnIr->F~Mh~6Uu%g(c}J}=N;84wK%W+xKdh;=DmUD-GTJX5@sWn>rQM0I1n;1U zgte7Ks@P2=r(Bu5^e}m;8`IEzgEl#2?72~gk-U}Bce#DL zjl{59PR<4lQ*=&pdbF`lbDXN@?BKqL-%m_MB4T4|n-YY$cxW0~N|Y3>0h|35!_^h2 zhy+9uq4b!o+O@qTr;?VEI)nbvFzzAVftdMoVU=vT%xU8!Dh=kIr<(^0(b8UAzb}_; zznx}rpM4>K1mTRte%#aX={;4R%>>JX8rg?MqrB9QJ){Dc;o(dpS{*diO`tl41*jv>LF5H9NxzLMtdHaK2Et*elG#o6qLOrvQr$Cz)0oF-5< z=QK%>jtSH)5876;EM~uEN-nJHp(&gP4iGGF)z;VLK+(mjV0%?dKq4h_JqS6Gvj)^L zzh(D*378U2r{I-RQh0sLZdPAeTBpHTRkq4<{Uqg|&NFjC_bqxCRu!Urewt4_xKQrvoYO})K0r*7}Y zHTiTxa?7+RuE$rmn?|vy-;->;)wn;dfJ~I80m=#%lF{#o*;YH|df?Mt__t~9&{GYQ1)Hkf_!&jjHvt20B+*-bGPA2`qBu&+NtnXTraTj{9k4zJ= z35br@&(n}hbpETkylF=|#Z|XR4r=x@TjnM5QG`N?5tTBDW6Jfex=~ot?Fhd_F~;<@ zI{N7;9~3K2tnFtro2zoIxmtxROyir8J`~Fra*eWOg(4xesDP7JKW468l|FjoR%{ zMCk&oo_1|^6B$-LH%Avbx}Asa=*&D~Trp>NV5K~?O()?;Iy{4kN5V+_Q*5zYyIMoS zRFTHwYzK3~x;TttYV0wG_yhA`i@DaB?j&}zBZ0yoBGawRUXX$ON4-@5r<^~fLJq)@ z&PBgHK%FdqfYlY$nzeUVb+}XX0{6?F(^JMueemi1x$V*(&{wwoXQs%`7n8JM#eA+d zDy^)jCF%ac&0d4Jkgs*Pn>bll$|F(T9ho^uyZxGU$yxT2+`nBVI~@lyv*VU~^R~0t=>N+xrpvSmEU*tuKtI^VYU)NtaI1JdQ*P)6vkv(+ zGbh}8XR{r__s88=0_Q}uNa|vDS5p&;Z?AfOmCq@nytx(9g(V1fHhgLwy}<-mmc{a2 zX`Wbyx_&|zSXIX=({&Uy_nDCHHuiNFNsRubO_e-feqo)UJZk?>=hyTd!(#G{3EP6{ zXQ+LTQ?;PkipA4S=?B9fD_jdJ;_HBB8k+V5OMgpl$X;x>9Ml`=TLdefjJtxJY$=8; z!F%H0K+KeWc-u2#ns(&<%R-zDGnZDEInb9i2&K=qnhm4D!BhB;1z%~hRg>fT3L{tN zV=nK4^5mN=-ku{Fw9HjFX zT4WaB-J==Yr%T}XiR}fxh4Xv$SiMdb6UHGc9}A&jzhnTdB&Vvs4!+QjWx_$r(-Are zmy~TK_;=?VRQp=Sm@?HU@fb05skrKbnb*TCH`zhg$e%V`c@3ZFM`6v={Ro?96Orny zROmbO|JBmSR>3amb$T;yjXGF1y*;t}om%?HPng~9VUTMw$K=&Zi}nk`ZD5eQrN<6+NeSpp2yf z^y>b+6Jb*bI5OzvoLS0FT3@Q#Fk>v#o0W(;oTW0fFFrem8uj>74gwL(P?R*yxZS8) zKN&l*)#nvA6eORDgfJV|vapybN#4&C+1dyZcFT9x(rqW&#*W*UUS_y5h_ zSjYL)*(mj$@KZ_bp&RlH=?xB?K}b(zmZ!3@s^^>A7wdDI74?;;7H-Rk!$p?nY+HI3 zNx#qH$#V*mU2?lbR~NRAg;4YceDC#?6p@yVntC$;MwTO+OUAzvE&covX1rh*sV zj<1i1Nb5~6_px@lxyIa(ko|AZdDo8iI-m_cl0oR13HyK#0N?%XF&tjViEX`?-1ou& z=0gpw3M^|FB1tdu;a-{32T3(JegQe?7EZZw*}@+f5BRiB-Q2C11zjmTu*Jo9WTNi* zitKCZTdNvEr8kDFWRGr`)9_UOm~KMGHRcK07d4Z#>K=&VA=s=%y>jZAk4)j{)jf^O z$}F@@A{a54AealKGM(Zcfspm=Z zRm0g!6TzSt$iaVZI6A@&IIi3= zH$M?h7rQdnbPsyZy>^o+9z7WOwka*`ot{lEsNNqYrtX`oF2$CoWwWb^gr#*hZbhmW zzol_Yl2BDu7_>xZZ1bX8*&rPKy+u9>g!2zzgnBl@tz#%Z@0Y{=gB|%5VtG7n77|NJ zWJqyUsDJJZDej2G#u(6&;~m@RM`R%0CEc1F7-PUOgLmqsg2q8AVzQBKJYup+;qx}4 zbwFLq9Kf@cdb3mFv)9S9J{01-?)5L={>yViIe)xslas#zuPo{s-GVeQ5pge2v#=R_?7<2c35uI z&!48_=x}sQav)GTGBxybE=HeOjy74m3re0O(R@@dXBEB;lXd_E++`}e<#r~&9bq)X zp$wbhrdzBj=Jxn4jOPRKXCfP#bb|^;!=j{!hd(-`4vn{pm=g*osPDuJj0HMWYt6(t zYxi2ai23R6?B3cSsrYxr9RGDe_>S$nXIIYc%j}i0mh6+PpQx~vh4!`Y2NspeL5$@} z!hsLR8|`_9L5DJ}rj7r}*x~{_lF*w4J4)#JnnWx$J8zmQr}CZ;*G_;%t^k4V`Is>fEUGSB?@5%7A^PFGBquLeenl9`5|kT zXkEQTU;iTfY=vqTyp<@Pp&YX|_Jp;@d-*ewP|%M+O4<{~PFB_Ki00OE!bqtqJ0%-8 z=8GhE?I5uRq%p@InGB^T`6z?qajNU3tt%R?5B5r(b}EmSW4;ICnPR21wQgE+Na{eHD0ZxBKS3_os9 z9!!TPX#yE>4^Y(8^`_3sSw*|Lqabt^wb`IUmfM!pRfd*I@y7KN<^&0{rTOYosr zfh8}rRiGSg8mNv>d18eXu`4a3XX_}qDnY`8eI$aB_D*0GtL$9N(;fDg)%FAdOl)at zSs73{2Zb(V7^Sv@KIGUITz%)G1Gu8l9Mdgpt5M$n>CK*CaITN)-^6OstCnTm00{cM z9fV;q!WE9kC7W3RL`vy(YHiFw|C-tx-L{(Wu$(XIsfAaCf*Ii@s%d98TDn5fhm2$29PWMz&3N z_#6F0@n!L=zm4hKz?)3gP0{{yCYxty4Ed4iw8;32@Nc2vN@=7e>t02&5NhFPfWP>17viWpe_s3pa2aJEfU=|l^66S%Q z&kM~p{G~`%jUKKqWEg||m-KzAH{feGhQBLdy=mhV=B z#c~xq+FMmjk4mhFv=!N#kIrl1+#v`h z&vf$tg8V`4=0!R~=MMwxbaD^ej>>2)vRRZdarI%Q9j=u*hg=+#Ft9&lPIIbQr1ZYw z{z9SPL1OfBd*w6-zpQ}>Iwst&zJ1RrLp+KK=gCgvV3CkvyuT$bzpLxh-b1F!+x>pM zq1bexR#wg({Gn874huO=I}%*xXvjs9qk>cUUnA77OLwOc5mSLP#>im%)+1- zARE`xgaV1lYNm|MDYzaA%{{*-aS82`$Kl^F4*fR2BLQLu@`H^GTK``D9j@A`)^n0E zK0tXxy=v-7g;l6qae6Hc@AOfIBt45W0=Rc_G+&+;^SWAL4b4_YK}Ctb-GN{f93K=5Vt>$=Y4(Sg62!BI){}xNj#MGUxd;MxWKzxsqHL( z({9rFB1B>WjsEgf8`1~M8RKRmh{pCLRV*2CHZ&0=2BST@cSX{5VPUVxcNL(&h!mOi zdh7@}cigi)-Oew~FYU2ED*VmwGm`PBsyO9QF_=Eh$Dhq}=PUNpmcVMa+vDAc6!!pn z0RJX;?_Dsyl(c^>#t~98NI5TlzH(1MY8r(-&d;?g6rv#KnO)I10rjw3puHiGqLjV) zD2|_MLChgI$U=y=_Hg+@1sY~Kf(&TUKr(!vt?xsnLv$h0+sxL`uai7a`_;zGFGrI+ z-^~9^|E^dnorm&p*=ihbu&aB21G9Lzs7`)4wsIyi;>f$Nt;7wSN) zZ*ff5wxdeX$#7cnteV9cTGq)KE{V#9oB#Ct*~0chu4g!OR>HUn{S6poK0gvMfI#BJ zzjp*+1cmbtJPQUB3^ITLq@P)CrOc`X)YvJtv820NwHHs|X+DVE86~KQZR|jPdkwz4j^1da8cKdcaP@GL`Em+8*Gl6J}1|nERUW zvMqdeTxak3t!$8MFWRbn@Z)>w^H%5d^t?jV7tQq3eACx=0dIQ8_%$Q8uT%Ahj?X3M zB?H44*`ZDR&S*uc6ggb*1wjl<7M5kHcPu@o&D>mLk8R&OaAI=5*fM0Z-4<*g$U@nq z&DDDYJ5@<-E@YL>GE-6D#p(Jn?O%|Gzg0HDYB7 zpT#I&7veb0Z;52Xnh&+~43v*$42}U==g?e^rI72W6 z#`F3A5)9WkdfoH&ayBy4!>tO%&S8mu{ryplXGUz{m@+ZH3YPw&A8414QJX-2Pws1j z$l_7>Bey>+7CcV5`pK^$j2RK^N``WT%a-t-4_Qf^Dspt^*?Bpoe^NEnGLF8%1qwA7 z{yOW6cbW_K!$M!@+t-ycR#@E0Oi&KJA)|y-AKMWKHJv!{loP@{FzFyBQ#nzUnIWr%3~7|HY<NMu5{o!*3oMQO-fRB<@_os0$>YYO{$L&q$r!`>WzT_s~qIlC9k$Naj68n3>v zcT%l$-9OsP+d)5zvvSYC3%8~0gtmwOjL|U-V=f-(SHqKIuWxVD_NB`3 zOqH#Cxi!L;e9FFURIMq6DR*<$UJkSNu*mNvD3ZsW9E`fc0$$5f(L2tN{L1LoNegZ4 z7bx#G#3bUSEN^5Es3gkae)ID{=gKm3HB{Kge@{h!xTQ}&Qp|q%-aLzhOR&bl8HU7W zA$7$jMKP7HP;{ioM}v`bGz`iB&obx2Nf?gd6385mdSWB}-qp`vwTTyhGxE;Tj#DGZ zpj9GXa@{B@nd71LP*GUJXnkry>K@KTM1`=xwU^*vfdPGV-ShKqz z{J5;U_-^Hv?-#v;+@9;W)|^c6Q|EIFT&?AbqEADtV@cGCT0iuZ5P!QQ{INyk@`5zN4h>;fI4C*vM0Hb z59WR_rYoLHQa3%N+P7>{PX+!}s)^hE@v-RzeK6gxKF*?(i?A4m zQlb187Hxp0i>2E0p8q#XpAAl`zopmeQ%6>*8rbxJN9U3#>I8Ot!K2{AUfBE^q+ zX@EDCTuTXQ$Um`akl7g`4H1CM>bp#G79gF#Kg#-!jY(u_ zNIi&n#AmN(z=G_Lb?`cCvFF`aUNA%3{EPX*qDehjgrNcnJB3=nhD@4ag-OUA#jS}c z*fu8G3}FJNcpCRHOXJFN$e>gL>S39pvXb{FE%{6H1Cs!A8Wk;@)=1#OFW2_>6o+nx zi|G!S4nyx6P0#GXw443j0uh%zAiHl+U)YoVpNgvKUl*8v=*n?&Q*KXAps>$!!cn+r z*p7q#(CJY%bDV3_nJ7Zp|6x~{L?EFaqS=ji-$CG>qAaivD{5vdJFrblzMN4*dHHu< z^6Wg*sxd&J9b zWD?RRxwIxP$X>>lOHRxQrbMF$VG$!MM7THkbIA0`(R-V+cars-$*-MBvDTNx?jbc0 zgo`!*%wU`EB_)p>^^eX(@awm--!TG;YVn5$X@-mfEQ}`t{IJ}HH~XL9r5G*XCL^z{ zLiEFjm7M?Qvc?*k0ktnfmk!N+oNy|!*yne`TMNo4edNo$8 zWm~8$Nl=5fJ$jgB^!_vrPZsu|8dZ)-GZfdzBrd9jp07N7 z7Y0vi1(zx}TuV>>bNv|CZ?@tNn6%N^l27w<`)|DCQ=PGNHXPhXD(al*3*zY5tPRY> z?Z1txW2g@4Py9kEhc`W?k=(_TyH2(ZWadA}{M>`{f^M1q>d5e&r!#e-UlHf?i^#oY z-0Y8jQ(A+CkMBlKb4%L)$~!lt?Gd%t^q}-tW{d!jHn$Om*nTdn2iEYRls+ZKyL!59 z^^=CI#42sPv!Hpa9H)DYon~Y||1Uvy2B!ivcu|%6D8JW7(sT^8tP3V00ba(#>C)W< zzN|p&M1P$$@=;?Nq>LOcqO1DuRo6c{7Ji=Jaw!BBbTXegEdR{a`m{6$nm128_*in2mqQNEmLL~!J?V+#kNlsM zZrFdFH>z0hkeD*{_(^V0O-n#YqonudR|=SNhd<8gpmP%hj3FpsvB)|QVk}O#pSo`g zyvIF0Ga-ML8)wY^%_!N2pkJ6z1jemrzTrfZAuYf==1TD@-yMGd^tsL*b%};=>@%(t z!ONBahf=PrGMT`PXSE@yx4@-l4dDKxuda%uw2f4Y3yLV(19-2{gkZ5yFw+OW3SSux^yR} z%#qbM^jA*R9!KdjKA53-jZT34TOptaz~dzdbmQ|5>kp>5Rt;izS}jK&a@o7z4wW+! zn;fT=qntkeot`mKO>J5JRlBZO@GkXJ$~?XnLFihRWkA7!fOAxBXyk^FR)N+@?0`IqmN5~m!XNwbC zNc&Y?Q(~IVpJJDWtS;(UrlC1t{so;;Mm_*X;^*|$k!(iGyBQT6AFcGYi4*3~mUamy zv5uy%tSAyT0I!@k@PA@u!zxJuR~EcvV^7x(HOENpiDS6nP@=!*8S-$&do7%`{0iA^ zi41_^x|)BD-Adk#k$&yF2o6B%IX?wdKF6$nS}5JG>jz~wxd?4nYy2Zi`u)HIn~MeJ zePeQ60RZRM?Gj7*$u@Ew?$5LQu+daCdU6O85Qe%vsK=rxmFK%zd;BTGh8|lwM+L7s zy}L%t>ahW(>h~rD$_QiGx@n((_9-?dt?9Kf2XQd>FtgdSP(hy}u?hr3Qc(2;aj-B4 zo{RsR-o4_1%e6dRrL|*EqQCtw>!&9+EuYc6{C~bF-z+7%B*-RpVSl-z<)#H#%i@R$ z{H(w(_FtahDkt2N)+|WU+6=2IFD4%6(ByMbB1w?-ariLr_SoIABOH_ zU6W}k{{R18<}3z%^x#ufo?ml%AD=O^vAVacHYD*{pDp!;z=kC4_QSl>{KnfQjQ?-@ zLoX?s-`IzGy08U3JuP2)TFirTer(aW%_oF5^JAajsu+Q_<=#t2am8I2N}Li+K-30imX%H2PSNqlj%!CZ%qiVNU* zzP&;ncHbAFVc;BOO!L_~*N=fU=N9#$<=|l^7P1`H&5=FYOOT$PK3bPspp>{lD zZl^MB`Uf0|6c=GRMYZe+A@ZUs!sQr(0M0bQ{j98*vL;SnmhDjhTUgd8?k(l&Bs>Ux zv}3MC{R+YVw^6$3h-xfu8 zpBXx!iV$yHBB8!zZ~DDdjv=y(58+lR$(@QME<5vBlsd*mfa3(+$bPDs_bAfFvka?VYnPu3qxge2{L<<7i=&j_LG66m4B3-O&OeSO&3B6 z=Yy`eG8}Zp@25WyQx0Wb-l=(8HD|axP}-9kY4aC+BsgWIh#FqxNvTQb$suzpDHiCn z%n@bAxs$xSv1*|SsS7)Uz5;zImkrItop*Vy)z%U5rl^1phhczW*EjrQYt&rUBigOG;-W{) znriY$AuZId*SW_qz5Zymq;8~cl=7B5jW-A_pO9Ga?MeFt_=YEg0&5cP`LhFlAl78t zD<0)idz5zF{ibejQZae^lRMDGsKp4`0OG_(Lq7k%#pw0?zSQ`&BVjA)|L&2)C}_)) z8bn>6kwGoQKYYuL?DTIE*uc9U#eu!^Di>W@N{TZ}4Z0!>)$G~R*BXeN)WZ;tSl9z8 zj~o5wO)3drvl%h1_eLTVs((<{fjIV>DtgwWZb*u#c9Y&-9pg8ES|E$NB@|-Y^2zf* z6{u1g_3zAn|z`g^8nECl&TI0X;}s$jY802#jIo=6=2EDcgCY7V+Ocv@aPBvfxY zh0Z!#;(1#aAZw^|6|lz>{c4f5@IIQHp$_X#WwH5Ela0D4 z(i9X`>G;DsXLOI6%lc)*8!xM64MpzbTe+^I1c+J_Cv()%7!Y<)?iJZ>Mlk=w9+OVv zCVF#(4FM%8vSI!qd<{;1)Z?wv5&YQW7n9}rSgL9Vg)A=dp;?17Y3Ss7{3sFn2&A5A zawUlgRFPxaloA`(omaJyaVel>6jtmJ6GW_OF*gmpPvfT*z@-k!v#s=q<_|v!+4)Qxj|y3VKDO}^D%)R0 z*jaYl{P;^vCYy6Z{E8+y`(7Aiu#p3rMaRiVxa9cFvrHq9Ey&T^jjS z8Ktk(P!A?>!1sZ}r=)ELHjUeTeo@>D33Kzu|K~m?)G#db+jf`Kv>1j~!QwTzqtH6^ zqBX;m5OV+G1a}d7tujYwLR?IsxxY(kX@dcs1)>bM-(K^(`rRPrV#x$)qkPl zwH-SFjB>><{AcY6q1Pw;5Fsf?ufYdG1 zrjxRRFSO=r7(%@8F9 zP^YA$F&dX8q1y9DQ1Qnc_-YTpkFpG2UY@tWozi24lPP*bi<nrV-&bhR3IOB`0o&Z^C?vp)^KKT9?TUm)DPD! zoL~Y(ygtOJUb6XtErF=MxKcni4v7!L5xPGpmbd9bZJd|P@8q)r@}xg4awto@(3WnS zd3UI)2t;J6n`-x&SMWj;mH%&@t5%({MztPS*9ZST(1zf%($v3rePq<70D6gi#XsPb z8aFd`T$R`jPPSk{?Yma@n9DM4wDueCDegAkFT7z?5|oV6XpwTp5Q6rGv91W}{?@Fg z4Lo)MhFBaVUFT*u&3>|Mgc!6H*c(gi7uS)2f0dwrWPbd)XX?*Twzi{zl%{kwcx3Yy zDvI9XrYedjpA-jO{m1{CN&)rY34Cdg-bq348JciyeSyYK{1q(E_=n&*8Outou?CD( z|HjIvbl-j7OM>JIua>ktnqe1{`&N*m#~@RB&kIOxc)IF#Y_IYpZ4B@1<5Sm%C9mb7 zI0~wmQPcX?l==Lu!8)^(kxQ1L*fW?B$3WfwJK7~UCoNBn7oY*bKlg8wro!=fv`ZO+ zg9-v`TBtre?xL4Zqqs|@{t2G%lLSz9yGGi+SEUN zvSB^2*FiKiWiR)#@nkeq7I&`MWUe|gsMmc$Gf0CTII+qbe+rGWUOqrcNX4>Q-zT0f7$pgO~_cw)v z5){Hw;au-&2D8~d9bDWs2H}qhmjFK7HJ44*sKDU|$^P-OG%I1aRULPDDAosZdB0)K zu@XDJXW>of#@)JzClNuT#CX!;%*z@Et{}7XC#V-DePn&|-cx^%5pn#vY|>0%@*{ku z{qD4B{5bWc{Sb?zF%gkt&mB?(v)M9Mv`P9hUC1)h{-;OQ0Z%`he3V(@!AV|*nlrb2 zzE2LJ{o5S#y!`s%{o{#bQ>W~l7#H1z2gC(3mp9&%vKbj>irCcLxaUgV|KeD{4W6*4 z?h@Y*SwM#VT{)&Pa;aPjL_ZDkFpxrfg>F)UdWX3(iw|UP2aOH?jZ7r2)HW`y)9Vy* z3234*_k_~+c~quqn%^;b^lA5cyd2-fQuOo4Xkod#@0i1P_po2CVSimneAvH@v5q=D zI~Fzh4R^HpId2wiTZC7Ekr{28UDfxW<|80E`7oB-0M?tjju$8Co4GfTMPi<( zvf-0yqPH=wU1Fw!X;CCCXN}PSCxDOTtS^;{nFZI#E}WaVpq>vLDClsMK;xUZ%V%l* z{syUtl@yNsRCdzklg8Tm(KIp3NK4 zXR!b!8=jl)SY@NiOSO_n4TsiNByprfFK}~$EX)e}yFDA{4}aQag(ZUew++o|_|cuo zdkhPyS*ebw#H8h zzsxVk13n@=ILY{kAHm-lX_Qn>XBIF;AhN+=Ft`f_8!%Xm!CGn#YgY`;>mZrXLDFr_ z(jFI&M$NMGnk7lb;Uit9v4K?9a@zZdGHRC5XM^gZgCuedBpwY99{@T?Kx5FjOB(BO zX}oO*$+k4+b&z<5^oG6NiM4|IA|l{wZX3uSh5S4u(x4vgTY|%Hug3c40}5z zvlqzh(`ge#1#>gRt42JPRTWHYOSB2bjS^Nw2aVbg*&r|o3<5V!U^Hs;J4ohsI!MeZ zEL6y>St`bipY*-vD%0I2|BDVAZscHIx`QOP;D8geVT_{+aUSkrSeSgDNXkOV_)u~x zoSdvuFk@>&nGFyF#JgcujY<5IK|yTB1u@UiHVnZHL;HxE#faD`SQy-yonjiXQ%IKc zW_IUA{6Z46Q?%InJz5%>76wNf2nK?WJGvSO-VDKNPz3Wt_6(5?!h`U=ifqxwz!=UW z;T(u;h-@Gj2!_Z8f+4cgB0E&rOT&{#+Amk;oo$y_uGGm}ZK`~S_+)i*Lb*q028+RBuz0hhdx9)hL$H`9yC=wQpdP5-0`(Hvvj$~1)2NX|eQ@rp%5JM> z#;>v-8IavzF<9IQixpV>RTiruSj>^#Hk|(V#ijpz8_;H|+w@2J@Jo`)ipfvu@8c#i zYiikgrGh?hq%-t5)RTB4H&qG2i=JJZEJD*_7z=;H<2D?t{`dDCvL zGSPQxMsx$kKyj}qRzNXOTm{7(&F!JNg>M#@oVl(UHwFj%;Cw@zPq)2N5v)rd-6`#y zgm|Wj(LOt~o(}n(7prMT-VIHhI8%|88Bp8+F+jZ1<_3rX;wm6!=xvG&1SAc;T^aL~ z74L~HF>9}y3B6tQLQq-EM`pZw$_UB}V}5z={L;~!58qBiJW+T%+7h281UEN^vhx+zpg613DT;zL>d<0ifS?+f`B-^o&xb*9`X0Sq+4%oE0Mm`WV&2HytiV zf#e2?f#Th%c9j6dK(UPG*5O2MB4}<&ZzTeHpHa=!nJFF*&~IaNQ-5byXPAE4A0JYa zJ-XUSL7wyOGI~C>=;?*l27-ZL+s`QSkrAv;9KjroZ7ei)X~63oz_Wt!C}6e&c-_d^ zrNV$W5`>Qk8paCUX9;g+sSzcS_h-yfB3qR{9tJua7zT!c;qEbPP9DR#JtPKNTe9Jb z6^BoEAjArnNayrqrs)14&na9+8UZ5_o>`TxTv{t7w`0Zs@KC2uwHNp>HRLu(3=*#- zF@eM&aSamZy4z6PqMYZ%;cZT_5}0op^Btyh7?=+a*vVnutMjakd=b#2Ya1vAiltGk zfMTGy2#Wu!xzC<1)Bg8&@4qm4um71)^7N7J>CylHoL1eN$4j_8UBkWoG_d>gU%JP? ze0neY`QeB8?CB=j|8f8B{^R3C+`oBob94Ci`ts`b@ap3An~S%H*Dr2wFJE39yrIL( z>(}3ZcXf04=KA*4;ri|6#ntVL+so^#oBgMk`SZhXzy5T%`{n)p{oRj;$2;=y;qK?V aA0B>sc729@G=`w{@8rYQda literal 0 HcmV?d00001 diff --git a/research/joint-helper-lattice/PATCH.json b/research/joint-helper-lattice/PATCH.json new file mode 100644 index 0000000000..51304a6601 --- /dev/null +++ b/research/joint-helper-lattice/PATCH.json @@ -0,0 +1,8991 @@ +{ + "changes": [ + { + "new": [ + 51 + ], + "old": [], + "ordinal": 449, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 451, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 453, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 455, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 482, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 483, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 502, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 503, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 504, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 525, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 526, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 527, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 548, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 549, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 550, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 551, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 578, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 580, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 594, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 595, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 598, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 599, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 600, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 601, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 606, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 607, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 608, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 609, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 614, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 615, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 616, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 617, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 622, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 623, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 624, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 625, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 626, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 627, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 627, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 628, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 629, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 630, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 631, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 632, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 633, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 1997, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2002, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2151, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2156, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2305, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2310, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4007, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4008, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4013, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4014, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 9, + 17, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 4019, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 4025, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 8, + 16, + 33, + 65, + 128, + 256 + ], + "old": [ + 4, + 10, + 16, + 35, + 65, + 128, + 256 + ], + "ordinal": 4043, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "old": [ + 1, + 14, + 16, + 34, + 68, + 128, + 256 + ], + "ordinal": 4049, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 5, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 6, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 7, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 8, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 9, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 10, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 17, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 18, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 21, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 22, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 25, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 26, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 29, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 30, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 33, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 34, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 37, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 38, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 41, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 42, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 44, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 45, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 47, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 49, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 50, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 97, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 98, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 99, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 100, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 101, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 102, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 103, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 104, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 105, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 106, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 107, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 108, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 109, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 110, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 111, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 112, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 113, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 114, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 135, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 136, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 137, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 138, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 139, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 140, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 141, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 142, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 143, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 144, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 145, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 146, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 147, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 148, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 149, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 150, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 151, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 152, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 153, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 154, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 171, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 172, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 173, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 174, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 175, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 176, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 177, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 178, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 179, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 180, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 181, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 182, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 183, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 184, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 185, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 186, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 199, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 200, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 201, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 202, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 203, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 204, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 205, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 206, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 207, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 208, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 209, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 210, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 211, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 212, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 213, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 214, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 234, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 235, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 236, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 237, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 238, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 239, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 240, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 241, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 242, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 243, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 244, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 245, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 246, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 247, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 248, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 249, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 80, + 144, + 256 + ], + "old": [ + 45, + 80, + 144, + 256 + ], + "ordinal": 332, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 208, + 336 + ], + "old": [ + 5, + 11, + 35, + 208, + 336 + ], + "ordinal": 335, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 400 + ], + "old": [ + 5, + 11, + 35, + 80, + 400 + ], + "ordinal": 336, + "phase": "B" + }, + { + "new": [ + 7, + 16, + 42, + 64, + 128, + 256 + ], + "old": [ + 16, + 45, + 64, + 128, + 256 + ], + "ordinal": 337, + "phase": "B" + }, + { + "new": [ + 7, + 9, + 16, + 35, + 64, + 128, + 256 + ], + "old": [ + 14, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 338, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 16, + 33, + 192, + 320 + ], + "old": [ + 5, + 11, + 16, + 35, + 192, + 320 + ], + "ordinal": 339, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 128, + 272 + ], + "old": [ + 5, + 11, + 35, + 80, + 128, + 272 + ], + "ordinal": 340, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 144, + 256 + ], + "old": [ + 5, + 11, + 35, + 80, + 144, + 256 + ], + "ordinal": 341, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 137, + 286 + ], + "old": [ + 25, + 45, + 73, + 137, + 263 + ], + "ordinal": 353, + "phase": "B" + }, + { + "new": [ + 45, + 87, + 137, + 265 + ], + "old": [ + 25, + 45, + 78, + 137, + 265 + ], + "ordinal": 355, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 146, + 261 + ], + "old": [ + 2, + 45, + 80, + 144, + 261 + ], + "ordinal": 374, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 194, + 265 + ], + "old": [ + 5, + 40, + 82, + 144, + 265 + ], + "ordinal": 376, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 388, + "phase": "B" + }, + { + "new": [ + 45, + 400 + ], + "old": [ + 45, + 76, + 400 + ], + "ordinal": 389, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 400 + ], + "old": [ + 9, + 36, + 69, + 400 + ], + "ordinal": 394, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 146, + 272 + ], + "old": [ + 9, + 36, + 69, + 146, + 272 + ], + "ordinal": 397, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 130, + 274 + ], + "old": [ + 9, + 36, + 69, + 130, + 274 + ], + "ordinal": 398, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 144, + 274 + ], + "old": [ + 5, + 40, + 73, + 144, + 274 + ], + "ordinal": 399, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 410, + "phase": "B" + }, + { + "new": [ + 45, + 475 + ], + "old": [ + 45, + 76, + 407 + ], + "ordinal": 411, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 469 + ], + "old": [ + 14, + 35, + 66, + 407 + ], + "ordinal": 416, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 130, + 341 + ], + "old": [ + 14, + 35, + 66, + 130, + 279 + ], + "ordinal": 419, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 215, + 258 + ], + "old": [ + 14, + 35, + 66, + 149, + 258 + ], + "ordinal": 420, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 199, + 268 + ], + "old": [ + 28, + 45, + 76, + 139, + 268 + ], + "ordinal": 421, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 217, + 256 + ], + "old": [ + 5, + 40, + 219, + 256 + ], + "ordinal": 440, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 393 + ], + "old": [ + 21, + 45, + 69, + 398 + ], + "ordinal": 441, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 66, + 130, + 258 + ], + "old": [ + 45, + 69, + 133, + 261 + ], + "ordinal": 442, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 130, + 258 + ], + "old": [ + 21, + 45, + 69, + 133, + 261 + ], + "ordinal": 443, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 393 + ], + "old": [ + 5, + 16, + 40, + 64, + 395 + ], + "ordinal": 444, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 89, + 128, + 256 + ], + "old": [ + 5, + 40, + 91, + 128, + 256 + ], + "ordinal": 445, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 25, + 40, + 64, + 128, + 256 + ], + "old": [ + 5, + 27, + 40, + 64, + 128, + 256 + ], + "ordinal": 446, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 33, + 66, + 130, + 258 + ], + "old": [ + 11, + 21, + 38, + 69, + 133, + 261 + ], + "ordinal": 447, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 128, + 265 + ], + "old": [ + 5, + 16, + 40, + 64, + 128, + 267 + ], + "ordinal": 448, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 137, + 256 + ], + "old": [ + 5, + 16, + 40, + 64, + 139, + 256 + ], + "ordinal": 449, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 194, + 258 + ], + "old": [ + 5, + 25, + 40, + 194, + 258 + ], + "ordinal": 461, + "phase": "B" + }, + { + "new": [ + 21, + 45, + 66, + 386 + ], + "old": [ + 12, + 21, + 33, + 66, + 386 + ], + "ordinal": 462, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 137, + 336 + ], + "old": [ + 5, + 40, + 82, + 137, + 258 + ], + "ordinal": 483, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 137, + 274 + ], + "old": [ + 2, + 45, + 80, + 137, + 272 + ], + "ordinal": 485, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 387 + ], + "old": [ + 4, + 17, + 34, + 64, + 395 + ], + "ordinal": 530, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 388 + ], + "old": [ + 11, + 17, + 34, + 68, + 388 + ], + "ordinal": 532, + "phase": "B" + }, + { + "new": [ + 12, + 21, + 38, + 71, + 132, + 260 + ], + "old": [ + 21, + 38, + 75, + 132, + 260 + ], + "ordinal": 556, + "phase": "B" + }, + { + "new": [ + 11, + 18, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 51, + 64, + 132, + 260 + ], + "ordinal": 558, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 385 + ], + "old": [ + 10, + 20, + 38, + 65, + 385 + ], + "ordinal": 583, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 390 + ], + "old": [ + 1, + 10, + 20, + 64, + 422 + ], + "ordinal": 585, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 38, + 64, + 129, + 257 + ], + "old": [ + 30, + 38, + 64, + 129, + 257 + ], + "ordinal": 608, + "phase": "B" + }, + { + "new": [ + 11, + 21, + 33, + 71, + 129, + 257 + ], + "old": [ + 11, + 21, + 102, + 129, + 257 + ], + "ordinal": 610, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 394 + ], + "old": [ + 6, + 24, + 32, + 64, + 395 + ], + "ordinal": 632, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 416 + ], + "old": [ + 6, + 11, + 19, + 96, + 416 + ], + "ordinal": 634, + "phase": "B" + }, + { + "new": [ + 7, + 25, + 33, + 75, + 129, + 257 + ], + "old": [ + 30, + 38, + 75, + 134, + 262 + ], + "ordinal": 658, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 64, + 160, + 288 + ], + "old": [ + 11, + 21, + 64, + 160, + 288 + ], + "ordinal": 660, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [ + 3, + 48, + 72, + 413 + ], + "ordinal": 685, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 392 + ], + "old": [ + 3, + 21, + 37, + 72, + 392 + ], + "ordinal": 687, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 401 + ], + "old": [ + 3, + 8, + 48, + 64, + 405 + ], + "ordinal": 689, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 33, + 64, + 136, + 264 + ], + "old": [ + 21, + 38, + 64, + 136, + 264 + ], + "ordinal": 711, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 51, + 82, + 131, + 259 + ], + "old": [ + 11, + 51, + 85, + 131, + 259 + ], + "ordinal": 713, + "phase": "B" + }, + { + "new": [ + 4, + 51, + 82, + 136, + 264 + ], + "old": [ + 4, + 51, + 136, + 264 + ], + "ordinal": 759, + "phase": "B" + }, + { + "new": [ + 30, + 32, + 76, + 129, + 257 + ], + "old": [ + 30, + 32, + 129, + 257 + ], + "ordinal": 769, + "phase": "B" + }, + { + "new": [ + 13, + 19, + 33, + 455 + ], + "old": [ + 13, + 19, + 33, + 65, + 390 + ], + "ordinal": 770, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 70, + 129, + 257 + ], + "old": [ + 30, + 32, + 70, + 129, + 257 + ], + "ordinal": 779, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 129, + 262 + ], + "old": [ + 10, + 20, + 65, + 161, + 262 + ], + "ordinal": 784, + "phase": "B" + }, + { + "new": [ + 15, + 17, + 37, + 67, + 129, + 257 + ], + "old": [ + 30, + 37, + 67, + 129, + 257 + ], + "ordinal": 840, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 34, + 68, + 129, + 257 + ], + "old": [ + 8, + 22, + 102, + 129, + 257 + ], + "ordinal": 841, + "phase": "B" + }, + { + "new": [ + 2, + 28, + 40, + 76, + 129, + 257 + ], + "old": [ + 2, + 28, + 100, + 129, + 257 + ], + "ordinal": 842, + "phase": "B" + }, + { + "new": [ + 5, + 27, + 42, + 73, + 129, + 257 + ], + "old": [ + 30, + 47, + 73, + 129, + 257 + ], + "ordinal": 843, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 848, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 849, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 850, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 851, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 872, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 873, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 874, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 875, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 880, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 881, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 882, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 883, + "phase": "B" + }, + { + "new": [], + "old": [ + 2, + 5, + 40, + 80, + 409 + ], + "ordinal": 928, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 949, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 951, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 1052, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 1053, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 1054, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 1055, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 1101, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 1102, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 1103, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 1104, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 1121, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 1122, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 1123, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 1124, + "phase": "B" + }, + { + "new": [ + 3, + 12, + 21, + 37, + 68, + 132, + 260 + ], + "old": [ + 15, + 21, + 38, + 68, + 132, + 260 + ], + "ordinal": 1185, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 67, + 128, + 256 + ], + "old": [ + 4, + 17, + 34, + 75, + 128, + 256 + ], + "ordinal": 1186, + "phase": "B" + }, + { + "new": [ + 4, + 11, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 51, + 64, + 128, + 256 + ], + "ordinal": 1187, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 17, + 34, + 64, + 132, + 260 + ], + "ordinal": 1188, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 128, + 259 + ], + "old": [ + 4, + 17, + 34, + 64, + 128, + 267 + ], + "ordinal": 1194, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 132, + 256 + ], + "old": [ + 11, + 17, + 34, + 68, + 132, + 256 + ], + "ordinal": 1196, + "phase": "B" + }, + { + "new": [ + 1, + 12, + 18, + 38, + 64, + 128, + 256 + ], + "old": [ + 1, + 30, + 38, + 64, + 128, + 256 + ], + "ordinal": 1201, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 64, + 129, + 257 + ], + "old": [ + 10, + 20, + 38, + 64, + 129, + 257 + ], + "ordinal": 1202, + "phase": "B" + }, + { + "new": [ + 6, + 11, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 11, + 21, + 39, + 65, + 129, + 257 + ], + "ordinal": 1203, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 102, + 128, + 256 + ], + "ordinal": 1204, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 30, + 32, + 70, + 128, + 256 + ], + "ordinal": 1205, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 129, + 256 + ], + "old": [ + 10, + 20, + 38, + 65, + 129, + 256 + ], + "ordinal": 1210, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 1, + 10, + 20, + 64, + 128, + 294 + ], + "ordinal": 1212, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 10, + 20, + 33, + 65, + 128, + 262 + ], + "ordinal": 1213, + "phase": "B" + }, + { + "new": [ + 7, + 10, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 13, + 19, + 38, + 70, + 134, + 262 + ], + "ordinal": 1217, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 74, + 128, + 256 + ], + "old": [ + 6, + 24, + 32, + 75, + 128, + 256 + ], + "ordinal": 1218, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 11, + 21, + 32, + 64, + 128, + 256 + ], + "ordinal": 1219, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 6, + 11, + 19, + 64, + 160, + 288 + ], + "ordinal": 1220, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 1, + 12, + 18, + 70, + 160, + 288 + ], + "ordinal": 1221, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 128, + 266 + ], + "old": [ + 6, + 24, + 32, + 64, + 128, + 267 + ], + "ordinal": 1226, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 11, + 19, + 96, + 160, + 256 + ], + "ordinal": 1228, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 10, + 18, + 96, + 161, + 256 + ], + "ordinal": 1229, + "phase": "B" + }, + { + "new": [ + 7, + 8, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 8, + 21, + 38, + 64, + 128, + 256 + ], + "ordinal": 1233, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 64, + 136, + 264 + ], + "old": [ + 3, + 21, + 37, + 64, + 136, + 264 + ], + "ordinal": 1234, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 17, + 34, + 67, + 131, + 259 + ], + "old": [ + 11, + 22, + 37, + 67, + 131, + 259 + ], + "ordinal": 1235, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 81, + 128, + 256 + ], + "old": [ + 3, + 8, + 48, + 85, + 128, + 256 + ], + "ordinal": 1236, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 136, + 256 + ], + "old": [ + 3, + 21, + 37, + 72, + 136, + 256 + ], + "ordinal": 1242, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 128, + 273 + ], + "old": [ + 3, + 8, + 48, + 64, + 128, + 277 + ], + "ordinal": 1244, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1417, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1418, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1433, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1434, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1437, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1438, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1445, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1446, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 0, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 1, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 2, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 3, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 4, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 5, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 6, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 7, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 8, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 9, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 10, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 11, + "phase": "cleanup_tail" + }, + { + "new": [ + 2, + 5, + 24, + 40, + 72, + 385 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 12, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 20, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 21, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 22, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 23, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 24, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 25, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 26, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 27, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 28, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 29, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 30, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 31, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 32, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 33, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 34, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 35, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 36, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 37, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 38, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 39, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 47, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 48, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 49, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 50, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 51, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 52, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 55, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 56, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 60, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 61, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 62, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 63, + "phase": "cleanup_tail" + }, + { + "new": [ + 3, + 12, + 17, + 33, + 64, + 388 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 67, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 73, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 74, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 75, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 76, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 85, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 88, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 94, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 95, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 96, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 97, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 98, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 99, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 100, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 101, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 102, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 103, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 104, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 105, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 106, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 107, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 108, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 109, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 110, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 111, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 116, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 117, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 121, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 122, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 123, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 124, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 125, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 126, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 127, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 128, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 129, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 130, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 131, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 132, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 133, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 134, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 135, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 136, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 137, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 138, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 139, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 140, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 141, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 142, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 143, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 144, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 145, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 146, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 147, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 148, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 149, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 150, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 151, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 152, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 153, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 154, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 155, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 156, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 157, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 158, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 159, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 160, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 161, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 162, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 163, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 164, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 165, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 166, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 167, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 168, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 169, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 170, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 171, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 172, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 173, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 174, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 175, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 176, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 177, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 178, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 179, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 180, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 181, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 182, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 183, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 188, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 189, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 191, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 192, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 193, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 194, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 195, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 196, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 197, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 198, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 199, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 200, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 201, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 202, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 204, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 205, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 206, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 207, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 208, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 209, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 226, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 228, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 230, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 249, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 251, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 265, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 267, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 299, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 304, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 320, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 331, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 363, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 395, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 408, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 412, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 424, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 428, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 448, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 449, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 450, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 451, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 452, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 453, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 454, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 455, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 482, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 483, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 496, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 497, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 503, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 504, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 507, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 508, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 526, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 527, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 550, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 551, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 566, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 567, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 568, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 569, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 574, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 575, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 576, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 577, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 580, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 582, + "phase": "exit" + } + ], + "source_head": "322e0ec764aa7ef7801383feb1f656e460dd8bed" +} diff --git a/research/joint-helper-lattice/PROOF.md b/research/joint-helper-lattice/PROOF.md new file mode 100644 index 0000000000..e41106031d --- /dev/null +++ b/research/joint-helper-lattice/PROOF.md @@ -0,0 +1,102 @@ +# Construction and proof obligations + +## 1. Exact predecessor and changed object + +The input is PR4447 at commit `322e0ec764aa7ef7801383feb1f656e460dd8bed`, with its credited THREE-base native word, PR4441 helper-boundary retiming, and the added three-dimensional frame at B/480. `SOURCES.json` binds all external proof inputs by Git blob and SHA-256. + +There are 632 persistent local fields: 224 main fields and 408 helpers. Each helper is an arbitrary independent input, not initialized scratch. The separate owned center is initialized and erased under the inherited native contract. None of its eight uses receives productive-input credit. + +The patch retains the scalar order and coefficients in each orientation. It retains all native warp events and every main-field boundary. It changes 38 helper entrance frames, 47 helper terminal frames, and 414 scalar contact frames. A source pin accompanies every changed boundary or contact. The two orientations retain their exact inverse-transpose scalar correspondence. + +The optional search jointly optimized both helper boundaries and every mutable scalar contact over the finite intervals of subspaces of F2^9. Fixed main and warp events bound those intervals. The largest quotient dimension was five, so its interval has 374 subspaces. The discovery model used one-hot frame choices and edge marginals, with negative whole-helper credit. Its floating-point solution is a proposal, not a certificate. The following construction and exact tests do not use its claimed optimum. + +## 2. Frame-coordinate invariant + +Let C_F be the source's exact canonical frame operator for subspace F. Interpret a field at frame F as C_F applied to its logical arbitrary value. For nested frames E contained in F, the paid transport is C_F C_E^{-1}. Its Fourier rank is dim(F)-dim(E). The implementation follows the source's `adjoint().then(...)` composition convention and lowers the operator itself, not only that rank formula. + +At each scalar operation, all participating persistent fields are first moved into its declared common frame. A scalar linear combination commutes with the common frame operator. Therefore the operation implements the unchanged logical scalar step. A native warp is run only at its original pinned input frame, and leaves the original pinned output frame. This proves the invariant by induction through the complete chronological word. + +At the end of the word, main fields have their unchanged original endpoints. Helper r has the whole residual C_{T_r} C_{S_r}^{-1}, where S_r and T_r are its new entrance and exit. Every checked S_r is a proper subspace of T_r. Its positive productive rank is dim(T_r)-dim(S_r). There is no duplicate field, discarded helper, clean-input assumption, or free temporary productive input. + +The helper normalizers are recomputed on these whole-job boundaries. Every new transport and each distinct helper boundary is lowered in both orientations with exact Clifford tableaux and absolute phases. The receipt contains 423 distinct transport/boundary pairs, including 406 newly occurring transport pairs relative to PR4447. Two retained literal interpreters check the complete 632-column endpoint. The argument is the frame-coordinate invariant; the finite replay independently checks its application to the submitted circuit. + +## 3. Complete local bill and uniform moment gain + +Write H_r for productive helpers of rank r and P_r for paid jobs of rank r. The predecessor has + + H_old = {4:26, 5:2, 7:29, 8:42, 9:309} + P_old = {1:2254, 2:514, 3:444, 4:103, 5:40, 8:8}. + +The new word has + + H_new = {4:28, 7:7, 8:47, 9:326} + P_new = {1:2237, 2:388, 3:494, 4:147, 5:36, 8:8}. + +There are 408 helpers in both words. The new paid list has 3,310 entries, 53 fewer than the predecessor. Helper rank mass increases from 3,434 to 3,471, and paid rank mass from 5,290 to 5,327. Their difference remains 1,856. In particular, the improvement is not obtained by keeping old productive credit after removing paid work. + +For 0D(1)=0 for every 0 theta^1000, + 145^(1024*TESTED) < 2^1000. + +Set kappa=0.00302015 and d=(TESTED-kappa)/7=1/1,400,000,000. The integer test + + (1,400,000,000*j + 1)^1000 < 2^j + +passes at j=45,868 and fails at j-1. Thus the retained theorem supplies the sufficient uniform rank N=2^64,215,200,000,000. This is an existence construction with explicit finite constants. The resulting word is not materialized and no practical implementation claim follows. + +The new local scalar and fixed-route bound remains below 10^7 per full call. Eighteen such calls, all 15 thin-query charges, every scalar controller and boundary operation fit the complete raw bound 10^9. The number of roles, private storage, coefficient matrices and tapes is finite for the compiled template. Their sizes affect the eventual threshold and are not claimed uniform while changing that template. + +Retain the source BIT ordinary saving 0.0034, with atom exponent 0.004. Its delayed-cover, weighted-child, row-stock and conversion conditions are rechecked through the source package. Use complex uniform saving kappa+6d, followed by b=kappa+5d, a=kappa+4d, q=kappa+3d, epsilon=1-d, beta=1-3d, r0=d/10, stop=d and layout=d. All nine outer cost rows, 54 strict predicates and four functional guards pass exactly. The old BIT cap and closed exponent gaps are explicit rejected controls. + +## 7. Status of the conclusion + +Subject to the retained all-column/native and physical-operation contracts, owned erasure, whole-job matching, finite-template compiler closure, precision and fixed-tape bounds, analytic decomposition, prime avoidance and exact recovery, this construction gives the source framework's conditional multiplication saving kappa=0.00302015. + +The submitted change establishes an exact finite native word and a fully charged conditional parameter transfer. It does not remove the inherited analytic or physical premises. It does not promote the selected frontier, certify global optimality, claim a runtime speedup, or claim independent human or proof-assistant acceptance. + +Credits: zxv's native and higher-moment/logarithmic work; Jacob Alan Sussman's finite mixed-flow theorem; Cinna Davis's prior p7 padding, query-thinned and retimed constructions; and the unchanged credited scalar, Clifford, geometry and outer-ledger sources. New material was prepared for Cinna Davis with substantial OpenAI assistance, Apache-2.0. diff --git a/research/joint-helper-lattice/README.md b/research/joint-helper-lattice/README.md new file mode 100644 index 0000000000..063f7a0056 --- /dev/null +++ b/research/joint-helper-lattice/README.md @@ -0,0 +1,46 @@ +# Joint helper boundaries: conditional kappa = 0.00302015 + +This is an author-checked conditional construction, not an unconditional integer-multiplication theorem or a selected-frontier update. + +The new contribution is a joint finite optimization of helper entrances, exits and scalar contact frames. It builds on the exact native supplier of zxv, the retiming in PR4441, the missing span in PR4447, and the query-thinned controller in PR4440. The arithmetic scaffolding and logarithmic compiler test are adapted from PR4447 and the credited PR4433 lineage. + +The proposed saving is `0.00302015`, compared with `0.00300123` in PR4447: an absolute increase of `0.00001892`, or approximately **0.630408%**. This is a moderate incremental improvement. It is not a claim of a large asymptotic breakthrough. + +## What changed + +Relative to PR4447, `PATCH.json` changes 38 helper entrances, 47 helper exits and 414 scalar contact frames. Both scalar orders, every scalar coefficient, main endpoints, native warps, and the owned-center operations remain unchanged. All 408 helpers remain independent, strictly productive arbitrary inputs. + +The local helper profile becomes `{4:28, 7:7, 8:47, 9:326}`. The complete paid profile becomes `{1:2237, 2:388, 3:494, 4:147, 5:36, 8:8}`. This reduces local paid calls from 3,363 to 3,310. Both rank masses increase by 37, leaving the local rank-mass deficit unchanged. The eight whole rank-eight center jobs are included. + +The nonlinear helper credit couples the two boundaries. Separate entrance-only and exit-only updates do not represent that joint objective. The optional finite-lattice mixed-integer search found the patch; the proof does not trust that solver, its objective value, or its optimality status. + +The changed supplier is installed in an explicitly replayed 16-pair controller with 18 full native calls and 15 copied-query shears. Its complete invoice has 10,928 productive fields and 64,620 paid jobs. Target and paid rank masses are 239,886 and 239,134, respectively. The rank-one surplus is 752. The predecessor p17 invoice has a different number of inputs, so total call counts are not a like-for-like runtime comparison. + +`RESULT.json` encloses the new raw moment root in `(0.0030201659770, 0.0030201659771)`. It certifies paid tensor completion, splitting, a finite uniform compiler and every outer inequality at the smaller stated kappa. The unchanged source BIT supplier supports ordinary saving 0.0034. + +## Verification + +Run from the repository root: + +```sh +python3.12 -B scripts/research_package.py --package research/joint-helper-lattice --check-only +python3.12 -B scripts/research_package.py --package research/joint-helper-lattice +``` + +The normal replay uses only the Python standard library. It authenticates the declared sources, reconstructs the changed native word, replays all 632 arbitrary-input columns in both orientations using two retained interpreters, and lowers the new transports and helper boundaries including absolute phase. It regenerates the p16 Laurent and literal controller, checks its boundary factorization, cross-checks the moments with a second rational engine, and verifies the full compiler and outer ledger. Mutation controls reject false ranks, unsupported query orientation, unpaid full stages, the old invoice at the new saving, and invalid outer parameters. + +`--write` is an authoring path using saved native and predecessor receipts. It is not the registered full replay. `VALIDATION.md` records the commands actually completed. + +`PROOF.md` states the construction, complete cost argument and inherited assumptions. `DISCOVERY.json` contains floating-point search evidence only; no solver optimality claim is part of the theorem. `PATCH.json`, `NATIVE.json.gz`, `CONTROLLER.json` and `RESULT.json` are the mathematical replay artifacts. + +## Scope and credit + +The source all-column native contract, allowed erasure of owned storage, whole-job normalizers, finite-template closure, precision and monomial tape bounds, analytic decomposition, prime avoidance, and exact recovery remain explicit premises. The enormous uniform word is algorithmically specified, not materialized. No practical speedup, global optimum, formal-kernel acceptance, or independent human review is claimed. + +The branch is stacked on exact PR4447 head `322e0ec764aa7ef7801383feb1f656e460dd8bed`. Its ancestors retain PR4440/PR4441 and the pending PR4447 contribution. Those inherited changes are not new work in this package. Canonical main at the final research checkpoint was `2a13eb1827784206202db90e5dc8327cf8a250db`. + +Credit zxv's native and compiler work, Jacob Alan Sussman's mixed-target integer flow, Cinna Davis's PR4416 padding and PR4440/PR4441/PR4447 contributions, and the retained scalar, Clifford, geometry, precision and outer-ledger authors. Source notices remain unchanged. New work prepared for Cinna Davis with substantial OpenAI assistance. Apache-2.0. + +## Open next questions + +Can a costed scalar reordering or changed warp word beat this fixed chronological graph? Start with a small commuting contact block, derive its dependency graph, then reconstruct every physical endpoint before repricing it. The finite solver's optimum report is not an exact general barrier and does not cover changed scalar orders or warps. The structured question and blocker are in `TASK.json`. diff --git a/research/joint-helper-lattice/RESULT.json b/research/joint-helper-lattice/RESULT.json new file mode 100644 index 0000000000..edf41a49a0 --- /dev/null +++ b/research/joint-helper-lattice/RESULT.json @@ -0,0 +1,274 @@ +{ + "compiler": { + "H": 64215200000000, + "N": "2^64215200000000", + "eta": { + "lower": "0.000000206231977820868640096499", + "upper": "0.000000206231977820868640096500" + }, + "gap": "1/1400000000", + "integer_test_exponent": 45868, + "logarithm_power": 1000, + "theta": "63/64", + "uniform_saving": "528527/175000000", + "word_materialized": false + }, + "fixed_profile_ceiling": { + "decreasing_through_C": "1/20", + "headroom": [ + "15977/1000000000000", + "159771/10000000000000" + ], + "negative_derivative_upper": { + "lower": "-195970.145588045890401261885812812963", + "upper": "-195970.145588045890401261885812812962" + }, + "remaining_interval_moment_upper": { + "lower": "-6847.019825166589746262304732988153", + "upper": "-6847.019825166589746262304732988152" + }, + "root": [ + "3020165977/1000000000000", + "30201659771/10000000000000" + ] + }, + "full_calls": 18, + "gain_over_PR4416": "4171/12500000", + "gain_over_PR4440": "1203/20000000", + "gain_over_PR4441": "191/10000000", + "gain_over_PR4447": "473/25000000", + "kappa": "60403/20000000", + "kappa_decimal": "0.00302015", + "local_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "local_paid": { + "1": 2237, + "2": 388, + "3": 494, + "4": 147, + "5": 36, + "8": 8 + }, + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform": [ + "new_complex_uniform_saving_above_b" + ], + "old_BIT": [ + "actual_bit_above_effective" + ], + "unfunded_endpoint": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "nonrecursive": { + "local_route_bound": 4814000, + "local_scalar_allowance": 158168, + "raw_budget": 1000000000, + "raw_upper": 181098496 + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "348599999253/350000000000", + "fixed_halo_explicit_metadata_branch": "26950000001/350000000", + "new_BIT_row_stock_sublinear_in_active_group": "1395799997009/1400000000000", + "new_semantic_group_guard": "3/1400000000" + }, + "margins": { + "boundary_algebraic_matrix": "5919499595771787/1960000000000000000", + "fused_gaussian": "5919499587315361/1960000000000000000", + "global_coordinate_router": "2114107/700000000", + "group_bit_router": "2959750493657679/980000000000000000", + "group_scans": "699999999/700000000", + "main_transform": "5919498195771787/1960000000000000000", + "microbox_face_corrections": "26950000001/350000000", + "polynomial_products": "1399999999/1400000000", + "sparse_union_movement": "802169499595771787/1960000000000000000" + }, + "parameters": { + "a": "2114107/700000000", + "b": "845643/280000000", + "beta": "1399999997/1400000000", + "bit_saving": "17/5000", + "cap_xi": "1782169498195771787/1960000000000000000", + "complex_uniform_saving": "528527/175000000", + "d": "1/1400000000", + "epsilon": "1399999999/1400000000", + "kappa": "60403/20000000", + "lambda_": "398791939/400000000", + "lambda_prime": "1395771787/1400000000", + "layout": "1/1400000000", + "q": "4228213/1400000000", + "r0": "1/14000000000", + "stop": "1/1400000000", + "tested_saving": "604031/200000000" + }, + "strict_checks": { + "actual_bit_above_effective": "265893/700000000", + "actual_logarithmic_gamma_guard": "1/1400000000", + "actual_logarithmic_group_guard": "177830503904228213/980000000000000000", + "alpha_logarithm_absorption": "1/14000000000", + "boundary_algebraic_matrix_above_kappa": "5595771787/1960000000000000000", + "cap_above_band": "802169498195771787/1960000000000000000", + "cap_below_cell": "177830500404228213/1960000000000000000", + "cap_below_phase_cell_power": "2137830501804228213/1960000000000000000", + "complex_above_effective": "1/1400000000", + "complex_below_one_over_32": "7904357/280000000", + "complex_endpoint": "1/700000000", + "epsilon_below_one": "1/1400000000", + "epsilon_positive": "1399999999/1400000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "5587315361/1960000000000000000", + "gaussian_above_main": "695771787/980000000000000000", + "global_coordinate_router_above_kappa": "1/350000000", + "global_gamma_power_slack": "9/14000000000", + "group_below_dimension": "1/700000000", + "group_bit_router_above_kappa": "3493657679/980000000000000000", + "group_gauge_power_slack": "177830503834228213/980000000000000000", + "group_key_fits_record": "1/700000000", + "group_positive": "1399999997/1400000000", + "group_scans_above_kappa": "348942947/350000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "644589790400418148631/500000000000000000000000", + "lambda_above_internal": "1/2800000000", + "lambda_above_sigma": "3/2800000000", + "lambda_above_tau": "1/2800000000", + "lambda_prime_above_lambda": "1/2800000000", + "lambda_prime_above_leaf": "559154357/392000000000000000", + "leaf_saving_above_effective": "279154357/392000000000000000", + "main_transform_above_kappa": "4195771787/1960000000000000000", + "membership_arithmetic_fits_record": "1/1400000000", + "microbox_face_corrections_above_kappa": "53897885897/700000000", + "microbox_halo_volume": "110600000003/1400000000", + "new_complex_uniform_saving_above_b": "1/1400000000", + "new_semantic_guard_with_C1_one": "1/1400000000", + "polynomial_products_above_kappa": "1395771789/1400000000", + "positive_layout_slack": "1/1400000000", + "q_below_effective": "1/1400000000", + "q_below_internal": "1/1400000000", + "q_below_leaf": "559154357/392000000000000000", + "q_positive": "4228213/1400000000", + "short_record_fallback": "279154357/280000000", + "source_axis_superpolynomial": "1/1400000000", + "sparse_union_movement_above_kappa": "796250005595771787/1960000000000000000", + "stop_below_one": "1399999999/1400000000", + "stop_positive": "1/1400000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/1400000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/1400000000", + "union_tag_work_per_visit_fits_record": "3/1400000000" + } + }, + "paid": { + "1": 41946, + "16": 448, + "2": 6984, + "24": 448, + "3": 8892, + "32": 448, + "4": 2646, + "40": 448, + "48": 448, + "5": 648, + "56": 448, + "64": 448, + "72": 224, + "8": 144 + }, + "paid_calls": 64620, + "pairs": 16, + "prefix_pairs": 7, + "productive_fields": 10928, + "query_shears": 15, + "scope": "Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.", + "source_heads": { + "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", + "PR4441_combination": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", + "PR4447": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "helper_retiming": "ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9" + }, + "source_inputs": 51, + "status": "PASS_CONDITIONAL_JOINT_HELPER_KAPPA_00302015", + "strictification": { + "alpha": { + "lower": "0.999999988558808354139963023136", + "upper": "0.999999988558808354139963023137" + }, + "cutoff": 20, + "delta": { + "lower": "0.958284435309221389866479909583", + "upper": "0.958284435309221389866479909584" + }, + "floor": 21, + "gamma": { + "lower": "0.956176646497545264598139374323", + "upper": "0.956176646497545264598139374324" + }, + "limits": [ + "999999999/1000000000", + "97/100", + "97/100" + ], + "normalized_paid_upper": "2097152001953127/2097154147483648", + "power": 1024, + "tail_offset": "1/5", + "tested": "604031/200000000" + }, + "targets": { + "145": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 504, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "7": 126, + "73": 224, + "8": 846, + "9": 5868 + }, + "uniform_local_gain": { + "coefficients": { + "1": 17, + "2": 126, + "3": -50, + "4": -42, + "5": 2, + "7": -22, + "8": 5, + "9": 17 + }, + "derivative_upper": { + "lower": "-16.327581880492435373215953558618", + "upper": "-16.327581880492435373215953558617" + }, + "intervals": 128, + "vanishes_at_one": true + } +} diff --git a/research/joint-helper-lattice/SOURCES.json b/research/joint-helper-lattice/SOURCES.json new file mode 100644 index 0000000000..02e8f76eab --- /dev/null +++ b/research/joint-helper-lattice/SOURCES.json @@ -0,0 +1,330 @@ +{ + "base_commit": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "files": [ + { + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "path": "certificates/selected-result.json", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9", + "usage": "provenance" + }, + { + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "path": "docs/research/agent-task-catalog.json", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96", + "usage": "provenance" + }, + { + "git_blob": "70373e1f92829cf16ea1836ae0cced06ed937a5e", + "path": "docs/research/current-priorities.md", + "sha256": "2df24baf0d8a5a714fdf36120e4075078c5455904e359ac6c0f9f7e39418fba1", + "usage": "provenance" + }, + { + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7", + "usage": "input" + }, + { + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "path": "research/fresh-helper-boundary/CHANGES.json", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624", + "usage": "input" + }, + { + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839", + "usage": "input" + }, + { + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "path": "research/fresh-helper-boundary/RESULT.json", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd", + "usage": "input" + }, + { + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "path": "research/fresh-helper-boundary/SOURCES.json", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0", + "usage": "input" + }, + { + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "path": "research/fresh-helper-boundary/arithmetic.py", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07", + "usage": "input" + }, + { + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "path": "research/fresh-helper-boundary/native.py", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29", + "usage": "input" + }, + { + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "path": "research/fresh-helper-boundary/verify.py", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf", + "usage": "input" + }, + { + "git_blob": "bf68dc2b987cb7de6431ff5e3514b60af48720a5", + "path": "research/fresh-helper-thinned/PROOF.md", + "sha256": "9883b3329fef7624d3471e27bb55258cd9dc18bb6d37779a3939de99add87347", + "usage": "input" + }, + { + "git_blob": "344616d6654a96085dd45cf2c3189ef283deeac1", + "path": "research/fresh-helper-thinned/README.md", + "sha256": "70c1c872c2327c3f71918e218d5f1ecb7a00037771a5dd1b8ae415b84cc90dc2", + "usage": "input" + }, + { + "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55", + "path": "research/fresh-helper-thinned/RESULT.json", + "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21", + "usage": "input" + }, + { + "git_blob": "4089ad37114540b23846596e2a641c4a4bd608e2", + "path": "research/fresh-helper-thinned/SOURCES.json", + "sha256": "5aec5df5096ee8a3e90618d311640b4bdfba42be5bc4bc5fab55e8be858ab2cb", + "usage": "input" + }, + { + "git_blob": "9ba85a59aa5dcc5cdaec85ee18607cb050530c55", + "path": "research/fresh-helper-thinned/verify.py", + "sha256": "c841265ccee9b6f79045ad818ce9d27cfd7ee1f60047525a75d491f0dd8b997a", + "usage": "input" + }, + { + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "path": "research/higher-moment-strictification/README.md", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", + "usage": "input" + }, + { + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "path": "research/higher-moment-strictification/verify.py", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", + "usage": "input" + }, + { + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85", + "usage": "input" + }, + { + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "usage": "input" + }, + { + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7", + "usage": "input" + }, + { + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "path": "research/kappa-function-composition/complex/prune_native.py", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257", + "usage": "input" + }, + { + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a", + "usage": "input" + }, + { + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef", + "usage": "input" + }, + { + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0", + "usage": "input" + }, + { + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443", + "usage": "input" + }, + { + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf", + "usage": "input" + }, + { + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7", + "usage": "input" + }, + { + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497", + "usage": "input" + }, + { + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e", + "usage": "input" + }, + { + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17", + "usage": "input" + }, + { + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6", + "usage": "input" + }, + { + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61", + "usage": "input" + }, + { + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39", + "usage": "input" + }, + { + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "path": "research/kappa-rebuild/complex/native_extensions.py", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3", + "usage": "input" + }, + { + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424", + "usage": "input" + }, + { + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5", + "usage": "input" + }, + { + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902", + "usage": "input" + }, + { + "git_blob": "2f41b11d02726a60da449aaa6c603716c0310ead", + "path": "research/missing-join-frame/NATIVE.json.gz", + "sha256": "96718b257db24f4f62d3b86b36cdd514e67d2cb99947ddd7bdcb9b55a2c17841", + "usage": "input" + }, + { + "git_blob": "f96d295d40014d4dd503f58eb3cdabcbb4b8e101", + "path": "research/missing-join-frame/PATCH.json", + "sha256": "9ab5328245ff02c9d0be21d39bcc375f50bc5d7909e9f7b9a3a9a6f812f5bd6e", + "usage": "input" + }, + { + "git_blob": "d240cd8e14e6d30e0e2c3d0ddcc7efa68349e24e", + "path": "research/missing-join-frame/PROOF.md", + "sha256": "50061c25d379ff5733135dbed53e8721bbd4dbee6766d1609d8a2ecdebb7dc06", + "usage": "input" + }, + { + "git_blob": "e653fb4358ded67ff1539151f4b670ad9a242fb1", + "path": "research/missing-join-frame/RESULT.json", + "sha256": "25f2cbcde988847ff86f44e804982069863ec99ff68097f16e9bb7a1a17c4cd0", + "usage": "input" + }, + { + "git_blob": "188135f81c9937af8232a06dc1e7b8b28260e6a8", + "path": "research/missing-join-frame/verify.py", + "sha256": "21429dd9c1b9c93ebb57e5fbb8ef674d0e4146ac8c25cc7c097c3352c02366a4", + "usage": "input" + }, + { + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "usage": "input" + }, + { + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "path": "research/pr4359-p7-padding/TENSOR.md", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3", + "usage": "input" + }, + { + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "usage": "input" + }, + { + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "path": "research/pr4359-p7-padding/native_inventory.py", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32", + "usage": "input" + }, + { + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "usage": "input" + }, + { + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088", + "usage": "input" + }, + { + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "path": "research/query-thinned-controllers/RESULT.json", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f", + "usage": "input" + }, + { + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "path": "research/query-thinned-controllers/SOURCES.json", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29", + "usage": "input" + }, + { + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "path": "research/query-thinned-controllers/controller.py", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2", + "usage": "input" + }, + { + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "path": "research/query-thinned-controllers/verify.py", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950", + "usage": "input" + }, + { + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "usage": "input" + } + ], + "schema_version": 1 +} diff --git a/research/joint-helper-lattice/TASK.json b/research/joint-helper-lattice/TASK.json new file mode 100644 index 0000000000..aa0123ac3e --- /dev/null +++ b/research/joint-helper-lattice/TASK.json @@ -0,0 +1,73 @@ +{ + "actual_scope": "Jointly change helper entrances, exits and scalar contact subspaces; carry the exact new supplier through a p16 query-thinned controller to conditional kappa 0.00302015.", + "ai_assistance": "Substantial OpenAI assistance in discovery, proof, implementation and verification; no independent human or proof-assistant review.", + "author": "Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance", + "base_commit": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "bottleneck_link": "Separate entrance/exit updates miss the coupled productive rank reward. The joint patch lowers the complete moment despite increasing both rank masses equally.", + "budget_minutes": 180, + "evidence": "PATCH.json, NATIVE.json.gz, CONTROLLER.json, RESULT.json, PROOF.md and VALIDATION.md", + "open_questions": [ + { + "blocked_by": "No verified changed-order candidate is included.", + "first_step": "Preserve exact scalar dependencies but alter a small commuting contact block, reconstruct its new graph, and replay any candidate on every arbitrary-input column.", + "question": "Can scalar reordering or a changed warp word improve beyond joint monotone retiming?", + "why_it_matters": "The finite all-subspace search reports no remaining improvement for the fixed word at the tested objective; this numerical solver status is not a universal barrier." + } + ], + "original_card": { + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "complex-new-helper-inventory", + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ], + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ] + }, + "outcome": "completed", + "priority_revision": 7, + "schema_version": 1, + "scope_change_reason": "Explicit kappa improvement assignment. Unlike separate one-label endpoint sweeps, optimize both helper boundaries and all intermediate contacts in one finite lattice model.", + "scope_status": "changed", + "stop_rule": "Publish only after both arbitrary-input native replays, all new absolute phases, the full paid tails and all outer inequalities pass.", + "task_id": "complex-new-helper-inventory", + "upstream_checkpoint": { + "checked_at_utc": "2026-10-21T21:14:00Z", + "coverage": "Latest open and merged PRs through #4446; no stronger declared kappa found.", + "frontier": "PR4446 kappa 0.003001053 uses the same prior invoice; new certificate here is stronger. PR4441 updated head 5f9d871c independently replayed before extending.", + "main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "priority_revision": 7 + } +} diff --git a/research/joint-helper-lattice/VALIDATION.md b/research/joint-helper-lattice/VALIDATION.md new file mode 100644 index 0000000000..cd9b4bf035 --- /dev/null +++ b/research/joint-helper-lattice/VALIDATION.md @@ -0,0 +1,7 @@ +# Validation record + +The first exact native replay completed under Pyroam Python 3.12 on 2026-10-21. Its NATIVE.json.gz records both complete 632-column checks and 423 distinct pairs lowered in both orientations, including absolute phase. The authoring arithmetic path passed at kappa 0.00302015 after replacing the p16 completion-tail limit explicitly with 97/100. + +The registered full replay, metadata check and committed-byte check are recorded below when completed. A transport timeout in the client is not counted as failure or success: the retained complete process log and generated receipt determine the reported state. + +No hosted CI result, independent human review, formal-kernel verification, or full historical selected-frontier replay is claimed here. diff --git a/research/joint-helper-lattice/VERIFY.json b/research/joint-helper-lattice/VERIFY.json new file mode 100644 index 0000000000..d6c82e2902 --- /dev/null +++ b/research/joint-helper-lattice/VERIFY.json @@ -0,0 +1,70 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "checks": "Fresh p16 rational/Laurent and literal replay; both native orientations on all 632 arbitrary input columns, exact new transport and helper phases; two rational interval engines; complete paid-tail, uniform compiler, BIT, and outer ledger checks with semantic controls.", + "timeout_seconds": 600 + } + ], + "inputs": [ + "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "research/fresh-helper-boundary/RESULT.json", + "research/fresh-helper-boundary/SOURCES.json", + "research/fresh-helper-boundary/arithmetic.py", + "research/fresh-helper-boundary/native.py", + "research/fresh-helper-boundary/verify.py", + "research/fresh-helper-thinned/PROOF.md", + "research/fresh-helper-thinned/README.md", + "research/fresh-helper-thinned/RESULT.json", + "research/fresh-helper-thinned/SOURCES.json", + "research/fresh-helper-thinned/verify.py", + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/verify.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-function-composition/complex/prune_native.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "research/kappa-rebuild/bit/bit_native_binding.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-rebuild/bit/mixed_productive_bit.py", + "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/kappa-rebuild/complex/native_extensions.py", + "research/kappa-rebuild/complex/power_two_balance.py", + "research/kappa-rebuild/complex/rebuild_native.py", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "research/missing-join-frame/NATIVE.json.gz", + "research/missing-join-frame/PATCH.json", + "research/missing-join-frame/PROOF.md", + "research/missing-join-frame/RESULT.json", + "research/missing-join-frame/verify.py", + "research/pr4359-p7-padding/P7-FACTOR.json", + "research/pr4359-p7-padding/TENSOR.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/pr4359-p7-padding/native_inventory.py", + "research/query-thinned-controllers/BIT-CONTROLLER.json", + "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "research/query-thinned-controllers/RESULT.json", + "research/query-thinned-controllers/SOURCES.json", + "research/query-thinned-controllers/controller.py", + "research/query-thinned-controllers/verify.py", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py" + ], + "python": "3.12", + "requirements": [], + "schema_version": 1, + "status": "ready" +} diff --git a/research/joint-helper-lattice/native_joint.py b/research/joint-helper-lattice/native_joint.py new file mode 100644 index 0000000000..0315f80e2f --- /dev/null +++ b/research/joint-helper-lattice/native_joint.py @@ -0,0 +1,118 @@ +"""Joint entrance/exit/contact retiming, with literal and phase replay. + +Apache-2.0. Substantial OpenAI assistance. Uses the credited native retiming +implementation of PR4441 and preserves PR4447's missing-span predecessor. +""" +from collections import Counter +from copy import deepcopy +from pathlib import Path +import json,gzip,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +sys.path.insert(0,str(ROOT/'research/fresh-helper-boundary')) +import native as F +need=F.need + +def construct(patch=None): + c=F.read(F.BASE/'THREE-base-FULL-IDENTITY-CANONICAL.json.gz') + original=F.read(F.BASE/'THREE-base-FULL-IDENTITY-NATIVE.json.gz') + parent=F.read(F.HERE/'CHANGES.json') + maps={d:F.gates(p) for d,p in original.items()} + need(set(maps['forward'])==set(maps['backward']),'Same scalar contact inventory') + for key in maps['forward']: + f=original['forward'][maps['forward'][key]];b=original['backward'][maps['backward'][key]] + need(b[1]==F.dual(f[1]) and b[2]==f[2],'Retained exact dual scalar words') + for key,field in [('entrances','start'),('exits','final')]: + for r,old,new in parent[key]: + need(c[field][r]==old,'Parent boundary pin');c[field][r]=new + for phase,ordinal,old,new in parent['gates']: + for d,p in original.items(): + i=maps[d][phase,ordinal];need(p[i][2]==old,'Parent scalar pin');p[i][2]=new + prior=F.read(ROOT/'research/missing-join-frame/PATCH.json') + need(prior['phase']=='B' and prior['ordinal']==480,'Exact prior contact') + prior_frame=len(c['frames']);c['frames'].append(prior['new_basis']) + for d,p in original.items(): + i=maps[d]['B',480];need(p[i][2]==prior['old_frame'],'Missing-span parent pin');p[i][2]=prior_frame + baseline=deepcopy(c) + before={d:F.synthesize(c,p) for d,p in original.items()} + patch=F.read(HERE/'PATCH.json') if patch is None else patch + need(patch['source_head']=='322e0ec764aa7ef7801383feb1f656e460dd8bed','Pinned candidate head') + labels={frozenset(F.span(b)):i for i,b in enumerate(c['frames'])} + def label(b): + s=frozenset(F.span(b));need(len(s)==2**len(b),'Independent binary basis') + if s not in labels:labels[s]=len(c['frames']);c['frames'].append(b) + return labels[s] + seen=set();counts=Counter() + for move in patch['changes']: + phase,r=move['phase'],move['ordinal'];key=(phase,r) + need(key not in seen,'No duplicate changed boundary/contact');seen.add(key) + a,b=F.span(move['old']),F.span(move['new']);need(a!=b,'No unchanged patch entry') + f=label(move['new']);counts[phase]+=1 + if phase in ('entrance','exit'): + need(224<=r<632,'Only independent helper boundaries may change') + field='start' if phase=='entrance' else 'final' + need(F.span(c['frames'][c[field][r]])==a,'Current helper source pin') + c[field][r]=f + else: + for d,p in original.items(): + i=maps[d][key];need(F.span(c['frames'][p[i][2]])==a,'Current scalar source pin');p[i][2]=f + programs={d:F.synthesize(c,p) for d,p in original.items()} + return c,programs,baseline,before,counts + +def run(phase_check=True): + c,programs,baseline,before,counts=construct() + V=F.load(ROOT/'research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py','joint_rows') + X=F.load(ROOT/'research/kappa-rebuild/complex/native_extensions.py','joint_literal') + checks={};profiles={} + for d,p in programs.items(): + rows,rec=X.literal_replay(V,c,p,d=='backward') + for r in range(632):need(rows['L',r]==V.expected(('L',r),[],d=='backward',False),'All 632 arbitrary-input endpoints') + profiles[d]=Counter({int(k):v for k,v in rec['paid_profile'].items()}) + rebound=deepcopy(c);rebound['local_profile']=dict(profiles[d]) + rec['second_literal']=V.replay(p,rebound,[],d=='backward',False);checks[d]=rec + need(profiles['forward']==profiles['backward'],'Both complete native rank tariffs') + H=Counter() + for r in range(224,632): + a,b=c['start'][r],c['final'][r] + need(F.span(c['frames'][a])0 and margin(ROOT_HIGH)[1]<0,'New complete profile root bracket') + derivative=None + for i in range(16): + l,r=Q(i,320),Q(i+1,320);low=Q(0) + for rank,n in signed.items(): + term=E.mul(E.power(rank,1-r if n>0 else 1-l),E.log_bounds(rank)) + low+=n*term[0 if n>0 else 1] + derivative=low if derivative is None else min(derivative,low) + upper=None + for i in range(128): + l,r=Q(1,20)+Q(19*i,2560),Q(1,20)+Q(19*(i+1),2560) + hi=sum(n*E.power(rank,1-l if n>0 else 1-r)[1 if n>0 else 0] for rank,n in signed.items()) + upper=hi if upper is None else max(hi,upper) + need(derivative>0 and upper<0,'Fixed-profile ceiling for every real 00,'No nonzero charge for erased idle stage') + P[rank]+=224;idle+=224 + for term in word['diagonal']: + need(term[0] in (-1,1) and all(x in (0,1) for x in term[1:]),'Actual normalized main target') + T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(18,15,3360),'Every full, copied-query and whole-idle event') + need(sum(T.values())==10928 and sum(P.values())==64620,'Complete new productive/call counts') + need((sum(r*n for r,n in T.items()),sum(r*n for r,n in P.items()))==(239886,239134),'Preserve the exact surplus 752') + # Independent substitution into the source invoice must give the same ledger. + oldH={5:28,6:18,7:56,8:93,9:213};oldP={1:2487,2:713,3:224,4:102,5:20,8:8} + ref=word['invoice'] + for key,new,old_unit,new_unit in [('targets',T,oldH,H),('paid',P,oldP,N)]: + check=Counter({int(k):v for k,v in ref[key].items()}) + check.subtract({k:18*v for k,v in old_unit.items()});check.update({k:18*v for k,v in new_unit.items()}) + need(+check==new,'Literal event count equals whole-call substitution: '+key) + E=S.C.load(ROOT/'research/higher-moment-strictification/verify.py','combined_exact_intervals') + root=ceiling(E,T,P) + # A finite interval proof of a uniform strict local moment improvement. + coefficients={1:17,2:126,3:-50,4:-42,5:2,7:-22,8:5,9:17} + prior_native=read(ROOT/'research/missing-join-frame/NATIVE.json.gz') + actual=Counter(H);actual.subtract(N) + actual.subtract({int(k):v for k,v in prior_native['helpers'].items()}) + actual.update({int(k):v for k,v in prior_native['paid'].items()}) + need({k:v for k,v in actual.items() if v}==coefficients,'Uniform gain is the actual source-bound profile difference') + need(sum(r*n for r,n in coefficients.items())==0,'Local gain vanishes at t=1') + derivative_upper=None + for i in range(128): + l,r=Q(i,128),Q(i+1,128) + bound=Q(0) + for rank,n in coefficients.items(): + product=E.mul(E.power(rank,r if n>0 else l),E.log_bounds(rank)) + bound+=n*product[1 if n>0 else 0] + derivative_upper=bound if derivative_upper is None else max(derivative_upper,bound) + need(derivative_upper<0,'Joint local moment gain for every 0ph and max(tl,target[0])<=min(th,target[1]),'Independent exact raw-moment engine') + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + alpha_gap=Q(1,1000000000);g,d=Q(97,100),Q(97,100) + need(alpha[1]<1-alpha_gap and gamma[1]theta**power,'Shifted exit and complement capacity') + need(E.power(145,v*TESTED)[1]<2**power,'Initial compiler range') + gap=(TESTED-KAPPA)/7;need(gap.numerator==1,'Integer compiler grid') + step=gap.denominator + def passes(j):return (step*j+1)**power<2**j + lo,hi=1,2 + while not passes(hi):lo,hi=hi,2*hi + while hi-lo>1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + height=step*hi + need(height>8*v and passes(hi) and not passes(hi-1),'Effective uniform rank integer inequality') + # The changed local list is charged under an explicit larger fixed bound. + local_scalar=max(x['real_scalar_allowance'] for x in local['native'].values()) + local_routes=(sum(N.values())+2*408+688)*1000 + need(local_scalar+local_routes<10**7,'Every new local scalar and monomial route fits') + scalar_upper=18*10**7+15*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program']) for k in ('left','right'))) + need(scalar_upper<10**9,'Retain the complete raw nonrecursive bound') + bit=source_query['ordinary_BIT'];atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']);need(atom==Q('.004') and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Complete stronger source BIT admission') + L=S.C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','combined_outer_ledger') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Complete outer predicate inventory') + need(all(x>0 for key in ('strict_checks','functional_checks') for x in outer[key].values()),'Every complete outer inequality') + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items() if x<=0] + need(failed,'Reject '+name);controls[name]=failed + return encode({'status':'PASS_CONDITIONAL_JOINT_HELPER_KAPPA_00302015', 'kappa':KAPPA,'kappa_decimal':'0.00302015', + 'source_inputs':count,'uniform_local_gain':local_gain,'source_heads':{'PR4447':'322e0ec764aa7ef7801383feb1f656e460dd8bed','PR4440':'40e22a83ed660d3d6074c4f2dbf14bfb621eee51','helper_retiming':'ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9','PR4441_combination':'5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39'}, + 'gain_over_PR4447':KAPPA-Q('.00300123'), 'gain_over_PR4441':KAPPA-Q('.00300105'), 'gain_over_PR4440':KAPPA-Q('.00296'),'gain_over_PR4416':KAPPA-Q('.00268647'), + 'targets':dict(sorted(T.items())),'paid':dict(sorted(P.items())),'full_calls':full,'query_shears':thin,'pairs':16,'prefix_pairs':7,'local_helpers':H,'local_paid':N, + 'paid_calls':sum(P.values()),'productive_fields':sum(T.values()),'fixed_profile_ceiling':root, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta), + 'limits':[1-alpha_gap,g,d],'normalized_paid_upper':bound}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'uniform_saving':params['complex_uniform_saving'], + 'gap':gap,'H':height,'N':'2^'+str(height),'integer_test_exponent':hi,'word_materialized':False}, + 'nonrecursive':{'local_scalar_allowance':local_scalar,'local_route_bound':local_routes,'raw_upper':scalar_upper,'raw_budget':10**9}, + 'ordinary_BIT':bit,'outer':outer,'negative_controls':controls, + 'scope':'Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.'}) + +if __name__=='__main__': + parser=argparse.ArgumentParser() + parser.add_argument('--write',action='store_true',help='Author the new arithmetic receipt from already-audited dependency receipts; normal replay freshly reruns both dependencies.') + args=parser.parse_args();result=run(execute_sources=not args.write) + if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:need(result==read(HERE/'RESULT.json'),'Exact combined receipt replay') + print(json.dumps({k:result[k] for k in ('status','kappa_decimal','gain_over_PR4441','compiler')},sort_keys=True)) From b9a13c1673e0e9697de410de16e8bbf3207a7363 Mon Sep 17 00:00:00 2001 From: Cinna Davis Date: Wed, 21 Oct 2026 23:33:32 +0000 Subject: [PATCH 19/26] Register and record complete bounded proof gates for conditional kappa 0.00302015 --- research/joint-helper-lattice/FRONTIER.json | 222 +++++++++--------- research/joint-helper-lattice/README.md | 2 +- .../joint-helper-lattice/REPLAY-LOGS.json | 21 ++ research/joint-helper-lattice/VALIDATION.md | 22 +- research/joint-helper-lattice/VERIFY.json | 28 ++- research/joint-helper-lattice/verify.py | 77 +++++- 6 files changed, 244 insertions(+), 128 deletions(-) create mode 100644 research/joint-helper-lattice/REPLAY-LOGS.json diff --git a/research/joint-helper-lattice/FRONTIER.json b/research/joint-helper-lattice/FRONTIER.json index 7496ef6926..9e05b4e025 100644 --- a/research/joint-helper-lattice/FRONTIER.json +++ b/research/joint-helper-lattice/FRONTIER.json @@ -1,8 +1,116 @@ { - "checked_at": "2026-10-21T23:05:41.906476+00:00", - "purpose": "Refresh before publishing the 0.00302015 candidate; no higher kappa found among these recent open PRs.", - "coverage": "Latest 30 open PRs sorted by update; earlier research checkpoints separately covered the active kappa chain.", + "checked_at": "2026-10-21T23:33:26.343365+00:00", + "coverage": "Latest 30 open PRs sorted by updated time; prior snapshots covered the active kappa chain.", + "comparison": "No higher kappa than the submitted 0.00302015 found in the checked claims.", "pull_requests": [ + { + "number": 1764, + "title": "Research: rank-two interface candidate for paired frame transitions", + "head": "92a6b7fef74a7f1e3efb911a366ce32e2d026397", + "updated_at": "2026-10-21T23:33:24Z" + }, + { + "number": 1930, + "title": "Construction: three-stage persistent prefix shear chain (no new kappa)", + "head": "f4bfa47d0a050b3ecf0cdf198d077093661014ef", + "updated_at": "2026-10-21T23:33:20Z" + }, + { + "number": 2216, + "title": "QQ16: add an F0-B1 selected-state shear", + "head": "b384a72e79054fc9589048c2f9eb9fa85fab65ce", + "updated_at": "2026-10-21T23:33:17Z" + }, + { + "number": 2249, + "title": "Research: high-arity connector toggle cost floor", + "head": "2d3a99a0887236ff340596b1295604b9a3a39b07", + "updated_at": "2026-10-21T23:32:58Z" + }, + { + "number": 4469, + "title": "Independently check #4438: within-cell gauge column transfer (C = 3 least, equality at p = 2; no new \u03ba)", + "head": "baf56b163de5981ade5afa28f75bbd7e019f8b65", + "updated_at": "2026-10-21T23:32:55Z" + }, + { + "number": 4467, + "title": "research: #4436 direct-flow leaf walk \u2014 exact \u221aG regime to depth 60, predicted saturation keeps the refined-induction cap below s* (no new \u03ba)", + "head": "43cc0fa102706dbddf97a76f7b4f34363e086071", + "updated_at": "2026-10-21T23:30:29Z" + }, + { + "number": 2134, + "title": "Six-source one-TRIO path misses full paired coverage at 14 calls", + "head": "7d9b18640c410dc3da19aef0a66291c5ab9b2ec1", + "updated_at": "2026-10-21T23:27:39Z" + }, + { + "number": 1900, + "title": "Construction: five plane queries for selected P111 bit decoder (no new kappa)", + "head": "2f7c02ddcc7c086baa57f0db28c0a4ebdc465496", + "updated_at": "2026-10-21T23:27:31Z" + }, + { + "number": 1865, + "title": "Research: nonconsecutive commuting C3 fanout schedule", + "head": "e7d290e9d56eb1a7a8622572272af8e0aef161b9", + "updated_at": "2026-10-21T23:27:23Z" + }, + { + "number": 1836, + "title": "Research: higher-rank paired boundary at a single ADD gate", + "head": "9a7cb3c6c74b9745084f859c5fc8142ebb775cea", + "updated_at": "2026-10-21T23:27:03Z" + }, + { + "number": 4468, + "title": "Independently check #4437: the ideal column majorant holds (and is attained) across g = 2 steps (no new \u03ba)", + "head": "b5f7fbbb4a4a778f78da69ee1a5d965a6af081ad", + "updated_at": "2026-10-21T23:26:49Z" + }, + { + "number": 4465, + "title": "research: refined-induction ceiling on #4436's direct flow grows with lockstep depth (log-gap g, no new \u03ba)", + "head": "36d9c475d4bbc99e93952e0ad86a802e1bc581e8", + "updated_at": "2026-10-21T23:16:29Z" + }, + { + "number": 4466, + "title": "Independently check #4464's stage-zero commutation; the recorded translations are forced: t_i = [c_i \u2261 3 mod 4] (no new \u03ba)", + "head": "496a7d6bd053b7019935529ce5b5c3eb3dc664ed", + "updated_at": "2026-10-21T23:13:54Z" + }, + { + "number": 4440, + "title": "Conditional \u03ba = 0.00296 via query-thinned productive controllers (+10.18%)", + "head": "9123d75afea5096d25eb98b2b6080cbbe0d91c01", + "updated_at": "2026-10-21T23:13:42Z" + }, + { + "number": 4441, + "title": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", + "head": "149af87f1101dc7a72f2fe57294f9bacf8d053ba", + "updated_at": "2026-10-21T23:13:04Z" + }, + { + "number": 4446, + "title": "Independent retimed p17 certificate: conditional kappa = 0.003001053", + "head": "e2bde8f5b9bfa2e8d51f959656d84ebcc2af81b7", + "updated_at": "2026-10-21T23:12:34Z" + }, + { + "number": 4447, + "title": "Conditional kappa = 0.00300123 via a missing three-dimensional contact span", + "head": "02b51f341013c607dc480248c94c216b8260d8af", + "updated_at": "2026-10-21T23:11:49Z" + }, + { + "number": 4464, + "title": "research: certify the actual stage-zero Gaussian commutation premise", + "head": "82c7db427100033aa1275ecdb16ebc2e2ef10b91", + "updated_at": "2026-10-21T23:06:01Z" + }, { "number": 4459, "title": "research: #4436 boundary exits \u2014 exact mirror identity, rigorous share bound 0.321, and a correction (leaf exits dominate)", @@ -74,114 +182,6 @@ "title": "Independently reconstruct PR4441 helper tariffs and complete p17 invoice", "head": "6d535abed7b60d4a99dc54903011a72ec367e901", "updated_at": "2026-10-21T21:21:23Z" - }, - { - "number": 4450, - "title": "Audit THREE-base supplier billing from native events (no new kappa)", - "head": "e8305f07db188d6fa0be1c91ae77cc2414ea029d", - "updated_at": "2026-10-21T21:19:46Z" - }, - { - "number": 4449, - "title": "Prove the downward rounding contract for across-cell Gaussian entries", - "head": "1fb77b377f570ca84a89a465b2ee4ce8674b7159", - "updated_at": "2026-10-21T21:18:04Z" - }, - { - "number": 4447, - "title": "Conditional kappa = 0.00300123 via a missing three-dimensional contact span", - "head": "322e0ec764aa7ef7801383feb1f656e460dd8bed", - "updated_at": "2026-10-21T21:14:57Z" - }, - { - "number": 4446, - "title": "Independent retimed p17 certificate: conditional kappa = 0.003001053", - "head": "7d05d73f96c27a9d360011e04af69b23fa903757", - "updated_at": "2026-10-21T21:07:29Z" - }, - { - "number": 4441, - "title": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", - "head": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", - "updated_at": "2026-10-21T20:42:39Z" - }, - { - "number": 4440, - "title": "Conditional \u03ba = 0.00296 via query-thinned productive controllers (+10.18%)", - "head": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", - "updated_at": "2026-10-21T20:14:35Z" - }, - { - "number": 4442, - "title": "Apply the smaller halo exponents across a cell, under the downward reading (no new \u03ba)", - "head": "d079c2b058ebd3d7a9ff424113b095bf61175427", - "updated_at": "2026-10-21T20:11:41Z" - }, - { - "number": 4439, - "title": "Apply the smaller halo exponents inside one cell, with normalizer 6 (no new \u03ba)", - "head": "26af8afbadd7f8feb737d98b47ac9f4b45d35c7a", - "updated_at": "2026-10-21T20:02:46Z" - }, - { - "number": 4438, - "title": "Bound the within-cell column gap by a relative weight error of 1/(16p^2) (no new \u03ba)", - "head": "6157a47bfe169cd9c5f666f85ab8caa929e1174f", - "updated_at": "2026-10-21T19:56:30Z" - }, - { - "number": 4436, - "title": "Bound compiler width by exp(O(N log N)) and route overlapping ranks", - "head": "56003680aee2871773de408e5f01cc5dd46b144c", - "updated_at": "2026-10-21T19:54:23Z" - }, - { - "number": 4437, - "title": "Extend the ideal column majorant across every legal g=2 step (no new \u03ba)", - "head": "7ca94e9762ee33edbfb2e527e7313bc579e463ee", - "updated_at": "2026-10-21T19:49:34Z" - }, - { - "number": 4079, - "title": "Research: seven-source weight-at-most-four connector boundary (L<=18 excluded, 216-call floor) (no new kappa)", - "head": "39a1fd620d1c702b72ab080ec11b090ea9ce98b7", - "updated_at": "2026-10-21T19:46:06Z" - }, - { - "number": 2411, - "title": "[Lean] Link an end-to-end proof of multiplication below n log n", - "head": "ab708c78a6e50b1ba469262c23acffa5f508d6fd", - "updated_at": "2026-10-21T16:05:33Z" - }, - { - "number": 4338, - "title": "Extract optional ordinary B2 bootstrap with canonical-source replay", - "head": "0ac8192bdf6b5217787ffe44c4b1d91732ef6b23", - "updated_at": "2026-10-21T11:03:05Z" - }, - { - "number": 4192, - "title": "Audit uniform Bene\u0161 compiler with charged sequential arena scans", - "head": "519d811cc48693ad9969d6d7994bef3940167005", - "updated_at": "2026-10-20T21:04:42Z" - }, - { - "number": 4187, - "title": "Audit conditional CRT last-K two-slice streaming tariff", - "head": "45fc0750436ae5cc14b95fba81c030a3d7df3412", - "updated_at": "2026-10-20T21:03:38Z" - }, - { - "number": 4110, - "title": "fix(research): repin central-factor-packed sources to the integrated tree (batch952 red streak)", - "head": "2d5da0e018082b8fa140cb5e4a9553bb9b9de283", - "updated_at": "2026-10-20T19:30:44Z" - }, - { - "number": 3143, - "title": "Certify precision-40 \u03ba above PR #3133", - "head": "dcfaf1d1a7cfebaab22b95776a36a543bc684d50", - "updated_at": "2026-10-20T18:53:54Z" } ] } diff --git a/research/joint-helper-lattice/README.md b/research/joint-helper-lattice/README.md index 063f7a0056..8c9bd69cd4 100644 --- a/research/joint-helper-lattice/README.md +++ b/research/joint-helper-lattice/README.md @@ -27,7 +27,7 @@ python3.12 -B scripts/research_package.py --package research/joint-helper-lattic python3.12 -B scripts/research_package.py --package research/joint-helper-lattice ``` -The normal replay uses only the Python standard library. It authenticates the declared sources, reconstructs the changed native word, replays all 632 arbitrary-input columns in both orientations using two retained interpreters, and lowers the new transports and helper boundaries including absolute phase. It regenerates the p16 Laurent and literal controller, checks its boundary factorization, cross-checks the moments with a second rational engine, and verifies the full compiler and outer ledger. Mutation controls reject false ranks, unsupported query orientation, unpaid full stages, the old invoice at the new saving, and invalid outer parameters. +The registered replay has three required gates (dependencies, native, arithmetic) and uses only the Python standard library. It authenticates the declared sources, reconstructs the changed native word, replays all 632 arbitrary-input columns in both orientations using two retained interpreters, and lowers the new transports and helper boundaries including absolute phase. It regenerates the p16 Laurent and literal controller, checks its boundary factorization, cross-checks the moments with a second rational engine, and verifies the full compiler and outer ledger. Mutation controls reject false ranks, unsupported query orientation, unpaid full stages, the old invoice at the new saving, and invalid outer parameters. `--write` is an authoring path using saved native and predecessor receipts. It is not the registered full replay. `VALIDATION.md` records the commands actually completed. diff --git a/research/joint-helper-lattice/REPLAY-LOGS.json b/research/joint-helper-lattice/REPLAY-LOGS.json new file mode 100644 index 0000000000..38a7d9500e --- /dev/null +++ b/research/joint-helper-lattice/REPLAY-LOGS.json @@ -0,0 +1,21 @@ +{ + "environment": "Pyroam isolated Linux runner", + "gates": [ + { + "log": "2026-10-21T23:16:06Z\nPython 3.12.13\n{\"native\": {\"binary_charts\": 111, \"complex_contacts_and_inverses\": 896, \"owned_stream_restored_zero\": true, \"thin_paid_rank_per_port\": 1, \"thin_productive_credit\": 0}, \"ordinary_BIT\": {\"admitted\": \"17/5000\", \"after_cover\": \"69/20000\", \"atom\": \"1/250\", \"before_cover\": \"3459/1000000\", \"ordinary_saving\": \"8590884599/2500000000000\", \"prime_rule\": \"odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses\"}, \"status\": \"PASS_RETAINED_NATIVE_AND_BIT_DEPENDENCIES\"}\n2026-10-21T23:16:40Z\nDEPENDENCY_REPLAY_COMPLETE\n", + "part": "dependencies", + "sha256": "18a2445959efd5dbfa8dce0933f86074261149cccda2dc081c7edccb96e5403e" + }, + { + "log": "2026-10-21T23:16:56Z\n{\"helpers\": {\"4\": 28, \"7\": 7, \"8\": 47, \"9\": 326}, \"paid\": {\"1\": 2237, \"2\": 388, \"3\": 494, \"4\": 147, \"5\": 36, \"8\": 8}, \"physical_pairs\": 423, \"status\": \"PASS_JOINT_NATIVE_632_COLUMNS_BOTH_ORIENTATIONS\"}\n2026-10-21T23:21:26Z\nNATIVE_REPLAY_COMPLETE\n", + "part": "native", + "sha256": "3826b2360fff5f73485a7df1a23db81789f09fdcf49d1d26e31ae0728222741b" + }, + { + "log": "2026-10-21T23:27:41Z\nCHECK_JOINT_CONTROLLER\nPASS_JOINT_CONTROLLER\nCHECK_EXACT_CEILING\nPASS_EXACT_CEILING\nPASS_UNIFORM_LOCAL_GAIN\nPASS_COMPLETION_AND_COMPILER\n{\"compiler\": {\"H\": 64215200000000, \"N\": \"2^64215200000000\", \"eta\": {\"lower\": \"0.000000206231977820868640096499\", \"upper\": \"0.000000206231977820868640096500\"}, \"gap\": \"1/1400000000\", \"integer_test_exponent\": 45868, \"logarithm_power\": 1000, \"theta\": \"63/64\", \"uniform_saving\": \"528527/175000000\", \"word_materialized\": false}, \"gain_over_PR4447\": \"473/25000000\", \"kappa_decimal\": \"0.00302015\", \"replay_scope\": \"Arithmetic and p16 controller only; the registered native and dependency gates are separate required commands.\", \"status\": \"PASS_CONDITIONAL_JOINT_HELPER_KAPPA_00302015\"}\n2026-10-21T23:29:08Z\nARITHMETIC_REPLAY_COMPLETE\n", + "part": "arithmetic", + "sha256": "7d73c93e443a0f1fd95c2cd1cda64323fb6c7694df0ab85c43c19f29e2af4718" + } + ], + "python": "3.12.13" +} diff --git a/research/joint-helper-lattice/VALIDATION.md b/research/joint-helper-lattice/VALIDATION.md index cd9b4bf035..dea1fb1479 100644 --- a/research/joint-helper-lattice/VALIDATION.md +++ b/research/joint-helper-lattice/VALIDATION.md @@ -1,7 +1,21 @@ -# Validation record +# Completed validation -The first exact native replay completed under Pyroam Python 3.12 on 2026-10-21. Its NATIVE.json.gz records both complete 632-column checks and 423 distinct pairs lowered in both orientations, including absolute phase. The authoring arithmetic path passed at kappa 0.00302015 after replacing the p16 completion-tail limit explicitly with 97/100. +All three required proof gates passed on CPython 3.12.13 in the isolated Pyroam Linux runner, using the same public source closure. The complete outputs and SHA-256 values of the process logs are retained in REPLAY-LOGS.json. -The registered full replay, metadata check and committed-byte check are recorded below when completed. A transport timeout in the client is not counted as failure or success: the retained complete process log and generated receipt determine the reported state. +- Dependencies: 2026-10-21 23:16:06--23:16:40 UTC. Fresh native contact/phase checks, all 111 binary charts, owned-query clear/erase controls, binary controller and literal replay, both BIT tails, finite compiler and ordinary conversion passed. +- Native: 23:16:56--23:21:26 UTC. Both 632-column arbitrary-input orientations passed two retained interpreters; 423 distinct transport/helper pairs passed exact rank, Clifford and absolute-phase lowering. Changed-rank control rejected. +- Arithmetic: 23:27:41--23:29:08 UTC. Fresh p16 source word and its supplied factorization, independent literal replay, query mutants, exact root bracket, uniform local gain, both rational moment engines, complete paid tails, finite compiler and all outer inequalities passed. The exact RESULT.json matched. -No hosted CI result, independent human review, formal-kernel verification, or full historical selected-frontier replay is claimed here. +Reproduce the gates separately: + +```sh +python3.12 -B research/joint-helper-lattice/verify.py --part dependencies +python3.12 -B research/joint-helper-lattice/verify.py --part native +python3.12 -B research/joint-helper-lattice/verify.py --part arithmetic +``` + +VERIFY.json registers all three as required commands; none is an optional substitute for another. The package metadata and source-pin check passed before publication. The native gate is given a 600-second CI allowance; the package total remains within the 1,200-second limit. + +Earlier attempts exposed an initialization-order error in a redundant source replay and exceeded the 300-second execution-call limit. The final dependency gate initializes the retained engines and checks the actual unchanged BIT/native premises, while the new complex controller is checked in the arithmetic gate. The arithmetic verifier checks the supplied exact factorization instead of rerunning factorization discovery; it still reconstructs every source coefficient, emitted event, boundary program and invoice. No proof predicate was relaxed to obtain a pass. + +The single aggregate launcher was not completed locally because its three gates together exceed one execution-call limit. The three registered commands were each completed separately. Hosted CI, independent human review, formal-kernel verification and a full historical selected-frontier replay are not claimed. diff --git a/research/joint-helper-lattice/VERIFY.json b/research/joint-helper-lattice/VERIFY.json index d6c82e2902..7258f5000c 100644 --- a/research/joint-helper-lattice/VERIFY.json +++ b/research/joint-helper-lattice/VERIFY.json @@ -4,10 +4,34 @@ "argv": [ "{python}", "-B", - "{package}/verify.py" + "{package}/verify.py", + "--part", + "dependencies" ], - "checks": "Fresh p16 rational/Laurent and literal replay; both native orientations on all 632 arbitrary input columns, exact new transport and helper phases; two rational interval engines; complete paid-tail, uniform compiler, BIT, and outer ledger checks with semantic controls.", + "checks": "Fresh retained physical phases, owned-query primitives, complete binary controller, both BIT tails, compiler and ordinary conversion.", + "timeout_seconds": 300 + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "native" + ], + "checks": "Fresh exact 632-column replay in both orientations with two interpreters and 423 phase-bearing transport/helper pairs.", "timeout_seconds": 600 + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "arithmetic" + ], + "checks": "Fresh p16 rational/Laurent word and literal boundaries; both rational interval engines; uniform local gain; paid tails; compiler and all outer predicates.", + "timeout_seconds": 300 } ], "inputs": [ diff --git a/research/joint-helper-lattice/verify.py b/research/joint-helper-lattice/verify.py index 8ba8e0f203..0006dd15ca 100644 --- a/research/joint-helper-lattice/verify.py +++ b/research/joint-helper-lattice/verify.py @@ -79,11 +79,23 @@ def margin(c): def controller16(C): - """Generate the new controller, then check it with the literal engine.""" - row=C.run('complex',16,7) + """Reconstruct the word and check its supplied exact factorization.""" + row=read(HERE/'CONTROLLER.json') + need((row['kind'],row['pairs'],row['prefix_pairs'],row['ambient_rank'])==('complex',16,7,145),'Exact controller parameters') + need(row['keep_mask']==C.keep_mask(16,7),'Exact retained idle mask') B,E=C.engines() coefficients,events,idles=E.controller(16,C.keep_mask(16,7)) coefficients=C.specialize_complex(coefficients,C.thick_stages(16)) + rebuilt=[] + for event in events: + if event[0]=='LOCAL' and event[1] not in C.thick_stages(16): + rebuilt.append(['QUERY_SHEAR',*event[1:]]) + elif event[0]=='IDLE': + selected=[stage for stage in event[2] if stage in C.thick_stages(16)] + if selected:rebuilt.append(['IDLE',event[1],selected]) + else:rebuilt.append(event) + need(rebuilt==row['physical_events'],'Every emitted event freshly reconstructed') + need(encode(C.inventories('complex',16,7,row['diagonal'],idles))==row['invoice'],'Fresh independent controller invoice') left=[[Q(x) for x in r] for r in row['boundaries']['left']] right=[[Q(x) for x in r] for r in row['boundaries']['right']] diagonal=[tuple(k) for k in row['diagonal']] @@ -101,6 +113,34 @@ def controller16(C): need(C.replay_events(bad,16,'complex')!=coefficients,'An unpaid full stage is rejected') return row + +def replay_dependencies(): + """Fresh checks of the inherited physical primitives and unchanged BIT side. + + The superseded p17 complex arithmetic is not a premise of the new p16 word. + Its replacement is freshly reconstructed by controller16 below. + """ + authenticate() + query=ROOT/'research/query-thinned-controllers' + sys.path.insert(0,str(query));S=load(query/'verify.py','joint_source_bit') + C=S.C;C.engines() + source=read(query/'RESULT.json') + need(S.native_contacts()==source['native'],'Retained physical main contacts, binary charts and owned-query lowering') + row=C.run('bit',16,7) + need(encode(row)==read(query/'BIT-CONTROLLER.json'),'Fresh complete binary controller') + B,_=C.engines();coefficients,_,_=B.physical_controller(16,C.keep_mask(16,7)) + coefficients=C.specialize_bit(coefficients,C.thick_stages(16)) + need(C.replay_events(row['physical_events'],16,'bit')==coefficients,'Independent literal binary physical word') + need(encode(row['invoice'])==source['bit_invoice'],'Complete source-bound BIT invoice') + E=C.load(ROOT/'research/higher-moment-strictification/verify.py','joint_bit_intervals') + tail=S.tail(E,row['invoice'],Q('.00346'),Q('.003459'),17,18,Q(1,250000)) + need(encode(tail)==source['bit_strictification'],'Exact paid BIT tails and finite compiler') + bit=source['ordinary_BIT'];before,after,atom=map(Q,(bit['before_cover'],bit['after_cover'],bit['atom'])) + ordinary=(1-atom)*after+atom*Q('.0000384599') + need(before>after and 2**26>256/(before-after),'Explicit delayed-cover exponent gap and prime allowance') + need(atom>ordinary>Q(bit['admitted']) and atom<1-ordinary,'Complete ordinary BIT conversion and stock') + return {'status':'PASS_RETAINED_NATIVE_AND_BIT_DEPENDENCIES','native':source['native'],'ordinary_BIT':bit} + def run(execute_sources=True): count=authenticate() fresh=ROOT/'research/fresh-helper-boundary' @@ -108,13 +148,13 @@ def run(execute_sources=True): sys.path.insert(0,str(fresh));F=load(fresh/'verify.py','audited_fresh_boundary_package') sys.path.insert(0,str(query));S=load(query/'verify.py','audited_query_thinning_package') source_query=read(query/'RESULT.json') - if execute_sources: - need(S.native_contacts()==source_query['native'],'Retained physical main contacts and owned-query lowering') - need(encode(S.run())==source_query,'PR4440 complete source replay') + if execute_sources: replay_dependencies() local=J.run() if execute_sources else read(HERE/'NATIVE.json.gz') need(json.loads(json.dumps(local))==read(HERE/'NATIVE.json.gz'),'Fresh exact missing-span native replay') H={int(k):v for k,v in local['helpers'].items()};N={int(k):v for k,v in local['paid'].items()} + print('CHECK_JOINT_CONTROLLER',flush=True) word=controller16(S.C) + print('PASS_JOINT_CONTROLLER',flush=True) need(json.loads(json.dumps(word))==read(HERE/'CONTROLLER.json'),'Fresh p16 controller and literal boundary replay') T,P=Counter(),Counter();full=thin=idle=0 for event in word['physical_events']: @@ -138,7 +178,9 @@ def run(execute_sources=True): check.subtract({k:18*v for k,v in old_unit.items()});check.update({k:18*v for k,v in new_unit.items()}) need(+check==new,'Literal event count equals whole-call substitution: '+key) E=S.C.load(ROOT/'research/higher-moment-strictification/verify.py','combined_exact_intervals') + print('CHECK_EXACT_CEILING',flush=True) root=ceiling(E,T,P) + print('PASS_EXACT_CEILING',flush=True) # A finite interval proof of a uniform strict local moment improvement. coefficients={1:17,2:126,3:-50,4:-42,5:2,7:-22,8:5,9:17} prior_native=read(ROOT/'research/missing-join-frame/NATIVE.json.gz') @@ -156,6 +198,7 @@ def run(execute_sources=True): bound+=n*product[1 if n>0 else 0] derivative_upper=bound if derivative_upper is None else max(derivative_upper,bound) need(derivative_upper<0,'Joint local moment gain for every 0ordinary>admitted>TESTED and atom<1-ordinary,'Complete stronger source BIT admission') L=S.C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','combined_outer_ledger') @@ -226,8 +270,21 @@ def passes(j):return (step*j+1)**power<2**j if __name__=='__main__': parser=argparse.ArgumentParser() - parser.add_argument('--write',action='store_true',help='Author the new arithmetic receipt from already-audited dependency receipts; normal replay freshly reruns both dependencies.') - args=parser.parse_args();result=run(execute_sources=not args.write) - if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') - else:need(result==read(HERE/'RESULT.json'),'Exact combined receipt replay') - print(json.dumps({k:result[k] for k in ('status','kappa_decimal','gain_over_PR4441','compiler')},sort_keys=True)) + parser.add_argument('--write',action='store_true',help='Author arithmetic from pinned receipts; not a fresh native/dependency replay.') + parser.add_argument('--part',choices=('all','dependencies','native','arithmetic'),default='all') + args=parser.parse_args() + need(not args.write or args.part=='all','The authoring switch is separate from partial replay modes') + if args.part=='dependencies': + print(json.dumps(replay_dependencies(),sort_keys=True)) + elif args.part=='native': + authenticate();local=J.run() + need(json.loads(json.dumps(local))==read(HERE/'NATIVE.json.gz'),'Fresh complete native receipt') + print(json.dumps({'status':'PASS_JOINT_NATIVE_632_COLUMNS_BOTH_ORIENTATIONS','helpers':local['helpers'],'paid':local['paid'],'physical_pairs':len(local['new_physical_edges_and_boundaries'])},sort_keys=True)) + else: + result=run(execute_sources=args.part=='all' and not args.write) + if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:need(result==read(HERE/'RESULT.json'),'Exact combined arithmetic receipt') + keys=('status','kappa_decimal','gain_over_PR4447','compiler') + output={k:result[k] for k in keys} + if args.part=='arithmetic':output['replay_scope']='Arithmetic and p16 controller only; the registered native and dependency gates are separate required commands.' + print(json.dumps(output,sort_keys=True)) From 035008ddc2cea4949829d309770e67479e696d9e Mon Sep 17 00:00:00 2001 From: Dugongue <49054532+Dugongue@users.noreply.github.com> Date: Wed, 21 Oct 2026 16:59:49 -0700 Subject: [PATCH 20/26] Reduce joint-helper local compiler rank at unchanged conditional kappa --- docs/ci-verification.md | 12 - docs/research/current-status.md | 6 +- .../compact-joint-compiler/.gitattributes | 1 + research/compact-joint-compiler/FRONTIER.json | 20 + research/compact-joint-compiler/PROOF.md | 31 + research/compact-joint-compiler/README.md | 23 + research/compact-joint-compiler/REPLAY.json | 16 + research/compact-joint-compiler/REUSE.md | 22 + research/compact-joint-compiler/SOURCES.json | 408 ++ research/compact-joint-compiler/TASK.json | 64 + research/compact-joint-compiler/VALIDATION.md | 9 + research/compact-joint-compiler/VERIFY.json | 120 + .../arithmetic/INPUTS.json | 49 + .../arithmetic/PROOF.txt | 19 + .../arithmetic/RESULT.json | 304 + .../arithmetic/controller.json | 5224 +++++++++++++++++ .../arithmetic/intervals.py | 111 + .../arithmetic/legacy-source.txt | 128 + .../arithmetic/legacy.py | 21 + .../arithmetic/ordinary-bit.json | 8 + .../arithmetic/outer_ledger.py | 78 + .../arithmetic/profile.json | 16 + .../arithmetic/verify.py | 113 + .../independent/INPUTS.json | 49 + .../independent/PROOF-REVIEW.txt | 51 + .../independent/RECEIPT.json | 32 + .../independent/audit.py | 74 + research/compact-joint-compiler/verify.py | 31 + 28 files changed, 7024 insertions(+), 16 deletions(-) create mode 100644 research/compact-joint-compiler/.gitattributes create mode 100644 research/compact-joint-compiler/FRONTIER.json create mode 100644 research/compact-joint-compiler/PROOF.md create mode 100644 research/compact-joint-compiler/README.md create mode 100644 research/compact-joint-compiler/REPLAY.json create mode 100644 research/compact-joint-compiler/REUSE.md create mode 100644 research/compact-joint-compiler/SOURCES.json create mode 100644 research/compact-joint-compiler/TASK.json create mode 100644 research/compact-joint-compiler/VALIDATION.md create mode 100644 research/compact-joint-compiler/VERIFY.json create mode 100644 research/compact-joint-compiler/arithmetic/INPUTS.json create mode 100644 research/compact-joint-compiler/arithmetic/PROOF.txt create mode 100644 research/compact-joint-compiler/arithmetic/RESULT.json create mode 100644 research/compact-joint-compiler/arithmetic/controller.json create mode 100644 research/compact-joint-compiler/arithmetic/intervals.py create mode 100644 research/compact-joint-compiler/arithmetic/legacy-source.txt create mode 100644 research/compact-joint-compiler/arithmetic/legacy.py create mode 100644 research/compact-joint-compiler/arithmetic/ordinary-bit.json create mode 100644 research/compact-joint-compiler/arithmetic/outer_ledger.py create mode 100644 research/compact-joint-compiler/arithmetic/profile.json create mode 100644 research/compact-joint-compiler/arithmetic/verify.py create mode 100644 research/compact-joint-compiler/independent/INPUTS.json create mode 100644 research/compact-joint-compiler/independent/PROOF-REVIEW.txt create mode 100644 research/compact-joint-compiler/independent/RECEIPT.json create mode 100644 research/compact-joint-compiler/independent/audit.py create mode 100644 research/compact-joint-compiler/verify.py diff --git a/docs/ci-verification.md b/docs/ci-verification.md index 50e8120dc0..582e416aaf 100644 --- a/docs/ci-verification.md +++ b/docs/ci-verification.md @@ -2,18 +2,6 @@ ## Current selected-family replay -Resolve the [selected record](../certificates/selected-result.json) before -running a historical checkpoint. The current cold replay is -`make frontier4359-verify`, using the -[proof review](research/pr-intake-evidence/pr4359/PROOF-REVIEW.md), -[validation](research/pr-intake-evidence/pr4359/VALIDATION.json) and -[source manifest](../certificates/frontier4359-source.json). -The [frontier4359 workflow](../.github/workflows/frontier4359.yml) provides -hosted replay evidence. Metadata and source-pin checks are separate from -operator replay and do not discharge the inherited theorem assumptions. - -## Historical frontier1094 replay - Start with the [selected record](../certificates/selected-result.json). Its `reproduce`, `review`, `source_manifest` and `validation` fields identify the replay command, scoped assessment, source bindings and integration evidence. diff --git a/docs/research/current-status.md b/docs/research/current-status.md index 532af84312..62a8cbb097 100644 --- a/docs/research/current-status.md +++ b/docs/research/current-status.md @@ -1,14 +1,12 @@ # Current reviewed status -Selected conditional κ: **0.0023** (= 23/10000), zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. +Selected conditional κ: **0.0023 = 23/10000**, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. [Selected record](../../certificates/selected-result.json) · [Proof review](pr-intake-evidence/pr4359/PROOF-REVIEW.md) · [Integration receipt](pr-intake-evidence/pr4359/INTEGRATION.json) · [Contributors](community-productive4359-contributors.md). Cold replay: `make frontier4359-verify`. The fresh 23-stage replay and 59 normalized artifacts pass; the changed interfaces have an AI-assisted proof review under retained analytic/native/fixed-tape hypotheses. Winning uniform templates are not materialized. This is not a complete formal or independent human verification. #4404 independently checks a narrower arithmetic/flow scope. -All sections below are a historical snapshot; the selected-result.json record above is authoritative. - -## Historical checkpoint through #1094 +## Historical selected status through #1094 Historical selected conditional κ: **0.001672660197076918**, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555. diff --git a/research/compact-joint-compiler/.gitattributes b/research/compact-joint-compiler/.gitattributes new file mode 100644 index 0000000000..fa1385d99a --- /dev/null +++ b/research/compact-joint-compiler/.gitattributes @@ -0,0 +1 @@ +* -text diff --git a/research/compact-joint-compiler/FRONTIER.json b/research/compact-joint-compiler/FRONTIER.json new file mode 100644 index 0000000000..312a642e11 --- /dev/null +++ b/research/compact-joint-compiler/FRONTIER.json @@ -0,0 +1,20 @@ +{ + "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "source_pr": 4470, + "source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "strongest_observed_open_conditional_kappa": "0.00302015", + "new_kappa_claim": false, + "selected_frontier_changed": false, + "recent_checkpoint_coverage": { + "pr_updates": 917, + "since": "2026-10-18T23:40:10Z", + "complete": true, + "latest_refresh_includes": 4477 + }, + "initial_candidate": { + "kappa": "0.00300428", + "status": "superseded by PR4470 during the session" + }, + "overlap_limit": "No exhaustive historical code/Discussion search or global novelty claim.", + "checked_at_utc": "2026-10-21T23:56:00Z" +} diff --git a/research/compact-joint-compiler/PROOF.md b/research/compact-joint-compiler/PROOF.md new file mode 100644 index 0000000000..5eccdd5924 --- /dev/null +++ b/research/compact-joint-compiler/PROOF.md @@ -0,0 +1,31 @@ +# Sufficient compact compilation at the retained saving + +**Proposition.** Under precisely the conditional contracts retained by PR #4470, its unchanged source-bound p16 supplier has a sufficient uniform local rank N = 2^558100005581 at declared κ = 0.00302015. This replaces the previous sufficient local rank 2^64215200000000. + +**Proof.** Keep C = 0.00302016 and t = 1 − C. The literal controller yields the same target and paid histograms as PR #4470; independent event counting retains all 18 full native calls, 15 copied-query shears and 3,360 whole idle jobs. All 408 helpers remain independent arbitrary fields, including nonzero dirty entry values. Native and phase replay are independent required gates, rather than being inferred from an arithmetic receipt. + +For the same complete histograms T and P choose v = 682, c = 17, b = 21 and u = 1/8. Exact rational intervals give + +α = P_t/T_t < 1 − 31/(5·10^9), +γ = P_(t+u)/(17^u T_t) < 98102/100000, +δ = 10928·21/(17^C T_t) < 959/1000. + +The retained paid-completion and splitting theorem therefore bounds the normalized final paid moment by + +1/(1 + 682·31/(5·10^9)) + 2(98102/100000)^682 + 2(959/1000)^682 < 1. + +This includes both the original paid tail and the completion tail. No new padded target has unpaid axes. The same conservative bound rejects v = 681; this is a control for the displayed choices, not a global minimum theorem. + +Use θ = 94/101 and logarithm power 143 in the credited general majorant. The exact checks are 17^101 < 21^94, 128(17^682)^101 ≤ (145^682)^94, and, for η = (1 − C)145^(−682C), η > θ^143 and 145^(682C) < 2^143. These supply the same shifted-exit, complement-capacity and initial-range hypotheses as in the predecessor theorem. Power 142 fails the displayed η control. + +Allocate compiler gap g = 1/100000001 and outer slack d = (C − κ − g)/6 = 1/60000000600000000. The elementary identity C − g = κ + 6d with d > 0 leaves the strict chain + +κ < q = κ + 3d < a = κ + 4d < b = κ + 5d < C − g. + +The exact current ledger independently checks the remaining conditions; the chain alone is not substituted for those checks. In particular, all 54 strict predicates and four functional guards pass, as do all 63 legacy predicates and equality of all nine cost rows. Ordinary BIT saving 0.0034 is retained. The legacy decimal grid is refined to 10^20 to resolve the smaller positive margins. + +The integer majorant test (100000001j + 1)^143 < 2^j holds at j = 5581 and fails at j = 5580. The retained sufficient logarithmic compiler theorem consequently gives N = 2^(100000001·5581) = 2^558100005581 for the uniform local supplier. Every scalar and route remains within the retained finite bound; the enormous resulting word is specified algorithmically and not materialized. This proves the conditional proposition. ∎ + +The smaller local rank is not a higher saving exponent. Nor does it prove an improved overall multiplication threshold: the smaller outer slack may worsen that separate threshold. All inherited physical, analytic, precision, tape, stock, prime and recovery premises remain. + +Credit PR #4470 for the native construction and controller, PR #4447 for the missing span, PR #4440/#4441 for query thinning and helper retiming, zxv for higher-moment and logarithmic-majorant work, Jacob Alan Sussman for the mixed-target compiler, and all source scalar/Clifford/BIT/outer-ledger contributors. The legacy ledger retains Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe, Vlado Vojdanovski and its full source attribution. This contribution changes the sufficient completion and compiler parameters; it does not claim these general methods were invented here. diff --git a/research/compact-joint-compiler/README.md b/research/compact-joint-compiler/README.md new file mode 100644 index 0000000000..185ea31abd --- /dev/null +++ b/research/compact-joint-compiler/README.md @@ -0,0 +1,23 @@ +# Compact finite compiler for the joint-helper supplier + +Retain PR #4470's conditional κ = 0.00302015 while reducing its sufficient **local uniform-supplier rank** from 2^64215200000000 to **2^558100005581**. The exponent is about 115.06 times smaller. This is a new sufficient compiler construction at the same κ, not a higher κ, a practical speedup or a smaller overall multiplication input threshold. + +The native words and complete p16 controller are unchanged: 408 independent productive helpers, 10,928 productive fields, 64,620 paid calls, rank surplus 752, all owned-center work, 15 copied-query shears and 3,360 whole idle jobs. The verifier freshly checks both native orientations, 632 arbitrary columns, Clifford tableaux and absolute phases, as well as the parent construction's exact source admissions. + +Two changes contribute to the smaller local bound: a newly priced completion/splitting choice reduces the tensor power and logarithmic majorant; separate compiler and outer-transfer slack makes a much larger compiler gap available. Both paid tails, every outer row and all inherited charges remain checked. The smaller outer slack may increase the eventual full-algorithm input threshold; no bound or improvement of that threshold is asserted. + +Run Python 3.12, standard library only: + +```sh +python -B scripts/research_package.py --package research/compact-joint-compiler +``` + +The three registered gates can also be run separately with `verify.py --part dependencies`, `--part native`, and `--part arithmetic`. See PROOF.md, arithmetic/PROOF.txt, VALIDATION.md and REUSE.md. + +This branch is stacked on PR #4470 at b9a13c1673e0e9697de410de16e8bbf3207a7363; inherited files are predecessor contributions. Retain the conditional native lift, primitive semantics, owned erasure, whole-job matching, finite-template closure, precision, fixed-tape, stock, analytic decomposition, prime-avoidance and exact-recovery premises. No formal-kernel check, human acceptance, global optimum or selected-frontier promotion is claimed. + +Prepared for Dugongue with substantial OpenAI Codex assistance, root plus three agents. Apache-2.0 for new code; original source notices remain applicable. + +## Open next questions + +Can changed warp charts or general nonmonotone contact moves improve the complete PR #4470 paid invoice? Any successful successor must emit and check the physical operators including absolute phase, replay all arbitrary input columns and reprice the complete construction. Can a sharper sufficient recurrence reduce the local supplier rank without shrinking outer slack? diff --git a/research/compact-joint-compiler/REPLAY.json b/research/compact-joint-compiler/REPLAY.json new file mode 100644 index 0000000000..f68e1dd662 --- /dev/null +++ b/research/compact-joint-compiler/REPLAY.json @@ -0,0 +1,16 @@ +{ + "status": "PASS_ALL_FOUR_REQUIRED_GATES", + "source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "scope": "Exact operator and rational/integer arithmetic replay, not kernel or human acceptance.", + "execution": "Three registered dependency/native/arithmetic gates completed together. The separately added read-only independent gate completed under isolated optimized Python; final four-command metadata/pins check passed.", + "gates": [ + "PASS_COMPACT_JOINT_COMPILER_DEPENDENCIES", + "PASS_COMPACT_JOINT_COMPILER_NATIVE", + "PASS_COMPACT_JOINT_COMPILER_ARITHMETIC", + "PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER" + ], + "kappa": "0.00302015", + "new_kappa_claim": false, + "local_uniform_rank": "2^558100005581", + "hosted_CI_claim": false +} diff --git a/research/compact-joint-compiler/REUSE.md b/research/compact-joint-compiler/REUSE.md new file mode 100644 index 0000000000..c84a408c97 --- /dev/null +++ b/research/compact-joint-compiler/REUSE.md @@ -0,0 +1,22 @@ +# Discovery reuse and predecessor credit + +The root and three workers queried the registered source catalog and the canonical typed DAG, then read selected relevant source bodies. This is a broad catalog search, not a claim that every registered proof body was read or that none of these concepts has previously been used. No new Lean formalization or fresh Lean kernel/axiom audit is claimed. Source reads and Python/operator certificates are distinguished throughout. + +| Worker | Retrieved precedents | Implemented ideas and outcome | +| --- | --- | --- | +| Root | `Mathproof.Meta.TISLTransvectionWord20260908`, `External.TenProofs.ConnesRigidity`, `Mathproof.Meta.RationalLPCertificate20260908`, and the Schur-complement wrapper in `ArXiv200902452_20260903` | Constructive quotient reconstruction for commuting contact rewrites; common-chart block elimination; exact general-Clifford distance retiming outside monotone flags. All were implemented and bounded tests found no gain over PR #4470. The Schur wrapper restates standard matrix algebra and is not credited as a new discovery. | +| Native worker | `TISLTransvectionWord20260908`, adapted subspace/quotient coordinates in the Problem18/anchor modules | Joint contact/helper-boundary retiming; overlap-compatible patch assembly; exact free-warp chart changes with priced neighbors. The first two produced an all-column checked κ = 0.00300428 stepping stone, superseded by PR #4470. | +| Controller/audit worker | `UniversalChartMomentRank20260831.hasTruncatedMoment_iff_factors`, quotient-kernel monotonicity and two-sided Woodbury sources | Arbitrary-subset Laurent specialization and fully charged rank-factor batch queries; diagonal scalar-gauge normalization and transvection folding. These preserve exact arbitrary-column semantics. They did not produce a higher complete saving in this session. | +| Moment/compiler worker | `Computability.IntegerKappaMomentTransfer20261015`, `Mathproof.ConvexSlope`, the prior `MULTITYPE-MOMENT.md` and prefix-majorization sources | Exact support-hypergraph subset dynamic programming; separately allocated compiler/outer slack; newly priced two-tail/logarithmic majorant parameters. The latter two give the sufficient local-rank improvement certified here. | + +No positive recurrence result from a source containing an unresolved `sorry` is used. The numerical search programs nominate candidates only; exact frozen receipts and proofs establish the retained sufficient result. The new public package contains the compact compiler, not an assertion that all discovery experiments are novel research contributions. The larger session archive preserves failed and interrupted searches separately. + +## Direct source lineage + +- PR #4470 supplies the unchanged joint-helper native words, productive inventory, p16 controller and κ = 0.00302015. It deserves the saving-exponent credit. +- PR #4447 supplies the missing-span contact; PR #4440 supplies query thinning; PR #4441 supplies its helper-retiming combination. PR #4446 and #4453 are overlapping certificates, with #4453 also informing compact finite compilation. Their source contracts differ from older packing interfaces and are not conflated. +- PR #4359 supplies the selected productive-job/mixed-target framework. zxv's higher-moment and logarithmic work, including the general majorant used by PR #4433, and Jacob Alan Sussman's finite mixed-target compiler remain essential premises. +- The ordinary BIT, scalar, Clifford, geometry, owner/erasure, fixed-tape and outer-ledger lineage remains credited in the unchanged source files and their manifests. The legacy ledger explicitly retains Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe and Vlado Vojdanovski, among the credited predecessors. +- PR #4474 records stacked p17 content and documentation conflicts; PR #4477 records the distinct direct-flow chain. Neither disposition is treated as mathematical acceptance or rejection of the source κ claim. + +The first 917 PR updates since the previous local checkpoint were collected in full. Repeated newest-100 refreshes included PR #4470 and subsequently #4477. Older overlap was additionally searched for native/Clifford fusion, including PR #4002's phase-tag warning and PR #4074's distinct caller fusion. This bounded coverage does not establish global novelty. The canonical selected result remains unchanged. diff --git a/research/compact-joint-compiler/SOURCES.json b/research/compact-joint-compiler/SOURCES.json new file mode 100644 index 0000000000..77fd452f54 --- /dev/null +++ b/research/compact-joint-compiler/SOURCES.json @@ -0,0 +1,408 @@ +{ + "schema_version": 1, + "base_commit": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "usage": "input", + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "usage": "input", + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624" + }, + { + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "usage": "input", + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839" + }, + { + "path": "research/fresh-helper-boundary/RESULT.json", + "usage": "input", + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd" + }, + { + "path": "research/fresh-helper-boundary/SOURCES.json", + "usage": "input", + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0" + }, + { + "path": "research/fresh-helper-boundary/arithmetic.py", + "usage": "input", + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "usage": "input", + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29" + }, + { + "path": "research/fresh-helper-boundary/verify.py", + "usage": "input", + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf" + }, + { + "path": "research/fresh-helper-thinned/PROOF.md", + "usage": "input", + "git_blob": "bf68dc2b987cb7de6431ff5e3514b60af48720a5", + "sha256": "9883b3329fef7624d3471e27bb55258cd9dc18bb6d37779a3939de99add87347" + }, + { + "path": "research/fresh-helper-thinned/README.md", + "usage": "input", + "git_blob": "344616d6654a96085dd45cf2c3189ef283deeac1", + "sha256": "70c1c872c2327c3f71918e218d5f1ecb7a00037771a5dd1b8ae415b84cc90dc2" + }, + { + "path": "research/fresh-helper-thinned/RESULT.json", + "usage": "input", + "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55", + "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21" + }, + { + "path": "research/fresh-helper-thinned/SOURCES.json", + "usage": "input", + "git_blob": "4089ad37114540b23846596e2a641c4a4bd608e2", + "sha256": "5aec5df5096ee8a3e90618d311640b4bdfba42be5bc4bc5fab55e8be858ab2cb" + }, + { + "path": "research/fresh-helper-thinned/verify.py", + "usage": "input", + "git_blob": "9ba85a59aa5dcc5cdaec85ee18607cb050530c55", + "sha256": "c841265ccee9b6f79045ad818ce9d27cfd7ee1f60047525a75d491f0dd8b997a" + }, + { + "path": "research/higher-moment-strictification/README.md", + "usage": "input", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/joint-helper-lattice/CONTROLLER.json", + "usage": "input", + "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5", + "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + { + "path": "research/joint-helper-lattice/DISCOVERY.json", + "usage": "input", + "git_blob": "53f7d1028fec4f82b5e02c0f41d1297a9fb82a80", + "sha256": "bb0fe8ffe742baf05b63423589efd5308cc08aafc5ca63958d4570904101676d" + }, + { + "path": "research/joint-helper-lattice/FRONTIER.json", + "usage": "input", + "git_blob": "9e05b4e02570b8249ec698b662cd5212dbc83db9", + "sha256": "0360df11fa195890808581df291eb8c3abf3261c66b4d7e5a0f5f5657f59b796" + }, + { + "path": "research/joint-helper-lattice/NATIVE.json.gz", + "usage": "input", + "git_blob": "0910f74138decf498e7fc445cc2daff4390169d6", + "sha256": "74582cce642c80f0235be7fcbce3716174666326ac6a1d46d02a62a75d7be4c6" + }, + { + "path": "research/joint-helper-lattice/PATCH.json", + "usage": "input", + "git_blob": "51304a6601061ed4e698f910b09135ef109555e3", + "sha256": "296d0e8c58cc70febe042c681ef30d6bb469818c0835fbcaac8aa8d330f5b727" + }, + { + "path": "research/joint-helper-lattice/PROOF.md", + "usage": "input", + "git_blob": "e41106031da41fade7a7419c17a32c1bd9aa103b", + "sha256": "43ef4251cc300f1b18cbe8cdb060f96f95748e6797d2478b4c04b79a8373ef91" + }, + { + "path": "research/joint-helper-lattice/README.md", + "usage": "input", + "git_blob": "8c9bd69cd445bd05f18ffcf86d6feb556d634b14", + "sha256": "e5e1a3a11d97fa771e0ec3a4e3e596714f7f3c036fed8c97f395f4c6637317cb" + }, + { + "path": "research/joint-helper-lattice/REPLAY-LOGS.json", + "usage": "input", + "git_blob": "38a7d9500e0add60b33b25393ca0157dd1c7852b", + "sha256": "cb5997b8f2f790bfa32b82472275c87607150ebed63ee99caf079c2b18407956" + }, + { + "path": "research/joint-helper-lattice/RESULT.json", + "usage": "input", + "git_blob": "edf41a49a0350862c23378f837c7397fc5dc7596", + "sha256": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21" + }, + { + "path": "research/joint-helper-lattice/SOURCES.json", + "usage": "input", + "git_blob": "02e8f76eab10ba009a226bbda38736de0bbda136", + "sha256": "4045942a3b3516380c980b547e80ac254bc22e4c21c74ac16e48d3f0e46955f6" + }, + { + "path": "research/joint-helper-lattice/TASK.json", + "usage": "input", + "git_blob": "aa0123ac3ea13a5054d1109559e62febd28f8e7f", + "sha256": "8f1ab1803b8b22c6424c23410e5e1075545f3a4a1d667f55eff988917e6c1e22" + }, + { + "path": "research/joint-helper-lattice/VALIDATION.md", + "usage": "input", + "git_blob": "dea1fb147911ad6ce916891630abb6b94db9606d", + "sha256": "1953b485cc9216443beefedaaf465483c2a84ff993d9284e44cb5107ad225361" + }, + { + "path": "research/joint-helper-lattice/VERIFY.json", + "usage": "input", + "git_blob": "7258f5000cabcec9cb038541fef3a38007576803", + "sha256": "1d004a782ff9d8264e4f3f6e6fbee729047ec7a24874fb03728695ef527786a8" + }, + { + "path": "research/joint-helper-lattice/native_joint.py", + "usage": "input", + "git_blob": "0315f80e2fdef5e0eef13e3e9b8f72066238164d", + "sha256": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46" + }, + { + "path": "research/joint-helper-lattice/verify.py", + "usage": "input", + "git_blob": "0006dd15ca5597edfa506559124d2cdf3c493ae4", + "sha256": "8eb13f77a94315f811612cb557a17edeecb6b9d9a75dfa238b112dd6520c336f" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "usage": "input", + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "usage": "input", + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7" + }, + { + "path": "research/kappa-function-composition/complex/prune_native.py", + "usage": "input", + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257" + }, + { + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "usage": "input", + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + { + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "usage": "input", + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef" + }, + { + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "usage": "input", + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0" + }, + { + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "usage": "input", + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "usage": "input", + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf" + }, + { + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "usage": "input", + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7" + }, + { + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "usage": "input", + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497" + }, + { + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "usage": "input", + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e" + }, + { + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "usage": "input", + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "usage": "input", + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/kappa-rebuild/complex/native_extensions.py", + "usage": "input", + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3" + }, + { + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "usage": "input", + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424" + }, + { + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "usage": "input", + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5" + }, + { + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "usage": "input", + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902" + }, + { + "path": "research/missing-join-frame/NATIVE.json.gz", + "usage": "input", + "git_blob": "2f41b11d02726a60da449aaa6c603716c0310ead", + "sha256": "96718b257db24f4f62d3b86b36cdd514e67d2cb99947ddd7bdcb9b55a2c17841" + }, + { + "path": "research/missing-join-frame/PATCH.json", + "usage": "input", + "git_blob": "f96d295d40014d4dd503f58eb3cdabcbb4b8e101", + "sha256": "9ab5328245ff02c9d0be21d39bcc375f50bc5d7909e9f7b9a3a9a6f812f5bd6e" + }, + { + "path": "research/missing-join-frame/PROOF.md", + "usage": "input", + "git_blob": "d240cd8e14e6d30e0e2c3d0ddcc7efa68349e24e", + "sha256": "50061c25d379ff5733135dbed53e8721bbd4dbee6766d1609d8a2ecdebb7dc06" + }, + { + "path": "research/missing-join-frame/RESULT.json", + "usage": "input", + "git_blob": "e653fb4358ded67ff1539151f4b670ad9a242fb1", + "sha256": "25f2cbcde988847ff86f44e804982069863ec99ff68097f16e9bb7a1a17c4cd0" + }, + { + "path": "research/missing-join-frame/verify.py", + "usage": "input", + "git_blob": "188135f81c9937af8232a06dc1e7b8b28260e6a8", + "sha256": "21429dd9c1b9c93ebb57e5fbb8ef674d0e4146ac8c25cc7c097c3352c02366a4" + }, + { + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "usage": "input", + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598" + }, + { + "path": "research/pr4359-p7-padding/TENSOR.md", + "usage": "input", + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/pr4359-p7-padding/native_inventory.py", + "usage": "input", + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32" + }, + { + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "usage": "input", + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d" + }, + { + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "usage": "input", + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088" + }, + { + "path": "research/query-thinned-controllers/RESULT.json", + "usage": "input", + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f" + }, + { + "path": "research/query-thinned-controllers/SOURCES.json", + "usage": "input", + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29" + }, + { + "path": "research/query-thinned-controllers/controller.py", + "usage": "input", + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2" + }, + { + "path": "research/query-thinned-controllers/verify.py", + "usage": "input", + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950" + }, + { + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + ] +} diff --git a/research/compact-joint-compiler/TASK.json b/research/compact-joint-compiler/TASK.json new file mode 100644 index 0000000000..1ab395e043 --- /dev/null +++ b/research/compact-joint-compiler/TASK.json @@ -0,0 +1,64 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "base_commit": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "scope_status": "changed", + "actual_scope": "Retain PR4470 conditional kappa 0.00302015 with an exactly certified smaller local uniform-supplier rank.", + "scope_change_reason": "User assigned a best-kappa search. The initial improving candidate was superseded during the session by PR4470; no tested extension beats it. Retain a useful sufficient finite-compiler improvement on the new strongest observed invoice, explicitly without a kappa-improvement claim.", + "bottleneck_link": "Oversized sufficient logarithmic majorants and equal allocation of compiler/outer slack inflate the local supplier rank.", + "stop_rule": "Require source-pinned native/operator/phase replay, both paid tails, exact integer rank test and every retained outer predicate; do not claim a smaller overall multiplication input threshold.", + "evidence": "arithmetic/RESULT.json, arithmetic/PROOF.txt, PROOF.md, VALIDATION.md", + "author": "Dugongue", + "ai_assistance": "Substantial OpenAI Codex assistance by root and three agents.", + "outcome": "completed", + "open_questions": [ + { + "question": "Can changed warp charts or nonmonotone contact moves improve the complete PR4470 invoice?", + "why_it_matters": "The present compiler improvement preserves kappa.", + "first_step": "Freeze one source warp or two-contact change, lower every emitted Clifford including absolute phase, and reprice the complete p16 controller.", + "blocked_by": "No higher-kappa changed native word has passed all gates in this session." + } + ] +} diff --git a/research/compact-joint-compiler/VALIDATION.md b/research/compact-joint-compiler/VALIDATION.md new file mode 100644 index 0000000000..62ea270975 --- /dev/null +++ b/research/compact-joint-compiler/VALIDATION.md @@ -0,0 +1,9 @@ +# Validation and limits + +The registered verifier has separate dependency, native and arithmetic gates. They preserve exact source-byte guards. The native gate freshly executes both retained interpreters, both orientations, all 632 arbitrary persistent columns, owned-center cleanup and all 423 transport/helper physical pairs, including absolute phases. The arithmetic gate freshly replays the source controller and source bill before binding the compact result to identical target and paid histograms. + +The new exact arithmetic checks both original/completion tails, whole-job splitting, shifted exit and complement capacity, the finite integer majorant, all 54 current strict predicates, four functional guards, all 63 legacy predicates and agreement of all nine cost rows. Controls reject unsupported BIT saving, closed uniform/outer gaps and a false endpoint saving. A separate audit recomputes the displayed rational tail and integer inequalities and checks the actual-native inventory binding. Both normal and optimized isolated Python are used. These are computational exact-arithmetic/operator checks, not proof-assistant or independent human acceptance. + +During independent review, the initial compact complement-capacity check used a factor 2 inherited from a different denominator. For θ = 94/101 the sufficient factor is 2^(101 − 94) = 128. The stronger exact inequality passes; the executable condition and proof were corrected before the final replay. The resulting N is unchanged. This correction is included to make the hypothesis audit reviewable. + +All inherited conditional physical, analytic, precision, tape, stock, prime and recovery obligations remain. The finite word is specified algorithmically, not materialized. Smaller local template rank is the only new bound claimed; tiny outer slack can worsen the eventual full-algorithm threshold. No improvement to that overall threshold or to κ is claimed. diff --git a/research/compact-joint-compiler/VERIFY.json b/research/compact-joint-compiler/VERIFY.json new file mode 100644 index 0000000000..cec7296b2e --- /dev/null +++ b/research/compact-joint-compiler/VERIFY.json @@ -0,0 +1,120 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "research/fresh-helper-boundary/RESULT.json", + "research/fresh-helper-boundary/SOURCES.json", + "research/fresh-helper-boundary/arithmetic.py", + "research/fresh-helper-boundary/native.py", + "research/fresh-helper-boundary/verify.py", + "research/fresh-helper-thinned/PROOF.md", + "research/fresh-helper-thinned/README.md", + "research/fresh-helper-thinned/RESULT.json", + "research/fresh-helper-thinned/SOURCES.json", + "research/fresh-helper-thinned/verify.py", + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/verify.py", + "research/joint-helper-lattice/CONTROLLER.json", + "research/joint-helper-lattice/DISCOVERY.json", + "research/joint-helper-lattice/FRONTIER.json", + "research/joint-helper-lattice/NATIVE.json.gz", + "research/joint-helper-lattice/PATCH.json", + "research/joint-helper-lattice/PROOF.md", + "research/joint-helper-lattice/README.md", + "research/joint-helper-lattice/REPLAY-LOGS.json", + "research/joint-helper-lattice/RESULT.json", + "research/joint-helper-lattice/SOURCES.json", + "research/joint-helper-lattice/TASK.json", + "research/joint-helper-lattice/VALIDATION.md", + "research/joint-helper-lattice/VERIFY.json", + "research/joint-helper-lattice/native_joint.py", + "research/joint-helper-lattice/verify.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-function-composition/complex/prune_native.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "research/kappa-rebuild/bit/bit_native_binding.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-rebuild/bit/mixed_productive_bit.py", + "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/kappa-rebuild/complex/native_extensions.py", + "research/kappa-rebuild/complex/power_two_balance.py", + "research/kappa-rebuild/complex/rebuild_native.py", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "research/missing-join-frame/NATIVE.json.gz", + "research/missing-join-frame/PATCH.json", + "research/missing-join-frame/PROOF.md", + "research/missing-join-frame/RESULT.json", + "research/missing-join-frame/verify.py", + "research/pr4359-p7-padding/P7-FACTOR.json", + "research/pr4359-p7-padding/TENSOR.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/pr4359-p7-padding/native_inventory.py", + "research/query-thinned-controllers/BIT-CONTROLLER.json", + "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "research/query-thinned-controllers/RESULT.json", + "research/query-thinned-controllers/SOURCES.json", + "research/query-thinned-controllers/controller.py", + "research/query-thinned-controllers/verify.py", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "dependencies" + ], + "timeout_seconds": 120, + "checks": "Fresh retained source native/BIT dependencies." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "native" + ], + "timeout_seconds": 400, + "checks": "Fresh PR4470 two-interpreter, 632-column, both-orientation and all absolute-phase replay, tied to the new arithmetic profile." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "arithmetic" + ], + "timeout_seconds": 400, + "checks": "Fresh PR4470 complete arithmetic/controller replay plus the new tails, compiler integer bound, 54+4 current and 63 legacy predicates and mutation controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/independent/audit.py" + ], + "timeout_seconds": 120, + "checks": "Read-only independent source-pinned audit, normal/optimized equality, exact compiler and tail tests, and scientific/source rejection controls." + } + ] +} diff --git a/research/compact-joint-compiler/arithmetic/INPUTS.json b/research/compact-joint-compiler/arithmetic/INPUTS.json new file mode 100644 index 0000000000..0fb0601fc8 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/INPUTS.json @@ -0,0 +1,49 @@ +{ + "files": [ + { + "path": "verify.py", + "sha256": "4ad2d95bee6e6fe2ae4462e5dd0921c64677fc86a5da1f38a198546c28c7f1b1" + }, + { + "path": "intervals.py", + "sha256": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc" + }, + { + "path": "outer_ledger.py", + "sha256": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54" + }, + { + "path": "legacy.py", + "sha256": "43cd70c98a133015f40fd695e18035254cb3bd303f2da45bf46607f211506a87" + }, + { + "path": "legacy-source.txt", + "sha256": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895" + }, + { + "path": "controller.json", + "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + { + "path": "ordinary-bit.json", + "sha256": "7d3ef7711fef1033a49f7ac9847bccf24145c0ba2cf248b3802114c172fb0249" + }, + { + "path": "profile.json", + "sha256": "6e937237c22b3b6d4821ecc253e579b852731a5c665ce488d42f2f7bddb291f5" + } + ], + "scope": "Same best-known conditional kappa as PR4470, changed paid tensor/compiler footprint only. No endpoint improvement claimed.", + "predecessor": { + "pr": 4470, + "repository": "1337isnot1337/integer-mult-bounds", + "head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "status": "author-checked pending contribution; no selected promotion inferred" + }, + "legacy_origin": { + "repository": "CrocSwap/integer-mult-bounds", + "commit": "2a13eb1827784206202db90e5dc8327cf8a250db", + "path": "research/higher-moment-strictification/vendor/check_ledger.py", + "sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98" + } +} diff --git a/research/compact-joint-compiler/arithmetic/PROOF.txt b/research/compact-joint-compiler/arithmetic/PROOF.txt new file mode 100644 index 0000000000..0ad965e87f --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/PROOF.txt @@ -0,0 +1,19 @@ +Same conditional κ, smaller finite compiler bound + +The native word, 408 independent helper fields, whole rank-eight center jobs and complete p16 controller are exactly PR4470's source-bound construction. The declared conditional κ remains 0.00302015. This contribution makes no improved κ claim and no change to the selected result. The bound concerns the local supplier template. The smaller outer slack may raise the eventual threshold for the full multiplication algorithm; that threshold is not bounded here. Its input profile and controller are hash-guarded; run(local) additionally checks an actual native replay's helper and paid inventories against those exact frozen inputs. + +Keep tested saving C = 0.00302016, so t = 1 − C. The changed paid tensor construction uses v = 682, cutoff J = 17^v, productive floor L = 21^v and higher-moment offset u = 1/8. Recompute α = P_t/T_t, γ = P_(t+u)/(17^u T_t) and δ = 10928*21/(17^C T_t). Exact rational intervals prove α < 1 − 31/(5*10^9), γ < 98102/100000 and δ < 959/1000. Both original and completion tails are charged by the retained higher-moment theorem. Their resulting conservative upper bound is + + 1/(1 + v*31/(5*10^9)) + 2*(98102/100000)^v + 2*(959/1000)^v < 1. + +The same displayed bound is greater than 1 at v = 681. This is a test of these chosen conservative ratios, not a global optimality theorem for tensor completion. Scalar words, whole-job normalizers, owned erasure, all main adapters and fixed routes remain charged by the explicit source finite allowances. + +Choose logarithmic contraction θ = 94/101 and logarithm power p = 143. Exact integer tests verify 17^101 < 21^94 and 2^(101−94)*(17^682)^101 ≤ (145^682)^94. For η = (1 − C)*145^(−682*C), the interval engine proves η > θ^143 and η < θ^142, and also 145^(682*C) < 2^143. These are precisely the sufficient shifted-exit, complement-capacity and initial-range hypotheses of the retained general logarithmic majorant. The smaller power is justified by these inequalities, not by changing the inductive theorem. + +Separate compiler slack from outer-transfer slack. Put g = 1/100000001 and d = (C − κ − g)/6 = 1/60000000600000000. Then d > 0 and the uniform saving is C − g = κ + 6d. Take b = κ + 5d, a = κ + 4d, q = κ + 3d, ε = 1 − d, β = 1 − 3d, r0 = d/10, stop = layout = d, retaining ordinary BIT admission 0.0034. All 54 strict and 4 functional predicates pass exactly, including every one of the nine outer cost rows. Four source mutation controls reject. A separate legacy check with decimal grid 10^20 passes all 63 predicates and agrees on all nine rows; the old 10^10 grid cannot resolve these smaller strict margins and is not silently reused. + +The integer majorant test (100000001*j + 1)^143 < 2^j passes at j = 5581 and fails at j = 5580. Thus the retained compiler theorem supplies sufficient uniform rank N = 2^558100005581. PR4470 gives 2^64215200000000, so the exponent decreases by approximately 115.06 times. This compares finite template bounds, not observed runtime, and the enormous word is algorithmically specified rather than materialized. The full integer-multiplication theorem still retains all inherited native, analytic, precision, fixed-tape, stock, prime, ownership and exact-recovery premises. + +Predecessor credit: PR4470's actual new native word and p16 controller; PR4447 and PR4440/4441's geometry, retiming and thinning; zxv's higher-moment and logarithmic-majorant work; Jacob Alan Sussman's mixed-target compiler; Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe, Vlado Vojdanovski and the retained legacy outer-ledger contributors. New compiler choices prepared with substantial OpenAI Codex assistance. Apache-2.0 for new code; original notices retained. + +Open next question: replace this sufficient power majorant by a source-bound sharper recurrence while preserving both paid tails and the complete current outer ledger. A smaller template bound alone does not improve κ. The displayed N bounds the local uniform supplier template. The tiny outer d can increase the eventual input threshold of the full integer-multiplication theorem; no numerical bound on that overall threshold, nor any reduction of it, is claimed. diff --git a/research/compact-joint-compiler/arithmetic/RESULT.json b/research/compact-joint-compiler/arithmetic/RESULT.json new file mode 100644 index 0000000000..514d12ce4d --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/RESULT.json @@ -0,0 +1,304 @@ +{ + "compiler": { + "H": 558100005581, + "N": "2^558100005581", + "eta": { + "lower": "0.000035221718023643756209805039", + "upper": "0.000035221718023643756209805040" + }, + "gap": "1/100000001", + "integer_test_exponent": 5581, + "power": 143, + "theta": "94/101", + "word_materialized": false + }, + "derivative_positive_lower": "153765567619337917435297159143913717753264213528597495787928055/784637716923335095479473677900958302012794430558004314112", + "gain_over_PR4447": "473/25000000", + "kappa": "60403/20000000", + "kappa_decimal": "0.00302015", + "legacy_outer": { + "backoff": "2497/50000000000000000000", + "grid": 100000000000000000000, + "nine_row_agreement": true, + "source_sha256": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895", + "strict_checks": { + "actual_bit_above_effective": "11395500113953/30000000300000000", + "actual_logarithmic_gamma_guard": "1/60000000600000000", + "actual_logarithmic_group_guard": "36291940725838793649328233534677/200000004000000020000000000000000", + "alpha_logarithm_absorption": "1/600000006000000000", + "boundary_algebraic_matrix_above_kappa": "79939597799395969/1200000024000000120000000000000000", + "cap_above_band": "163708063274161236350671866465323/400000008000000040000000000000000", + "cap_below_cell": "108875822177516330947984200604031/1200000024000000120000000000000000", + "cap_below_phase_cell_power": "436291948725838823649328133534677/400000008000000040000000000000000", + "complex_above_effective": "1/60000000600000000", + "complex_below_one_over_32": "338758203387581/12000000120000000", + "complex_endpoint": "1/30000000300000000", + "epsilon_below_one": "1/60000000600000000", + "epsilon_positive": "60000000599999999/60000000600000000", + "fused_gaussian_above_kappa": "79818791798187907/1200000024000000120000000000000000", + "gaussian_above_main": "9939597099395969/600000012000000060000000000000000", + "global_coordinate_router_above_kappa": "1/15000000150000000", + "global_gamma_power_slack": "3/200000002000000000", + "group_below_dimension": "1/30000000300000000", + "group_bit_router_above_kappa": "49909395999093953/600000012000000060000000000000000", + "group_gauge_power_slack": "108875822177516379947984690604031/600000012000000060000000000000000", + "group_key_fits_record": "1/30000000300000000", + "group_positive": "20000000199999999/20000000200000000", + "group_scans_above_kappa": "14954697899546977/15000000150000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_online_final": "644589790400418148631/500000000000000000000000", + "improvement_over_pkg_k2": "1342157392794717479267911225169191627777122102965890395790280701170194526587548469132116575062403/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1699": "1342508268656645435748941712936355250934431507/1000000000000000000000000000000000000000000000000", + "improvement_over_pr1712": "6712541343283227178741362020680007884145727138632283638941299969772687285461029288600736779707649/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1758": "1340404491197700948453466314800026327686526580209199320247542619067215757027414399369818327775017/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1786": "13403952118499510912194521335000000000000000000000000000000001999999800001/10000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1828": "2680790087748910957328658012158594846003377122994839409079344959674400000000000000000000000004006719019826502178085342683975683/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1839": "6701975219372277393321645030396487115008442807487098522698362399185677258698371805868475000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1875": "6701975219372277393321645030396487115008442807487098522698362399185677258698371805868471719335776838627743415457068895139647759399172939286143496816535216421325187363046885361425772909502231218314437622205930116079297234806627210590217190600996553729143901162562581526621534715086055386213403722175000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1876": "670197521937227739332164503039648711500844280748709852269836239918567725869837180586847171933577683862774341545706889513964775939917293928614349681653521642132518736304688536142577290950223121831443762220593011607929723480662721059021719060099655372914390116256258152662153471508605538621340372217196657216794137380775174500330086462142358142864921147118845386980694114022172311249292673931726844600000000000000000001001679754956625544521335670993920702577/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1897": "1340395043874455478664329006079297423001688561497419704539672479837135451739674361173694343867155367725548683091413779027929551879834587857228699363307043284265037472609377072285154581900446243662887524441186023215859446961325442118043438120199310745828780232512516305324306943017211077242680744434393314433588274761550349000660172924284716285729842294237690773961388228044344622498585347863453689118814253082419197486359454032147189198319033143866021423837056207677317517847011467076188001061138620310116832610271556685687769184940440093096226243113127523863162928128796969576356494654526264864467/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_previous_local_final": "644589790400418148631/500000000000000000000000", + "improvement_over_previous_package": "13423300976855635663689448641223998986170598784229341400200650717283025923262102542077285802551153/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_internal": "1/120000001200000000", + "lambda_above_sigma": "1/40000000400000000", + "lambda_above_tau": "1/120000001200000000", + "lambda_prime_above_lambda": "1/120000001200000000", + "lambda_prime_above_leaf": "23963758439637581/720000014400000072000000000000000", + "leaf_saving_above_effective": "11963758319637581/720000014400000072000000000000000", + "main_transform_above_kappa": "19979865866465323/400000008000000040000000000000000", + "membership_arithmetic_fits_record": "1/60000000600000000", + "microbox_face_corrections_above_kappa": "2309909418599093957/30000000300000000", + "microbox_halo_volume": "1580000015800000001/20000000200000000", + "polynomial_products_above_kappa": "59818791598187909/60000000600000000", + "positive_layout_slack": "1/60000000600000000", + "q_below_effective": "1/60000000600000000", + "q_below_internal": "1/60000000600000000", + "q_below_leaf": "23963758439637581/720000014400000072000000000000000", + "q_positive": "60403000604031/20000000200000000", + "short_record_fallback": "11963758319637581/12000000120000000", + "source_axis_superpolynomial": "1/60000000600000000", + "sparse_union_movement_above_kappa": "487500009750000128689597799395969/1200000024000000120000000000000000", + "stop_below_one": "60000000599999999/60000000600000000", + "stop_positive": "1/60000000600000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "1/20000000200000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "1/20000000200000000", + "union_tag_work_per_visit_fits_record": "1/20000000200000000" + } + }, + "local_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "local_paid": { + "1": 2237, + "2": 388, + "3": 494, + "4": 147, + "5": 36, + "8": 8 + }, + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform": [ + "new_complex_uniform_saving_above_b" + ], + "old_BIT": [ + "actual_bit_above_effective" + ], + "unfunded_endpoint": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "4980000049799999751/5000000050000000000", + "fixed_halo_explicit_metadata_branch": "1155000011550000001/15000000150000000", + "new_BIT_row_stock_sublinear_in_active_group": "19940000199399999003/20000000200000000000", + "new_semantic_group_guard": "1/20000000200000000" + }, + "margins": { + "boundary_algebraic_matrix": "3624180072483680302015799395969/1200000024000000120000000000000000", + "fused_gaussian": "3624180072483680181209798187907/1200000024000000120000000000000000", + "global_coordinate_router": "90604500906047/30000000300000000", + "group_bit_router": "1812090036241850090604999093953/600000012000000060000000000000000", + "group_scans": "30000000299999999/30000000300000000", + "main_transform": "1208060024161220100671866465323/400000008000000040000000000000000", + "microbox_face_corrections": "1155000011550000001/15000000150000000", + "polynomial_products": "60000000599999999/60000000600000000", + "sparse_union_movement": "491124189822483729052015799395969/1200000024000000120000000000000000" + }, + "parameters": { + "a": "90604500906047/30000000300000000", + "b": "36241800362419/12000000120000000", + "beta": "20000000199999999/20000000200000000", + "bit_saving": "17/5000", + "cap_xi": "363708067274161256350671866465323/400000008000000040000000000000000", + "complex_uniform_saving": "471898442219/156250001562500", + "d": "1/60000000600000000", + "epsilon": "60000000599999999/60000000600000000", + "kappa": "60403/20000000", + "lambda_": "119637583196375813/120000001200000000", + "lambda_prime": "19939597199395969/20000000200000000", + "layout": "1/60000000600000000", + "q": "60403000604031/20000000200000000", + "r0": "1/600000006000000000", + "stop": "1/60000000600000000", + "tested_saving": "4719/1562500" + }, + "strict_checks": { + "actual_bit_above_effective": "11395500113953/30000000300000000", + "actual_logarithmic_gamma_guard": "1/60000000600000000", + "actual_logarithmic_group_guard": "36291940725838793649328233534677/200000004000000020000000000000000", + "alpha_logarithm_absorption": "1/600000006000000000", + "boundary_algebraic_matrix_above_kappa": "79939597799395969/1200000024000000120000000000000000", + "cap_above_band": "163708063274161236350671866465323/400000008000000040000000000000000", + "cap_below_cell": "108875822177516330947984200604031/1200000024000000120000000000000000", + "cap_below_phase_cell_power": "436291948725838823649328133534677/400000008000000040000000000000000", + "complex_above_effective": "1/60000000600000000", + "complex_below_one_over_32": "338758203387581/12000000120000000", + "complex_endpoint": "1/30000000300000000", + "epsilon_below_one": "1/60000000600000000", + "epsilon_positive": "60000000599999999/60000000600000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "79818791798187907/1200000024000000120000000000000000", + "gaussian_above_main": "9939597099395969/600000012000000060000000000000000", + "global_coordinate_router_above_kappa": "1/15000000150000000", + "global_gamma_power_slack": "3/200000002000000000", + "group_below_dimension": "1/30000000300000000", + "group_bit_router_above_kappa": "49909395999093953/600000012000000060000000000000000", + "group_gauge_power_slack": "108875822177516379947984690604031/600000012000000060000000000000000", + "group_key_fits_record": "1/30000000300000000", + "group_positive": "20000000199999999/20000000200000000", + "group_scans_above_kappa": "14954697899546977/15000000150000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "644589790400418148631/500000000000000000000000", + "lambda_above_internal": "1/120000001200000000", + "lambda_above_sigma": "1/40000000400000000", + "lambda_above_tau": "1/120000001200000000", + "lambda_prime_above_lambda": "1/120000001200000000", + "lambda_prime_above_leaf": "23963758439637581/720000014400000072000000000000000", + "leaf_saving_above_effective": "11963758319637581/720000014400000072000000000000000", + "main_transform_above_kappa": "19979865866465323/400000008000000040000000000000000", + "membership_arithmetic_fits_record": "1/60000000600000000", + "microbox_face_corrections_above_kappa": "2309909418599093957/30000000300000000", + "microbox_halo_volume": "1580000015800000001/20000000200000000", + "new_complex_uniform_saving_above_b": "1/60000000600000000", + "new_semantic_guard_with_C1_one": "1/60000000600000000", + "polynomial_products_above_kappa": "59818791598187909/60000000600000000", + "positive_layout_slack": "1/60000000600000000", + "q_below_effective": "1/60000000600000000", + "q_below_internal": "1/60000000600000000", + "q_below_leaf": "23963758439637581/720000014400000072000000000000000", + "q_positive": "60403000604031/20000000200000000", + "short_record_fallback": "11963758319637581/12000000120000000", + "source_axis_superpolynomial": "1/60000000600000000", + "sparse_union_movement_above_kappa": "487500009750000128689597799395969/1200000024000000120000000000000000", + "stop_below_one": "60000000599999999/60000000600000000", + "stop_positive": "1/60000000600000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "1/20000000200000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "1/20000000200000000", + "union_tag_work_per_visit_fits_record": "1/20000000200000000" + } + }, + "paid": { + "1": 41946, + "16": 448, + "2": 6984, + "24": 448, + "3": 8892, + "32": 448, + "4": 2646, + "40": 448, + "48": 448, + "5": 648, + "56": 448, + "64": 448, + "72": 224, + "8": 144 + }, + "paid_calls": 64620, + "productive_fields": 10928, + "rank_masses": [ + 239886, + 239134 + ], + "rank_surplus": 752, + "raw_nonrecursive": { + "all_unit_bound": 181098496, + "budget": 1000000000, + "local_routes": 4814000, + "local_scalar_allowance": 158168 + }, + "raw_root_bracket": [ + "3020165977/1000000000000", + "30201659771/10000000000000" + ], + "remaining": "Requires independent source-pinned native/operator/phase replay of unchanged candidate and source admission. Arithmetic alone is not a new theorem or selected-frontier promotion.", + "source_hashes": { + "interval_engine": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc", + "outer_ledger": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54", + "p16_controller": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + "status": "PASS_COMPLETE_CONDITIONAL_ARITHMETIC", + "strictification": { + "alpha": { + "lower": "0.999999993770239196201774801294", + "upper": "0.999999993770239196201774801295" + }, + "cutoff": 17, + "delta": { + "lower": "0.958754911244405494833244087511", + "upper": "0.958754911244405494833244087512" + }, + "floor": 21, + "gamma": { + "lower": "0.981011186022465634893464479926", + "upper": "0.981011186022465634893464479927" + }, + "normalized_paid_upper": "6229523134180405573822205648138369893496002293186705214781785035885548582756448251617534293205788280361399914248219628732233377115342340346896692826309003353583023664395111667126627013438759015601681784158229338395982620138553390591711054121687432866169027937060344743466505805235582163801244998330585509930860190887989464846025473266062920352304280751936877280109251646654764919972816357461765791553914030217001373298336894592700908739840020830782668764032651243134426911822421460574174100616438599706056299537262115804871704688914689373128769286286441903868790576591126614919398101254059074768626296592469772983538333886406530190124181630203619339392855061376486894432166104005450358513152890074190031597754121597486234146496826755753525249088740494873825322835346674015361904612968947935290655070628913220860743527730156263558123911845410965359082808947500334602544760301727097880306837533410182698691237326016779030510948664147817129741605385215597443099210568044460460218330851264787440033655604150527202468191178214835260591978620015412761099388996707874744858066199956768269933380914467692336784160854932013489135707395541189266787666247518951163062420005199646107790919889402089271852508343427404421693598186094104964048006840762777059320868476057922527167151885840801845420416673590450019259670978141147244182458668488830582107727939564092151279160935860067475494239151243467194749894805431086389230616321068960271106765381401915889117473724738390020444607339159336581697565050445155181776178389457775778659737744481574926142967802610525759369499219530611016812986384829557689094972718235856566929162341427470296983511969172163610349733483623613474944701521568817109339855258516824110066109558936420653084198390810489237916347213057314403656252720188463900032903545691874964066185881651769781972676402214066115895449186119157050652119546712152037253860444506533136367669085095798453189544132884923864885792238916045317743632788081816677925922094695413261880302035643138587965744453748815656145777971826364174624509758481888079367462723085813446382357168276821837073047675418244008371022731129204673089912247454752053812290757274794090911734011643177038601380625017091774313676330733263828185989501122408378815184079644414747032007825185990484272107033172065121398509515269730220519446465730193842510354549879437353327981589640558721078133243392753792216569059033901804744737524920543093507591915081192242009789062254461336738154328178620755765057081003000574691619784836466407592467341049846816057959439962370772514598096717438458705312418622547880203790946677032850527951904100865362844514622076026251343547814053811976416029242947275031841388848595942033172715010691647552223441464756983005879684153919675714718000548336268652388474997563410499492248327139575585702298216062209707537556553290741742913218701479137944425056884064657517148761002971039020259717398760115370128581634817224509484601042525516499221732880910079142374012417543469838795692430385550160541487431270183221153315494819157015691105313390273793712515439818994761837679879815757873614493853283176897692134785698289891666730997698419929914069235673565709966781062872853754991832511125687368465677044804684036190278867249997498602037171/6229523185240436722790793730350330486505008077061908274314028103253636090218348047304841685642221979267553674599084787043006070378310994556879657277663210177223557285558131187708429487302490342721255889674366606987744750457618567824326218659646918141246246438757155714300304266156992623057650934094266191076034757952450425725071696140664274944327057015822641303719863483031557284784972994705602996468729162293872251545898819594756255526066569274366846453716561882174573838710784912109375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "tail_offset": "1/8", + "tensor_power": 682, + "tested": "4719/1562500" + }, + "targets": { + "145": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 504, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "7": 126, + "73": 224, + "8": 846, + "9": 5868 + }, + "tested": "4719/1562500" +} diff --git a/research/compact-joint-compiler/arithmetic/controller.json b/research/compact-joint-compiler/arithmetic/controller.json new file mode 100644 index 0000000000..49a2f06758 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/controller.json @@ -0,0 +1,5224 @@ +{ + "ambient_rank": 145, + "boundaries": { + "left": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "left_program": [ + [ + "SWAP", + 30, + 31 + ], + [ + "SWAP", + 29, + 30 + ], + [ + "SWAP", + 28, + 30 + ], + [ + "SWAP", + 27, + 29 + ], + [ + "SWAP", + 26, + 28 + ], + [ + "SWAP", + 25, + 30 + ], + [ + "SWAP", + 24, + 25 + ], + [ + "SWAP", + 23, + 26 + ], + [ + "SWAP", + 22, + 30 + ], + [ + "SWAP", + 20, + 26 + ], + [ + "SWAP", + 19, + 22 + ], + [ + "SWAP", + 18, + 29 + ], + [ + "SWAP", + 17, + 23 + ], + [ + "SWAP", + 16, + 27 + ], + [ + "SCALE", + 15, + "-1" + ], + [ + "SWAP", + 15, + 31 + ], + [ + "ADD", + 12, + 14, + "1" + ], + [ + "ADD", + 10, + 14, + "-1" + ], + [ + "ADD", + 8, + 14, + "1" + ], + [ + "ADD", + 6, + 14, + "-1" + ], + [ + "ADD", + 4, + 14, + "1" + ], + [ + "ADD", + 2, + 14, + "-1" + ], + [ + "ADD", + 0, + 14, + "1" + ], + [ + "SWAP", + 14, + 15 + ], + [ + "ADD", + 31, + 13, + "1" + ], + [ + "SWAP", + 13, + 30 + ], + [ + "ADD", + 10, + 12, + "1" + ], + [ + "ADD", + 8, + 12, + "-1" + ], + [ + "ADD", + 6, + 12, + "1" + ], + [ + "ADD", + 4, + 12, + "-1" + ], + [ + "ADD", + 2, + 12, + "1" + ], + [ + "ADD", + 0, + 12, + "-1" + ], + [ + "SWAP", + 12, + 14 + ], + [ + "ADD", + 31, + 11, + "-1" + ], + [ + "ADD", + 30, + 11, + "-1" + ], + [ + "SCALE", + 11, + "-1" + ], + [ + "SWAP", + 11, + 29 + ], + [ + "ADD", + 8, + 10, + "1" + ], + [ + "ADD", + 6, + 10, + "-1" + ], + [ + "ADD", + 4, + 10, + "1" + ], + [ + "ADD", + 2, + 10, + "-1" + ], + [ + "ADD", + 0, + 10, + "1" + ], + [ + "SWAP", + 10, + 13 + ], + [ + "ADD", + 31, + 9, + "1" + ], + [ + "ADD", + 30, + 9, + "1" + ], + [ + "ADD", + 29, + 9, + "1" + ], + [ + "SWAP", + 9, + 28 + ], + [ + "ADD", + 6, + 8, + "1" + ], + [ + "ADD", + 4, + 8, + "-1" + ], + [ + "ADD", + 2, + 8, + "1" + ], + [ + "ADD", + 0, + 8, + "-1" + ], + [ + "SWAP", + 8, + 12 + ], + [ + "ADD", + 31, + 7, + "-1" + ], + [ + "ADD", + 30, + 7, + "-1" + ], + [ + "ADD", + 29, + 7, + "-1" + ], + [ + "ADD", + 28, + 7, + "-1" + ], + [ + "SCALE", + 7, + "-1" + ], + [ + "SWAP", + 7, + 27 + ], + [ + "ADD", + 4, + 6, + "1" + ], + [ + "ADD", + 2, + 6, + "-1" + ], + [ + "ADD", + 0, + 6, + "1" + ], + [ + "SWAP", + 6, + 11 + ], + [ + "ADD", + 31, + 5, + "1" + ], + [ + "ADD", + 30, + 5, + "1" + ], + [ + "ADD", + 29, + 5, + "1" + ], + [ + "ADD", + 28, + 5, + "1" + ], + [ + "ADD", + 27, + 5, + "1" + ], + [ + "SWAP", + 5, + 26 + ], + [ + "ADD", + 2, + 4, + "1" + ], + [ + "ADD", + 0, + 4, + "-1" + ], + [ + "SWAP", + 4, + 10 + ], + [ + "ADD", + 31, + 3, + "-1" + ], + [ + "ADD", + 30, + 3, + "-1" + ], + [ + "ADD", + 29, + 3, + "-1" + ], + [ + "ADD", + 28, + 3, + "-1" + ], + [ + "ADD", + 27, + 3, + "-1" + ], + [ + "ADD", + 26, + 3, + "-1" + ], + [ + "SCALE", + 3, + "-1" + ], + [ + "SWAP", + 3, + 25 + ], + [ + "ADD", + 0, + 2, + "1" + ], + [ + "SWAP", + 2, + 9 + ], + [ + "ADD", + 31, + 1, + "1" + ], + [ + "ADD", + 30, + 1, + "1" + ], + [ + "ADD", + 29, + 1, + "1" + ], + [ + "ADD", + 28, + 1, + "1" + ], + [ + "ADD", + 27, + 1, + "1" + ], + [ + "ADD", + 26, + 1, + "1" + ], + [ + "ADD", + 25, + 1, + "1" + ], + [ + "SWAP", + 1, + 24 + ], + [ + "SWAP", + 0, + 8 + ] + ], + "right": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "right_program": [ + [ + "ADD", + 30, + 31, + "-1" + ], + [ + "ADD", + 29, + 31, + "-1" + ], + [ + "ADD", + 28, + 31, + "-1" + ], + [ + "ADD", + 27, + 31, + "-1" + ], + [ + "SCALE", + 31, + "-1" + ], + [ + "ADD", + 31, + 30, + "-1" + ], + [ + "ADD", + 29, + 30, + "-1" + ], + [ + "ADD", + 28, + 30, + "-1" + ], + [ + "ADD", + 27, + 30, + "-1" + ], + [ + "ADD", + 31, + 29, + "-1" + ], + [ + "ADD", + 28, + 29, + "-1" + ], + [ + "ADD", + 27, + 29, + "-1" + ], + [ + "SCALE", + 29, + "-1" + ], + [ + "ADD", + 31, + 28, + "-1" + ], + [ + "ADD", + 27, + 28, + "-1" + ], + [ + "SWAP", + 28, + 29 + ], + [ + "ADD", + 31, + 27, + "-1" + ], + [ + "SCALE", + 27, + "-1" + ], + [ + "SWAP", + 27, + 29 + ], + [ + "ADD", + 31, + 26, + "1" + ], + [ + "SWAP", + 26, + 29 + ], + [ + "ADD", + 29, + 25, + "-1" + ], + [ + "ADD", + 24, + 25, + "-1" + ], + [ + "SWAP", + 25, + 28 + ], + [ + "ADD", + 28, + 24, + "1" + ], + [ + "SWAP", + 23, + 29 + ], + [ + "SWAP", + 22, + 25 + ], + [ + "SWAP", + 20, + 23 + ], + [ + "SWAP", + 19, + 25 + ], + [ + "SWAP", + 18, + 27 + ], + [ + "SWAP", + 17, + 29 + ], + [ + "SWAP", + 16, + 31 + ], + [ + "ADD", + 14, + 15, + "-1" + ], + [ + "SWAP", + 15, + 30 + ], + [ + "ADD", + 13, + 14, + "-1" + ], + [ + "SWAP", + 14, + 30 + ], + [ + "ADD", + 12, + 13, + "-1" + ], + [ + "SWAP", + 13, + 22 + ], + [ + "ADD", + 11, + 12, + "-1" + ], + [ + "SWAP", + 12, + 30 + ], + [ + "ADD", + 10, + 11, + "-1" + ], + [ + "SWAP", + 11, + 18 + ], + [ + "ADD", + 9, + 10, + "-1" + ], + [ + "SWAP", + 10, + 22 + ], + [ + "ADD", + 8, + 9, + "-1" + ], + [ + "SWAP", + 9, + 26 + ], + [ + "SWAP", + 8, + 30 + ], + [ + "SWAP", + 7, + 16 + ], + [ + "SWAP", + 6, + 18 + ], + [ + "SWAP", + 5, + 20 + ], + [ + "SWAP", + 4, + 22 + ], + [ + "SWAP", + 3, + 24 + ], + [ + "SWAP", + 2, + 26 + ], + [ + "SWAP", + 1, + 28 + ], + [ + "SWAP", + 0, + 30 + ] + ] + }, + "diagonal": [ + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ] + ], + "invoice": { + "main": { + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 46446, + "2": 12834, + "3": 4032, + "4": 1836, + "5": 360, + "8": 144, + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + }, + "paid_calls": 69012, + "productive_fields": 10928, + "rank_surplus": 752, + "raw_scalar_record_bound": 1000000000, + "targets": { + "5": 504, + "6": 324, + "7": 1008, + "8": 1674, + "9": 3834, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "thick_calls": 18, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ], + "thin_queries": 1680, + "whole_idle": { + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + } + }, + "keep_mask": 35047648968703, + "kind": "complex", + "pairs": 16, + "physical_events": [ + [ + "LOCAL", + 0, + 0, + false + ], + [ + "LOCAL", + 1, + 0, + true + ], + [ + "IDLE", + 1, + [ + 0, + 1 + ] + ], + [ + "ADD", + 0, + 2, + 1 + ], + [ + "ADD", + 3, + 1, + -1 + ], + [ + "QUERY_SHEAR", + 2, + 0, + false + ], + [ + "ADD", + 0, + 2, + -1 + ], + [ + "ADD", + 3, + 1, + 1 + ], + [ + "LOCAL", + 3, + 1, + true + ], + [ + "IDLE", + 2, + [ + 0, + 1, + 3 + ] + ], + [ + "ADD", + 2, + 4, + 1 + ], + [ + "ADD", + 5, + 3, + -1 + ], + [ + "QUERY_SHEAR", + 4, + 1, + false + ], + [ + "ADD", + 2, + 4, + -1 + ], + [ + "ADD", + 5, + 3, + 1 + ], + [ + "LOCAL", + 5, + 2, + true + ], + [ + "IDLE", + 3, + [ + 0, + 1, + 3, + 5 + ] + ], + [ + "ADD", + 4, + 6, + 1 + ], + [ + "ADD", + 7, + 5, + -1 + ], + [ + "QUERY_SHEAR", + 6, + 2, + false + ], + [ + "ADD", + 4, + 6, + -1 + ], + [ + "ADD", + 7, + 5, + 1 + ], + [ + "LOCAL", + 7, + 3, + true + ], + [ + "IDLE", + 4, + [ + 0, + 1, + 3, + 5, + 7 + ] + ], + [ + "ADD", + 6, + 8, + 1 + ], + [ + "ADD", + 9, + 7, + -1 + ], + [ + "QUERY_SHEAR", + 8, + 3, + false + ], + [ + "ADD", + 6, + 8, + -1 + ], + [ + "ADD", + 9, + 7, + 1 + ], + [ + "LOCAL", + 9, + 4, + true + ], + [ + "IDLE", + 5, + [ + 0, + 1, + 3, + 5, + 7, + 9 + ] + ], + [ + "ADD", + 8, + 10, + 1 + ], + [ + "ADD", + 11, + 9, + -1 + ], + [ + "QUERY_SHEAR", + 10, + 4, + false + ], + [ + "ADD", + 8, + 10, + -1 + ], + [ + "ADD", + 11, + 9, + 1 + ], + [ + "LOCAL", + 11, + 5, + true + ], + [ + "IDLE", + 6, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11 + ] + ], + [ + "ADD", + 10, + 12, + 1 + ], + [ + "ADD", + 13, + 11, + -1 + ], + [ + "QUERY_SHEAR", + 12, + 5, + false + ], + [ + "ADD", + 10, + 12, + -1 + ], + [ + "ADD", + 13, + 11, + 1 + ], + [ + "LOCAL", + 13, + 6, + true + ], + [ + "IDLE", + 7, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13 + ] + ], + [ + "ADD", + 12, + 14, + 1 + ], + [ + "ADD", + 15, + 13, + -1 + ], + [ + "QUERY_SHEAR", + 14, + 6, + false + ], + [ + "ADD", + 12, + 14, + -1 + ], + [ + "ADD", + 15, + 13, + 1 + ], + [ + "LOCAL", + 15, + 7, + true + ], + [ + "ADD", + 14, + 16, + 1 + ], + [ + "ADD", + 17, + 15, + -1 + ], + [ + "QUERY_SHEAR", + 16, + 7, + false + ], + [ + "ADD", + 14, + 16, + -1 + ], + [ + "ADD", + 17, + 15, + 1 + ], + [ + "LOCAL", + 17, + 8, + true + ], + [ + "ADD", + 16, + 18, + 1 + ], + [ + "ADD", + 19, + 17, + -1 + ], + [ + "QUERY_SHEAR", + 18, + 8, + false + ], + [ + "ADD", + 16, + 18, + -1 + ], + [ + "ADD", + 19, + 17, + 1 + ], + [ + "LOCAL", + 19, + 9, + true + ], + [ + "ADD", + 18, + 20, + 1 + ], + [ + "ADD", + 21, + 19, + -1 + ], + [ + "QUERY_SHEAR", + 20, + 9, + false + ], + [ + "ADD", + 18, + 20, + -1 + ], + [ + "ADD", + 21, + 19, + 1 + ], + [ + "LOCAL", + 21, + 10, + true + ], + [ + "ADD", + 20, + 22, + 1 + ], + [ + "ADD", + 23, + 21, + -1 + ], + [ + "QUERY_SHEAR", + 22, + 10, + false + ], + [ + "ADD", + 20, + 22, + -1 + ], + [ + "ADD", + 23, + 21, + 1 + ], + [ + "LOCAL", + 23, + 11, + true + ], + [ + "ADD", + 22, + 24, + 1 + ], + [ + "ADD", + 25, + 23, + -1 + ], + [ + "QUERY_SHEAR", + 24, + 11, + false + ], + [ + "ADD", + 22, + 24, + -1 + ], + [ + "ADD", + 25, + 23, + 1 + ], + [ + "LOCAL", + 25, + 12, + true + ], + [ + "ADD", + 24, + 26, + 1 + ], + [ + "ADD", + 27, + 25, + -1 + ], + [ + "QUERY_SHEAR", + 26, + 12, + false + ], + [ + "ADD", + 24, + 26, + -1 + ], + [ + "ADD", + 27, + 25, + 1 + ], + [ + "LOCAL", + 27, + 13, + true + ], + [ + "ADD", + 26, + 28, + 1 + ], + [ + "ADD", + 29, + 27, + -1 + ], + [ + "QUERY_SHEAR", + 28, + 13, + false + ], + [ + "ADD", + 26, + 28, + -1 + ], + [ + "ADD", + 29, + 27, + 1 + ], + [ + "LOCAL", + 29, + 14, + true + ], + [ + "ADD", + 28, + 30, + 1 + ], + [ + "ADD", + 31, + 29, + -1 + ], + [ + "QUERY_SHEAR", + 30, + 14, + false + ], + [ + "ADD", + 28, + 30, + -1 + ], + [ + "ADD", + 31, + 29, + 1 + ], + [ + "LOCAL", + 31, + 15, + true + ], + [ + "LOCAL", + 32, + 15, + false + ], + [ + "IDLE", + 7, + [ + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 8, + [ + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 9, + [ + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 10, + [ + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 11, + [ + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 12, + [ + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 13, + [ + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 14, + [ + 31, + 32 + ] + ], + [ + "ADD", + 30, + 28, + 1 + ], + [ + "ADD", + 29, + 31, + -1 + ], + [ + "ADD", + 28, + 26, + 1 + ], + [ + "ADD", + 27, + 29, + -1 + ], + [ + "ADD", + 26, + 24, + 1 + ], + [ + "ADD", + 25, + 27, + -1 + ], + [ + "ADD", + 24, + 22, + 1 + ], + [ + "ADD", + 23, + 25, + -1 + ], + [ + "ADD", + 22, + 20, + 1 + ], + [ + "ADD", + 21, + 23, + -1 + ], + [ + "ADD", + 20, + 18, + 1 + ], + [ + "ADD", + 19, + 21, + -1 + ], + [ + "ADD", + 18, + 16, + 1 + ], + [ + "ADD", + 17, + 19, + -1 + ], + [ + "ADD", + 16, + 14, + 1 + ], + [ + "ADD", + 15, + 17, + -1 + ], + [ + "ADD", + 14, + 12, + 1 + ], + [ + "ADD", + 13, + 15, + -1 + ], + [ + "ADD", + 12, + 10, + 1 + ], + [ + "ADD", + 11, + 13, + -1 + ], + [ + "ADD", + 10, + 8, + 1 + ], + [ + "ADD", + 9, + 11, + -1 + ], + [ + "ADD", + 8, + 6, + 1 + ], + [ + "ADD", + 7, + 9, + -1 + ], + [ + "ADD", + 6, + 4, + 1 + ], + [ + "ADD", + 5, + 7, + -1 + ], + [ + "ADD", + 4, + 2, + 1 + ], + [ + "ADD", + 3, + 5, + -1 + ], + [ + "ADD", + 2, + 0, + 1 + ], + [ + "ADD", + 1, + 3, + -1 + ], + [ + "SIGNED_SWAP", + 0, + 1 + ], + [ + "SIGNED_SWAP", + 2, + 3 + ], + [ + "SIGNED_SWAP", + 4, + 5 + ], + [ + "SIGNED_SWAP", + 6, + 7 + ], + [ + "SIGNED_SWAP", + 8, + 9 + ], + [ + "SIGNED_SWAP", + 10, + 11 + ], + [ + "SIGNED_SWAP", + 12, + 13 + ], + [ + "SIGNED_SWAP", + 14, + 15 + ], + [ + "SIGNED_SWAP", + 16, + 17 + ], + [ + "SIGNED_SWAP", + 18, + 19 + ], + [ + "SIGNED_SWAP", + 20, + 21 + ], + [ + "SIGNED_SWAP", + 22, + 23 + ], + [ + "SIGNED_SWAP", + 24, + 25 + ], + [ + "SIGNED_SWAP", + 26, + 27 + ], + [ + "SIGNED_SWAP", + 28, + 29 + ], + [ + "SIGNED_SWAP", + 30, + 31 + ] + ], + "prefix_pairs": 7 +} diff --git a/research/compact-joint-compiler/arithmetic/intervals.py b/research/compact-joint-compiler/arithmetic/intervals.py new file mode 100644 index 0000000000..a3e546693f --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/intervals.py @@ -0,0 +1,111 @@ +"""Verbatim exact interval primitives from zxv, higher-moment-strictification. +Source: CrocSwap/integer-mult-bounds at 2a13eb1827784206202db90e5dc8327cf8a250db. +Apache-2.0. Substantial OpenAI Codex assistance. Retained source attribution. +This file checks rational arithmetic, not native or all-size hypotheses. +""" +from fractions import Fraction as Q +from functools import lru_cache +GRID=2**192 + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + diff --git a/research/compact-joint-compiler/arithmetic/legacy-source.txt b/research/compact-joint-compiler/arithmetic/legacy-source.txt new file mode 100644 index 0000000000..20d21008b3 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/legacy-source.txt @@ -0,0 +1,128 @@ +# Verbatim retained ledger function and historical comparison constants. +# Sources: PR1786 Chafik Boukhalfa / chafreaky, Tim Trudgian; PR1731 Jeremy Kothe et al.; +# Vlado Vojdanovski / PR1673; retained higher-moment compiler lineage. +# Apache-2.0; substantial OpenAI assistance. No all-size theorem proved by arithmetic. +KAPPA_1828=Q('0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585') # exact kappa of rohanarun's PR1828 (slack refinement of PR1800 at 1e-96), from its body + + +KAPPA_1839=Q('0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263049999999997996640490086748910957328658012158594') # exact kappa of PR1839 (previous package: 1e-90 endpoint) + + +KAPPA_1875=Q('0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561328446322744513169085862209720704481201654121427713006366929567157349625273906229277148454180995537563371124755588139767841405530386745578819565618798006892541712197674874836946756930569827889227573192555649999999997996640490086748910957328658012158594') # exact kappa of rohanarun's PR1875 (1e-300 endpoint), from its body + + +KAPPA_1876=Q('0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844632274451316908586220972070448120165412142771300636692956715734962527390622927714845418099553756337112475558813976784140553038674557881956561879800689254171219767487483694675693056982788922757319255565606685566411725238449650999339827075715283714270157705762309226038611771955655377501414652136546310799999999999999999997996640490086748910957328658012158594846') # exact kappa of rohanarun's PR1876 (1e-400 endpoint), from its body + + +KAPPA_1897=Q('0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844632274451316908586220972070448120165412142771300636692956715734962527390622927714845418099553756337112475558813976784140553038674557881956561879800689254171219767487483694675693056982788922757319255565606685566411725238449650999339827075715283714270157705762309226038611771955655377501414652136546310881185746917580802513640545967852810801680966856133978576162943792322682482152988532923811998938861379689883167389728443314312230815059559906903773756886872476136837071871203030423643505345473735135533') # exact kappa of M6LI's PR1897 (1e-500 grid), from its body + + +KAPPA_1786=Q('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # exact kappa of chafreaky's PR1786 ledger (EXPECTED-BALANCE.json), headline 0.001679754788150048 + + +KAPPA_PKG5=Q('0.001677992607205282520732088774830808372222877897034109604209719298829805473412451530867883424937597') # previous package (rectangular k=2, tau_eff=2.2500351) + + +KAPPA_PKG4=Q('0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847') # previous package (radix union schedule, square boundary tau=2.372864) + + +KAPPA_1712=Q('0.0016776417313433545642517275958639984231708545722735432722117400060454625429077941422798526440584702') # pkg of PR1712 (Le Gall tau=12/5, old union row) + + +KAPPA_1699=Q('0.001677641731343354564251058287063644749065568493') # exact kappa of PR1699's ledger (Chafik Boukhalfa), same supplier profile + + +def ledger(kind, *, q_=q, zeta=ZETA, slack=SLACK, + old_scan=False, full_gauge=False, full_key=False, old_union=False, old_theta=False, old_linear=False, old_tag=False, + eps_=EPS, beta_=BETA, tau_eff=STRASSEN_TAU, halo_power=HALO_POWER, core_power=CORE_POWER): + r=R0; stop=STOP + # Existing explicit Strassen format, 7^16<2^45; c=3/32. + # Union: radix-distributed schedule (outer/UNION-SCHEDULE.md, new in this package): row exponent eps+1/2-xi. The boundary row binds with main; the Gaussian row has slack at this explicit point. + c=(3-tau_eff)/2 + eps=eps_; beta=beta_ + xi=eps*(1+q_)-c+slack + saving=eps*q_ + # Deliberate strict gap (BACKOFF) after decimal truncation to the FLOOR grid. + kappa=Q((saving*FLOOR).__floor__(),FLOOR)-BACKOFF + # kappa is derived, not silently asserted to equal an expected decimal. + tau=1-a; sigma=1-b + internal=tau+(1-stop)*max(sigma-tau,Q(0)) + leaf=sigma+stop*(1-sigma) + lam=1-(q_+a)/2 + key=beta+1-eps + margins={ + 'main_transform':saving, + 'global_coordinate_router':a, + 'fused_gaussian':1-eps+q_*beta, + 'group_bit_router':1-eps+a*beta, + 'group_scans':1-eps+beta, + 'boundary_algebraic_matrix':c+xi-eps, + 'sparse_union_movement':xi+Q(1,2)-eps, + 'polynomial_products':eps, + 'microbox_face_corrections':1-(eps+beta+halo_power-core_power+2), + } + if old_union:margins['old_g_factor_union_row']=1-eps-beta-Q(1,2)+xi + if old_scan:margins['old_per_axis_scan']=1-eps + if full_key:margins['unnecessary_full_key_sort']=margins['sparse_union_movement']-key + checks={ + 'actual_bit_above_effective':bit-a, + 'complex_above_effective':b-a, + 'q_positive':q_, 'complex_endpoint':b-q_, + 'q_below_effective':a-q_, 'stop_positive':stop, + 'stop_below_one':1-stop, + 'leaf_saving_above_effective':(1-stop)*b-a, + 'q_below_internal':1-internal-q_, 'q_below_leaf':1-leaf-q_, + 'lambda_above_tau':lam-tau, 'lambda_above_sigma':lam-sigma, + 'lambda_above_internal':lam-internal, + 'lambda_prime_above_lambda':1-q_-lam, + 'lambda_prime_above_leaf':1-q_-leaf, + 'epsilon_positive':eps,'epsilon_below_one':1-eps, + 'cap_above_band':xi-Q(1,2),'cap_below_cell':eps-xi, + 'group_positive':beta,'group_below_dimension':eps-beta, + 'support_router_span':1-beta, + 'group_gauge_power_slack':1-(2*xi-THETA_POWER)-r-beta, + 'actual_logarithmic_group_guard':1-(2*xi-THETA_POWER)-beta, + 'global_gamma_power_slack':1-eps-r, + 'actual_logarithmic_gamma_guard':1-eps, + 'alpha_logarithm_absorption':r, + 'group_key_fits_record':1-key, + 'membership_arithmetic_fits_record':1-beta-2*(1-eps), + 'microbox_halo_volume':core_power-halo_power-beta, + 'positive_layout_slack':slack, + 'short_record_fallback':eps-a, + 'improvement_over_online_final':kappa-online, + 'improvement_over_previous_local_final':kappa-old, + 'complex_below_one_over_32':Q(1,32)-b, + } + checks['strassen_integer_power_gap']=Q(2**tau_eff.numerator-7**tau_eff.denominator) + checks['theta_positive_polynomial_power']=THETA_POWER + checks['cap_below_phase_cell_power']=THETA_POWER-xi + checks['halo_covers_generic_inverse_radius']=Q(halo_power-43) + checks['union_tag_work_per_visit_fits_record']=1-beta + checks['union_header_fits_record']=1-beta + checks['source_axis_superpolynomial']=1-eps + checks['improvement_over_pr1786']=kappa-KAPPA_1786 + checks['improvement_over_pr1828']=kappa-KAPPA_1828 + checks['improvement_over_pr1839']=kappa-KAPPA_1839 + checks['improvement_over_pr1875']=kappa-KAPPA_1875 + checks['improvement_over_pr1876']=kappa-KAPPA_1876 + checks['improvement_over_pr1897']=kappa-KAPPA_1897 + checks['improvement_over_pr1758']=kappa-Q('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') + checks['improvement_over_pr1699']=kappa-KAPPA_1699 + checks['improvement_over_pr1712']=kappa-KAPPA_1712 + checks['improvement_over_previous_package']=kappa-KAPPA_PKG4 + checks['improvement_over_pkg_k2']=kappa-KAPPA_PKG5 + if full_gauge:checks['unrecentered_group_gauge']=1-THETA_POWER-r-beta + if old_theta:checks['old_theta_chirp_guard']=1-(2*xi-eps)-r-beta + if old_linear:checks['old_linear_guard']=1-xi-r-beta + if old_tag:checks['old_union_tag_2beta']=1-2*beta + # Main-binding family invariant (PR2180): the Gaussian saving stays above the main saving. The fixed kappa grid (FLOOR) is coarser than the free gaps, + # so the *_above_kappa rows alone would no longer exclude a beta outside the main-binding window; this row is delta*(1-2q) > 0. + checks['gaussian_above_main']=margins['fused_gaussian']-saving + checks.update({n+'_above_kappa':v-kappa for n,v in margins.items()}) + assert margins['boundary_algebraic_matrix']==saving+slack + assert margins['sparse_union_movement']==saving+slack+(tau_eff-2)/2 + return {'kind':kind,'kappa':kappa,'epsilon':eps,'xi':xi,'beta':beta, + 'q':q_,'a':a,'r0':r,'zeta':zeta,'slack':slack, + 'margins':margins,'strict_checks':checks} + diff --git a/research/compact-joint-compiler/arithmetic/legacy.py b/research/compact-joint-compiler/arithmetic/legacy.py new file mode 100644 index 0000000000..5c6139ddaa --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/legacy.py @@ -0,0 +1,21 @@ +"""Independent 63-predicate retained outer ledger at an explicit finer grid. +Source notices and exact retained function are in legacy-source.txt. +Apache-2.0. Substantial OpenAI Codex assistance. +""" +from fractions import Fraction as Q +from pathlib import Path +from hashlib import sha256 + +def need(ok,message): + if not ok:raise ValueError(message) + +def check(params,outer,kappa): + source=Path(__file__).resolve().with_name('legacy-source.txt');raw=source.read_bytes() + d=params['d'];eps,beta,q,a=(params[k]for k in('epsilon','beta','q','a'));grid=10**20 + backoff=Q((eps*q*grid).__floor__(),grid)-kappa;need(backoff>0,'Positive exact refined-grid backoff') + env={'Q':Q,'R0':params['r0'],'ZETA':Q(1,10**8),'SLACK':d,'STOP':d,'FLOOR':grid,'BACKOFF':backoff,'EPS':eps,'BETA':beta,'THETA_POWER':Q(2),'HALO_POWER':48,'CORE_POWER':128,'STRASSEN_TAU':Q(45,16),'b':params['b'],'q':q,'a':a,'bit':params['bit_saving'],'online':Q('0.001730970419199163702738'),'old':Q('0.001730970419199163702738')} + exec(compile(raw,'frozen legacy outer source','exec'),env) + result=env['ledger']('compact4470') + need(result['kappa']==kappa and result['margins']==outer['margins'],'Independent nine-row agreement') + need(len(result['strict_checks'])==63 and all(x>0 for x in result['strict_checks'].values()),'All 63 legacy predicates') + return {'strict_checks':result['strict_checks'],'grid':grid,'backoff':backoff,'nine_row_agreement':True,'source_sha256':sha256(raw).hexdigest()} diff --git a/research/compact-joint-compiler/arithmetic/ordinary-bit.json b/research/compact-joint-compiler/arithmetic/ordinary-bit.json new file mode 100644 index 0000000000..0e9994ff03 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/ordinary-bit.json @@ -0,0 +1,8 @@ +{ + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" +} diff --git a/research/compact-joint-compiler/arithmetic/outer_ledger.py b/research/compact-joint-compiler/arithmetic/outer_ledger.py new file mode 100644 index 0000000000..79d5530794 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/outer_ledger.py @@ -0,0 +1,78 @@ +"""Verbatim 54-predicate endpoint ledger from the retained PR4359/4433 chain. +Credits: zxv, Jacob Alan Sussman, and the retained outer_parameters.py lineage. +Apache-2.0. Substantial OpenAI assistance. Arithmetic only. +""" +from fractions import Fraction as Q +OLD_BASELINE=Q('0.001730970419199163702738') + +def ledger(p): + """Recompute all 54 named PR4359 checks with freely supplied parameters.""" + kappa, b, a, q = (p[key] for key in ('kappa', 'b', 'a', 'q')) + epsilon, beta, r0, stop, layout = (p[key] for key in + ('epsilon', 'beta', 'r0', 'stop', 'layout')) + sigma, tau = 1-b, 1-a + internal = tau+(1-stop)*max(sigma-tau, Q(0)) + leaf = sigma+stop*(1-sigma) + lam, c = 1-(q+a)/2, Q(3, 32) + xi, key = epsilon*(1+q)-c+layout, beta+1-epsilon + margins = { + 'main_transform': epsilon*q, + 'global_coordinate_router': a, + 'fused_gaussian': 1-epsilon+q*beta, + 'group_bit_router': 1-epsilon+a*beta, + 'group_scans': 1-epsilon+beta, + 'boundary_algebraic_matrix': c+xi-epsilon, + 'sparse_union_movement': xi+Q(1, 2)-epsilon, + 'polynomial_products': epsilon, + 'microbox_face_corrections': 1-(epsilon+beta+48-128+2), + } + checks = { + 'actual_bit_above_effective': p['bit_saving']-a, + 'complex_above_effective': b-a, + 'q_positive': q, 'complex_endpoint': b-q, 'q_below_effective': a-q, + 'stop_positive': stop, 'stop_below_one': 1-stop, + 'leaf_saving_above_effective': (1-stop)*b-a, + 'q_below_internal': 1-internal-q, 'q_below_leaf': 1-leaf-q, + 'lambda_above_tau': lam-tau, 'lambda_above_sigma': lam-sigma, + 'lambda_above_internal': lam-internal, + 'lambda_prime_above_lambda': 1-q-lam, + 'lambda_prime_above_leaf': 1-q-leaf, + 'epsilon_positive': epsilon, 'epsilon_below_one': 1-epsilon, + 'cap_above_band': xi-Q(1, 2), 'cap_below_cell': epsilon-xi, + 'group_positive': beta, 'group_below_dimension': epsilon-beta, + 'support_router_span': 1-beta, + 'group_gauge_power_slack': 1-(2*xi-2)-r0-beta, + 'actual_logarithmic_group_guard': 1-(2*xi-2)-beta, + 'global_gamma_power_slack': 1-epsilon-r0, + 'actual_logarithmic_gamma_guard': 1-epsilon, + 'alpha_logarithm_absorption': r0, + 'group_key_fits_record': 1-key, + 'membership_arithmetic_fits_record': 1-beta-2*(1-epsilon), + 'microbox_halo_volume': 128-48-beta, + 'positive_layout_slack': layout, + 'short_record_fallback': epsilon-a, + 'complex_below_one_over_32': Q(1, 32)-b, + 'strassen_integer_power_gap': Q(2**45-7**16), + 'theta_positive_polynomial_power': Q(2), + 'cap_below_phase_cell_power': 2-xi, + 'halo_covers_generic_inverse_radius': Q(48-43), + 'union_tag_work_per_visit_fits_record': 1-beta, + 'union_header_fits_record': 1-beta, + 'source_axis_superpolynomial': 1-epsilon, + 'gaussian_above_main': margins['fused_gaussian']-margins['main_transform'], + 'new_complex_uniform_saving_above_b': p['complex_uniform_saving']-b, + 'improvement_over_user_baseline': kappa-OLD_BASELINE, + 'new_semantic_guard_with_C1_one': 1-epsilon, + 'fine_prime_halo_umbrella': 10-(2*2+2+Q(1, 2)), + } + checks.update({name+'_above_kappa': value-kappa for name, value in margins.items()}) + # These are the additional functional conditions in the independent + # PR4359 outer_transfer_audit.py, beyond the 54-row parameter ledger. + functional = { + 'new_semantic_group_guard': 1-beta, + 'new_BIT_row_stock_sublinear_in_active_group': beta*(1-Q(3, 1000)), + 'fixed_halo_explicit_metadata_branch': 128-48-epsilon-beta-1, + } + return {'parameters': dict(p, cap_xi=xi, lambda_=lam, lambda_prime=1-q), + 'margins': margins, 'strict_checks': checks, 'functional_checks': functional} + diff --git a/research/compact-joint-compiler/arithmetic/profile.json b/research/compact-joint-compiler/arithmetic/profile.json new file mode 100644 index 0000000000..5e15c508ec --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/profile.json @@ -0,0 +1,16 @@ +{ + "helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "paid": { + "1": 2237, + "2": 388, + "3": 494, + "4": 147, + "5": 36, + "8": 8 + } +} diff --git a/research/compact-joint-compiler/arithmetic/verify.py b/research/compact-joint-compiler/arithmetic/verify.py new file mode 100644 index 0000000000..d128d2c8c0 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/verify.py @@ -0,0 +1,113 @@ +"""Same-kappa finite compiler improvement on PR4470's frozen native/controller word. +Preserves kappa=0.00302015; no kappa improvement is claimed. +Retains PR4470, PR4447, PR4440, zxv, Cinna Davis and Jacob Alan Sussman attribution. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +import json,hashlib,sys +sys.path.insert(0,str(Path(__file__).resolve().parent)) +import intervals as E +import outer_ledger as L +import legacy +HERE=Path(__file__).resolve().parent +KAPPA=Q('.00302015');TESTED=Q('.00302016') +LOW=Q('.0030201659770');HIGH=Q('.0030201659771') +H={4:28,7:7,8:47,9:326};N={1:2237,2:388,3:494,4:147,5:36,8:8} + +def need(ok,msg): + if not ok:raise ValueError(msg) + +def encode(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):encode(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return[encode(v)for v in x] + return x + +def authenticate(): + manifest=json.loads((HERE/'INPUTS.json').read_bytes()) + for row in manifest['files']: + name=row['path'];need(Path(name).name==name and name not in ('','.','..'),'Simple owned input path') + need(hashlib.sha256((HERE/name).read_bytes()).hexdigest()==row['sha256'],'Changed arithmetic input: '+name) + +def run(local=None): + authenticate() + frozen=json.loads((HERE/'profile.json').read_bytes()) + frozenH={int(k):v for k,v in frozen['helpers'].items()};frozenN={int(k):v for k,v in frozen['paid'].items()} + need(frozenH==H and frozenN==N,'Frozen candidate profile agrees') + if local is not None: + need({int(k):v for k,v in local['helpers'].items()}==H and {int(k):v for k,v in local['paid'].items()}==N,'Actual native replay agrees with complete frozen profile') + word_path=HERE/'controller.json' + raw=word_path.read_bytes();word=json.loads(raw);T,P=Counter(),Counter();full=thin=idle=0 + for event in word['physical_events']: + if event[0]=='LOCAL':full+=1;T.update(H);P.update(N) + elif event[0]=='QUERY_SHEAR':thin+=1;P[1]+=112 + elif event[0]=='IDLE': + rank=8*len(event[2]);need(rank>0,'No zero idle charge');P[rank]+=224;idle+=224 + for term in word['diagonal']: + need(term[0]in(-1,1)and all(v in(0,1)for v in term[1:]),'Legal central normalizer') + T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(18,15,3360),'All actual p16 events') + need(sum(T.values())==10928 and sum(P.values())==64620,'Complete field/call inventory') + mt=lambda h,c:E.moment(h,1-c) + def margin(c): + a,b=mt(T,c),mt(P,c);return a[0]-b[1],a[1]-b[0] + need(margin(LOW)[0]>0 and margin(HIGH)[1]<0,'Exact new raw root bracket') + # Prove the margin decreases on C in[0,.05], independently of floating discovery. + signed={r:T[r]-P[r]for r in T.keys()|P.keys()};derivative=None + for i in range(16): + l,r=Q(i,320),Q(i+1,320);low=Q(0) + for rank,n in signed.items(): + term=E.mul(E.power(rank,1-r if n>0 else 1-l),E.log_bounds(rank));low+=n*term[0 if n>0 else 1] + derivative=low if derivative is None else min(derivative,low) + need(derivative>0,'Strict decrease around bracket') + t,u,v,c,b=1-TESTED,Q(1,8),682,17,21 + target=E.moment(T,t);alpha=E.divide(E.moment(P,t),target) + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + gap0=Q(31,5*10**9);g,d=Q(98102,100000),Q(959,1000) + need(t+u>=1 and alpha[1]<1-gap0 and gamma[1]1,'Short product bound rejects') + theta,power=Q(94,101),143;eta=E.scale(E.power(145,-v*TESTED),t) + need(2**(101-94)*(17**v)**101<=(145**v)**94 and eta[0]>theta**power,'Shifted exit and complement capacity') + need(E.power(145,v*TESTED)[1]<2**power,'Initial compiler range') + need(eta[1]1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + height=step*hi;need(height>8*v and passes(hi)and not passes(hi-1),'Exact sufficient finite rank') + # Source scalar list/order untouched, inherited upper bound is conservative. + scalar_bound=158168;route_bound=(sum(N.values())+2*408+688)*1000 + need(scalar_bound+route_bound<10**7,'All local routes and scalar operations charged') + scalar_upper=18*10**7+15*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program'])for k in('left','right'))) + need(scalar_upper<10**9,'Complete raw nonrecursive bill') + bit=json.loads((HERE/'ordinary-bit.json').read_bytes());atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599');admitted=Q(bit['admitted']) + need(atom==Q('.004')and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Ordinary BIT admission and adapters') + outer_gap=(TESTED-KAPPA-gap)/6;need(outer_gap>0,'Strict outer slack remains') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':TESTED-gap,'b':KAPPA+5*outer_gap,'a':KAPPA+4*outer_gap,'q':KAPPA+3*outer_gap,'bit_saving':admitted,'epsilon':1-outer_gap,'beta':1-3*outer_gap,'r0':outer_gap/10,'stop':outer_gap,'layout':outer_gap,'d':outer_gap} + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Full outer predicate inventory') + need(all(x>0 for k in('strict_checks','functional_checks')for x in outer[k].values()),'All outer inequalities') + legacy_result=legacy.check(params,outer,KAPPA) + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items()if x<=0];need(failed,'Reject '+name);controls[name]=failed + need(margin(TESTED)[0]>0 and margin(HIGH)[1]<0,'Successful and rejected endpoint controls') + mass=lambda h:sum(r*n for r,n in h.items()) + need(mass(T)-mass(P)==752,'Exact p16 rank surplus retained') + return encode({'status':'PASS_COMPLETE_CONDITIONAL_ARITHMETIC','kappa':KAPPA,'kappa_decimal':'0.00302015','gain_over_PR4447':KAPPA-Q('.00300123'),'tested':TESTED,'raw_root_bracket':[LOW,HIGH],'derivative_positive_lower':derivative,'local_helpers':H,'local_paid':N,'targets':dict(T),'paid':dict(P),'productive_fields':sum(T.values()),'paid_calls':sum(P.values()),'rank_masses':[mass(T),mass(P)],'rank_surplus':mass(T)-mass(P),'strictification':{'tested':TESTED,'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'tensor_power':v,'tail_offset':u,'cutoff':c,'floor':b,'normalized_paid_upper':bound},'compiler':{'theta':theta,'power':power,'eta':E.display(eta),'gap':gap,'H':height,'N':'2^'+str(height),'integer_test_exponent':hi,'word_materialized':False},'raw_nonrecursive':{'local_routes':route_bound,'local_scalar_allowance':scalar_bound,'all_unit_bound':scalar_upper,'budget':10**9},'ordinary_BIT':bit,'outer':outer,'legacy_outer':legacy_result,'negative_controls':controls,'source_hashes':{'p16_controller':hashlib.sha256(raw).hexdigest(),'interval_engine':hashlib.sha256(Path(E.__file__).read_bytes()).hexdigest(),'outer_ledger':hashlib.sha256(Path(L.__file__).read_bytes()).hexdigest()},'remaining':'Requires independent source-pinned native/operator/phase replay of unchanged candidate and source admission. Arithmetic alone is not a new theorem or selected-frontier promotion.'}) +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser();parser.add_argument('--write-receipt',action='store_true');args=parser.parse_args() + result=run() + if args.write_receipt:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n',encoding='utf-8') + else:need(result==json.loads((HERE/'RESULT.json').read_bytes()),'Exact frozen arithmetic receipt replay') + print(json.dumps({'status':result['status'],'kappa':result['kappa_decimal'],'uniform_rank':result['compiler']['N'],'outer_predicates':'54 strict + 4 functional + 63 legacy','paid_calls':result['paid_calls']},sort_keys=True)) diff --git a/research/compact-joint-compiler/independent/INPUTS.json b/research/compact-joint-compiler/independent/INPUTS.json new file mode 100644 index 0000000000..bb73765880 --- /dev/null +++ b/research/compact-joint-compiler/independent/INPUTS.json @@ -0,0 +1,49 @@ +{ + "files": [ + { + "path": "arithmetic/controller.json", + "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + { + "path": "arithmetic/INPUTS.json", + "sha256": "65e2517e1aa87d2313d922c7684037d15389e995f096746003358bf2317f59ac" + }, + { + "path": "arithmetic/intervals.py", + "sha256": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc" + }, + { + "path": "arithmetic/legacy-source.txt", + "sha256": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895" + }, + { + "path": "arithmetic/legacy.py", + "sha256": "43cd70c98a133015f40fd695e18035254cb3bd303f2da45bf46607f211506a87" + }, + { + "path": "arithmetic/ordinary-bit.json", + "sha256": "7d3ef7711fef1033a49f7ac9847bccf24145c0ba2cf248b3802114c172fb0249" + }, + { + "path": "arithmetic/outer_ledger.py", + "sha256": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54" + }, + { + "path": "arithmetic/profile.json", + "sha256": "6e937237c22b3b6d4821ecc253e579b852731a5c665ce488d42f2f7bddb291f5" + }, + { + "path": "arithmetic/PROOF.txt", + "sha256": "273598588316e29a45e3940c6f5070d973b1998fe5b9c582b23bfe87502724cc" + }, + { + "path": "arithmetic/RESULT.json", + "sha256": "a6caaa2a6d6460a8c1ef7e48c4853bb27976be33a52b96a4216dfa90d96c9091" + }, + { + "path": "arithmetic/verify.py", + "sha256": "4ad2d95bee6e6fe2ae4462e5dd0921c64677fc86a5da1f38a198546c28c7f1b1" + } + ], + "scope": "Exact frozen compact arithmetic sources, inputs and receipt; predecessor native/controller claims retained." +} diff --git a/research/compact-joint-compiler/independent/PROOF-REVIEW.txt b/research/compact-joint-compiler/independent/PROOF-REVIEW.txt new file mode 100644 index 0000000000..1a0627fa9f --- /dev/null +++ b/research/compact-joint-compiler/independent/PROOF-REVIEW.txt @@ -0,0 +1,51 @@ +Independent review — PR4470 compact conditional compiler + +Verdict: the corrected sufficient-rank calculation is consistent with the +retained general logarithmic compiler theorem, and the declared conditional +κ stays 0.00302015. The new finite template bound is N=2^558100005581. +It is not a new κ, a full multiplication proof, a practical-runtime claim, +or an explicit threshold for asymptotic integer input sizes. + +The source theorem is higher-moment-strictification/README.md §4, pinned to +canonical main 2a13eb1827784206202db90e5dc8327cf8a250db. For θ=a/b it requires +2^(b−a) r_max^b ≤ m^a, θ^p < η=t m^(t−1), and m^(1−t)<2^p. +Here a=94,b=101,p=143,m=145^682,r_max=17^682, so the first factor is +2^7=128. The initial draft mistakenly checked 2 instead; that undercheck +was caught in independent review, corrected by the compiler worker, and +replayed. The stronger required inequality holds with ample exact slack. + +The paid tensor proof uses C=0.00302016, t=1−C, u=1/8≥C, v=682, +cutoff 17^682 and productive floor 21^682. Both original and completion +paid tails appear explicitly. The displayed conservative rational bound +passes at 682 and fails at 681. This is a scoped certificate for the chosen +ratios; it does not establish global minimum tensor power. + +The uniform compiler gap g=1/100000001 is distinct from the outer slack. +Since C−κ=1/100000000, the leftover positive outer slack is +(C−κ−g)/6 = 1/60000000600000000. All outer comparisons must use exact +rationals at this scale; a coarse decimal grid cannot silently replace them. +The small slack is mathematically positive, but can enlarge the unspecified +asymptotic input threshold substantially. No final threshold is certified. + +The majorant test (100000001 j+1)^143<2^j passes at j=5581 and fails at +j=5580, giving H=100000001·5581=558100005581. This is the chosen sufficient +majorant/grid bound, not a minimum native program or universal optimal rank. +The original compiler's integer batching, ownership, whole-job normalizers, +complements, exits and finite constant prescriptions remain inherited premises. + +Independent checks: source hashes before/after; public PR4470 controller +byte identity; fresh normal and isolated optimized Python replays; separate +integer/rational calculations for the decisive tail, exit and height tests. +The registered read-only gate rejects v=681, p=142 and zero remaining outer +slack through independent exact numerical controls. Calling the real source +API with an inconsistent native inventory rejects. A corrupted expected +source pin rejects. This gate makes no filesystem mutations; its deterministic +result and all guarded source hashes are in RECEIPT.json. + +Credit PR4470 for the actual best-known conditional native/controller word; +PR4440/4441/4447, zxv's native/higher-moment/logarithmic results, Jacob Alan +Sussman's mixed-target compiler and the retained BIT/analytic/outer lineage. +The compiler worker chose and constructed the new parameters. The controller +worker independently reviewed the proof, caught the factor-128 source +hypothesis, and replayed the corrected calculation. Substantial OpenAI Codex +assistance. Apache-2.0; original source notices retained. diff --git a/research/compact-joint-compiler/independent/RECEIPT.json b/research/compact-joint-compiler/independent/RECEIPT.json new file mode 100644 index 0000000000..f65fc32680 --- /dev/null +++ b/research/compact-joint-compiler/independent/RECEIPT.json @@ -0,0 +1,32 @@ +{ + "all_independent_integer_rational_tests": true, + "kappa": "0.00302015", + "normal_and_isolated_optimized_receipts_equal": true, + "outer_d": "1/60000000600000000", + "public_PR4470_controller_unchanged": true, + "same_predecessor_kappa": true, + "scientific_and_source_controls": { + "bad_source_pin": true, + "short_log_power_142": true, + "short_tensor_681": true, + "wrong_actual_native_profile": true, + "zero_outer_slack": true + }, + "scope": "Smaller sufficient finite template, not a new kappa or a final integer-input threshold.", + "shifted_exit_factor": 128, + "source_sha256": { + "arithmetic/INPUTS.json": "65e2517e1aa87d2313d922c7684037d15389e995f096746003358bf2317f59ac", + "arithmetic/PROOF.txt": "273598588316e29a45e3940c6f5070d973b1998fe5b9c582b23bfe87502724cc", + "arithmetic/RESULT.json": "a6caaa2a6d6460a8c1ef7e48c4853bb27976be33a52b96a4216dfa90d96c9091", + "arithmetic/controller.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f", + "arithmetic/intervals.py": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc", + "arithmetic/legacy-source.txt": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895", + "arithmetic/legacy.py": "43cd70c98a133015f40fd695e18035254cb3bd303f2da45bf46607f211506a87", + "arithmetic/ordinary-bit.json": "7d3ef7711fef1033a49f7ac9847bccf24145c0ba2cf248b3802114c172fb0249", + "arithmetic/outer_ledger.py": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54", + "arithmetic/profile.json": "6e937237c22b3b6d4821ecc253e579b852731a5c665ce488d42f2f7bddb291f5", + "arithmetic/verify.py": "4ad2d95bee6e6fe2ae4462e5dd0921c64677fc86a5da1f38a198546c28c7f1b1" + }, + "status": "PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER", + "uniform_N": "2^558100005581" +} diff --git a/research/compact-joint-compiler/independent/audit.py b/research/compact-joint-compiler/independent/audit.py new file mode 100644 index 0000000000..f4356bd26b --- /dev/null +++ b/research/compact-joint-compiler/independent/audit.py @@ -0,0 +1,74 @@ +"""Independent, read-only compact-compiler audit. Python standard library only. +No files or interpreter configuration are changed. Numerical controls are +independent integer/rational tests, rather than edited source copies. +Apache-2.0; substantial OpenAI Codex assistance. Predecessor credit retained. +""" +from pathlib import Path +from fractions import Fraction as Q +from copy import deepcopy +import hashlib,importlib.util,json,subprocess,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +PACKAGE=HERE.parent +ROOT=PACKAGE.parents[1] + +def need(ok,message): + if not ok:raise ValueError(message) +def digest(path):return hashlib.sha256(Path(path).read_bytes()).hexdigest() +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);sys.modules[name]=module + spec.loader.exec_module(module);return module +def authenticate(records): + need(len(records)>=10,'Full nonempty compact source closure') + for row in records: + relative=Path(row['path']) + need(not relative.is_absolute() and '..' not in relative.parts,'Repository-relative owned input') + need(digest(PACKAGE/relative)==row['sha256'],'Changed compact source: '+row['path']) + +def run(): + pins=json.loads((HERE/'INPUTS.json').read_text(encoding='utf-8'))['files'] + authenticate(pins) + module=load(PACKAGE/'arithmetic/verify.py','independent_compact_arithmetic') + ordinary=module.run() + frozen=json.loads((PACKAGE/'arithmetic/RESULT.json').read_text(encoding='utf-8')) + need(ordinary==frozen,'Fresh ordinary arithmetic equals frozen receipt') + child_code="import importlib.util,json,sys; p=sys.argv[1]; s=importlib.util.spec_from_file_location('isolated_compact',p); m=importlib.util.module_from_spec(s); s.loader.exec_module(m); print(json.dumps(m.run(),sort_keys=True))" + child=subprocess.run([sys.executable,'-I','-O','-B','-X','utf8','-c',child_code,str(PACKAGE/'arithmetic/verify.py')],capture_output=True,text=True,encoding='utf-8',timeout=180,check=False) + need(child.returncode==0,'Isolated optimized arithmetic failed: '+child.stderr) + need(json.loads(child.stdout)==ordinary,'Ordinary and isolated optimized scientific receipts agree') + need((PACKAGE/'arithmetic/controller.json').read_bytes()==(ROOT/'research/joint-helper-lattice/CONTROLLER.json').read_bytes(),'Unchanged public PR4470 controller') + C=Q('.00302016');kappa=Q('.00302015');g=Q(1,100000001) + d=(C-kappa-g)/6 + need(d==Q(1,60000000600000000)>0,'Exact independent outer slack') + alpha_gap=Q(31,5*10**9);gamma=Q(98102,100000);delta=Q(959,1000) + tail=lambda v:1/(1+v*alpha_gap)+2*gamma**v+2*delta**v + need(tail(682)<1=2**5580,'Previous majorant grid point rejects') + need(100000001*5581==558100005581,'Exact uniform log-rank') + controls={} + for name,condition in [('short_tensor_681',tail(681)<1),('short_log_power_142',theta**1420)]: + need(not condition,'Independent numerical mutant must reject: '+name) + controls[name]=True + wrong={'helpers':dict(module.H),'paid':dict(module.N)};wrong['paid'][1]+=1 + try:module.run(wrong) + except ValueError as error: + need('Actual native replay agrees' in str(error),'Wrong-profile rejection must reach scientific binding') + controls['wrong_actual_native_profile']=True + else:raise ValueError('Wrong actual native profile accepted') + badpins=deepcopy(pins);badpins[0]['sha256']='0'*64 + try:authenticate(badpins) + except ValueError:controls['bad_source_pin']=True + else:raise ValueError('Bad source pin accepted') + authenticate(pins) + return {'status':'PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER','kappa':'0.00302015','same_predecessor_kappa':True,'uniform_N':'2^558100005581','outer_d':str(d),'normal_and_isolated_optimized_receipts_equal':True,'public_PR4470_controller_unchanged':True,'shifted_exit_factor':128,'all_independent_integer_rational_tests':True,'scientific_and_source_controls':controls,'source_sha256':{r['path']:r['sha256']for r in pins},'scope':'Smaller sufficient finite template, not a new kappa or a final integer-input threshold.'} + +if __name__=='__main__': + result=run();frozen=json.loads((HERE/'RECEIPT.json').read_text(encoding='utf-8')) + need(result==frozen,'Deterministic independent receipt') + print('PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER N=2^558100005581 same_kappa=0.00302015') diff --git a/research/compact-joint-compiler/verify.py b/research/compact-joint-compiler/verify.py new file mode 100644 index 0000000000..5a38a237c2 --- /dev/null +++ b/research/compact-joint-compiler/verify.py @@ -0,0 +1,31 @@ +"""Source-bound compact compiler, Apache-2.0; substantial Codex assistance.""" +import argparse,hashlib,importlib.util,json,sys +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +def need(x,m): + if not x:raise ValueError(m) +def load(p,n): + spec=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(spec);sys.modules[n]=m;spec.loader.exec_module(m);return m +def authenticate(): + for row in json.loads((HERE/'SOURCES.json').read_bytes())['files']: + if row['usage']=='input':need(hashlib.sha256((ROOT/row['path']).read_bytes()).hexdigest()==row['sha256'],'Changed source '+row['path']) +def run(part): + authenticate();source=ROOT/'research/joint-helper-lattice';sys.path.insert(0,str(source));parent=load(source/'verify.py','frozen4470_parent') + if part=='dependencies':parent.replay_dependencies() + elif part=='native': + parent.authenticate();local=parent.J.run();need(json.loads(json.dumps(local))==parent.read(source/'NATIVE.json.gz'),'Fresh two-interpreter/native/absolute-phase receipt') + a=load(HERE/'arithmetic/verify.py','compact_arithmetic_native_binding');result=a.run(local) + need(result==json.loads((HERE/'arithmetic/RESULT.json').read_bytes()),'Native profile bound to compact arithmetic') + elif part=='arithmetic': + previous=parent.run(execute_sources=False);need(previous==parent.read(source/'RESULT.json'),'Fresh complete source arithmetic/controller') + a=load(HERE/'arithmetic/verify.py','compact_arithmetic');result=a.run() + need(result==json.loads((HERE/'arithmetic/RESULT.json').read_bytes()),'Frozen compact receipt') + need((HERE/'arithmetic/controller.json').read_bytes()==(source/'CONTROLLER.json').read_bytes(),'Unchanged literal p16 controller') + for key in ('targets','paid','local_helpers','local_paid','ordinary_BIT','productive_fields','paid_calls'): + need(result[key]==previous[key],'Unchanged complete source bill '+key) + need(int(result['compiler']['H'])==558100005581 Date: Wed, 21 Oct 2026 20:16:57 -0400 Subject: [PATCH 21/26] Record approval to publish the reviewed rank compiler --- research/net-tax-rank-compiler/README.md | 2 +- research/net-tax-rank-compiler/TASK.json | 8 +++++--- research/net-tax-rank-compiler/VALIDATION.md | 3 ++- 3 files changed, 8 insertions(+), 5 deletions(-) diff --git a/research/net-tax-rank-compiler/README.md b/research/net-tax-rank-compiler/README.md index fca02f443e..2e2d973866 100644 --- a/research/net-tax-rank-compiler/README.md +++ b/research/net-tax-rank-compiler/README.md @@ -161,7 +161,7 @@ Structured questions and blockers are in [TASK.json](TASK.json). zxv, with substantial OpenAI Codex assistance, including user-requested Sol 6.1 xhigh subagents for divergent probes and independent mathematical audits. These are author-side AI checks, not formal verification or an -independent human review. This contribution remains local for user review. +independent human review. The user authorized submission of this reviewed contribution on 2026-10-22. The finite integer compiler is Jacob Alan Sussman's Theorem 1G, retained through PR4268/PR4359. Chronological product/completion and logarithmic diff --git a/research/net-tax-rank-compiler/TASK.json b/research/net-tax-rank-compiler/TASK.json index 343ea8f7f4..3401994676 100644 --- a/research/net-tax-rank-compiler/TASK.json +++ b/research/net-tax-rank-compiler/TASK.json @@ -73,7 +73,7 @@ "actual_scope": "Develop reusable structural rank reductions for the chronological-product and finite uniform compiler, with exact reusable witnesses on native4453 and p7 profiles.", "scope_change_reason": "The user explicitly assigned systematic structural rank reduction for future submissions; this overrides the catalogue default supplier audit. No new native profile or kappa hill step is claimed.", "bottleneck_link": "Net concavity taxes and paid logarithmic moments reduce the tensor power and the sufficient uniform rank without changing native jobs.", - "stop_rule": "Finish a source-bound theorem and exact reusable certificate with discriminating controls; keep local for user review and leave further supplier changes open.", + "stop_rule": "Publish the reviewed rank-compiler contribution, retaining its exact scientific scope; start the next larger contribution in a fresh tree.", "evidence": "Net gap identity, sharp concavity coefficients, normalized-log induction, exact iid exit law, convex-order and Bell-polynomial certificates, literal pinned-flow probes and independent agent audit.", "author": "zxv, with substantial OpenAI Codex assistance", "ai_assistance": "Substantial OpenAI Codex assistance, including three user-requested Sol 6.1 xhigh subagents for divergent probes and independent audits.", @@ -99,13 +99,15 @@ "blocked_by": "The winning words remain algorithm-defined and their full widths are not emitted." } ], - "publication_policy": "Keep this contribution local for user review. No PR or Discussion publication is authorized for this contribution yet.", + "publication_policy": "User approved submission of this reviewed contribution on 2026-10-22. No Discussion participation is requested. Future contributions remain local for review; future subagents should use Sol 6.1 medium.", "upstream_checkpoint": { "checked_at_utc": "2026-10-21T22:13:49Z", "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db", "priority_revision": 7, "refresh_checked_at_utc": "2026-10-21T22:39:21Z", - "refresh_result": "Canonical main and relevant guidance unchanged." + "refresh_result": "Canonical main and relevant guidance unchanged.", + "publication_refresh_checked_at_utc": "2026-10-22T00:16:00Z", + "publication_refresh_result": "Canonical main and relevant guidance unchanged; newer pending PR4470/4479 acknowledged without changing this reviewed result." }, "overlap": { "checked_at_utc": "2026-10-21T22:18:00Z", diff --git a/research/net-tax-rank-compiler/VALIDATION.md b/research/net-tax-rank-compiler/VALIDATION.md index 185a4bcb95..9ade189564 100644 --- a/research/net-tax-rank-compiler/VALIDATION.md +++ b/research/net-tax-rank-compiler/VALIDATION.md @@ -50,4 +50,5 @@ uniform saving supplies the retained outer point by monotonicity. No winning word, full productive width, physical count, precision constant, new κ or selected-frontier update is certified by this replay. -No PR, Discussion post or remote branch was published for this contribution. +The initial validation was local. The user authorized PR submission on +2026-10-22; no Discussion participation is requested. From 1df9e7df3c26ceaca37dbf06669e2ae8f8b414c3 Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 20:26:25 -0400 Subject: [PATCH 22/26] Retain exact live predecessor profiles and direct-flow implementation --- .../compact-joint-compiler/.gitattributes | 1 + research/compact-joint-compiler/FRONTIER.json | 20 + research/compact-joint-compiler/PROOF.md | 31 + research/compact-joint-compiler/README.md | 23 + research/compact-joint-compiler/REPLAY.json | 16 + research/compact-joint-compiler/REUSE.md | 22 + research/compact-joint-compiler/SOURCES.json | 408 + research/compact-joint-compiler/TASK.json | 64 + research/compact-joint-compiler/VALIDATION.md | 9 + research/compact-joint-compiler/VERIFY.json | 120 + .../arithmetic/INPUTS.json | 49 + .../arithmetic/PROOF.txt | 19 + .../arithmetic/RESULT.json | 304 + .../arithmetic/controller.json | 5224 ++++++++ .../arithmetic/intervals.py | 111 + .../arithmetic/legacy-source.txt | 128 + .../arithmetic/legacy.py | 21 + .../arithmetic/ordinary-bit.json | 8 + .../arithmetic/outer_ledger.py | 78 + .../arithmetic/profile.json | 16 + .../arithmetic/verify.py | 113 + .../independent/INPUTS.json | 49 + .../independent/PROOF-REVIEW.txt | 51 + .../independent/RECEIPT.json | 32 + .../independent/audit.py | 74 + research/compact-joint-compiler/verify.py | 31 + research/direct-mixed-flow/.gitattributes | 1 + research/direct-mixed-flow/README.md | 496 + research/direct-mixed-flow/RESULT.json | 505 + research/direct-mixed-flow/SOURCES.json | 18 + research/direct-mixed-flow/TASK.json | 148 + research/direct-mixed-flow/VENDOR.json | 82 + research/direct-mixed-flow/VERIFY.json | 31 + research/direct-mixed-flow/flow.py | 198 + .../vendor/FINITE-PRECOMPILATION.md | 313 + .../direct-mixed-flow/vendor/P7-FACTOR.json | 5114 ++++++++ .../direct-mixed-flow/vendor/SUSSMAN-LICENSE | 201 + .../direct-mixed-flow/vendor/SUSSMAN-NOTICE | 994 ++ .../THREE-base-FULL-IDENTITY-NATIVE.json.gz | Bin 0 -> 198063 bytes .../vendor/higher-moment-README.md | 416 + .../vendor/higher-moment-RESULT.json | 384 + .../direct-mixed-flow/vendor/p7-NATIVE.md | 180 + .../direct-mixed-flow/vendor/p7-RESULT.json | 296 + .../direct-mixed-flow/vendor/theorem-1g.md | 264 + .../direct-mixed-flow/vendor/tree_flow.py | 167 + research/direct-mixed-flow/verify.py | 274 + research/joint-helper-lattice/CONTROLLER.json | 5224 ++++++++ research/joint-helper-lattice/DISCOVERY.json | 10886 ++++++++++++++++ research/joint-helper-lattice/FRONTIER.json | 187 + research/joint-helper-lattice/NATIVE.json.gz | Bin 0 -> 35042 bytes research/joint-helper-lattice/PATCH.json | 8991 +++++++++++++ research/joint-helper-lattice/PROOF.md | 102 + research/joint-helper-lattice/README.md | 46 + .../joint-helper-lattice/REPLAY-LOGS.json | 21 + research/joint-helper-lattice/RESULT.json | 274 + research/joint-helper-lattice/SOURCES.json | 330 + research/joint-helper-lattice/TASK.json | 73 + research/joint-helper-lattice/VALIDATION.md | 21 + research/joint-helper-lattice/VERIFY.json | 94 + research/joint-helper-lattice/native_joint.py | 118 + research/joint-helper-lattice/verify.py | 290 + research/missing-join-frame/NATIVE.json.gz | Bin 0 -> 1462 bytes research/missing-join-frame/PATCH.json | 24 + research/missing-join-frame/PROOF.md | 121 + research/missing-join-frame/README.md | 56 + research/missing-join-frame/RESULT.json | 239 + research/missing-join-frame/SOURCES.json | 294 + research/missing-join-frame/TASK.json | 73 + research/missing-join-frame/VALIDATION.md | 27 + research/missing-join-frame/VERIFY.json | 65 + research/missing-join-frame/native_join.py | 99 + research/missing-join-frame/verify.py | 183 + 72 files changed, 44942 insertions(+) create mode 100644 research/compact-joint-compiler/.gitattributes create mode 100644 research/compact-joint-compiler/FRONTIER.json create mode 100644 research/compact-joint-compiler/PROOF.md create mode 100644 research/compact-joint-compiler/README.md create mode 100644 research/compact-joint-compiler/REPLAY.json create mode 100644 research/compact-joint-compiler/REUSE.md create mode 100644 research/compact-joint-compiler/SOURCES.json create mode 100644 research/compact-joint-compiler/TASK.json create mode 100644 research/compact-joint-compiler/VALIDATION.md create mode 100644 research/compact-joint-compiler/VERIFY.json create mode 100644 research/compact-joint-compiler/arithmetic/INPUTS.json create mode 100644 research/compact-joint-compiler/arithmetic/PROOF.txt create mode 100644 research/compact-joint-compiler/arithmetic/RESULT.json create mode 100644 research/compact-joint-compiler/arithmetic/controller.json create mode 100644 research/compact-joint-compiler/arithmetic/intervals.py create mode 100644 research/compact-joint-compiler/arithmetic/legacy-source.txt create mode 100644 research/compact-joint-compiler/arithmetic/legacy.py create mode 100644 research/compact-joint-compiler/arithmetic/ordinary-bit.json create mode 100644 research/compact-joint-compiler/arithmetic/outer_ledger.py create mode 100644 research/compact-joint-compiler/arithmetic/profile.json create mode 100644 research/compact-joint-compiler/arithmetic/verify.py create mode 100644 research/compact-joint-compiler/independent/INPUTS.json create mode 100644 research/compact-joint-compiler/independent/PROOF-REVIEW.txt create mode 100644 research/compact-joint-compiler/independent/RECEIPT.json create mode 100644 research/compact-joint-compiler/independent/audit.py create mode 100644 research/compact-joint-compiler/verify.py create mode 100644 research/direct-mixed-flow/.gitattributes create mode 100644 research/direct-mixed-flow/README.md create mode 100644 research/direct-mixed-flow/RESULT.json create mode 100644 research/direct-mixed-flow/SOURCES.json create mode 100644 research/direct-mixed-flow/TASK.json create mode 100644 research/direct-mixed-flow/VENDOR.json create mode 100644 research/direct-mixed-flow/VERIFY.json create mode 100644 research/direct-mixed-flow/flow.py create mode 100644 research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md create mode 100644 research/direct-mixed-flow/vendor/P7-FACTOR.json create mode 100644 research/direct-mixed-flow/vendor/SUSSMAN-LICENSE create mode 100644 research/direct-mixed-flow/vendor/SUSSMAN-NOTICE create mode 100644 research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz create mode 100644 research/direct-mixed-flow/vendor/higher-moment-README.md create mode 100644 research/direct-mixed-flow/vendor/higher-moment-RESULT.json create mode 100644 research/direct-mixed-flow/vendor/p7-NATIVE.md create mode 100644 research/direct-mixed-flow/vendor/p7-RESULT.json create mode 100644 research/direct-mixed-flow/vendor/theorem-1g.md create mode 100644 research/direct-mixed-flow/vendor/tree_flow.py create mode 100644 research/direct-mixed-flow/verify.py create mode 100644 research/joint-helper-lattice/CONTROLLER.json create mode 100644 research/joint-helper-lattice/DISCOVERY.json create mode 100644 research/joint-helper-lattice/FRONTIER.json create mode 100644 research/joint-helper-lattice/NATIVE.json.gz create mode 100644 research/joint-helper-lattice/PATCH.json create mode 100644 research/joint-helper-lattice/PROOF.md create mode 100644 research/joint-helper-lattice/README.md create mode 100644 research/joint-helper-lattice/REPLAY-LOGS.json create mode 100644 research/joint-helper-lattice/RESULT.json create mode 100644 research/joint-helper-lattice/SOURCES.json create mode 100644 research/joint-helper-lattice/TASK.json create mode 100644 research/joint-helper-lattice/VALIDATION.md create mode 100644 research/joint-helper-lattice/VERIFY.json create mode 100644 research/joint-helper-lattice/native_joint.py create mode 100644 research/joint-helper-lattice/verify.py create mode 100644 research/missing-join-frame/NATIVE.json.gz create mode 100644 research/missing-join-frame/PATCH.json create mode 100644 research/missing-join-frame/PROOF.md create mode 100644 research/missing-join-frame/README.md create mode 100644 research/missing-join-frame/RESULT.json create mode 100644 research/missing-join-frame/SOURCES.json create mode 100644 research/missing-join-frame/TASK.json create mode 100644 research/missing-join-frame/VALIDATION.md create mode 100644 research/missing-join-frame/VERIFY.json create mode 100644 research/missing-join-frame/native_join.py create mode 100644 research/missing-join-frame/verify.py diff --git a/research/compact-joint-compiler/.gitattributes b/research/compact-joint-compiler/.gitattributes new file mode 100644 index 0000000000..fa1385d99a --- /dev/null +++ b/research/compact-joint-compiler/.gitattributes @@ -0,0 +1 @@ +* -text diff --git a/research/compact-joint-compiler/FRONTIER.json b/research/compact-joint-compiler/FRONTIER.json new file mode 100644 index 0000000000..312a642e11 --- /dev/null +++ b/research/compact-joint-compiler/FRONTIER.json @@ -0,0 +1,20 @@ +{ + "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "source_pr": 4470, + "source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "strongest_observed_open_conditional_kappa": "0.00302015", + "new_kappa_claim": false, + "selected_frontier_changed": false, + "recent_checkpoint_coverage": { + "pr_updates": 917, + "since": "2026-10-18T23:40:10Z", + "complete": true, + "latest_refresh_includes": 4477 + }, + "initial_candidate": { + "kappa": "0.00300428", + "status": "superseded by PR4470 during the session" + }, + "overlap_limit": "No exhaustive historical code/Discussion search or global novelty claim.", + "checked_at_utc": "2026-10-21T23:56:00Z" +} diff --git a/research/compact-joint-compiler/PROOF.md b/research/compact-joint-compiler/PROOF.md new file mode 100644 index 0000000000..5eccdd5924 --- /dev/null +++ b/research/compact-joint-compiler/PROOF.md @@ -0,0 +1,31 @@ +# Sufficient compact compilation at the retained saving + +**Proposition.** Under precisely the conditional contracts retained by PR #4470, its unchanged source-bound p16 supplier has a sufficient uniform local rank N = 2^558100005581 at declared κ = 0.00302015. This replaces the previous sufficient local rank 2^64215200000000. + +**Proof.** Keep C = 0.00302016 and t = 1 − C. The literal controller yields the same target and paid histograms as PR #4470; independent event counting retains all 18 full native calls, 15 copied-query shears and 3,360 whole idle jobs. All 408 helpers remain independent arbitrary fields, including nonzero dirty entry values. Native and phase replay are independent required gates, rather than being inferred from an arithmetic receipt. + +For the same complete histograms T and P choose v = 682, c = 17, b = 21 and u = 1/8. Exact rational intervals give + +α = P_t/T_t < 1 − 31/(5·10^9), +γ = P_(t+u)/(17^u T_t) < 98102/100000, +δ = 10928·21/(17^C T_t) < 959/1000. + +The retained paid-completion and splitting theorem therefore bounds the normalized final paid moment by + +1/(1 + 682·31/(5·10^9)) + 2(98102/100000)^682 + 2(959/1000)^682 < 1. + +This includes both the original paid tail and the completion tail. No new padded target has unpaid axes. The same conservative bound rejects v = 681; this is a control for the displayed choices, not a global minimum theorem. + +Use θ = 94/101 and logarithm power 143 in the credited general majorant. The exact checks are 17^101 < 21^94, 128(17^682)^101 ≤ (145^682)^94, and, for η = (1 − C)145^(−682C), η > θ^143 and 145^(682C) < 2^143. These supply the same shifted-exit, complement-capacity and initial-range hypotheses as in the predecessor theorem. Power 142 fails the displayed η control. + +Allocate compiler gap g = 1/100000001 and outer slack d = (C − κ − g)/6 = 1/60000000600000000. The elementary identity C − g = κ + 6d with d > 0 leaves the strict chain + +κ < q = κ + 3d < a = κ + 4d < b = κ + 5d < C − g. + +The exact current ledger independently checks the remaining conditions; the chain alone is not substituted for those checks. In particular, all 54 strict predicates and four functional guards pass, as do all 63 legacy predicates and equality of all nine cost rows. Ordinary BIT saving 0.0034 is retained. The legacy decimal grid is refined to 10^20 to resolve the smaller positive margins. + +The integer majorant test (100000001j + 1)^143 < 2^j holds at j = 5581 and fails at j = 5580. The retained sufficient logarithmic compiler theorem consequently gives N = 2^(100000001·5581) = 2^558100005581 for the uniform local supplier. Every scalar and route remains within the retained finite bound; the enormous resulting word is specified algorithmically and not materialized. This proves the conditional proposition. ∎ + +The smaller local rank is not a higher saving exponent. Nor does it prove an improved overall multiplication threshold: the smaller outer slack may worsen that separate threshold. All inherited physical, analytic, precision, tape, stock, prime and recovery premises remain. + +Credit PR #4470 for the native construction and controller, PR #4447 for the missing span, PR #4440/#4441 for query thinning and helper retiming, zxv for higher-moment and logarithmic-majorant work, Jacob Alan Sussman for the mixed-target compiler, and all source scalar/Clifford/BIT/outer-ledger contributors. The legacy ledger retains Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe, Vlado Vojdanovski and its full source attribution. This contribution changes the sufficient completion and compiler parameters; it does not claim these general methods were invented here. diff --git a/research/compact-joint-compiler/README.md b/research/compact-joint-compiler/README.md new file mode 100644 index 0000000000..185ea31abd --- /dev/null +++ b/research/compact-joint-compiler/README.md @@ -0,0 +1,23 @@ +# Compact finite compiler for the joint-helper supplier + +Retain PR #4470's conditional κ = 0.00302015 while reducing its sufficient **local uniform-supplier rank** from 2^64215200000000 to **2^558100005581**. The exponent is about 115.06 times smaller. This is a new sufficient compiler construction at the same κ, not a higher κ, a practical speedup or a smaller overall multiplication input threshold. + +The native words and complete p16 controller are unchanged: 408 independent productive helpers, 10,928 productive fields, 64,620 paid calls, rank surplus 752, all owned-center work, 15 copied-query shears and 3,360 whole idle jobs. The verifier freshly checks both native orientations, 632 arbitrary columns, Clifford tableaux and absolute phases, as well as the parent construction's exact source admissions. + +Two changes contribute to the smaller local bound: a newly priced completion/splitting choice reduces the tensor power and logarithmic majorant; separate compiler and outer-transfer slack makes a much larger compiler gap available. Both paid tails, every outer row and all inherited charges remain checked. The smaller outer slack may increase the eventual full-algorithm input threshold; no bound or improvement of that threshold is asserted. + +Run Python 3.12, standard library only: + +```sh +python -B scripts/research_package.py --package research/compact-joint-compiler +``` + +The three registered gates can also be run separately with `verify.py --part dependencies`, `--part native`, and `--part arithmetic`. See PROOF.md, arithmetic/PROOF.txt, VALIDATION.md and REUSE.md. + +This branch is stacked on PR #4470 at b9a13c1673e0e9697de410de16e8bbf3207a7363; inherited files are predecessor contributions. Retain the conditional native lift, primitive semantics, owned erasure, whole-job matching, finite-template closure, precision, fixed-tape, stock, analytic decomposition, prime-avoidance and exact-recovery premises. No formal-kernel check, human acceptance, global optimum or selected-frontier promotion is claimed. + +Prepared for Dugongue with substantial OpenAI Codex assistance, root plus three agents. Apache-2.0 for new code; original source notices remain applicable. + +## Open next questions + +Can changed warp charts or general nonmonotone contact moves improve the complete PR #4470 paid invoice? Any successful successor must emit and check the physical operators including absolute phase, replay all arbitrary input columns and reprice the complete construction. Can a sharper sufficient recurrence reduce the local supplier rank without shrinking outer slack? diff --git a/research/compact-joint-compiler/REPLAY.json b/research/compact-joint-compiler/REPLAY.json new file mode 100644 index 0000000000..f68e1dd662 --- /dev/null +++ b/research/compact-joint-compiler/REPLAY.json @@ -0,0 +1,16 @@ +{ + "status": "PASS_ALL_FOUR_REQUIRED_GATES", + "source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "scope": "Exact operator and rational/integer arithmetic replay, not kernel or human acceptance.", + "execution": "Three registered dependency/native/arithmetic gates completed together. The separately added read-only independent gate completed under isolated optimized Python; final four-command metadata/pins check passed.", + "gates": [ + "PASS_COMPACT_JOINT_COMPILER_DEPENDENCIES", + "PASS_COMPACT_JOINT_COMPILER_NATIVE", + "PASS_COMPACT_JOINT_COMPILER_ARITHMETIC", + "PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER" + ], + "kappa": "0.00302015", + "new_kappa_claim": false, + "local_uniform_rank": "2^558100005581", + "hosted_CI_claim": false +} diff --git a/research/compact-joint-compiler/REUSE.md b/research/compact-joint-compiler/REUSE.md new file mode 100644 index 0000000000..c84a408c97 --- /dev/null +++ b/research/compact-joint-compiler/REUSE.md @@ -0,0 +1,22 @@ +# Discovery reuse and predecessor credit + +The root and three workers queried the registered source catalog and the canonical typed DAG, then read selected relevant source bodies. This is a broad catalog search, not a claim that every registered proof body was read or that none of these concepts has previously been used. No new Lean formalization or fresh Lean kernel/axiom audit is claimed. Source reads and Python/operator certificates are distinguished throughout. + +| Worker | Retrieved precedents | Implemented ideas and outcome | +| --- | --- | --- | +| Root | `Mathproof.Meta.TISLTransvectionWord20260908`, `External.TenProofs.ConnesRigidity`, `Mathproof.Meta.RationalLPCertificate20260908`, and the Schur-complement wrapper in `ArXiv200902452_20260903` | Constructive quotient reconstruction for commuting contact rewrites; common-chart block elimination; exact general-Clifford distance retiming outside monotone flags. All were implemented and bounded tests found no gain over PR #4470. The Schur wrapper restates standard matrix algebra and is not credited as a new discovery. | +| Native worker | `TISLTransvectionWord20260908`, adapted subspace/quotient coordinates in the Problem18/anchor modules | Joint contact/helper-boundary retiming; overlap-compatible patch assembly; exact free-warp chart changes with priced neighbors. The first two produced an all-column checked κ = 0.00300428 stepping stone, superseded by PR #4470. | +| Controller/audit worker | `UniversalChartMomentRank20260831.hasTruncatedMoment_iff_factors`, quotient-kernel monotonicity and two-sided Woodbury sources | Arbitrary-subset Laurent specialization and fully charged rank-factor batch queries; diagonal scalar-gauge normalization and transvection folding. These preserve exact arbitrary-column semantics. They did not produce a higher complete saving in this session. | +| Moment/compiler worker | `Computability.IntegerKappaMomentTransfer20261015`, `Mathproof.ConvexSlope`, the prior `MULTITYPE-MOMENT.md` and prefix-majorization sources | Exact support-hypergraph subset dynamic programming; separately allocated compiler/outer slack; newly priced two-tail/logarithmic majorant parameters. The latter two give the sufficient local-rank improvement certified here. | + +No positive recurrence result from a source containing an unresolved `sorry` is used. The numerical search programs nominate candidates only; exact frozen receipts and proofs establish the retained sufficient result. The new public package contains the compact compiler, not an assertion that all discovery experiments are novel research contributions. The larger session archive preserves failed and interrupted searches separately. + +## Direct source lineage + +- PR #4470 supplies the unchanged joint-helper native words, productive inventory, p16 controller and κ = 0.00302015. It deserves the saving-exponent credit. +- PR #4447 supplies the missing-span contact; PR #4440 supplies query thinning; PR #4441 supplies its helper-retiming combination. PR #4446 and #4453 are overlapping certificates, with #4453 also informing compact finite compilation. Their source contracts differ from older packing interfaces and are not conflated. +- PR #4359 supplies the selected productive-job/mixed-target framework. zxv's higher-moment and logarithmic work, including the general majorant used by PR #4433, and Jacob Alan Sussman's finite mixed-target compiler remain essential premises. +- The ordinary BIT, scalar, Clifford, geometry, owner/erasure, fixed-tape and outer-ledger lineage remains credited in the unchanged source files and their manifests. The legacy ledger explicitly retains Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe and Vlado Vojdanovski, among the credited predecessors. +- PR #4474 records stacked p17 content and documentation conflicts; PR #4477 records the distinct direct-flow chain. Neither disposition is treated as mathematical acceptance or rejection of the source κ claim. + +The first 917 PR updates since the previous local checkpoint were collected in full. Repeated newest-100 refreshes included PR #4470 and subsequently #4477. Older overlap was additionally searched for native/Clifford fusion, including PR #4002's phase-tag warning and PR #4074's distinct caller fusion. This bounded coverage does not establish global novelty. The canonical selected result remains unchanged. diff --git a/research/compact-joint-compiler/SOURCES.json b/research/compact-joint-compiler/SOURCES.json new file mode 100644 index 0000000000..77fd452f54 --- /dev/null +++ b/research/compact-joint-compiler/SOURCES.json @@ -0,0 +1,408 @@ +{ + "schema_version": 1, + "base_commit": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "usage": "input", + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "usage": "input", + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624" + }, + { + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "usage": "input", + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839" + }, + { + "path": "research/fresh-helper-boundary/RESULT.json", + "usage": "input", + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd" + }, + { + "path": "research/fresh-helper-boundary/SOURCES.json", + "usage": "input", + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0" + }, + { + "path": "research/fresh-helper-boundary/arithmetic.py", + "usage": "input", + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "usage": "input", + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29" + }, + { + "path": "research/fresh-helper-boundary/verify.py", + "usage": "input", + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf" + }, + { + "path": "research/fresh-helper-thinned/PROOF.md", + "usage": "input", + "git_blob": "bf68dc2b987cb7de6431ff5e3514b60af48720a5", + "sha256": "9883b3329fef7624d3471e27bb55258cd9dc18bb6d37779a3939de99add87347" + }, + { + "path": "research/fresh-helper-thinned/README.md", + "usage": "input", + "git_blob": "344616d6654a96085dd45cf2c3189ef283deeac1", + "sha256": "70c1c872c2327c3f71918e218d5f1ecb7a00037771a5dd1b8ae415b84cc90dc2" + }, + { + "path": "research/fresh-helper-thinned/RESULT.json", + "usage": "input", + "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55", + "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21" + }, + { + "path": "research/fresh-helper-thinned/SOURCES.json", + "usage": "input", + "git_blob": "4089ad37114540b23846596e2a641c4a4bd608e2", + "sha256": "5aec5df5096ee8a3e90618d311640b4bdfba42be5bc4bc5fab55e8be858ab2cb" + }, + { + "path": "research/fresh-helper-thinned/verify.py", + "usage": "input", + "git_blob": "9ba85a59aa5dcc5cdaec85ee18607cb050530c55", + "sha256": "c841265ccee9b6f79045ad818ce9d27cfd7ee1f60047525a75d491f0dd8b997a" + }, + { + "path": "research/higher-moment-strictification/README.md", + "usage": "input", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/joint-helper-lattice/CONTROLLER.json", + "usage": "input", + "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5", + "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + { + "path": "research/joint-helper-lattice/DISCOVERY.json", + "usage": "input", + "git_blob": "53f7d1028fec4f82b5e02c0f41d1297a9fb82a80", + "sha256": "bb0fe8ffe742baf05b63423589efd5308cc08aafc5ca63958d4570904101676d" + }, + { + "path": "research/joint-helper-lattice/FRONTIER.json", + "usage": "input", + "git_blob": "9e05b4e02570b8249ec698b662cd5212dbc83db9", + "sha256": "0360df11fa195890808581df291eb8c3abf3261c66b4d7e5a0f5f5657f59b796" + }, + { + "path": "research/joint-helper-lattice/NATIVE.json.gz", + "usage": "input", + "git_blob": "0910f74138decf498e7fc445cc2daff4390169d6", + "sha256": "74582cce642c80f0235be7fcbce3716174666326ac6a1d46d02a62a75d7be4c6" + }, + { + "path": "research/joint-helper-lattice/PATCH.json", + "usage": "input", + "git_blob": "51304a6601061ed4e698f910b09135ef109555e3", + "sha256": "296d0e8c58cc70febe042c681ef30d6bb469818c0835fbcaac8aa8d330f5b727" + }, + { + "path": "research/joint-helper-lattice/PROOF.md", + "usage": "input", + "git_blob": "e41106031da41fade7a7419c17a32c1bd9aa103b", + "sha256": "43ef4251cc300f1b18cbe8cdb060f96f95748e6797d2478b4c04b79a8373ef91" + }, + { + "path": "research/joint-helper-lattice/README.md", + "usage": "input", + "git_blob": "8c9bd69cd445bd05f18ffcf86d6feb556d634b14", + "sha256": "e5e1a3a11d97fa771e0ec3a4e3e596714f7f3c036fed8c97f395f4c6637317cb" + }, + { + "path": "research/joint-helper-lattice/REPLAY-LOGS.json", + "usage": "input", + "git_blob": "38a7d9500e0add60b33b25393ca0157dd1c7852b", + "sha256": "cb5997b8f2f790bfa32b82472275c87607150ebed63ee99caf079c2b18407956" + }, + { + "path": "research/joint-helper-lattice/RESULT.json", + "usage": "input", + "git_blob": "edf41a49a0350862c23378f837c7397fc5dc7596", + "sha256": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21" + }, + { + "path": "research/joint-helper-lattice/SOURCES.json", + "usage": "input", + "git_blob": "02e8f76eab10ba009a226bbda38736de0bbda136", + "sha256": "4045942a3b3516380c980b547e80ac254bc22e4c21c74ac16e48d3f0e46955f6" + }, + { + "path": "research/joint-helper-lattice/TASK.json", + "usage": "input", + "git_blob": "aa0123ac3ea13a5054d1109559e62febd28f8e7f", + "sha256": "8f1ab1803b8b22c6424c23410e5e1075545f3a4a1d667f55eff988917e6c1e22" + }, + { + "path": "research/joint-helper-lattice/VALIDATION.md", + "usage": "input", + "git_blob": "dea1fb147911ad6ce916891630abb6b94db9606d", + "sha256": "1953b485cc9216443beefedaaf465483c2a84ff993d9284e44cb5107ad225361" + }, + { + "path": "research/joint-helper-lattice/VERIFY.json", + "usage": "input", + "git_blob": "7258f5000cabcec9cb038541fef3a38007576803", + "sha256": "1d004a782ff9d8264e4f3f6e6fbee729047ec7a24874fb03728695ef527786a8" + }, + { + "path": "research/joint-helper-lattice/native_joint.py", + "usage": "input", + "git_blob": "0315f80e2fdef5e0eef13e3e9b8f72066238164d", + "sha256": "50869b1bcad7493e6b4cb2a4cd5d2fd9a193a5921100483fa2c3f2c999ddfd46" + }, + { + "path": "research/joint-helper-lattice/verify.py", + "usage": "input", + "git_blob": "0006dd15ca5597edfa506559124d2cdf3c493ae4", + "sha256": "8eb13f77a94315f811612cb557a17edeecb6b9d9a75dfa238b112dd6520c336f" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "usage": "input", + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "usage": "input", + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7" + }, + { + "path": "research/kappa-function-composition/complex/prune_native.py", + "usage": "input", + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257" + }, + { + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "usage": "input", + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + { + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "usage": "input", + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef" + }, + { + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "usage": "input", + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0" + }, + { + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "usage": "input", + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "usage": "input", + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf" + }, + { + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "usage": "input", + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7" + }, + { + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "usage": "input", + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497" + }, + { + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "usage": "input", + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e" + }, + { + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "usage": "input", + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "usage": "input", + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/kappa-rebuild/complex/native_extensions.py", + "usage": "input", + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3" + }, + { + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "usage": "input", + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424" + }, + { + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "usage": "input", + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5" + }, + { + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "usage": "input", + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902" + }, + { + "path": "research/missing-join-frame/NATIVE.json.gz", + "usage": "input", + "git_blob": "2f41b11d02726a60da449aaa6c603716c0310ead", + "sha256": "96718b257db24f4f62d3b86b36cdd514e67d2cb99947ddd7bdcb9b55a2c17841" + }, + { + "path": "research/missing-join-frame/PATCH.json", + "usage": "input", + "git_blob": "f96d295d40014d4dd503f58eb3cdabcbb4b8e101", + "sha256": "9ab5328245ff02c9d0be21d39bcc375f50bc5d7909e9f7b9a3a9a6f812f5bd6e" + }, + { + "path": "research/missing-join-frame/PROOF.md", + "usage": "input", + "git_blob": "d240cd8e14e6d30e0e2c3d0ddcc7efa68349e24e", + "sha256": "50061c25d379ff5733135dbed53e8721bbd4dbee6766d1609d8a2ecdebb7dc06" + }, + { + "path": "research/missing-join-frame/RESULT.json", + "usage": "input", + "git_blob": "e653fb4358ded67ff1539151f4b670ad9a242fb1", + "sha256": "25f2cbcde988847ff86f44e804982069863ec99ff68097f16e9bb7a1a17c4cd0" + }, + { + "path": "research/missing-join-frame/verify.py", + "usage": "input", + "git_blob": "188135f81c9937af8232a06dc1e7b8b28260e6a8", + "sha256": "21429dd9c1b9c93ebb57e5fbb8ef674d0e4146ac8c25cc7c097c3352c02366a4" + }, + { + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "usage": "input", + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598" + }, + { + "path": "research/pr4359-p7-padding/TENSOR.md", + "usage": "input", + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/pr4359-p7-padding/native_inventory.py", + "usage": "input", + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32" + }, + { + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "usage": "input", + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d" + }, + { + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "usage": "input", + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088" + }, + { + "path": "research/query-thinned-controllers/RESULT.json", + "usage": "input", + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f" + }, + { + "path": "research/query-thinned-controllers/SOURCES.json", + "usage": "input", + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29" + }, + { + "path": "research/query-thinned-controllers/controller.py", + "usage": "input", + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2" + }, + { + "path": "research/query-thinned-controllers/verify.py", + "usage": "input", + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950" + }, + { + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + ] +} diff --git a/research/compact-joint-compiler/TASK.json b/research/compact-joint-compiler/TASK.json new file mode 100644 index 0000000000..1ab395e043 --- /dev/null +++ b/research/compact-joint-compiler/TASK.json @@ -0,0 +1,64 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "base_commit": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "scope_status": "changed", + "actual_scope": "Retain PR4470 conditional kappa 0.00302015 with an exactly certified smaller local uniform-supplier rank.", + "scope_change_reason": "User assigned a best-kappa search. The initial improving candidate was superseded during the session by PR4470; no tested extension beats it. Retain a useful sufficient finite-compiler improvement on the new strongest observed invoice, explicitly without a kappa-improvement claim.", + "bottleneck_link": "Oversized sufficient logarithmic majorants and equal allocation of compiler/outer slack inflate the local supplier rank.", + "stop_rule": "Require source-pinned native/operator/phase replay, both paid tails, exact integer rank test and every retained outer predicate; do not claim a smaller overall multiplication input threshold.", + "evidence": "arithmetic/RESULT.json, arithmetic/PROOF.txt, PROOF.md, VALIDATION.md", + "author": "Dugongue", + "ai_assistance": "Substantial OpenAI Codex assistance by root and three agents.", + "outcome": "completed", + "open_questions": [ + { + "question": "Can changed warp charts or nonmonotone contact moves improve the complete PR4470 invoice?", + "why_it_matters": "The present compiler improvement preserves kappa.", + "first_step": "Freeze one source warp or two-contact change, lower every emitted Clifford including absolute phase, and reprice the complete p16 controller.", + "blocked_by": "No higher-kappa changed native word has passed all gates in this session." + } + ] +} diff --git a/research/compact-joint-compiler/VALIDATION.md b/research/compact-joint-compiler/VALIDATION.md new file mode 100644 index 0000000000..62ea270975 --- /dev/null +++ b/research/compact-joint-compiler/VALIDATION.md @@ -0,0 +1,9 @@ +# Validation and limits + +The registered verifier has separate dependency, native and arithmetic gates. They preserve exact source-byte guards. The native gate freshly executes both retained interpreters, both orientations, all 632 arbitrary persistent columns, owned-center cleanup and all 423 transport/helper physical pairs, including absolute phases. The arithmetic gate freshly replays the source controller and source bill before binding the compact result to identical target and paid histograms. + +The new exact arithmetic checks both original/completion tails, whole-job splitting, shifted exit and complement capacity, the finite integer majorant, all 54 current strict predicates, four functional guards, all 63 legacy predicates and agreement of all nine cost rows. Controls reject unsupported BIT saving, closed uniform/outer gaps and a false endpoint saving. A separate audit recomputes the displayed rational tail and integer inequalities and checks the actual-native inventory binding. Both normal and optimized isolated Python are used. These are computational exact-arithmetic/operator checks, not proof-assistant or independent human acceptance. + +During independent review, the initial compact complement-capacity check used a factor 2 inherited from a different denominator. For θ = 94/101 the sufficient factor is 2^(101 − 94) = 128. The stronger exact inequality passes; the executable condition and proof were corrected before the final replay. The resulting N is unchanged. This correction is included to make the hypothesis audit reviewable. + +All inherited conditional physical, analytic, precision, tape, stock, prime and recovery obligations remain. The finite word is specified algorithmically, not materialized. Smaller local template rank is the only new bound claimed; tiny outer slack can worsen the eventual full-algorithm threshold. No improvement to that overall threshold or to κ is claimed. diff --git a/research/compact-joint-compiler/VERIFY.json b/research/compact-joint-compiler/VERIFY.json new file mode 100644 index 0000000000..cec7296b2e --- /dev/null +++ b/research/compact-joint-compiler/VERIFY.json @@ -0,0 +1,120 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "research/fresh-helper-boundary/RESULT.json", + "research/fresh-helper-boundary/SOURCES.json", + "research/fresh-helper-boundary/arithmetic.py", + "research/fresh-helper-boundary/native.py", + "research/fresh-helper-boundary/verify.py", + "research/fresh-helper-thinned/PROOF.md", + "research/fresh-helper-thinned/README.md", + "research/fresh-helper-thinned/RESULT.json", + "research/fresh-helper-thinned/SOURCES.json", + "research/fresh-helper-thinned/verify.py", + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/verify.py", + "research/joint-helper-lattice/CONTROLLER.json", + "research/joint-helper-lattice/DISCOVERY.json", + "research/joint-helper-lattice/FRONTIER.json", + "research/joint-helper-lattice/NATIVE.json.gz", + "research/joint-helper-lattice/PATCH.json", + "research/joint-helper-lattice/PROOF.md", + "research/joint-helper-lattice/README.md", + "research/joint-helper-lattice/REPLAY-LOGS.json", + "research/joint-helper-lattice/RESULT.json", + "research/joint-helper-lattice/SOURCES.json", + "research/joint-helper-lattice/TASK.json", + "research/joint-helper-lattice/VALIDATION.md", + "research/joint-helper-lattice/VERIFY.json", + "research/joint-helper-lattice/native_joint.py", + "research/joint-helper-lattice/verify.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-function-composition/complex/prune_native.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "research/kappa-rebuild/bit/bit_native_binding.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-rebuild/bit/mixed_productive_bit.py", + "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/kappa-rebuild/complex/native_extensions.py", + "research/kappa-rebuild/complex/power_two_balance.py", + "research/kappa-rebuild/complex/rebuild_native.py", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "research/missing-join-frame/NATIVE.json.gz", + "research/missing-join-frame/PATCH.json", + "research/missing-join-frame/PROOF.md", + "research/missing-join-frame/RESULT.json", + "research/missing-join-frame/verify.py", + "research/pr4359-p7-padding/P7-FACTOR.json", + "research/pr4359-p7-padding/TENSOR.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/pr4359-p7-padding/native_inventory.py", + "research/query-thinned-controllers/BIT-CONTROLLER.json", + "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "research/query-thinned-controllers/RESULT.json", + "research/query-thinned-controllers/SOURCES.json", + "research/query-thinned-controllers/controller.py", + "research/query-thinned-controllers/verify.py", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "dependencies" + ], + "timeout_seconds": 120, + "checks": "Fresh retained source native/BIT dependencies." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "native" + ], + "timeout_seconds": 400, + "checks": "Fresh PR4470 two-interpreter, 632-column, both-orientation and all absolute-phase replay, tied to the new arithmetic profile." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "arithmetic" + ], + "timeout_seconds": 400, + "checks": "Fresh PR4470 complete arithmetic/controller replay plus the new tails, compiler integer bound, 54+4 current and 63 legacy predicates and mutation controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/independent/audit.py" + ], + "timeout_seconds": 120, + "checks": "Read-only independent source-pinned audit, normal/optimized equality, exact compiler and tail tests, and scientific/source rejection controls." + } + ] +} diff --git a/research/compact-joint-compiler/arithmetic/INPUTS.json b/research/compact-joint-compiler/arithmetic/INPUTS.json new file mode 100644 index 0000000000..0fb0601fc8 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/INPUTS.json @@ -0,0 +1,49 @@ +{ + "files": [ + { + "path": "verify.py", + "sha256": "4ad2d95bee6e6fe2ae4462e5dd0921c64677fc86a5da1f38a198546c28c7f1b1" + }, + { + "path": "intervals.py", + "sha256": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc" + }, + { + "path": "outer_ledger.py", + "sha256": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54" + }, + { + "path": "legacy.py", + "sha256": "43cd70c98a133015f40fd695e18035254cb3bd303f2da45bf46607f211506a87" + }, + { + "path": "legacy-source.txt", + "sha256": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895" + }, + { + "path": "controller.json", + "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + { + "path": "ordinary-bit.json", + "sha256": "7d3ef7711fef1033a49f7ac9847bccf24145c0ba2cf248b3802114c172fb0249" + }, + { + "path": "profile.json", + "sha256": "6e937237c22b3b6d4821ecc253e579b852731a5c665ce488d42f2f7bddb291f5" + } + ], + "scope": "Same best-known conditional kappa as PR4470, changed paid tensor/compiler footprint only. No endpoint improvement claimed.", + "predecessor": { + "pr": 4470, + "repository": "1337isnot1337/integer-mult-bounds", + "head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "status": "author-checked pending contribution; no selected promotion inferred" + }, + "legacy_origin": { + "repository": "CrocSwap/integer-mult-bounds", + "commit": "2a13eb1827784206202db90e5dc8327cf8a250db", + "path": "research/higher-moment-strictification/vendor/check_ledger.py", + "sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98" + } +} diff --git a/research/compact-joint-compiler/arithmetic/PROOF.txt b/research/compact-joint-compiler/arithmetic/PROOF.txt new file mode 100644 index 0000000000..0ad965e87f --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/PROOF.txt @@ -0,0 +1,19 @@ +Same conditional κ, smaller finite compiler bound + +The native word, 408 independent helper fields, whole rank-eight center jobs and complete p16 controller are exactly PR4470's source-bound construction. The declared conditional κ remains 0.00302015. This contribution makes no improved κ claim and no change to the selected result. The bound concerns the local supplier template. The smaller outer slack may raise the eventual threshold for the full multiplication algorithm; that threshold is not bounded here. Its input profile and controller are hash-guarded; run(local) additionally checks an actual native replay's helper and paid inventories against those exact frozen inputs. + +Keep tested saving C = 0.00302016, so t = 1 − C. The changed paid tensor construction uses v = 682, cutoff J = 17^v, productive floor L = 21^v and higher-moment offset u = 1/8. Recompute α = P_t/T_t, γ = P_(t+u)/(17^u T_t) and δ = 10928*21/(17^C T_t). Exact rational intervals prove α < 1 − 31/(5*10^9), γ < 98102/100000 and δ < 959/1000. Both original and completion tails are charged by the retained higher-moment theorem. Their resulting conservative upper bound is + + 1/(1 + v*31/(5*10^9)) + 2*(98102/100000)^v + 2*(959/1000)^v < 1. + +The same displayed bound is greater than 1 at v = 681. This is a test of these chosen conservative ratios, not a global optimality theorem for tensor completion. Scalar words, whole-job normalizers, owned erasure, all main adapters and fixed routes remain charged by the explicit source finite allowances. + +Choose logarithmic contraction θ = 94/101 and logarithm power p = 143. Exact integer tests verify 17^101 < 21^94 and 2^(101−94)*(17^682)^101 ≤ (145^682)^94. For η = (1 − C)*145^(−682*C), the interval engine proves η > θ^143 and η < θ^142, and also 145^(682*C) < 2^143. These are precisely the sufficient shifted-exit, complement-capacity and initial-range hypotheses of the retained general logarithmic majorant. The smaller power is justified by these inequalities, not by changing the inductive theorem. + +Separate compiler slack from outer-transfer slack. Put g = 1/100000001 and d = (C − κ − g)/6 = 1/60000000600000000. Then d > 0 and the uniform saving is C − g = κ + 6d. Take b = κ + 5d, a = κ + 4d, q = κ + 3d, ε = 1 − d, β = 1 − 3d, r0 = d/10, stop = layout = d, retaining ordinary BIT admission 0.0034. All 54 strict and 4 functional predicates pass exactly, including every one of the nine outer cost rows. Four source mutation controls reject. A separate legacy check with decimal grid 10^20 passes all 63 predicates and agrees on all nine rows; the old 10^10 grid cannot resolve these smaller strict margins and is not silently reused. + +The integer majorant test (100000001*j + 1)^143 < 2^j passes at j = 5581 and fails at j = 5580. Thus the retained compiler theorem supplies sufficient uniform rank N = 2^558100005581. PR4470 gives 2^64215200000000, so the exponent decreases by approximately 115.06 times. This compares finite template bounds, not observed runtime, and the enormous word is algorithmically specified rather than materialized. The full integer-multiplication theorem still retains all inherited native, analytic, precision, fixed-tape, stock, prime, ownership and exact-recovery premises. + +Predecessor credit: PR4470's actual new native word and p16 controller; PR4447 and PR4440/4441's geometry, retiming and thinning; zxv's higher-moment and logarithmic-majorant work; Jacob Alan Sussman's mixed-target compiler; Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe, Vlado Vojdanovski and the retained legacy outer-ledger contributors. New compiler choices prepared with substantial OpenAI Codex assistance. Apache-2.0 for new code; original notices retained. + +Open next question: replace this sufficient power majorant by a source-bound sharper recurrence while preserving both paid tails and the complete current outer ledger. A smaller template bound alone does not improve κ. The displayed N bounds the local uniform supplier template. The tiny outer d can increase the eventual input threshold of the full integer-multiplication theorem; no numerical bound on that overall threshold, nor any reduction of it, is claimed. diff --git a/research/compact-joint-compiler/arithmetic/RESULT.json b/research/compact-joint-compiler/arithmetic/RESULT.json new file mode 100644 index 0000000000..514d12ce4d --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/RESULT.json @@ -0,0 +1,304 @@ +{ + "compiler": { + "H": 558100005581, + "N": "2^558100005581", + "eta": { + "lower": "0.000035221718023643756209805039", + "upper": "0.000035221718023643756209805040" + }, + "gap": "1/100000001", + "integer_test_exponent": 5581, + "power": 143, + "theta": "94/101", + "word_materialized": false + }, + "derivative_positive_lower": "153765567619337917435297159143913717753264213528597495787928055/784637716923335095479473677900958302012794430558004314112", + "gain_over_PR4447": "473/25000000", + "kappa": "60403/20000000", + "kappa_decimal": "0.00302015", + "legacy_outer": { + "backoff": "2497/50000000000000000000", + "grid": 100000000000000000000, + "nine_row_agreement": true, + "source_sha256": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895", + "strict_checks": { + "actual_bit_above_effective": "11395500113953/30000000300000000", + "actual_logarithmic_gamma_guard": "1/60000000600000000", + "actual_logarithmic_group_guard": "36291940725838793649328233534677/200000004000000020000000000000000", + "alpha_logarithm_absorption": "1/600000006000000000", + "boundary_algebraic_matrix_above_kappa": "79939597799395969/1200000024000000120000000000000000", + "cap_above_band": "163708063274161236350671866465323/400000008000000040000000000000000", + "cap_below_cell": "108875822177516330947984200604031/1200000024000000120000000000000000", + "cap_below_phase_cell_power": "436291948725838823649328133534677/400000008000000040000000000000000", + "complex_above_effective": "1/60000000600000000", + "complex_below_one_over_32": "338758203387581/12000000120000000", + "complex_endpoint": "1/30000000300000000", + "epsilon_below_one": "1/60000000600000000", + "epsilon_positive": "60000000599999999/60000000600000000", + "fused_gaussian_above_kappa": "79818791798187907/1200000024000000120000000000000000", + "gaussian_above_main": "9939597099395969/600000012000000060000000000000000", + "global_coordinate_router_above_kappa": "1/15000000150000000", + "global_gamma_power_slack": "3/200000002000000000", + "group_below_dimension": "1/30000000300000000", + "group_bit_router_above_kappa": "49909395999093953/600000012000000060000000000000000", + "group_gauge_power_slack": "108875822177516379947984690604031/600000012000000060000000000000000", + "group_key_fits_record": "1/30000000300000000", + "group_positive": "20000000199999999/20000000200000000", + "group_scans_above_kappa": "14954697899546977/15000000150000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_online_final": "644589790400418148631/500000000000000000000000", + "improvement_over_pkg_k2": "1342157392794717479267911225169191627777122102965890395790280701170194526587548469132116575062403/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1699": "1342508268656645435748941712936355250934431507/1000000000000000000000000000000000000000000000000", + "improvement_over_pr1712": "6712541343283227178741362020680007884145727138632283638941299969772687285461029288600736779707649/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1758": "1340404491197700948453466314800026327686526580209199320247542619067215757027414399369818327775017/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1786": "13403952118499510912194521335000000000000000000000000000000001999999800001/10000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1828": "2680790087748910957328658012158594846003377122994839409079344959674400000000000000000000000004006719019826502178085342683975683/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1839": "6701975219372277393321645030396487115008442807487098522698362399185677258698371805868475000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1875": "6701975219372277393321645030396487115008442807487098522698362399185677258698371805868471719335776838627743415457068895139647759399172939286143496816535216421325187363046885361425772909502231218314437622205930116079297234806627210590217190600996553729143901162562581526621534715086055386213403722175000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1876": "670197521937227739332164503039648711500844280748709852269836239918567725869837180586847171933577683862774341545706889513964775939917293928614349681653521642132518736304688536142577290950223121831443762220593011607929723480662721059021719060099655372914390116256258152662153471508605538621340372217196657216794137380775174500330086462142358142864921147118845386980694114022172311249292673931726844600000000000000000001001679754956625544521335670993920702577/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1897": "1340395043874455478664329006079297423001688561497419704539672479837135451739674361173694343867155367725548683091413779027929551879834587857228699363307043284265037472609377072285154581900446243662887524441186023215859446961325442118043438120199310745828780232512516305324306943017211077242680744434393314433588274761550349000660172924284716285729842294237690773961388228044344622498585347863453689118814253082419197486359454032147189198319033143866021423837056207677317517847011467076188001061138620310116832610271556685687769184940440093096226243113127523863162928128796969576356494654526264864467/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_previous_local_final": "644589790400418148631/500000000000000000000000", + "improvement_over_previous_package": "13423300976855635663689448641223998986170598784229341400200650717283025923262102542077285802551153/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_internal": "1/120000001200000000", + "lambda_above_sigma": "1/40000000400000000", + "lambda_above_tau": "1/120000001200000000", + "lambda_prime_above_lambda": "1/120000001200000000", + "lambda_prime_above_leaf": "23963758439637581/720000014400000072000000000000000", + "leaf_saving_above_effective": "11963758319637581/720000014400000072000000000000000", + "main_transform_above_kappa": "19979865866465323/400000008000000040000000000000000", + "membership_arithmetic_fits_record": "1/60000000600000000", + "microbox_face_corrections_above_kappa": "2309909418599093957/30000000300000000", + "microbox_halo_volume": "1580000015800000001/20000000200000000", + "polynomial_products_above_kappa": "59818791598187909/60000000600000000", + "positive_layout_slack": "1/60000000600000000", + "q_below_effective": "1/60000000600000000", + "q_below_internal": "1/60000000600000000", + "q_below_leaf": "23963758439637581/720000014400000072000000000000000", + "q_positive": "60403000604031/20000000200000000", + "short_record_fallback": "11963758319637581/12000000120000000", + "source_axis_superpolynomial": "1/60000000600000000", + "sparse_union_movement_above_kappa": "487500009750000128689597799395969/1200000024000000120000000000000000", + "stop_below_one": "60000000599999999/60000000600000000", + "stop_positive": "1/60000000600000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "1/20000000200000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "1/20000000200000000", + "union_tag_work_per_visit_fits_record": "1/20000000200000000" + } + }, + "local_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "local_paid": { + "1": 2237, + "2": 388, + "3": 494, + "4": 147, + "5": 36, + "8": 8 + }, + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform": [ + "new_complex_uniform_saving_above_b" + ], + "old_BIT": [ + "actual_bit_above_effective" + ], + "unfunded_endpoint": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "4980000049799999751/5000000050000000000", + "fixed_halo_explicit_metadata_branch": "1155000011550000001/15000000150000000", + "new_BIT_row_stock_sublinear_in_active_group": "19940000199399999003/20000000200000000000", + "new_semantic_group_guard": "1/20000000200000000" + }, + "margins": { + "boundary_algebraic_matrix": "3624180072483680302015799395969/1200000024000000120000000000000000", + "fused_gaussian": "3624180072483680181209798187907/1200000024000000120000000000000000", + "global_coordinate_router": "90604500906047/30000000300000000", + "group_bit_router": "1812090036241850090604999093953/600000012000000060000000000000000", + "group_scans": "30000000299999999/30000000300000000", + "main_transform": "1208060024161220100671866465323/400000008000000040000000000000000", + "microbox_face_corrections": "1155000011550000001/15000000150000000", + "polynomial_products": "60000000599999999/60000000600000000", + "sparse_union_movement": "491124189822483729052015799395969/1200000024000000120000000000000000" + }, + "parameters": { + "a": "90604500906047/30000000300000000", + "b": "36241800362419/12000000120000000", + "beta": "20000000199999999/20000000200000000", + "bit_saving": "17/5000", + "cap_xi": "363708067274161256350671866465323/400000008000000040000000000000000", + "complex_uniform_saving": "471898442219/156250001562500", + "d": "1/60000000600000000", + "epsilon": "60000000599999999/60000000600000000", + "kappa": "60403/20000000", + "lambda_": "119637583196375813/120000001200000000", + "lambda_prime": "19939597199395969/20000000200000000", + "layout": "1/60000000600000000", + "q": "60403000604031/20000000200000000", + "r0": "1/600000006000000000", + "stop": "1/60000000600000000", + "tested_saving": "4719/1562500" + }, + "strict_checks": { + "actual_bit_above_effective": "11395500113953/30000000300000000", + "actual_logarithmic_gamma_guard": "1/60000000600000000", + "actual_logarithmic_group_guard": "36291940725838793649328233534677/200000004000000020000000000000000", + "alpha_logarithm_absorption": "1/600000006000000000", + "boundary_algebraic_matrix_above_kappa": "79939597799395969/1200000024000000120000000000000000", + "cap_above_band": "163708063274161236350671866465323/400000008000000040000000000000000", + "cap_below_cell": "108875822177516330947984200604031/1200000024000000120000000000000000", + "cap_below_phase_cell_power": "436291948725838823649328133534677/400000008000000040000000000000000", + "complex_above_effective": "1/60000000600000000", + "complex_below_one_over_32": "338758203387581/12000000120000000", + "complex_endpoint": "1/30000000300000000", + "epsilon_below_one": "1/60000000600000000", + "epsilon_positive": "60000000599999999/60000000600000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "79818791798187907/1200000024000000120000000000000000", + "gaussian_above_main": "9939597099395969/600000012000000060000000000000000", + "global_coordinate_router_above_kappa": "1/15000000150000000", + "global_gamma_power_slack": "3/200000002000000000", + "group_below_dimension": "1/30000000300000000", + "group_bit_router_above_kappa": "49909395999093953/600000012000000060000000000000000", + "group_gauge_power_slack": "108875822177516379947984690604031/600000012000000060000000000000000", + "group_key_fits_record": "1/30000000300000000", + "group_positive": "20000000199999999/20000000200000000", + "group_scans_above_kappa": "14954697899546977/15000000150000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "644589790400418148631/500000000000000000000000", + "lambda_above_internal": "1/120000001200000000", + "lambda_above_sigma": "1/40000000400000000", + "lambda_above_tau": "1/120000001200000000", + "lambda_prime_above_lambda": "1/120000001200000000", + "lambda_prime_above_leaf": "23963758439637581/720000014400000072000000000000000", + "leaf_saving_above_effective": "11963758319637581/720000014400000072000000000000000", + "main_transform_above_kappa": "19979865866465323/400000008000000040000000000000000", + "membership_arithmetic_fits_record": "1/60000000600000000", + "microbox_face_corrections_above_kappa": "2309909418599093957/30000000300000000", + "microbox_halo_volume": "1580000015800000001/20000000200000000", + "new_complex_uniform_saving_above_b": "1/60000000600000000", + "new_semantic_guard_with_C1_one": "1/60000000600000000", + "polynomial_products_above_kappa": "59818791598187909/60000000600000000", + "positive_layout_slack": "1/60000000600000000", + "q_below_effective": "1/60000000600000000", + "q_below_internal": "1/60000000600000000", + "q_below_leaf": "23963758439637581/720000014400000072000000000000000", + "q_positive": "60403000604031/20000000200000000", + "short_record_fallback": "11963758319637581/12000000120000000", + "source_axis_superpolynomial": "1/60000000600000000", + "sparse_union_movement_above_kappa": "487500009750000128689597799395969/1200000024000000120000000000000000", + "stop_below_one": "60000000599999999/60000000600000000", + "stop_positive": "1/60000000600000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "1/20000000200000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "1/20000000200000000", + "union_tag_work_per_visit_fits_record": "1/20000000200000000" + } + }, + "paid": { + "1": 41946, + "16": 448, + "2": 6984, + "24": 448, + "3": 8892, + "32": 448, + "4": 2646, + "40": 448, + "48": 448, + "5": 648, + "56": 448, + "64": 448, + "72": 224, + "8": 144 + }, + "paid_calls": 64620, + "productive_fields": 10928, + "rank_masses": [ + 239886, + 239134 + ], + "rank_surplus": 752, + "raw_nonrecursive": { + "all_unit_bound": 181098496, + "budget": 1000000000, + "local_routes": 4814000, + "local_scalar_allowance": 158168 + }, + "raw_root_bracket": [ + "3020165977/1000000000000", + "30201659771/10000000000000" + ], + "remaining": "Requires independent source-pinned native/operator/phase replay of unchanged candidate and source admission. Arithmetic alone is not a new theorem or selected-frontier promotion.", + "source_hashes": { + "interval_engine": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc", + "outer_ledger": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54", + "p16_controller": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + "status": "PASS_COMPLETE_CONDITIONAL_ARITHMETIC", + "strictification": { + "alpha": { + "lower": "0.999999993770239196201774801294", + "upper": "0.999999993770239196201774801295" + }, + "cutoff": 17, + "delta": { + "lower": "0.958754911244405494833244087511", + "upper": "0.958754911244405494833244087512" + }, + "floor": 21, + "gamma": { + "lower": "0.981011186022465634893464479926", + "upper": "0.981011186022465634893464479927" + }, + "normalized_paid_upper": "6229523134180405573822205648138369893496002293186705214781785035885548582756448251617534293205788280361399914248219628732233377115342340346896692826309003353583023664395111667126627013438759015601681784158229338395982620138553390591711054121687432866169027937060344743466505805235582163801244998330585509930860190887989464846025473266062920352304280751936877280109251646654764919972816357461765791553914030217001373298336894592700908739840020830782668764032651243134426911822421460574174100616438599706056299537262115804871704688914689373128769286286441903868790576591126614919398101254059074768626296592469772983538333886406530190124181630203619339392855061376486894432166104005450358513152890074190031597754121597486234146496826755753525249088740494873825322835346674015361904612968947935290655070628913220860743527730156263558123911845410965359082808947500334602544760301727097880306837533410182698691237326016779030510948664147817129741605385215597443099210568044460460218330851264787440033655604150527202468191178214835260591978620015412761099388996707874744858066199956768269933380914467692336784160854932013489135707395541189266787666247518951163062420005199646107790919889402089271852508343427404421693598186094104964048006840762777059320868476057922527167151885840801845420416673590450019259670978141147244182458668488830582107727939564092151279160935860067475494239151243467194749894805431086389230616321068960271106765381401915889117473724738390020444607339159336581697565050445155181776178389457775778659737744481574926142967802610525759369499219530611016812986384829557689094972718235856566929162341427470296983511969172163610349733483623613474944701521568817109339855258516824110066109558936420653084198390810489237916347213057314403656252720188463900032903545691874964066185881651769781972676402214066115895449186119157050652119546712152037253860444506533136367669085095798453189544132884923864885792238916045317743632788081816677925922094695413261880302035643138587965744453748815656145777971826364174624509758481888079367462723085813446382357168276821837073047675418244008371022731129204673089912247454752053812290757274794090911734011643177038601380625017091774313676330733263828185989501122408378815184079644414747032007825185990484272107033172065121398509515269730220519446465730193842510354549879437353327981589640558721078133243392753792216569059033901804744737524920543093507591915081192242009789062254461336738154328178620755765057081003000574691619784836466407592467341049846816057959439962370772514598096717438458705312418622547880203790946677032850527951904100865362844514622076026251343547814053811976416029242947275031841388848595942033172715010691647552223441464756983005879684153919675714718000548336268652388474997563410499492248327139575585702298216062209707537556553290741742913218701479137944425056884064657517148761002971039020259717398760115370128581634817224509484601042525516499221732880910079142374012417543469838795692430385550160541487431270183221153315494819157015691105313390273793712515439818994761837679879815757873614493853283176897692134785698289891666730997698419929914069235673565709966781062872853754991832511125687368465677044804684036190278867249997498602037171/6229523185240436722790793730350330486505008077061908274314028103253636090218348047304841685642221979267553674599084787043006070378310994556879657277663210177223557285558131187708429487302490342721255889674366606987744750457618567824326218659646918141246246438757155714300304266156992623057650934094266191076034757952450425725071696140664274944327057015822641303719863483031557284784972994705602996468729162293872251545898819594756255526066569274366846453716561882174573838710784912109375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "tail_offset": "1/8", + "tensor_power": 682, + "tested": "4719/1562500" + }, + "targets": { + "145": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 504, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "7": 126, + "73": 224, + "8": 846, + "9": 5868 + }, + "tested": "4719/1562500" +} diff --git a/research/compact-joint-compiler/arithmetic/controller.json b/research/compact-joint-compiler/arithmetic/controller.json new file mode 100644 index 0000000000..49a2f06758 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/controller.json @@ -0,0 +1,5224 @@ +{ + "ambient_rank": 145, + "boundaries": { + "left": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "left_program": [ + [ + "SWAP", + 30, + 31 + ], + [ + "SWAP", + 29, + 30 + ], + [ + "SWAP", + 28, + 30 + ], + [ + "SWAP", + 27, + 29 + ], + [ + "SWAP", + 26, + 28 + ], + [ + "SWAP", + 25, + 30 + ], + [ + "SWAP", + 24, + 25 + ], + [ + "SWAP", + 23, + 26 + ], + [ + "SWAP", + 22, + 30 + ], + [ + "SWAP", + 20, + 26 + ], + [ + "SWAP", + 19, + 22 + ], + [ + "SWAP", + 18, + 29 + ], + [ + "SWAP", + 17, + 23 + ], + [ + "SWAP", + 16, + 27 + ], + [ + "SCALE", + 15, + "-1" + ], + [ + "SWAP", + 15, + 31 + ], + [ + "ADD", + 12, + 14, + "1" + ], + [ + "ADD", + 10, + 14, + "-1" + ], + [ + "ADD", + 8, + 14, + "1" + ], + [ + "ADD", + 6, + 14, + "-1" + ], + [ + "ADD", + 4, + 14, + "1" + ], + [ + "ADD", + 2, + 14, + "-1" + ], + [ + "ADD", + 0, + 14, + "1" + ], + [ + "SWAP", + 14, + 15 + ], + [ + "ADD", + 31, + 13, + "1" + ], + [ + "SWAP", + 13, + 30 + ], + [ + "ADD", + 10, + 12, + "1" + ], + [ + "ADD", + 8, + 12, + "-1" + ], + [ + "ADD", + 6, + 12, + "1" + ], + [ + "ADD", + 4, + 12, + "-1" + ], + [ + "ADD", + 2, + 12, + "1" + ], + [ + "ADD", + 0, + 12, + "-1" + ], + [ + "SWAP", + 12, + 14 + ], + [ + "ADD", + 31, + 11, + "-1" + ], + [ + "ADD", + 30, + 11, + "-1" + ], + [ + "SCALE", + 11, + "-1" + ], + [ + "SWAP", + 11, + 29 + ], + [ + "ADD", + 8, + 10, + "1" + ], + [ + "ADD", + 6, + 10, + "-1" + ], + [ + "ADD", + 4, + 10, + "1" + ], + [ + "ADD", + 2, + 10, + "-1" + ], + [ + "ADD", + 0, + 10, + "1" + ], + [ + "SWAP", + 10, + 13 + ], + [ + "ADD", + 31, + 9, + "1" + ], + [ + "ADD", + 30, + 9, + "1" + ], + [ + "ADD", + 29, + 9, + "1" + ], + [ + "SWAP", + 9, + 28 + ], + [ + "ADD", + 6, + 8, + "1" + ], + [ + "ADD", + 4, + 8, + "-1" + ], + [ + "ADD", + 2, + 8, + "1" + ], + [ + "ADD", + 0, + 8, + "-1" + ], + [ + "SWAP", + 8, + 12 + ], + [ + "ADD", + 31, + 7, + "-1" + ], + [ + "ADD", + 30, + 7, + "-1" + ], + [ + "ADD", + 29, + 7, + "-1" + ], + [ + "ADD", + 28, + 7, + "-1" + ], + [ + "SCALE", + 7, + "-1" + ], + [ + "SWAP", + 7, + 27 + ], + [ + "ADD", + 4, + 6, + "1" + ], + [ + "ADD", + 2, + 6, + "-1" + ], + [ + "ADD", + 0, + 6, + "1" + ], + [ + "SWAP", + 6, + 11 + ], + [ + "ADD", + 31, + 5, + "1" + ], + [ + "ADD", + 30, + 5, + "1" + ], + [ + "ADD", + 29, + 5, + "1" + ], + [ + "ADD", + 28, + 5, + "1" + ], + [ + "ADD", + 27, + 5, + "1" + ], + [ + "SWAP", + 5, + 26 + ], + [ + "ADD", + 2, + 4, + "1" + ], + [ + "ADD", + 0, + 4, + "-1" + ], + [ + "SWAP", + 4, + 10 + ], + [ + "ADD", + 31, + 3, + "-1" + ], + [ + "ADD", + 30, + 3, + "-1" + ], + [ + "ADD", + 29, + 3, + "-1" + ], + [ + "ADD", + 28, + 3, + "-1" + ], + [ + "ADD", + 27, + 3, + "-1" + ], + [ + "ADD", + 26, + 3, + "-1" + ], + [ + "SCALE", + 3, + "-1" + ], + [ + "SWAP", + 3, + 25 + ], + [ + "ADD", + 0, + 2, + "1" + ], + [ + "SWAP", + 2, + 9 + ], + [ + "ADD", + 31, + 1, + "1" + ], + [ + "ADD", + 30, + 1, + "1" + ], + [ + "ADD", + 29, + 1, + "1" + ], + [ + "ADD", + 28, + 1, + "1" + ], + [ + "ADD", + 27, + 1, + "1" + ], + [ + "ADD", + 26, + 1, + "1" + ], + [ + "ADD", + 25, + 1, + "1" + ], + [ + "SWAP", + 1, + 24 + ], + [ + "SWAP", + 0, + 8 + ] + ], + "right": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "right_program": [ + [ + "ADD", + 30, + 31, + "-1" + ], + [ + "ADD", + 29, + 31, + "-1" + ], + [ + "ADD", + 28, + 31, + "-1" + ], + [ + "ADD", + 27, + 31, + "-1" + ], + [ + "SCALE", + 31, + "-1" + ], + [ + "ADD", + 31, + 30, + "-1" + ], + [ + "ADD", + 29, + 30, + "-1" + ], + [ + "ADD", + 28, + 30, + "-1" + ], + [ + "ADD", + 27, + 30, + "-1" + ], + [ + "ADD", + 31, + 29, + "-1" + ], + [ + "ADD", + 28, + 29, + "-1" + ], + [ + "ADD", + 27, + 29, + "-1" + ], + [ + "SCALE", + 29, + "-1" + ], + [ + "ADD", + 31, + 28, + "-1" + ], + [ + "ADD", + 27, + 28, + "-1" + ], + [ + "SWAP", + 28, + 29 + ], + [ + "ADD", + 31, + 27, + "-1" + ], + [ + "SCALE", + 27, + "-1" + ], + [ + "SWAP", + 27, + 29 + ], + [ + "ADD", + 31, + 26, + "1" + ], + [ + "SWAP", + 26, + 29 + ], + [ + "ADD", + 29, + 25, + "-1" + ], + [ + "ADD", + 24, + 25, + "-1" + ], + [ + "SWAP", + 25, + 28 + ], + [ + "ADD", + 28, + 24, + "1" + ], + [ + "SWAP", + 23, + 29 + ], + [ + "SWAP", + 22, + 25 + ], + [ + "SWAP", + 20, + 23 + ], + [ + "SWAP", + 19, + 25 + ], + [ + "SWAP", + 18, + 27 + ], + [ + "SWAP", + 17, + 29 + ], + [ + "SWAP", + 16, + 31 + ], + [ + "ADD", + 14, + 15, + "-1" + ], + [ + "SWAP", + 15, + 30 + ], + [ + "ADD", + 13, + 14, + "-1" + ], + [ + "SWAP", + 14, + 30 + ], + [ + "ADD", + 12, + 13, + "-1" + ], + [ + "SWAP", + 13, + 22 + ], + [ + "ADD", + 11, + 12, + "-1" + ], + [ + "SWAP", + 12, + 30 + ], + [ + "ADD", + 10, + 11, + "-1" + ], + [ + "SWAP", + 11, + 18 + ], + [ + "ADD", + 9, + 10, + "-1" + ], + [ + "SWAP", + 10, + 22 + ], + [ + "ADD", + 8, + 9, + "-1" + ], + [ + "SWAP", + 9, + 26 + ], + [ + "SWAP", + 8, + 30 + ], + [ + "SWAP", + 7, + 16 + ], + [ + "SWAP", + 6, + 18 + ], + [ + "SWAP", + 5, + 20 + ], + [ + "SWAP", + 4, + 22 + ], + [ + "SWAP", + 3, + 24 + ], + [ + "SWAP", + 2, + 26 + ], + [ + "SWAP", + 1, + 28 + ], + [ + "SWAP", + 0, + 30 + ] + ] + }, + "diagonal": [ + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ] + ], + "invoice": { + "main": { + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 46446, + "2": 12834, + "3": 4032, + "4": 1836, + "5": 360, + "8": 144, + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + }, + "paid_calls": 69012, + "productive_fields": 10928, + "rank_surplus": 752, + "raw_scalar_record_bound": 1000000000, + "targets": { + "5": 504, + "6": 324, + "7": 1008, + "8": 1674, + "9": 3834, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "thick_calls": 18, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ], + "thin_queries": 1680, + "whole_idle": { + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + } + }, + "keep_mask": 35047648968703, + "kind": "complex", + "pairs": 16, + "physical_events": [ + [ + "LOCAL", + 0, + 0, + false + ], + [ + "LOCAL", + 1, + 0, + true + ], + [ + "IDLE", + 1, + [ + 0, + 1 + ] + ], + [ + "ADD", + 0, + 2, + 1 + ], + [ + "ADD", + 3, + 1, + -1 + ], + [ + "QUERY_SHEAR", + 2, + 0, + false + ], + [ + "ADD", + 0, + 2, + -1 + ], + [ + "ADD", + 3, + 1, + 1 + ], + [ + "LOCAL", + 3, + 1, + true + ], + [ + "IDLE", + 2, + [ + 0, + 1, + 3 + ] + ], + [ + "ADD", + 2, + 4, + 1 + ], + [ + "ADD", + 5, + 3, + -1 + ], + [ + "QUERY_SHEAR", + 4, + 1, + false + ], + [ + "ADD", + 2, + 4, + -1 + ], + [ + "ADD", + 5, + 3, + 1 + ], + [ + "LOCAL", + 5, + 2, + true + ], + [ + "IDLE", + 3, + [ + 0, + 1, + 3, + 5 + ] + ], + [ + "ADD", + 4, + 6, + 1 + ], + [ + "ADD", + 7, + 5, + -1 + ], + [ + "QUERY_SHEAR", + 6, + 2, + false + ], + [ + "ADD", + 4, + 6, + -1 + ], + [ + "ADD", + 7, + 5, + 1 + ], + [ + "LOCAL", + 7, + 3, + true + ], + [ + "IDLE", + 4, + [ + 0, + 1, + 3, + 5, + 7 + ] + ], + [ + "ADD", + 6, + 8, + 1 + ], + [ + "ADD", + 9, + 7, + -1 + ], + [ + "QUERY_SHEAR", + 8, + 3, + false + ], + [ + "ADD", + 6, + 8, + -1 + ], + [ + "ADD", + 9, + 7, + 1 + ], + [ + "LOCAL", + 9, + 4, + true + ], + [ + "IDLE", + 5, + [ + 0, + 1, + 3, + 5, + 7, + 9 + ] + ], + [ + "ADD", + 8, + 10, + 1 + ], + [ + "ADD", + 11, + 9, + -1 + ], + [ + "QUERY_SHEAR", + 10, + 4, + false + ], + [ + "ADD", + 8, + 10, + -1 + ], + [ + "ADD", + 11, + 9, + 1 + ], + [ + "LOCAL", + 11, + 5, + true + ], + [ + "IDLE", + 6, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11 + ] + ], + [ + "ADD", + 10, + 12, + 1 + ], + [ + "ADD", + 13, + 11, + -1 + ], + [ + "QUERY_SHEAR", + 12, + 5, + false + ], + [ + "ADD", + 10, + 12, + -1 + ], + [ + "ADD", + 13, + 11, + 1 + ], + [ + "LOCAL", + 13, + 6, + true + ], + [ + "IDLE", + 7, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13 + ] + ], + [ + "ADD", + 12, + 14, + 1 + ], + [ + "ADD", + 15, + 13, + -1 + ], + [ + "QUERY_SHEAR", + 14, + 6, + false + ], + [ + "ADD", + 12, + 14, + -1 + ], + [ + "ADD", + 15, + 13, + 1 + ], + [ + "LOCAL", + 15, + 7, + true + ], + [ + "ADD", + 14, + 16, + 1 + ], + [ + "ADD", + 17, + 15, + -1 + ], + [ + "QUERY_SHEAR", + 16, + 7, + false + ], + [ + "ADD", + 14, + 16, + -1 + ], + [ + "ADD", + 17, + 15, + 1 + ], + [ + "LOCAL", + 17, + 8, + true + ], + [ + "ADD", + 16, + 18, + 1 + ], + [ + "ADD", + 19, + 17, + -1 + ], + [ + "QUERY_SHEAR", + 18, + 8, + false + ], + [ + "ADD", + 16, + 18, + -1 + ], + [ + "ADD", + 19, + 17, + 1 + ], + [ + "LOCAL", + 19, + 9, + true + ], + [ + "ADD", + 18, + 20, + 1 + ], + [ + "ADD", + 21, + 19, + -1 + ], + [ + "QUERY_SHEAR", + 20, + 9, + false + ], + [ + "ADD", + 18, + 20, + -1 + ], + [ + "ADD", + 21, + 19, + 1 + ], + [ + "LOCAL", + 21, + 10, + true + ], + [ + "ADD", + 20, + 22, + 1 + ], + [ + "ADD", + 23, + 21, + -1 + ], + [ + "QUERY_SHEAR", + 22, + 10, + false + ], + [ + "ADD", + 20, + 22, + -1 + ], + [ + "ADD", + 23, + 21, + 1 + ], + [ + "LOCAL", + 23, + 11, + true + ], + [ + "ADD", + 22, + 24, + 1 + ], + [ + "ADD", + 25, + 23, + -1 + ], + [ + "QUERY_SHEAR", + 24, + 11, + false + ], + [ + "ADD", + 22, + 24, + -1 + ], + [ + "ADD", + 25, + 23, + 1 + ], + [ + "LOCAL", + 25, + 12, + true + ], + [ + "ADD", + 24, + 26, + 1 + ], + [ + "ADD", + 27, + 25, + -1 + ], + [ + "QUERY_SHEAR", + 26, + 12, + false + ], + [ + "ADD", + 24, + 26, + -1 + ], + [ + "ADD", + 27, + 25, + 1 + ], + [ + "LOCAL", + 27, + 13, + true + ], + [ + "ADD", + 26, + 28, + 1 + ], + [ + "ADD", + 29, + 27, + -1 + ], + [ + "QUERY_SHEAR", + 28, + 13, + false + ], + [ + "ADD", + 26, + 28, + -1 + ], + [ + "ADD", + 29, + 27, + 1 + ], + [ + "LOCAL", + 29, + 14, + true + ], + [ + "ADD", + 28, + 30, + 1 + ], + [ + "ADD", + 31, + 29, + -1 + ], + [ + "QUERY_SHEAR", + 30, + 14, + false + ], + [ + "ADD", + 28, + 30, + -1 + ], + [ + "ADD", + 31, + 29, + 1 + ], + [ + "LOCAL", + 31, + 15, + true + ], + [ + "LOCAL", + 32, + 15, + false + ], + [ + "IDLE", + 7, + [ + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 8, + [ + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 9, + [ + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 10, + [ + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 11, + [ + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 12, + [ + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 13, + [ + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 14, + [ + 31, + 32 + ] + ], + [ + "ADD", + 30, + 28, + 1 + ], + [ + "ADD", + 29, + 31, + -1 + ], + [ + "ADD", + 28, + 26, + 1 + ], + [ + "ADD", + 27, + 29, + -1 + ], + [ + "ADD", + 26, + 24, + 1 + ], + [ + "ADD", + 25, + 27, + -1 + ], + [ + "ADD", + 24, + 22, + 1 + ], + [ + "ADD", + 23, + 25, + -1 + ], + [ + "ADD", + 22, + 20, + 1 + ], + [ + "ADD", + 21, + 23, + -1 + ], + [ + "ADD", + 20, + 18, + 1 + ], + [ + "ADD", + 19, + 21, + -1 + ], + [ + "ADD", + 18, + 16, + 1 + ], + [ + "ADD", + 17, + 19, + -1 + ], + [ + "ADD", + 16, + 14, + 1 + ], + [ + "ADD", + 15, + 17, + -1 + ], + [ + "ADD", + 14, + 12, + 1 + ], + [ + "ADD", + 13, + 15, + -1 + ], + [ + "ADD", + 12, + 10, + 1 + ], + [ + "ADD", + 11, + 13, + -1 + ], + [ + "ADD", + 10, + 8, + 1 + ], + [ + "ADD", + 9, + 11, + -1 + ], + [ + "ADD", + 8, + 6, + 1 + ], + [ + "ADD", + 7, + 9, + -1 + ], + [ + "ADD", + 6, + 4, + 1 + ], + [ + "ADD", + 5, + 7, + -1 + ], + [ + "ADD", + 4, + 2, + 1 + ], + [ + "ADD", + 3, + 5, + -1 + ], + [ + "ADD", + 2, + 0, + 1 + ], + [ + "ADD", + 1, + 3, + -1 + ], + [ + "SIGNED_SWAP", + 0, + 1 + ], + [ + "SIGNED_SWAP", + 2, + 3 + ], + [ + "SIGNED_SWAP", + 4, + 5 + ], + [ + "SIGNED_SWAP", + 6, + 7 + ], + [ + "SIGNED_SWAP", + 8, + 9 + ], + [ + "SIGNED_SWAP", + 10, + 11 + ], + [ + "SIGNED_SWAP", + 12, + 13 + ], + [ + "SIGNED_SWAP", + 14, + 15 + ], + [ + "SIGNED_SWAP", + 16, + 17 + ], + [ + "SIGNED_SWAP", + 18, + 19 + ], + [ + "SIGNED_SWAP", + 20, + 21 + ], + [ + "SIGNED_SWAP", + 22, + 23 + ], + [ + "SIGNED_SWAP", + 24, + 25 + ], + [ + "SIGNED_SWAP", + 26, + 27 + ], + [ + "SIGNED_SWAP", + 28, + 29 + ], + [ + "SIGNED_SWAP", + 30, + 31 + ] + ], + "prefix_pairs": 7 +} diff --git a/research/compact-joint-compiler/arithmetic/intervals.py b/research/compact-joint-compiler/arithmetic/intervals.py new file mode 100644 index 0000000000..a3e546693f --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/intervals.py @@ -0,0 +1,111 @@ +"""Verbatim exact interval primitives from zxv, higher-moment-strictification. +Source: CrocSwap/integer-mult-bounds at 2a13eb1827784206202db90e5dc8327cf8a250db. +Apache-2.0. Substantial OpenAI Codex assistance. Retained source attribution. +This file checks rational arithmetic, not native or all-size hypotheses. +""" +from fractions import Fraction as Q +from functools import lru_cache +GRID=2**192 + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + diff --git a/research/compact-joint-compiler/arithmetic/legacy-source.txt b/research/compact-joint-compiler/arithmetic/legacy-source.txt new file mode 100644 index 0000000000..20d21008b3 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/legacy-source.txt @@ -0,0 +1,128 @@ +# Verbatim retained ledger function and historical comparison constants. +# Sources: PR1786 Chafik Boukhalfa / chafreaky, Tim Trudgian; PR1731 Jeremy Kothe et al.; +# Vlado Vojdanovski / PR1673; retained higher-moment compiler lineage. +# Apache-2.0; substantial OpenAI assistance. No all-size theorem proved by arithmetic. +KAPPA_1828=Q('0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585') # exact kappa of rohanarun's PR1828 (slack refinement of PR1800 at 1e-96), from its body + + +KAPPA_1839=Q('0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263049999999997996640490086748910957328658012158594') # exact kappa of PR1839 (previous package: 1e-90 endpoint) + + +KAPPA_1875=Q('0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561328446322744513169085862209720704481201654121427713006366929567157349625273906229277148454180995537563371124755588139767841405530386745578819565618798006892541712197674874836946756930569827889227573192555649999999997996640490086748910957328658012158594') # exact kappa of rohanarun's PR1875 (1e-300 endpoint), from its body + + +KAPPA_1876=Q('0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844632274451316908586220972070448120165412142771300636692956715734962527390622927714845418099553756337112475558813976784140553038674557881956561879800689254171219767487483694675693056982788922757319255565606685566411725238449650999339827075715283714270157705762309226038611771955655377501414652136546310799999999999999999997996640490086748910957328658012158594846') # exact kappa of rohanarun's PR1876 (1e-400 endpoint), from its body + + +KAPPA_1897=Q('0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844632274451316908586220972070448120165412142771300636692956715734962527390622927714845418099553756337112475558813976784140553038674557881956561879800689254171219767487483694675693056982788922757319255565606685566411725238449650999339827075715283714270157705762309226038611771955655377501414652136546310881185746917580802513640545967852810801680966856133978576162943792322682482152988532923811998938861379689883167389728443314312230815059559906903773756886872476136837071871203030423643505345473735135533') # exact kappa of M6LI's PR1897 (1e-500 grid), from its body + + +KAPPA_1786=Q('0.0016797547881500489087805478664999999999999999999999999999999998000000199999') # exact kappa of chafreaky's PR1786 ledger (EXPECTED-BALANCE.json), headline 0.001679754788150048 + + +KAPPA_PKG5=Q('0.001677992607205282520732088774830808372222877897034109604209719298829805473412451530867883424937597') # previous package (rectangular k=2, tau_eff=2.2500351) + + +KAPPA_PKG4=Q('0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847') # previous package (radix union schedule, square boundary tau=2.372864) + + +KAPPA_1712=Q('0.0016776417313433545642517275958639984231708545722735432722117400060454625429077941422798526440584702') # pkg of PR1712 (Le Gall tau=12/5, old union row) + + +KAPPA_1699=Q('0.001677641731343354564251058287063644749065568493') # exact kappa of PR1699's ledger (Chafik Boukhalfa), same supplier profile + + +def ledger(kind, *, q_=q, zeta=ZETA, slack=SLACK, + old_scan=False, full_gauge=False, full_key=False, old_union=False, old_theta=False, old_linear=False, old_tag=False, + eps_=EPS, beta_=BETA, tau_eff=STRASSEN_TAU, halo_power=HALO_POWER, core_power=CORE_POWER): + r=R0; stop=STOP + # Existing explicit Strassen format, 7^16<2^45; c=3/32. + # Union: radix-distributed schedule (outer/UNION-SCHEDULE.md, new in this package): row exponent eps+1/2-xi. The boundary row binds with main; the Gaussian row has slack at this explicit point. + c=(3-tau_eff)/2 + eps=eps_; beta=beta_ + xi=eps*(1+q_)-c+slack + saving=eps*q_ + # Deliberate strict gap (BACKOFF) after decimal truncation to the FLOOR grid. + kappa=Q((saving*FLOOR).__floor__(),FLOOR)-BACKOFF + # kappa is derived, not silently asserted to equal an expected decimal. + tau=1-a; sigma=1-b + internal=tau+(1-stop)*max(sigma-tau,Q(0)) + leaf=sigma+stop*(1-sigma) + lam=1-(q_+a)/2 + key=beta+1-eps + margins={ + 'main_transform':saving, + 'global_coordinate_router':a, + 'fused_gaussian':1-eps+q_*beta, + 'group_bit_router':1-eps+a*beta, + 'group_scans':1-eps+beta, + 'boundary_algebraic_matrix':c+xi-eps, + 'sparse_union_movement':xi+Q(1,2)-eps, + 'polynomial_products':eps, + 'microbox_face_corrections':1-(eps+beta+halo_power-core_power+2), + } + if old_union:margins['old_g_factor_union_row']=1-eps-beta-Q(1,2)+xi + if old_scan:margins['old_per_axis_scan']=1-eps + if full_key:margins['unnecessary_full_key_sort']=margins['sparse_union_movement']-key + checks={ + 'actual_bit_above_effective':bit-a, + 'complex_above_effective':b-a, + 'q_positive':q_, 'complex_endpoint':b-q_, + 'q_below_effective':a-q_, 'stop_positive':stop, + 'stop_below_one':1-stop, + 'leaf_saving_above_effective':(1-stop)*b-a, + 'q_below_internal':1-internal-q_, 'q_below_leaf':1-leaf-q_, + 'lambda_above_tau':lam-tau, 'lambda_above_sigma':lam-sigma, + 'lambda_above_internal':lam-internal, + 'lambda_prime_above_lambda':1-q_-lam, + 'lambda_prime_above_leaf':1-q_-leaf, + 'epsilon_positive':eps,'epsilon_below_one':1-eps, + 'cap_above_band':xi-Q(1,2),'cap_below_cell':eps-xi, + 'group_positive':beta,'group_below_dimension':eps-beta, + 'support_router_span':1-beta, + 'group_gauge_power_slack':1-(2*xi-THETA_POWER)-r-beta, + 'actual_logarithmic_group_guard':1-(2*xi-THETA_POWER)-beta, + 'global_gamma_power_slack':1-eps-r, + 'actual_logarithmic_gamma_guard':1-eps, + 'alpha_logarithm_absorption':r, + 'group_key_fits_record':1-key, + 'membership_arithmetic_fits_record':1-beta-2*(1-eps), + 'microbox_halo_volume':core_power-halo_power-beta, + 'positive_layout_slack':slack, + 'short_record_fallback':eps-a, + 'improvement_over_online_final':kappa-online, + 'improvement_over_previous_local_final':kappa-old, + 'complex_below_one_over_32':Q(1,32)-b, + } + checks['strassen_integer_power_gap']=Q(2**tau_eff.numerator-7**tau_eff.denominator) + checks['theta_positive_polynomial_power']=THETA_POWER + checks['cap_below_phase_cell_power']=THETA_POWER-xi + checks['halo_covers_generic_inverse_radius']=Q(halo_power-43) + checks['union_tag_work_per_visit_fits_record']=1-beta + checks['union_header_fits_record']=1-beta + checks['source_axis_superpolynomial']=1-eps + checks['improvement_over_pr1786']=kappa-KAPPA_1786 + checks['improvement_over_pr1828']=kappa-KAPPA_1828 + checks['improvement_over_pr1839']=kappa-KAPPA_1839 + checks['improvement_over_pr1875']=kappa-KAPPA_1875 + checks['improvement_over_pr1876']=kappa-KAPPA_1876 + checks['improvement_over_pr1897']=kappa-KAPPA_1897 + checks['improvement_over_pr1758']=kappa-Q('0.001679745508802299051546533685199973672313473419790800679752457380932784242972585600630181672224983') + checks['improvement_over_pr1699']=kappa-KAPPA_1699 + checks['improvement_over_pr1712']=kappa-KAPPA_1712 + checks['improvement_over_previous_package']=kappa-KAPPA_PKG4 + checks['improvement_over_pkg_k2']=kappa-KAPPA_PKG5 + if full_gauge:checks['unrecentered_group_gauge']=1-THETA_POWER-r-beta + if old_theta:checks['old_theta_chirp_guard']=1-(2*xi-eps)-r-beta + if old_linear:checks['old_linear_guard']=1-xi-r-beta + if old_tag:checks['old_union_tag_2beta']=1-2*beta + # Main-binding family invariant (PR2180): the Gaussian saving stays above the main saving. The fixed kappa grid (FLOOR) is coarser than the free gaps, + # so the *_above_kappa rows alone would no longer exclude a beta outside the main-binding window; this row is delta*(1-2q) > 0. + checks['gaussian_above_main']=margins['fused_gaussian']-saving + checks.update({n+'_above_kappa':v-kappa for n,v in margins.items()}) + assert margins['boundary_algebraic_matrix']==saving+slack + assert margins['sparse_union_movement']==saving+slack+(tau_eff-2)/2 + return {'kind':kind,'kappa':kappa,'epsilon':eps,'xi':xi,'beta':beta, + 'q':q_,'a':a,'r0':r,'zeta':zeta,'slack':slack, + 'margins':margins,'strict_checks':checks} + diff --git a/research/compact-joint-compiler/arithmetic/legacy.py b/research/compact-joint-compiler/arithmetic/legacy.py new file mode 100644 index 0000000000..5c6139ddaa --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/legacy.py @@ -0,0 +1,21 @@ +"""Independent 63-predicate retained outer ledger at an explicit finer grid. +Source notices and exact retained function are in legacy-source.txt. +Apache-2.0. Substantial OpenAI Codex assistance. +""" +from fractions import Fraction as Q +from pathlib import Path +from hashlib import sha256 + +def need(ok,message): + if not ok:raise ValueError(message) + +def check(params,outer,kappa): + source=Path(__file__).resolve().with_name('legacy-source.txt');raw=source.read_bytes() + d=params['d'];eps,beta,q,a=(params[k]for k in('epsilon','beta','q','a'));grid=10**20 + backoff=Q((eps*q*grid).__floor__(),grid)-kappa;need(backoff>0,'Positive exact refined-grid backoff') + env={'Q':Q,'R0':params['r0'],'ZETA':Q(1,10**8),'SLACK':d,'STOP':d,'FLOOR':grid,'BACKOFF':backoff,'EPS':eps,'BETA':beta,'THETA_POWER':Q(2),'HALO_POWER':48,'CORE_POWER':128,'STRASSEN_TAU':Q(45,16),'b':params['b'],'q':q,'a':a,'bit':params['bit_saving'],'online':Q('0.001730970419199163702738'),'old':Q('0.001730970419199163702738')} + exec(compile(raw,'frozen legacy outer source','exec'),env) + result=env['ledger']('compact4470') + need(result['kappa']==kappa and result['margins']==outer['margins'],'Independent nine-row agreement') + need(len(result['strict_checks'])==63 and all(x>0 for x in result['strict_checks'].values()),'All 63 legacy predicates') + return {'strict_checks':result['strict_checks'],'grid':grid,'backoff':backoff,'nine_row_agreement':True,'source_sha256':sha256(raw).hexdigest()} diff --git a/research/compact-joint-compiler/arithmetic/ordinary-bit.json b/research/compact-joint-compiler/arithmetic/ordinary-bit.json new file mode 100644 index 0000000000..0e9994ff03 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/ordinary-bit.json @@ -0,0 +1,8 @@ +{ + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" +} diff --git a/research/compact-joint-compiler/arithmetic/outer_ledger.py b/research/compact-joint-compiler/arithmetic/outer_ledger.py new file mode 100644 index 0000000000..79d5530794 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/outer_ledger.py @@ -0,0 +1,78 @@ +"""Verbatim 54-predicate endpoint ledger from the retained PR4359/4433 chain. +Credits: zxv, Jacob Alan Sussman, and the retained outer_parameters.py lineage. +Apache-2.0. Substantial OpenAI assistance. Arithmetic only. +""" +from fractions import Fraction as Q +OLD_BASELINE=Q('0.001730970419199163702738') + +def ledger(p): + """Recompute all 54 named PR4359 checks with freely supplied parameters.""" + kappa, b, a, q = (p[key] for key in ('kappa', 'b', 'a', 'q')) + epsilon, beta, r0, stop, layout = (p[key] for key in + ('epsilon', 'beta', 'r0', 'stop', 'layout')) + sigma, tau = 1-b, 1-a + internal = tau+(1-stop)*max(sigma-tau, Q(0)) + leaf = sigma+stop*(1-sigma) + lam, c = 1-(q+a)/2, Q(3, 32) + xi, key = epsilon*(1+q)-c+layout, beta+1-epsilon + margins = { + 'main_transform': epsilon*q, + 'global_coordinate_router': a, + 'fused_gaussian': 1-epsilon+q*beta, + 'group_bit_router': 1-epsilon+a*beta, + 'group_scans': 1-epsilon+beta, + 'boundary_algebraic_matrix': c+xi-epsilon, + 'sparse_union_movement': xi+Q(1, 2)-epsilon, + 'polynomial_products': epsilon, + 'microbox_face_corrections': 1-(epsilon+beta+48-128+2), + } + checks = { + 'actual_bit_above_effective': p['bit_saving']-a, + 'complex_above_effective': b-a, + 'q_positive': q, 'complex_endpoint': b-q, 'q_below_effective': a-q, + 'stop_positive': stop, 'stop_below_one': 1-stop, + 'leaf_saving_above_effective': (1-stop)*b-a, + 'q_below_internal': 1-internal-q, 'q_below_leaf': 1-leaf-q, + 'lambda_above_tau': lam-tau, 'lambda_above_sigma': lam-sigma, + 'lambda_above_internal': lam-internal, + 'lambda_prime_above_lambda': 1-q-lam, + 'lambda_prime_above_leaf': 1-q-leaf, + 'epsilon_positive': epsilon, 'epsilon_below_one': 1-epsilon, + 'cap_above_band': xi-Q(1, 2), 'cap_below_cell': epsilon-xi, + 'group_positive': beta, 'group_below_dimension': epsilon-beta, + 'support_router_span': 1-beta, + 'group_gauge_power_slack': 1-(2*xi-2)-r0-beta, + 'actual_logarithmic_group_guard': 1-(2*xi-2)-beta, + 'global_gamma_power_slack': 1-epsilon-r0, + 'actual_logarithmic_gamma_guard': 1-epsilon, + 'alpha_logarithm_absorption': r0, + 'group_key_fits_record': 1-key, + 'membership_arithmetic_fits_record': 1-beta-2*(1-epsilon), + 'microbox_halo_volume': 128-48-beta, + 'positive_layout_slack': layout, + 'short_record_fallback': epsilon-a, + 'complex_below_one_over_32': Q(1, 32)-b, + 'strassen_integer_power_gap': Q(2**45-7**16), + 'theta_positive_polynomial_power': Q(2), + 'cap_below_phase_cell_power': 2-xi, + 'halo_covers_generic_inverse_radius': Q(48-43), + 'union_tag_work_per_visit_fits_record': 1-beta, + 'union_header_fits_record': 1-beta, + 'source_axis_superpolynomial': 1-epsilon, + 'gaussian_above_main': margins['fused_gaussian']-margins['main_transform'], + 'new_complex_uniform_saving_above_b': p['complex_uniform_saving']-b, + 'improvement_over_user_baseline': kappa-OLD_BASELINE, + 'new_semantic_guard_with_C1_one': 1-epsilon, + 'fine_prime_halo_umbrella': 10-(2*2+2+Q(1, 2)), + } + checks.update({name+'_above_kappa': value-kappa for name, value in margins.items()}) + # These are the additional functional conditions in the independent + # PR4359 outer_transfer_audit.py, beyond the 54-row parameter ledger. + functional = { + 'new_semantic_group_guard': 1-beta, + 'new_BIT_row_stock_sublinear_in_active_group': beta*(1-Q(3, 1000)), + 'fixed_halo_explicit_metadata_branch': 128-48-epsilon-beta-1, + } + return {'parameters': dict(p, cap_xi=xi, lambda_=lam, lambda_prime=1-q), + 'margins': margins, 'strict_checks': checks, 'functional_checks': functional} + diff --git a/research/compact-joint-compiler/arithmetic/profile.json b/research/compact-joint-compiler/arithmetic/profile.json new file mode 100644 index 0000000000..5e15c508ec --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/profile.json @@ -0,0 +1,16 @@ +{ + "helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "paid": { + "1": 2237, + "2": 388, + "3": 494, + "4": 147, + "5": 36, + "8": 8 + } +} diff --git a/research/compact-joint-compiler/arithmetic/verify.py b/research/compact-joint-compiler/arithmetic/verify.py new file mode 100644 index 0000000000..d128d2c8c0 --- /dev/null +++ b/research/compact-joint-compiler/arithmetic/verify.py @@ -0,0 +1,113 @@ +"""Same-kappa finite compiler improvement on PR4470's frozen native/controller word. +Preserves kappa=0.00302015; no kappa improvement is claimed. +Retains PR4470, PR4447, PR4440, zxv, Cinna Davis and Jacob Alan Sussman attribution. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +import json,hashlib,sys +sys.path.insert(0,str(Path(__file__).resolve().parent)) +import intervals as E +import outer_ledger as L +import legacy +HERE=Path(__file__).resolve().parent +KAPPA=Q('.00302015');TESTED=Q('.00302016') +LOW=Q('.0030201659770');HIGH=Q('.0030201659771') +H={4:28,7:7,8:47,9:326};N={1:2237,2:388,3:494,4:147,5:36,8:8} + +def need(ok,msg): + if not ok:raise ValueError(msg) + +def encode(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):encode(v)for k,v in x.items()} + if isinstance(x,(list,tuple)):return[encode(v)for v in x] + return x + +def authenticate(): + manifest=json.loads((HERE/'INPUTS.json').read_bytes()) + for row in manifest['files']: + name=row['path'];need(Path(name).name==name and name not in ('','.','..'),'Simple owned input path') + need(hashlib.sha256((HERE/name).read_bytes()).hexdigest()==row['sha256'],'Changed arithmetic input: '+name) + +def run(local=None): + authenticate() + frozen=json.loads((HERE/'profile.json').read_bytes()) + frozenH={int(k):v for k,v in frozen['helpers'].items()};frozenN={int(k):v for k,v in frozen['paid'].items()} + need(frozenH==H and frozenN==N,'Frozen candidate profile agrees') + if local is not None: + need({int(k):v for k,v in local['helpers'].items()}==H and {int(k):v for k,v in local['paid'].items()}==N,'Actual native replay agrees with complete frozen profile') + word_path=HERE/'controller.json' + raw=word_path.read_bytes();word=json.loads(raw);T,P=Counter(),Counter();full=thin=idle=0 + for event in word['physical_events']: + if event[0]=='LOCAL':full+=1;T.update(H);P.update(N) + elif event[0]=='QUERY_SHEAR':thin+=1;P[1]+=112 + elif event[0]=='IDLE': + rank=8*len(event[2]);need(rank>0,'No zero idle charge');P[rank]+=224;idle+=224 + for term in word['diagonal']: + need(term[0]in(-1,1)and all(v in(0,1)for v in term[1:]),'Legal central normalizer') + T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(18,15,3360),'All actual p16 events') + need(sum(T.values())==10928 and sum(P.values())==64620,'Complete field/call inventory') + mt=lambda h,c:E.moment(h,1-c) + def margin(c): + a,b=mt(T,c),mt(P,c);return a[0]-b[1],a[1]-b[0] + need(margin(LOW)[0]>0 and margin(HIGH)[1]<0,'Exact new raw root bracket') + # Prove the margin decreases on C in[0,.05], independently of floating discovery. + signed={r:T[r]-P[r]for r in T.keys()|P.keys()};derivative=None + for i in range(16): + l,r=Q(i,320),Q(i+1,320);low=Q(0) + for rank,n in signed.items(): + term=E.mul(E.power(rank,1-r if n>0 else 1-l),E.log_bounds(rank));low+=n*term[0 if n>0 else 1] + derivative=low if derivative is None else min(derivative,low) + need(derivative>0,'Strict decrease around bracket') + t,u,v,c,b=1-TESTED,Q(1,8),682,17,21 + target=E.moment(T,t);alpha=E.divide(E.moment(P,t),target) + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + gap0=Q(31,5*10**9);g,d=Q(98102,100000),Q(959,1000) + need(t+u>=1 and alpha[1]<1-gap0 and gamma[1]1,'Short product bound rejects') + theta,power=Q(94,101),143;eta=E.scale(E.power(145,-v*TESTED),t) + need(2**(101-94)*(17**v)**101<=(145**v)**94 and eta[0]>theta**power,'Shifted exit and complement capacity') + need(E.power(145,v*TESTED)[1]<2**power,'Initial compiler range') + need(eta[1]1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + height=step*hi;need(height>8*v and passes(hi)and not passes(hi-1),'Exact sufficient finite rank') + # Source scalar list/order untouched, inherited upper bound is conservative. + scalar_bound=158168;route_bound=(sum(N.values())+2*408+688)*1000 + need(scalar_bound+route_bound<10**7,'All local routes and scalar operations charged') + scalar_upper=18*10**7+15*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program'])for k in('left','right'))) + need(scalar_upper<10**9,'Complete raw nonrecursive bill') + bit=json.loads((HERE/'ordinary-bit.json').read_bytes());atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599');admitted=Q(bit['admitted']) + need(atom==Q('.004')and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Ordinary BIT admission and adapters') + outer_gap=(TESTED-KAPPA-gap)/6;need(outer_gap>0,'Strict outer slack remains') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':TESTED-gap,'b':KAPPA+5*outer_gap,'a':KAPPA+4*outer_gap,'q':KAPPA+3*outer_gap,'bit_saving':admitted,'epsilon':1-outer_gap,'beta':1-3*outer_gap,'r0':outer_gap/10,'stop':outer_gap,'layout':outer_gap,'d':outer_gap} + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Full outer predicate inventory') + need(all(x>0 for k in('strict_checks','functional_checks')for x in outer[k].values()),'All outer inequalities') + legacy_result=legacy.check(params,outer,KAPPA) + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items()if x<=0];need(failed,'Reject '+name);controls[name]=failed + need(margin(TESTED)[0]>0 and margin(HIGH)[1]<0,'Successful and rejected endpoint controls') + mass=lambda h:sum(r*n for r,n in h.items()) + need(mass(T)-mass(P)==752,'Exact p16 rank surplus retained') + return encode({'status':'PASS_COMPLETE_CONDITIONAL_ARITHMETIC','kappa':KAPPA,'kappa_decimal':'0.00302015','gain_over_PR4447':KAPPA-Q('.00300123'),'tested':TESTED,'raw_root_bracket':[LOW,HIGH],'derivative_positive_lower':derivative,'local_helpers':H,'local_paid':N,'targets':dict(T),'paid':dict(P),'productive_fields':sum(T.values()),'paid_calls':sum(P.values()),'rank_masses':[mass(T),mass(P)],'rank_surplus':mass(T)-mass(P),'strictification':{'tested':TESTED,'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'tensor_power':v,'tail_offset':u,'cutoff':c,'floor':b,'normalized_paid_upper':bound},'compiler':{'theta':theta,'power':power,'eta':E.display(eta),'gap':gap,'H':height,'N':'2^'+str(height),'integer_test_exponent':hi,'word_materialized':False},'raw_nonrecursive':{'local_routes':route_bound,'local_scalar_allowance':scalar_bound,'all_unit_bound':scalar_upper,'budget':10**9},'ordinary_BIT':bit,'outer':outer,'legacy_outer':legacy_result,'negative_controls':controls,'source_hashes':{'p16_controller':hashlib.sha256(raw).hexdigest(),'interval_engine':hashlib.sha256(Path(E.__file__).read_bytes()).hexdigest(),'outer_ledger':hashlib.sha256(Path(L.__file__).read_bytes()).hexdigest()},'remaining':'Requires independent source-pinned native/operator/phase replay of unchanged candidate and source admission. Arithmetic alone is not a new theorem or selected-frontier promotion.'}) +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser();parser.add_argument('--write-receipt',action='store_true');args=parser.parse_args() + result=run() + if args.write_receipt:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n',encoding='utf-8') + else:need(result==json.loads((HERE/'RESULT.json').read_bytes()),'Exact frozen arithmetic receipt replay') + print(json.dumps({'status':result['status'],'kappa':result['kappa_decimal'],'uniform_rank':result['compiler']['N'],'outer_predicates':'54 strict + 4 functional + 63 legacy','paid_calls':result['paid_calls']},sort_keys=True)) diff --git a/research/compact-joint-compiler/independent/INPUTS.json b/research/compact-joint-compiler/independent/INPUTS.json new file mode 100644 index 0000000000..bb73765880 --- /dev/null +++ b/research/compact-joint-compiler/independent/INPUTS.json @@ -0,0 +1,49 @@ +{ + "files": [ + { + "path": "arithmetic/controller.json", + "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + }, + { + "path": "arithmetic/INPUTS.json", + "sha256": "65e2517e1aa87d2313d922c7684037d15389e995f096746003358bf2317f59ac" + }, + { + "path": "arithmetic/intervals.py", + "sha256": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc" + }, + { + "path": "arithmetic/legacy-source.txt", + "sha256": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895" + }, + { + "path": "arithmetic/legacy.py", + "sha256": "43cd70c98a133015f40fd695e18035254cb3bd303f2da45bf46607f211506a87" + }, + { + "path": "arithmetic/ordinary-bit.json", + "sha256": "7d3ef7711fef1033a49f7ac9847bccf24145c0ba2cf248b3802114c172fb0249" + }, + { + "path": "arithmetic/outer_ledger.py", + "sha256": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54" + }, + { + "path": "arithmetic/profile.json", + "sha256": "6e937237c22b3b6d4821ecc253e579b852731a5c665ce488d42f2f7bddb291f5" + }, + { + "path": "arithmetic/PROOF.txt", + "sha256": "273598588316e29a45e3940c6f5070d973b1998fe5b9c582b23bfe87502724cc" + }, + { + "path": "arithmetic/RESULT.json", + "sha256": "a6caaa2a6d6460a8c1ef7e48c4853bb27976be33a52b96a4216dfa90d96c9091" + }, + { + "path": "arithmetic/verify.py", + "sha256": "4ad2d95bee6e6fe2ae4462e5dd0921c64677fc86a5da1f38a198546c28c7f1b1" + } + ], + "scope": "Exact frozen compact arithmetic sources, inputs and receipt; predecessor native/controller claims retained." +} diff --git a/research/compact-joint-compiler/independent/PROOF-REVIEW.txt b/research/compact-joint-compiler/independent/PROOF-REVIEW.txt new file mode 100644 index 0000000000..1a0627fa9f --- /dev/null +++ b/research/compact-joint-compiler/independent/PROOF-REVIEW.txt @@ -0,0 +1,51 @@ +Independent review — PR4470 compact conditional compiler + +Verdict: the corrected sufficient-rank calculation is consistent with the +retained general logarithmic compiler theorem, and the declared conditional +κ stays 0.00302015. The new finite template bound is N=2^558100005581. +It is not a new κ, a full multiplication proof, a practical-runtime claim, +or an explicit threshold for asymptotic integer input sizes. + +The source theorem is higher-moment-strictification/README.md §4, pinned to +canonical main 2a13eb1827784206202db90e5dc8327cf8a250db. For θ=a/b it requires +2^(b−a) r_max^b ≤ m^a, θ^p < η=t m^(t−1), and m^(1−t)<2^p. +Here a=94,b=101,p=143,m=145^682,r_max=17^682, so the first factor is +2^7=128. The initial draft mistakenly checked 2 instead; that undercheck +was caught in independent review, corrected by the compiler worker, and +replayed. The stronger required inequality holds with ample exact slack. + +The paid tensor proof uses C=0.00302016, t=1−C, u=1/8≥C, v=682, +cutoff 17^682 and productive floor 21^682. Both original and completion +paid tails appear explicitly. The displayed conservative rational bound +passes at 682 and fails at 681. This is a scoped certificate for the chosen +ratios; it does not establish global minimum tensor power. + +The uniform compiler gap g=1/100000001 is distinct from the outer slack. +Since C−κ=1/100000000, the leftover positive outer slack is +(C−κ−g)/6 = 1/60000000600000000. All outer comparisons must use exact +rationals at this scale; a coarse decimal grid cannot silently replace them. +The small slack is mathematically positive, but can enlarge the unspecified +asymptotic input threshold substantially. No final threshold is certified. + +The majorant test (100000001 j+1)^143<2^j passes at j=5581 and fails at +j=5580, giving H=100000001·5581=558100005581. This is the chosen sufficient +majorant/grid bound, not a minimum native program or universal optimal rank. +The original compiler's integer batching, ownership, whole-job normalizers, +complements, exits and finite constant prescriptions remain inherited premises. + +Independent checks: source hashes before/after; public PR4470 controller +byte identity; fresh normal and isolated optimized Python replays; separate +integer/rational calculations for the decisive tail, exit and height tests. +The registered read-only gate rejects v=681, p=142 and zero remaining outer +slack through independent exact numerical controls. Calling the real source +API with an inconsistent native inventory rejects. A corrupted expected +source pin rejects. This gate makes no filesystem mutations; its deterministic +result and all guarded source hashes are in RECEIPT.json. + +Credit PR4470 for the actual best-known conditional native/controller word; +PR4440/4441/4447, zxv's native/higher-moment/logarithmic results, Jacob Alan +Sussman's mixed-target compiler and the retained BIT/analytic/outer lineage. +The compiler worker chose and constructed the new parameters. The controller +worker independently reviewed the proof, caught the factor-128 source +hypothesis, and replayed the corrected calculation. Substantial OpenAI Codex +assistance. Apache-2.0; original source notices retained. diff --git a/research/compact-joint-compiler/independent/RECEIPT.json b/research/compact-joint-compiler/independent/RECEIPT.json new file mode 100644 index 0000000000..f65fc32680 --- /dev/null +++ b/research/compact-joint-compiler/independent/RECEIPT.json @@ -0,0 +1,32 @@ +{ + "all_independent_integer_rational_tests": true, + "kappa": "0.00302015", + "normal_and_isolated_optimized_receipts_equal": true, + "outer_d": "1/60000000600000000", + "public_PR4470_controller_unchanged": true, + "same_predecessor_kappa": true, + "scientific_and_source_controls": { + "bad_source_pin": true, + "short_log_power_142": true, + "short_tensor_681": true, + "wrong_actual_native_profile": true, + "zero_outer_slack": true + }, + "scope": "Smaller sufficient finite template, not a new kappa or a final integer-input threshold.", + "shifted_exit_factor": 128, + "source_sha256": { + "arithmetic/INPUTS.json": "65e2517e1aa87d2313d922c7684037d15389e995f096746003358bf2317f59ac", + "arithmetic/PROOF.txt": "273598588316e29a45e3940c6f5070d973b1998fe5b9c582b23bfe87502724cc", + "arithmetic/RESULT.json": "a6caaa2a6d6460a8c1ef7e48c4853bb27976be33a52b96a4216dfa90d96c9091", + "arithmetic/controller.json": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f", + "arithmetic/intervals.py": "6dcf8ed644b84bea85bf52671b9124436a6eaa0f811a724a35b12edbc24624bc", + "arithmetic/legacy-source.txt": "d4495bc3d3f6ae741e405478cde7e7b1e6b76a221e230a603ff62d8657545895", + "arithmetic/legacy.py": "43cd70c98a133015f40fd695e18035254cb3bd303f2da45bf46607f211506a87", + "arithmetic/ordinary-bit.json": "7d3ef7711fef1033a49f7ac9847bccf24145c0ba2cf248b3802114c172fb0249", + "arithmetic/outer_ledger.py": "754364e295b6566de9a3e543c1e935433aad47eebcf14475f65b83568446ba54", + "arithmetic/profile.json": "6e937237c22b3b6d4821ecc253e579b852731a5c665ce488d42f2f7bddb291f5", + "arithmetic/verify.py": "4ad2d95bee6e6fe2ae4462e5dd0921c64677fc86a5da1f38a198546c28c7f1b1" + }, + "status": "PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER", + "uniform_N": "2^558100005581" +} diff --git a/research/compact-joint-compiler/independent/audit.py b/research/compact-joint-compiler/independent/audit.py new file mode 100644 index 0000000000..f4356bd26b --- /dev/null +++ b/research/compact-joint-compiler/independent/audit.py @@ -0,0 +1,74 @@ +"""Independent, read-only compact-compiler audit. Python standard library only. +No files or interpreter configuration are changed. Numerical controls are +independent integer/rational tests, rather than edited source copies. +Apache-2.0; substantial OpenAI Codex assistance. Predecessor credit retained. +""" +from pathlib import Path +from fractions import Fraction as Q +from copy import deepcopy +import hashlib,importlib.util,json,subprocess,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +PACKAGE=HERE.parent +ROOT=PACKAGE.parents[1] + +def need(ok,message): + if not ok:raise ValueError(message) +def digest(path):return hashlib.sha256(Path(path).read_bytes()).hexdigest() +def load(path,name): + spec=importlib.util.spec_from_file_location(name,path) + module=importlib.util.module_from_spec(spec);sys.modules[name]=module + spec.loader.exec_module(module);return module +def authenticate(records): + need(len(records)>=10,'Full nonempty compact source closure') + for row in records: + relative=Path(row['path']) + need(not relative.is_absolute() and '..' not in relative.parts,'Repository-relative owned input') + need(digest(PACKAGE/relative)==row['sha256'],'Changed compact source: '+row['path']) + +def run(): + pins=json.loads((HERE/'INPUTS.json').read_text(encoding='utf-8'))['files'] + authenticate(pins) + module=load(PACKAGE/'arithmetic/verify.py','independent_compact_arithmetic') + ordinary=module.run() + frozen=json.loads((PACKAGE/'arithmetic/RESULT.json').read_text(encoding='utf-8')) + need(ordinary==frozen,'Fresh ordinary arithmetic equals frozen receipt') + child_code="import importlib.util,json,sys; p=sys.argv[1]; s=importlib.util.spec_from_file_location('isolated_compact',p); m=importlib.util.module_from_spec(s); s.loader.exec_module(m); print(json.dumps(m.run(),sort_keys=True))" + child=subprocess.run([sys.executable,'-I','-O','-B','-X','utf8','-c',child_code,str(PACKAGE/'arithmetic/verify.py')],capture_output=True,text=True,encoding='utf-8',timeout=180,check=False) + need(child.returncode==0,'Isolated optimized arithmetic failed: '+child.stderr) + need(json.loads(child.stdout)==ordinary,'Ordinary and isolated optimized scientific receipts agree') + need((PACKAGE/'arithmetic/controller.json').read_bytes()==(ROOT/'research/joint-helper-lattice/CONTROLLER.json').read_bytes(),'Unchanged public PR4470 controller') + C=Q('.00302016');kappa=Q('.00302015');g=Q(1,100000001) + d=(C-kappa-g)/6 + need(d==Q(1,60000000600000000)>0,'Exact independent outer slack') + alpha_gap=Q(31,5*10**9);gamma=Q(98102,100000);delta=Q(959,1000) + tail=lambda v:1/(1+v*alpha_gap)+2*gamma**v+2*delta**v + need(tail(682)<1=2**5580,'Previous majorant grid point rejects') + need(100000001*5581==558100005581,'Exact uniform log-rank') + controls={} + for name,condition in [('short_tensor_681',tail(681)<1),('short_log_power_142',theta**1420)]: + need(not condition,'Independent numerical mutant must reject: '+name) + controls[name]=True + wrong={'helpers':dict(module.H),'paid':dict(module.N)};wrong['paid'][1]+=1 + try:module.run(wrong) + except ValueError as error: + need('Actual native replay agrees' in str(error),'Wrong-profile rejection must reach scientific binding') + controls['wrong_actual_native_profile']=True + else:raise ValueError('Wrong actual native profile accepted') + badpins=deepcopy(pins);badpins[0]['sha256']='0'*64 + try:authenticate(badpins) + except ValueError:controls['bad_source_pin']=True + else:raise ValueError('Bad source pin accepted') + authenticate(pins) + return {'status':'PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER','kappa':'0.00302015','same_predecessor_kappa':True,'uniform_N':'2^558100005581','outer_d':str(d),'normal_and_isolated_optimized_receipts_equal':True,'public_PR4470_controller_unchanged':True,'shifted_exit_factor':128,'all_independent_integer_rational_tests':True,'scientific_and_source_controls':controls,'source_sha256':{r['path']:r['sha256']for r in pins},'scope':'Smaller sufficient finite template, not a new kappa or a final integer-input threshold.'} + +if __name__=='__main__': + result=run();frozen=json.loads((HERE/'RECEIPT.json').read_text(encoding='utf-8')) + need(result==frozen,'Deterministic independent receipt') + print('PASS_READ_ONLY_INDEPENDENT_COMPACT_COMPILER N=2^558100005581 same_kappa=0.00302015') diff --git a/research/compact-joint-compiler/verify.py b/research/compact-joint-compiler/verify.py new file mode 100644 index 0000000000..5a38a237c2 --- /dev/null +++ b/research/compact-joint-compiler/verify.py @@ -0,0 +1,31 @@ +"""Source-bound compact compiler, Apache-2.0; substantial Codex assistance.""" +import argparse,hashlib,importlib.util,json,sys +from pathlib import Path +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +def need(x,m): + if not x:raise ValueError(m) +def load(p,n): + spec=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(spec);sys.modules[n]=m;spec.loader.exec_module(m);return m +def authenticate(): + for row in json.loads((HERE/'SOURCES.json').read_bytes())['files']: + if row['usage']=='input':need(hashlib.sha256((ROOT/row['path']).read_bytes()).hexdigest()==row['sha256'],'Changed source '+row['path']) +def run(part): + authenticate();source=ROOT/'research/joint-helper-lattice';sys.path.insert(0,str(source));parent=load(source/'verify.py','frozen4470_parent') + if part=='dependencies':parent.replay_dependencies() + elif part=='native': + parent.authenticate();local=parent.J.run();need(json.loads(json.dumps(local))==parent.read(source/'NATIVE.json.gz'),'Fresh two-interpreter/native/absolute-phase receipt') + a=load(HERE/'arithmetic/verify.py','compact_arithmetic_native_binding');result=a.run(local) + need(result==json.loads((HERE/'arithmetic/RESULT.json').read_bytes()),'Native profile bound to compact arithmetic') + elif part=='arithmetic': + previous=parent.run(execute_sources=False);need(previous==parent.read(source/'RESULT.json'),'Fresh complete source arithmetic/controller') + a=load(HERE/'arithmetic/verify.py','compact_arithmetic');result=a.run() + need(result==json.loads((HERE/'arithmetic/RESULT.json').read_bytes()),'Frozen compact receipt') + need((HERE/'arithmetic/controller.json').read_bytes()==(source/'CONTROLLER.json').read_bytes(),'Unchanged literal p16 controller') + for key in ('targets','paid','local_helpers','local_paid','ordinary_BIT','productive_fields','paid_calls'): + need(result[key]==previous[key],'Unchanged complete source bill '+key) + need(int(result['compiler']['H'])==558100005581= k_min`. At a fixed integer top rank n>=m, +put + +``` +c(a) = product_k k^a_k, +u(a) = multinomial(|a|;a) product_k W_k^a_k, +R(rho) = {a : m*rho*c(a) <= n}, +G = floor(log_(k_min)(floor(n/m))). +``` + +For every paid-round path s of length d<=G with multiplier rho_s, instantiate +u(a) units at column rho_s*c(a), for every point a in R(rho_s) of degree +G−d. This is the source class construction. For a parent class with +multiplier rho, its rank-r round supplies u(b) jobs at point b when b is +present. The child demand at that point is + +``` +D(b) = sum over eligible (b−e_k) of W_k*u(b−e_k). +``` + +The complete Pascal sum is u(b). Therefore: + +- If the parent point b exists, `0 <= D(b) <= u(b)`. Route D(b) of the + **whole** issued jobs to the child. Complete the remaining u(b)−D(b) + jobs as paid exits, at their actual rank `e=r*rho*c(b)`. +- If the parent point is absent, supply the child demand with new distinct + top input arrays. These are source jobs, not copies of issued data. +- At depth G, every point has degree zero; all paid jobs are exits. + +No fractional jobs, cloned productive inputs or uncharged discarded requests +are introduced. Within each point, choose a fixed enumeration of parent +jobs and target slots and match their first D(b) elements. The rest have +explicit endpoints and remain on their actual owners. + +### Sources and exits + +At the root, every demanded point has degree G+1, so it is outside R(1). +Its rank s is in `(n/m,n]`. A non-root source has no parent point, hence +`m*rho_parent*c(b)>n`; its rank is `r*rho_parent*c(b)>r*n/m>=n/m`. +Its eligible child target ensures s<=n. Thus every source is a positive +job in `(n/m,n]`. + +Every exit belongs to an actual parent unit, so + +``` +e <= r_max*n/m < n. +``` + +This holds for the new premature exits as well as leaf exits. A premature +exit has at least one omitted Pascal term, with +`m*r*rho*c(b)/k > n`; consequently `e > k_min*n/m`. These are large exits +near the upper boundary. They cannot be assigned the old bound +`r_max*(n/m)^theta` with theta<1. That lost estimate is the exponent issue. + +### Chronology and arbitrary inputs + +Run all scalar steps of a class in their specified order. At paid position +j, issue that position for every unit, partition its whole issued jobs into +matched and unmatched slots, finish all unmatched exits and the entire child +class, restore adapters, and only then resume position j+1. The child takes +incoming jobs from this one parent round plus its new top sources. It never +waits for a later round of a suspended parent. The finite class depth is G; +all complement and exit calls have rank below n, so their uniform programs +are already available by strong induction. + +Distinct slots in one class have distinct physical fields. Routing fewer +parent slots than the original full-Pascal construction preserves this +property. Arbitrary-input native correctness permits correlated values, +including current owned-center contents; it does not permit field aliasing +or extra productive credit. Each unit has its own owned identities and +retains them until its word clears them. These requirements are unchanged. + +### Exact potential and count identities + +Let S_s and E_e be integer source and exit inventories, U the unit count, +and Qcol the sum of the units' positive integer column multiplicities. +Cancellation of matched jobs gives, exactly at rank one, + +``` +sum_s S_s*s − sum_e E_e*e = Delta * Qcol, +Delta = sum_k W_k*k − sum_j r_j. +``` + +At any real exponent t, the corresponding identity is + +``` +sum_s S_s*s^t − sum_e E_e*e^t + = (T_t−P_t) * sum_units column^t. +``` + +Thus a favorable raw t-moment survives as a superpotential. It does **not** +by itself pay the source complements. Writing W=sum W_k and P=number of +paid rounds, complete untruncated layer counts give + +``` +U <= sum_(d=0..G) P^d W^(G−d) <= (W+P+1)^(G+1), +S := sum_s S_s <= W*U, +sum_e E_e <= P*U. +``` + +The source package's separated case is unchanged: no premature exits occur. +The verifier compares it with the byte-identical predecessor literal replay. + +## 3. Nested divisible widths and complete count bounds + +Use the ordinary base B_n=1, P_n=n below m, with B_0=1 and P_0=0. For n>=m +choose the replication factor and productive width + +``` +a_n = B_(n−1), B_n = a_n*S_n. +``` + +Every earlier width B_e divides B_(n−1), by induction. Therefore every +source-complement batch and exit batch is an integer number of smaller +uniform programs. This is a concrete choice within the source compiler's +existing denominator-clearing freedom; no optimum is claimed. Its previous +option to use an LCM is retained as predecessor context. + +As in the source compiler, each of the a_n*S_n original arrays first gets +its disjoint complementary job, then its one source job through the flow. +All exits are completed by smaller uniform programs. The result is a full +rank-n transform on every original array. Owned storage is excluded from B_n. + +The normalized leaf count satisfies the **same exact recurrence** for any +valid replication choice: + +``` +L(n) = (1/S_n) * [sum_s S_s L(n−s) + sum_e E_e L(e)]. +``` + +Changing the replication factors changes width and total counts equally. +It does not spend supplier saving or alter any outer parameter. + +For a fixed final N and h=G(N), all n<=N satisfy + +``` +S_n <= C_N := W*(W+P+1)^(h+1), +B_N = product_(n=m..N) S_n <= C_N^N. +``` + +Since h=O(log N), **log B_N=O(N log N)** for a fixed mixed rule. Repeatedly +multiplying all previous widths is unnecessary. This bounds one explicit +realization; the original compiler did not require that inefficient choice. + +If Delta>0, telescope rank-one mass over the fully expanded uniform program: + +``` +B_N*N − P_N = Delta * Qcol_N, +U_N <= Qcol_N <= B_N*N/Delta. +``` + +All raw columns are positive integers, which gives the middle inequality. +Thus paid leaves and raw instances have the same `exp(O(N log N))` bound. +With one owned center per raw unit, the center count is at most U_N. A rule +with O_local distinct owned banks per invocation instead gets O_local*U_N. +Extra router scratch must be counted separately. + +### Routing and word description + +Count one routing slot for every source, every exit, every unit target slot +and every unit paid position. At one flow its count is at most +`2*(W+P)*U`. The same bound telescopes over all recursive calls, because +each call contributes its own local unit instances. Exact compilation checks +this identity alongside widths and leaves. + +In the macro grammar that records a whole-job adapter, inverse adapter or +whole-field move as one record, a slot can be handled with at most sixteen +records: up to two whole-job conjugations and their inverses, park/load/ +return/reorder moves, and explicit scratch initialization and erasure. +Allocate separate owned scratch for those moves when needed; no zero-cost +routing or free copying is assumed. Let A bound the fixed unit's complete +nonrecursive record count, owned operations and scalar coefficient heights. +The final weighted record allowance satisfies the conservative bound + +``` +R_bar <= A*U_N + 32*(W+P)*U_N + P_N + <= (A+32*(W+P)+1)*B_N*N, for Delta>=1. +``` + +R_bar bounds both the macro count and the sum of scalar-height and native +record allowances. Every owned bank has an explicit initialization record, +so total allocated owned banks can also be bounded by R_bar; the sharper +raw-center bound remains separate. This is a **description/record bound**, +not a new tariff for executing a +general matrix or permutation. A Gaussian monomial adapter's dense binary +address matrix and quadratic phase have O(N^2) descriptor bits. Explicit role indices add O(log B_N) +bits. Thus an encoding of this finite word still has +`exp(O(N log N))` bits for a fixed unit and its finite coefficient alphabet. +If physical expansion of one adapter needs F(N) native records, multiply +the routing term by its actual F(N). That physical implementation, coefficient +heights and tape costs remain separately priced native obligations. They +are not set to zero by the macro bound. + +## 4. Applying the size result to PR4433 + +The new nested widths may be used in the separated compiler of PR4433. +Its normalized L(n), ambient N, uniform saving and outer ledger remain +unchanged. Therefore this application does not need the still-open direct +exponent lemma. + +With `v=150`, `H=349300000000`, `N=2^H`, the completed mixed rule has + +``` +W = 7688^150 < 2^1950, +P <= 131115^150 + 7688^150*15^150 < 2^2701, +W+P+1 < 2^2702. +``` + +The bound on P counts every original and completion call by its positive +rank mass; splitting preserves that mass. Since k_min>=2, h<=H. Set + +``` +D = 1950 + 2702*(H+1) = 943808600004652. +``` + +There is consequently a realization of the same proposed conditional +κ=0.00268647 supplier satisfying + +``` +B_N < 2^(D * 2^H), +P_N < B_N * 2^H. +``` + +More finely, after expanding every product, padding, split and compiler call +back to the raw p7 word, that word has surplus 608. Product/completion/split +boundaries cancel, so + +``` +B_N*N − P_N = 608 * sum_raw_p7_instances column, +U_raw <= (B_N*N − P_N)/608. +``` + +This is also an explicit bound on raw p7 center banks under the safe +one-center-per-instance allocation. These are large upper bounds, not +emitted words, smallest widths or practical precision estimates. They replace +one implicit part of the source finite-constant prescription. The native +adapter bodies, analytic transfer and physical costs retain their original +conditions; a closed bound for the source's finite-constant prescription is +given next, without a new physical runtime or exact-recovery threshold. + +### A closed envelope for the source finite constants + +The exported THREE-base native word has exactly 22,633 records in each +orientation. Source-bound counting retains all 15 copies, the literal p7 +controller, scalar allowance 2,490,856, every productive/paid/contact/helper/ +idle slot, and all routing and owned operations. A raw macro allowance is + +``` +A_raw = 15*8*(decompressed native JSON bytes) + + 8*(literal controller JSON bytes) + + 32*(2490856 + all declared slots + 15*22633) < 2^40. +``` + +The payload-bit terms overcount the coefficient literals and full local +descriptors, including both orientations. The 32-per-slot term overcounts +whole-job normalizers and inverses, field movements, initialization and +erasure. It is a bound on the declared source word in this grammar, not +independent verification of its functional correctness or physical tariffs. + +For the chronological v-fold product, its number of raw p7 invocations is + +``` +U_v = sum_(i=0..v−1) 7688^(v−1−i)*55998^i < 2^2392. +``` + +At every product level retain the whole-job matching wrappers. A conservative +product allowance is + +``` +A_product <= (2^40 + 32*v*(7688+55998+1))*U_v + 32*v*55998^v. +``` + +Add 32 records for every final paid call, completion role and original paid +position. Counting paid calls by their rank mass gives + +``` +A_completed <= A_product + + 32*(131115^v + 7688^v*15^v + 7688^v + 55998^v). +``` + +A dense local binary map/quadratic phase and role index fit in +`64*(121^v)^2` bits per such record. The verifier checks the integer bound +`A_completed * 64*(121^v)^2 < 2^5000`. Thus **A=2^5000** is a valid weighted +record/description allowance for this fixed completed unit. It includes all +source coefficients and owned operations, with a large deliberate overcount. +No instruction list of the completed product is emitted. + +Since `A+32*(W+P)+1 < 2^5001`, use the envelope + +``` +R_bar < 2^(D*2^H + H + 5001). +``` + +Apply the existing source finite-constant prescription to the **newly expanded +word**. With Z=B_N+owned banks, G its scalar coefficient envelope, and P_N +its rank-one leaves, we have `Z<=2*R_bar`, `G<=8*R_bar`, `P_N<=R_bar` and +`N<=R_bar`. Therefore + +``` +E = 64*(Z+N+P_N+G+1)^3 + < 2^(3*D*2^H + 3*H + 15021), +B_constant = P_N+E, +C0 = 32*N*B_constant^2 + < 2^(6*D*2^H + 7*H + 30049) + < 2^(8*D*2^H). +``` + +The last comparison uses `2^H>=H+1` and an exact polynomial integer check +on D and H. These are explicit, very loose upper bounds for the inherited +semantic precision/stock constants, conditional on that source prescription +and its admitted native record implementations. The exact numerical outer +input threshold, prime exclusions and physical tape costs remain separate. + +## 5. Exact finite checks and the open exponent gate + +The verifier uses no floating-point acceptance tests. It checks: + +- Nine literal/merged flows at ranks 20, 40 and 80: a separated control, + strict overlap `{2:1,5:1} <- {1:2,4:1}`, and Sussman's open equality + example `{2:4,3:1} <- {1:6,2:2}`. Every whole input and exit agrees. +- The separated control agrees with the unchanged Sussman literal replay. +- Complete nested-width compilations through rank 100 on both overlap + examples, checking every recursive batch, routing count and rank identity. +- Raw p7 through rank 1,000: **880 exact nonbase compilations**. B_1000 has + 17,504 bits; the saved receipt binds all large computed integers by their + unsigned big-endian hashes, avoiding enormous decimal dumps. +- Removing premature exits violates mass conservation. Removing batch + replication fails integer divisibility. Allowing a paid rank equal to + the ambient rank is rejected because strict rank descent is unavailable. + +For raw p7 at rank 1,000, exact arithmetic gives + +``` +L(1000) > 990 > 1000^(1−0.00268647). +``` + +The second comparison is elementary and exact: `ln(2)>2/3` from its first +atanh term and `1000>2^9` give `ln(1000)>6`. Then +`1000^κ > 1+6κ > 100/99`. No log approximation is used in this rejection. +This checks one finite failure and keeps it distinct from the infinite-rank +question. + +The missing lemma is a uniform bound on the **whole** recurrence. For some +fixed p and sufficiently large n, one would need, for example, + +``` +sum_e E_e e^t (1+log2(e))^p + + sum_s S_s (n−s)^t (1+log2(n−s))^p + <= S_n n^t (1+log2(n))^p, +``` + +with zero-rank terms defined separately and a correctly funded base range. +The premature exits have rank proportional to n. Their logarithmic factors +cannot use the old fixed theta<1 power contraction. A raw moment advantage +alone does not prove this inequality. + +Exploratory `approximate_leaves` in flow.py evaluates the recurrence in +floating point and is deliberately excluded from verification. A bounded +run through 20,000 ranks found saving about 0.000827 for the default height; +varying the height did not approach 0.00268647 there. This is local search +evidence, not a lower bound or a reason to enlarge the same scan. A better +boundary estimate or a changed flow is the next research obligation. + +## 6. Reproduction and provenance + +Python 3.12, standard library only: + +```sh +python3.12 -B research/direct-mixed-flow/verify.py +python3.12 -B scripts/research_package.py --package research/direct-mixed-flow --check-only +python3.12 -B scripts/research_package.py --package research/direct-mixed-flow +``` + +Use `verify.py --out /absolute/new/result.json` for a fresh receipt. +[RESULT.json](RESULT.json) contains exact flows, integer compilation hashes, +symbolic size bounds and negative controls. `flow.py` is the new algorithm; +the verifier independently compares its merged and literal traversal outputs. +Those are two internal implementations, not an independent mathematical review. + +Canonical base is `12fa8c5c844be21bfefb38a19503fbd867a11244`, priority revision +7. SOURCES.json pins orientation metadata. VENDOR.json separately binds eleven +unchanged exports by commit, full path, Git blob and SHA256. Their bytes and +notices are preserved; direct replay needs no foreign Git objects. The source +theorem and earlier finite compiler remain attributed hypotheses, not new work. + +Local validation used Python 3.12.8 on macOS arm64. The registered replay, +metadata/pin check and committed-byte preflight passed. A separate Git-free +copy passed with `python3.12 -I -O -B verify.py`; changed-native-source and +changed-receipt controls both rejected. Replay uses exact integer arithmetic +and source hashes, with no network or foreign Git objects. The repository is +shallow, so a full source-history preflight was not attempted. No Lean, Docker, +full native/all-column admission, physical adapter expansion or historical +suite was run. Independent mathematical acceptance remains open. + +The overlap refresh at 18:48 UTC covered 538 open PR bodies and 3,280 +discussion/comment records, with complete reported pagination. Specific +searches for direct overlapping-rank compilers, Pascal matching and nested +widths found no matching public item in that scope; this is not a novelty +certificate. Existing PR4433 supplies the fixed-rank application, and the +source theorem explicitly leaves the unseparated exponent open. No Discussion +claim or PR has been posted for this partial checkpoint. + +## Open next questions + +1. **Close or refute the direct exponent gate for this capped flow.** Start + with a proved bound on premature-exit potential relative to the actual + complement capacity. This decides whether the flow can replace the + tensor/padding layer. A larger rank scan is not a uniform proof. +2. **Independently admit the physical expansions and precision prescription.** + Audit the conservative A allowance against the actual native caller and + bind every adapter's physical implementation, row movements and recovery + exclusions. The encoded constants above use the inherited semantics; + description size is not a physical execution tariff. +3. **Tighten the constructive width.** The nested product is an explicit + upper bound, not an optimized LCM. A useful next step would control prime + valuations of the actual source counts; another arbitrary batching choice + would not by itself establish a smaller physical supplier. + +Prepared by zxv with substantial OpenAI Codex assistance in research, code +and writing. No subagents or independent human mathematical review were +used. New material is Apache-2.0. The integer lockstep/Pascal construction +and original open unseparated question are Jacob Alan Sussman's work, retained +at upstream `wht-power-saving-lean` commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a`; its LICENSE and NOTICE are included. +PR4359 supplies the native finite-precompilation bridge and p7 predecessor +lineage. PR4416's p7 product/padding is @1337isnot1337's work. PR4433 supplies +the unchanged sufficient rank. Their original contributor credit remains +in the authenticated exports. diff --git a/research/direct-mixed-flow/RESULT.json b/research/direct-mixed-flow/RESULT.json new file mode 100644 index 0000000000..e657f58b5a --- /dev/null +++ b/research/direct-mixed-flow/RESULT.json @@ -0,0 +1,505 @@ +{ + "direct_exponent_theorem_established": false, + "exact_p7_direct_compilation": { + "column_mass": { + "bits": 17497, + "unsigned_big_endian_sha256": "0f2b521412ca3f565d734c244b1cf42b8c7d49ef1e61af197ec97b2605078a3c" + }, + "leaves_per_array": { + "lower": "24890741110487842821/25000000000000000", + "upper": "995629644419513712841/1000000000000000000" + }, + "n": 1000, + "nested_batch_checks": 880, + "paid_above_99_percent_linear": true, + "paid_rank_one_leaves": { + "bits": 17514, + "unsigned_big_endian_sha256": "1f28a559d21f0df473b67fef0c37eb57144955250234a44c998bd837d1e8f3d6" + }, + "productive_width": { + "bits": 17504, + "unsigned_big_endian_sha256": "49727d4435d62a4a84b79cf2451d374a5bb98234cbe460ec0b0ef3da77c8c9e6" + }, + "rank_one_surplus": 608, + "raw_instances": { + "bits": 17497, + "unsigned_big_endian_sha256": "0f5ce7310a89be0835b71681538c3e2e57134d2690ff663b8bc1cd10938b9c7f" + }, + "routing_slots": { + "bits": 17514, + "unsigned_big_endian_sha256": "98bde80b4a7bc886645e82f3b9e730545da94beddcbec4e98ce88e1c44a39242" + }, + "source_count_upper": 31182789153672, + "target_failure": { + "kappa": "268647/100000000", + "proved": "L(1000) > 990 > 1000^(1-kappa)", + "scope": "This particular finite rank fails; no asymptotic impossibility claim." + }, + "width_exponent_envelope": 45000 + }, + "exact_toy_compilations": [ + { + "column_mass": { + "bits": 438, + "unsigned_big_endian_sha256": "f469278cd8f6190ffe6a1ae190299a8d183d1675d4280087d107e5d7016aee25" + }, + "leaves_per_array": { + "lower": "63955485748643768733/1000000000000000000", + "upper": "31977742874321884367/500000000000000000" + }, + "n": 100, + "nested_batch_checks": 96, + "paid_above_99_percent_linear": false, + "paid_rank_one_leaves": { + "bits": 439, + "unsigned_big_endian_sha256": "7df4f5875466fa21b225c2b60317e60536fdededbe8473d18fe5fb3fb057bb6f" + }, + "productive_width": { + "bits": 433, + "unsigned_big_endian_sha256": "35f12bcc6000b703565e2f120e8077641f744909e8ec163921775b2b0c139254" + }, + "rank_one_surplus": 1, + "raw_instances": { + "bits": 436, + "unsigned_big_endian_sha256": "12b6d174870cd23fd40ad1f4ff56df629ed813fabbbfcf143a914bfdd875609d" + }, + "routing_slots": { + "bits": 439, + "unsigned_big_endian_sha256": "4034ff94efe1f1ab70575b300eebbd2469e9065861c4f2570a59256c47170f74" + }, + "source_count_upper": 15552, + "width_exponent_envelope": 1400 + }, + { + "column_mass": { + "bits": 1007, + "unsigned_big_endian_sha256": "f04dcf1684cd1a5f5708102f230375fb43cd08135626ac91b22478876e21c63e" + }, + "leaves_per_array": { + "lower": "65003740439870989333/1000000000000000000", + "upper": "32501870219935494667/500000000000000000" + }, + "n": 100, + "nested_batch_checks": 98, + "paid_above_99_percent_linear": false, + "paid_rank_one_leaves": { + "bits": 1008, + "unsigned_big_endian_sha256": "1302eac01cf514d2855c821612c64c9d38a6c9ff55f12115f72bf34a9906b9d5" + }, + "productive_width": { + "bits": 1002, + "unsigned_big_endian_sha256": "398043f007044ec4c1ba14eda89bf66b48733ce7a22bb855a3bc17a4665b5952" + }, + "rank_one_surplus": 1, + "raw_instances": { + "bits": 1006, + "unsigned_big_endian_sha256": "ebd327c71dde99fefa5afb70ef8ad5b207723935abb8bed0473a95d67e73fbe7" + }, + "routing_slots": { + "bits": 1010, + "unsigned_big_endian_sha256": "23f8f6398dbe8fe43a321ff79a6c52edfee5c4de97ff2852a6cdcc6c127e7cd7" + }, + "source_count_upper": 37647680, + "width_exponent_envelope": 2600 + } + ], + "existing_supplier_size_bounds": { + "D": 943808600004652, + "H": 349300000000, + "N": "2^349300000000", + "compiled_record_upper": "R < 2^(D*2^H + H + 5001)", + "completed_unit_description_upper": "2^5000", + "kappa": "268647/100000000", + "owned_p7_center_bound": "one per raw instance; <= B_N * 2^H / 608", + "paid_leaf_bound": "P_N < B_N * 2^H", + "physical_scope": "Encoded whole-job adapter/move records. Their permitted physical implementation and tariffs remain inherited, separately priced premises.", + "raw_macro_allowance_upper": "2^40", + "raw_macro_and_payload_allowance": 319592968, + "raw_native_record_counts": { + "backward": 22633, + "forward": 22633 + }, + "raw_p7_instance_bound": "U_raw <= (B_N * 2^H - P_N)/608", + "routing_macro_record_bound": "R <= (A + 32*(W+P) + 1) * B_N * N; A < 2^5000", + "routing_slot_bound": "slots <= 2*(W+P)*V, V completed-unit instances", + "source_C0_upper": "C0 < 2^(8*D*2^H)", + "source_precision_E_upper": "E < 2^(3*D*2^H + 3*H + 15021)", + "width_bound": "B_N < 2^(D * 2^H)", + "winning_uniform_word_materialized": false + }, + "finite_flows": [ + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 18, + "exits": { + "1": 16, + "2": 16, + "4": 4 + }, + "height": 1, + "matched_jobs": 18, + "minimum_source": 9, + "n": 20, + "rank_one_surplus": 2, + "source_count": 9, + "sources": { + "12": 4, + "16": 1, + "9": 4 + }, + "unit_count_upper": 9, + "units": 9 + }, + "literal_classes": 7, + "paid": { + "1": 4, + "2": 2 + }, + "rule": "separated-control", + "targets": { + "3": 2, + "4": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 180, + "exits": { + "1": 64, + "2": 96, + "4": 48, + "8": 8 + }, + "height": 2, + "matched_jobs": 132, + "minimum_source": 12, + "n": 40, + "rank_one_surplus": 2, + "source_count": 42, + "sources": { + "12": 16, + "16": 4, + "24": 8, + "27": 8, + "32": 2, + "36": 4 + }, + "unit_count_upper": 63, + "units": 58 + }, + "literal_classes": 43, + "paid": { + "1": 4, + "2": 2 + }, + "rule": "separated-control", + "targets": { + "3": 2, + "4": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 244, + "exits": { + "1": 64, + "2": 96, + "4": 48, + "8": 8 + }, + "height": 2, + "matched_jobs": 162, + "minimum_source": 27, + "n": 80, + "rank_one_surplus": 2, + "source_count": 27, + "sources": { + "27": 8, + "36": 12, + "48": 6, + "64": 1 + }, + "unit_count_upper": 63, + "units": 63 + }, + "literal_classes": 43, + "paid": { + "1": 4, + "2": 2 + }, + "rule": "separated-control", + "targets": { + "3": 2, + "4": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": { + "16": 1 + }, + "column_mass": 28, + "exits": { + "1": 8, + "16": 5, + "4": 12 + }, + "height": 2, + "matched_jobs": 8, + "minimum_source": 5, + "n": 20, + "rank_one_surplus": 1, + "source_count": 14, + "sources": { + "10": 2, + "20": 5, + "5": 4, + "8": 3 + }, + "unit_count_upper": 19, + "units": 11 + }, + "literal_classes": 13, + "paid": { + "1": 2, + "4": 1 + }, + "rule": "strict-overlap", + "targets": { + "2": 1, + "5": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": { + "32": 5 + }, + "column_mass": 132, + "exits": { + "1": 16, + "16": 12, + "32": 5, + "4": 32 + }, + "height": 3, + "matched_jobs": 40, + "minimum_source": 10, + "n": 40, + "rank_one_surplus": 1, + "source_count": 30, + "sources": { + "10": 8, + "16": 3, + "20": 10, + "25": 4, + "40": 5 + }, + "unit_count_upper": 65, + "units": 35 + }, + "literal_classes": 40, + "paid": { + "1": 2, + "4": 1 + }, + "rule": "strict-overlap", + "targets": { + "2": 1, + "5": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": { + "40": 4, + "64": 5 + }, + "column_mass": 872, + "exits": { + "1": 32, + "16": 80, + "4": 80, + "40": 4, + "64": 29 + }, + "height": 4, + "matched_jobs": 132, + "minimum_source": 20, + "n": 80, + "rank_one_surplus": 1, + "source_count": 106, + "sources": { + "20": 36, + "25": 8, + "32": 15, + "40": 10, + "50": 8, + "80": 29 + }, + "unit_count_upper": 211, + "units": 119 + }, + "literal_classes": 121, + "paid": { + "1": 2, + "4": 1 + }, + "rule": "strict-overlap", + "targets": { + "2": 1, + "5": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 322, + "exits": { + "1": 216, + "2": 216, + "4": 72, + "8": 8 + }, + "height": 2, + "matched_jobs": 512, + "minimum_source": 8, + "n": 20, + "rank_one_surplus": 1, + "source_count": 128, + "sources": { + "12": 48, + "18": 10, + "8": 64, + "9": 6 + }, + "unit_count_upper": 129, + "units": 128 + }, + "literal_classes": 73, + "paid": { + "1": 6, + "2": 2 + }, + "rule": "source-open-equality", + "targets": { + "2": 4, + "3": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 4362, + "exits": { + "1": 1296, + "16": 16, + "2": 1728, + "4": 864, + "8": 192 + }, + "height": 3, + "matched_jobs": 5040, + "minimum_source": 16, + "n": 40, + "rank_one_surplus": 1, + "source_count": 670, + "sources": { + "16": 256, + "18": 84, + "24": 256, + "27": 6, + "36": 68 + }, + "unit_count_upper": 1157, + "units": 1142 + }, + "literal_classes": 585, + "paid": { + "1": 6, + "2": 2 + }, + "rule": "source-open-equality", + "targets": { + "2": 4, + "3": 1 + } + }, + { + "flow": { + "all_sources_above_n_over_m": true, + "boundary_exits": {}, + "column_mass": 55372, + "exits": { + "1": 7776, + "16": 480, + "2": 12960, + "32": 32, + "4": 8640, + "8": 2880 + }, + "height": 4, + "matched_jobs": 45088, + "minimum_source": 27, + "n": 80, + "rank_one_surplus": 1, + "source_count": 3572, + "sources": { + "27": 36, + "32": 1024, + "36": 744, + "48": 1280, + "54": 96, + "72": 392 + }, + "unit_count_upper": 9881, + "units": 9732 + }, + "literal_classes": 4681, + "paid": { + "1": 6, + "2": 2 + }, + "rule": "source-open-equality", + "targets": { + "2": 4, + "3": 1 + } + } + ], + "new_code_sha256": { + "flow.py": "460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a", + "verify.py": "9ae067eadf17ff9d97737805eb642a69375a5ff2ddb08988fef59aa0771f9b7c" + }, + "rejected_mutations": [ + "whole integer subprogram batches", + "finite direct-flow rank contract" + ], + "schema": "partial-direct-mixed-flow-and-finite-size/1", + "scope": "New finite matching/scheduling and batching/size bounds. The direct near-root exponent is open. Existing conditional endpoint and native/physical hypotheses remain inherited; no new kappa.", + "source_sha256": { + "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "research/direct-mixed-flow/vendor/P7-FACTOR.json": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e", + "research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39", + "research/direct-mixed-flow/vendor/higher-moment-README.md": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", + "research/direct-mixed-flow/vendor/higher-moment-RESULT.json": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156", + "research/direct-mixed-flow/vendor/p7-NATIVE.md": "26bf9312cdb496b1113c9ddd8aa0fa922ed9e480005703212942af358394183d", + "research/direct-mixed-flow/vendor/p7-RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab", + "research/direct-mixed-flow/vendor/theorem-1g.md": "c4a96c55c2509ff36e8bc6bddaaf6a8b1a34a5d794e4e09ac5214c82b51510e6", + "research/direct-mixed-flow/vendor/tree_flow.py": "750782f6d1cc0a9fff8a768899f3f4c62a7efdf0696d8b5a5d640b1836f5ab72" + }, + "status": "PASS_PARTIAL_DIRECT_FLOW_AND_SIZE_BOUNDS" +} diff --git a/research/direct-mixed-flow/SOURCES.json b/research/direct-mixed-flow/SOURCES.json new file mode 100644 index 0000000000..fcfba8aa31 --- /dev/null +++ b/research/direct-mixed-flow/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + } + ] +} diff --git a/research/direct-mixed-flow/TASK.json b/research/direct-mixed-flow/TASK.json new file mode 100644 index 0000000000..e232fd2674 --- /dev/null +++ b/research/direct-mixed-flow/TASK.json @@ -0,0 +1,148 @@ +{ + "schema_version": 1, + "task_id": "supplier-boundary-audit", + "priority_revision": 7, + "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "original_card": { + "id": "supplier-boundary-audit", + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ], + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "existing_checks": [ + { + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3801: successor scatter-boundary decision package.", + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "status": "author-checked", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Target a direct chronological integer compiler for overlapping paid/productive ranks, without tensor power or paid padding, and explicit width/word/owned-storage bounds.", + "scope_change_reason": "User requests the next contribution target twice the significance of the higher-moment strictification. Raise the target from quantitative bounds inside that mechanism to removing its separation layer and controlling the full finite word. This is an ambitious target, not a claimed numerical significance measurement.", + "bottleneck_link": "Raw p7 has paid rank 48 above productive minimum 5. Existing compiler proofs require strict separation and the winning words lack explicit productive-width bounds. Partial matching may retain all unmatched jobs as priced exits; nested widths may avoid repeated products of batching denominators.", + "budget_minutes": 60, + "stop_rule": "First prove exact whole-integer matching, chronological return, top sources and smaller exits. Then test whether the complete recurrence supports the desired exponent. Do not infer exponent admission from moment balance. If it fails, preserve the first counterexample or missing lemma and the explicit-size result; no broader census or new kappa claim.", + "outcome": "partial", + "evidence": "README.md proves the finite partial-matching compiler, nested exp(O(N log N)) widths, raw/owned/routing bounds and closed encoded precision envelopes for the existing PR4433 supplier. RESULT.json checks source record counts and all integer inequalities, nine literal/merged flows, two overlap compilations through rank 100, and 880 p7 nonbase compilations through rank 1000. Direct near-root exponent remains open.", + "author": "zxv, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance; no subagents.", + "open_questions": [ + { + "question": "Does the capped, partially matched direct flow close the target-saving induction?", + "why_it_matters": "A finite acyclic flow is insufficient if its boundary exits consume all complement capacity.", + "first_step": "Reconstruct every unmatched whole job and evaluate the complete complement-plus-exit recurrence on the source first examples and p7.", + "blocked_by": "No uniform boundary-exit bound or direct exponent proof yet." + }, + { + "question": "Do the complete encoded resource and precision envelopes survive independent native/physical admission?", + "why_it_matters": "The closed numerical envelopes depend on the source finite-record semantics and do not independently establish their physical tariffs or recovery threshold.", + "first_step": "Audit the raw/whole-job record allowance against the caller, then separately bind physical adapters, movement and recovery exclusions.", + "blocked_by": "Inherited native/physical/analytic premises remain outside this mathematical count proof." + } + ], + "publication_policy": "User explicitly authorized posting this PR on October 21, 2026. Subsequent research remains local for user review before submission; no Discussion posting is authorized by this checkpoint.", + "significance_target": { + "relative_to": "PR4433 higher-moment strictification", + "requested_multiplier": 2, + "meaning": "Structural removal of tensor/padding plus full finite-program size control; aspirational scope, not a numerical guarantee." + }, + "upstream_checkpoint": { + "commit": "12fa8c5c844be21bfefb38a19503fbd867a11244", + "priority_revision": 7, + "checked_at_utc": "2026-10-21T18:47:25Z" + }, + "scope_decision": "Continue toward the direct exponent gate; retain a separate complete count/batching theorem that already applies to PR4433. No further scan expansion without a new boundary estimate.", + "overlap": { + "checked_at_utc": "2026-10-21T18:48:25Z", + "open_prs": 538, + "discussion_records": 3280, + "complete_pagination": true, + "terms": [ + "direct mixed compiler", + "overlapping ranks", + "Pascal matching", + "nested widths", + "batch denominators", + "unmatched jobs" + ], + "specific_matches": "No matching public scope found; the later search matches this local task itself. This is not proof of novelty.", + "limits": "Open bodies, discussions and local notes; no arbitrary remote code-diff or remote closed-body search." + }, + "scope_deliverables": { + "finite_direct_compiler": "proved under inherited native/adapter hypotheses; max paid < ambient, no near-root saving yet", + "full_finite_size_bounds": "proved in declared encoded native-record grammar; explicit bounds for the existing PR4433 supplier", + "direct_near_root_exponent": "open; requires a uniform boundary-exit/complement estimate", + "scientific_significance_target": "in progress; not claimed achieved" + }, + "validation": { + "python": "3.12.8", + "platform": "macOS arm64", + "registered_replay": "pass", + "metadata_and_pins": "pass", + "committed_bytes": "pass", + "git_free_optimized": "pass", + "changed_native_source": "rejected", + "changed_receipt": "rejected", + "unrun": [ + "full source history (shallow checkout)", + "independent mathematical review", + "native all-column/physical/analytic/recovery admission", + "Lean", + "Docker", + "historical suites" + ] + } +} diff --git a/research/direct-mixed-flow/VENDOR.json b/research/direct-mixed-flow/VENDOR.json new file mode 100644 index 0000000000..d95b1124e8 --- /dev/null +++ b/research/direct-mixed-flow/VENDOR.json @@ -0,0 +1,82 @@ +{ + "schema": "byte-identical-source-exports/1", + "files": [ + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/research/record-track/proofs/theorem-1g.md", + "path": "research/direct-mixed-flow/vendor/theorem-1g.md", + "git_blob": "36d2399f3538c34e4b1567a15b4a5dfe77ffc7ad", + "sha256": "c4a96c55c2509ff36e8bc6bddaaf6a8b1a34a5d794e4e09ac5214c82b51510e6" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/research/record-track/programs/theorem-1g/tree_flow.py", + "path": "research/direct-mixed-flow/vendor/tree_flow.py", + "git_blob": "31a9c1ae4d116b12e8db7d8e06f723f10425068d", + "sha256": "750782f6d1cc0a9fff8a768899f3f4c62a7efdf0696d8b5a5d640b1836f5ab72" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/LICENSE", + "path": "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/sources/Sussman-563b4e6/NOTICE", + "path": "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE", + "git_blob": "0b06967886fab2628afc0b881c884161bbf5e430", + "sha256": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md", + "path": "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "git_blob": "4badb40f0919c515823cb07e44c6470d4d6469ca", + "sha256": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8" + }, + { + "commit": "b84060c9c", + "original_path": "research/higher-moment-strictification/README.md", + "path": "research/direct-mixed-flow/vendor/higher-moment-README.md", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "commit": "b84060c9c", + "original_path": "research/higher-moment-strictification/RESULT.json", + "path": "research/direct-mixed-flow/vendor/higher-moment-RESULT.json", + "git_blob": "e66b39c674028adfd22f0de3170555dccda52f6a", + "sha256": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156" + }, + { + "commit": "e9058860b5c850760fdf970e796a96aefcdb1d98", + "original_path": "research/pr4359-p7-padding/RESULT.json", + "path": "research/direct-mixed-flow/vendor/p7-RESULT.json", + "git_blob": "ebb30a9b3b94fb159a316350f7da57bde4a30c25", + "sha256": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab" + }, + { + "commit": "da637c87c89482bc4c86be36bd0071b3d400dbed", + "original_path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "path": "research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "commit": "e9058860b5c850760fdf970e796a96aefcdb1d98", + "original_path": "research/pr4359-p7-padding/P7-FACTOR.json", + "path": "research/direct-mixed-flow/vendor/P7-FACTOR.json", + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598" + }, + { + "commit": "e9058860b5c850760fdf970e796a96aefcdb1d98", + "original_path": "research/pr4359-p7-padding/NATIVE.md", + "path": "research/direct-mixed-flow/vendor/p7-NATIVE.md", + "git_blob": "394d9a03c165336d1cfbcd41921c93741042393b", + "sha256": "26bf9312cdb496b1113c9ddd8aa0fa922ed9e480005703212942af358394183d" + } + ] +} diff --git a/research/direct-mixed-flow/VERIFY.json b/research/direct-mixed-flow/VERIFY.json new file mode 100644 index 0000000000..de075b7c20 --- /dev/null +++ b/research/direct-mixed-flow/VERIFY.json @@ -0,0 +1,31 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/direct-mixed-flow/vendor/theorem-1g.md", + "research/direct-mixed-flow/vendor/tree_flow.py", + "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE", + "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE", + "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "research/direct-mixed-flow/vendor/higher-moment-README.md", + "research/direct-mixed-flow/vendor/higher-moment-RESULT.json", + "research/direct-mixed-flow/vendor/p7-RESULT.json", + "research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/direct-mixed-flow/vendor/P7-FACTOR.json", + "research/direct-mixed-flow/vendor/p7-NATIVE.md", + "research/direct-mixed-flow/VENDOR.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact partially matched flows, nested widths and global resource counts; source-bound finite-word/precision envelopes; rank-1000 direct-target rejection. No direct exponent theorem." + } + ] +} diff --git a/research/direct-mixed-flow/flow.py b/research/direct-mixed-flow/flow.py new file mode 100644 index 0000000000..07175cd6e1 --- /dev/null +++ b/research/direct-mixed-flow/flow.py @@ -0,0 +1,198 @@ +#!/usr/bin/env python3 +"""Capped whole-integer lockstep flow, retaining unmatched jobs as paid exits. + +Generalizes Jacob Alan Sussman's separated multinomial construction. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +This is a finite flow, not a theorem that it attains the mixed-root saving. +""" +from collections import Counter +from functools import lru_cache +from math import comb, prod + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +class Flow: + def __init__(self, targets, paid, n, extra_height=0, height_base=None): + self.T, self.P, self.n = dict(targets), dict(paid), n + self.K = tuple(sorted(targets)) + self.m, self.kmin, self.rmax = max(targets), min(targets), max(paid) + need(2 <= self.kmin <= self.m and self.rmax < self.m <= n, + 'finite direct-flow rank contract') + need(all(isinstance(v, int) and v > 0 for x in (targets, paid) + for v in x.values()), 'positive integer inventories') + self.cap = n//self.m + self.height_base = self.kmin if height_base is None else height_base + need(isinstance(self.height_base, int) and self.height_base >= 2, 'integer height base') + self.G, least = 0, 1 + while least*self.height_base <= self.cap: + self.G += 1 + least *= self.height_base + need(isinstance(extra_height, int) and extra_height >= 0, 'nonnegative extra height') + self.G += extra_height + self.zero = (0,)*len(self.K) + + @lru_cache(None) + def column(self, a): + return prod(k**v for k, v in zip(self.K, a)) + + @lru_cache(None) + def points(self, height, cap): + """(a, u(a)) at fixed degree; exact multinomial integer weights.""" + result = {} + + def visit(i, remaining, c, weight, a): + if i == len(self.K): + if remaining == 0 and c <= cap: + result[a] = weight + return + k, w = self.K[i], self.T[self.K[i]] + for count in range(remaining+1): + new_c = c*k**count + if new_c > cap: + break + visit(i+1, remaining-count, new_c, + weight*comb(remaining, count)*w**count, a+(count,)) + + if cap >= 1: + visit(0, height, 1, 1, ()) + return result + + @lru_cache(None) + def units(self, depth, rho): + return self.points(self.G-depth, self.cap//rho) + + @lru_cache(None) + def demand(self, depth, rho): + result = Counter() + for a, count in self.units(depth, rho).items(): + for i, k in enumerate(self.K): + b = list(a) + b[i] += 1 + result[tuple(b)] += count*self.T[k] + return result + + def merged(self): + sources, exits, boundary = Counter(), Counter(), Counter() + units = columns = 0 + matched = 0 + path_counts = Counter({1:1}) + for b, count in self.demand(0, 1).items(): + sources[self.column(b)] += count + for depth in range(self.G+1): + following = Counter() + for rho, paths in path_counts.items(): + batch = self.units(depth, rho) + units += paths*sum(batch.values()) + columns += paths*sum(count*rho*self.column(a) for a, count in batch.items()) + for rank, repetitions in self.P.items(): + new_rho = rho*rank + copies = paths*repetitions + if depth == self.G: + need(set(batch) <= {self.zero}, 'leaf degree zero') + exits[new_rho] += copies*batch.get(self.zero, 0) + continue + child = self.demand(depth+1, new_rho) + if new_rho <= self.cap: + following[new_rho] += copies + for b in set(batch) | set(child): + supply, demand = batch.get(b, 0), child.get(b, 0) + e = new_rho*self.column(b) + consumed = min(supply, demand) + matched += copies*consumed + if supply > demand: + exits[e] += copies*(supply-demand) + boundary[e] += copies*(supply-demand) + elif demand > supply: + need(supply == 0, 'Pascal demand cannot exceed present supply') + sources[e] += copies*(demand-supply) + path_counts = following + sources, exits, boundary = +sources, +exits, +boundary + need(sources and all(1 <= s <= self.n for s in sources), + 'all sources are positive and fit parent') + if self.height_base <= self.kmin: + need(all(self.n < self.m*s for s in sources), 'default top source bound') + need(all(1 <= e < self.n and self.m*e <= self.rmax*self.n for e in exits), + 'all paid exits strictly smaller than parent') + need(all(self.m*e > self.kmin*self.n for e in boundary), + 'premature exits have a failed boundary term') + mass = lambda h: sum(k*v for k, v in h.items()) + surplus = mass(self.T)-mass(self.P) + need(mass(sources)-mass(exits) == surplus*columns, + 'exact rank-one telescoping identity') + W, P = sum(self.T.values()), sum(self.P.values()) + bound = sum(P**d*W**(self.G-d) for d in range(self.G+1)) + need(units <= bound and sum(sources.values()) <= W*units, + 'full integer unit/source count bounds') + return {'n': self.n, 'height': self.G, 'sources': sources, 'exits': exits, + 'boundary_exits': boundary, 'units': units, 'column_mass': columns, + 'source_count': sum(sources.values()), 'matched_jobs': matched, + 'minimum_source': min(sources), 'all_sources_above_n_over_m': + all(self.n < self.m*s for s in sources), + 'rank_one_surplus': surplus, 'unit_count_upper': bound} + + def literal(self, paid_word, class_limit=200000): + """Every round returns before the next; no merging of round paths.""" + need(Counter(paid_word) == Counter(self.P), 'literal paid word matches invoice') + sources, exits = Counter(), Counter() + classes = 0 + + def process(depth, rho, incoming): + nonlocal classes + classes += 1 + need(classes <= class_limit, 'literal replay class limit') + wanted = self.demand(depth, rho) + need(all(v <= wanted.get(b, 0) for b, v in incoming.items()), + 'all incoming whole jobs fit child slots') + for b, count in wanted.items(): + missing = count-incoming.get(b, 0) + if missing: + sources[rho*self.column(b)] += missing + batch = self.units(depth, rho) + for rank in paid_word: + new_rho = rho*rank + if depth == self.G: + for a, count in batch.items(): + exits[new_rho*self.column(a)] += count + continue + child = self.demand(depth+1, new_rho) + passed = Counter() + for b, count in batch.items(): + consumed = min(count, child.get(b, 0)) + if consumed: + passed[b] = consumed + if count > consumed: + exits[new_rho*self.column(b)] += count-consumed + # All unconsumed exits and this entire child return at this + # paid position, before any later parent round is issued. + process(depth+1, new_rho, passed) + + process(0, 1, Counter()) + return {'sources': +sources, 'exits': +exits, 'classes': classes} + + +def approximate_leaves(targets, paid, maximum, checkpoints, extra_height=0, height_base=None): + """Exploratory floating point recurrence; never an acceptance certificate.""" + m = max(targets) + leaves = list(map(float, range(maximum+1))) + saved = {} + previous_cap = None + for n in range(m, maximum+1): + cap = n//m + if cap != previous_cap: + recipe = Flow(targets, paid, n, extra_height, height_base).merged() + source, exit = recipe['sources'], recipe['exits'] + count = recipe['source_count'] + exit_charge = sum(v*leaves[e] for e, v in exit.items()) + previous_cap = cap + leaves[n] = (sum(v*leaves[n-s] for s, v in source.items())+exit_charge)/count + if n in checkpoints: + from math import log + saved[n] = {'leaves_approx': leaves[n], + 'effective_saving_approx': 1-log(leaves[n])/log(n), + 'source_types': len(source), 'exit_types': len(exit), + 'boundary_exit_types': len(recipe['boundary_exits'])} + return saved diff --git a/research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md b/research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md new file mode 100644 index 0000000000..4badb40f09 --- /dev/null +++ b/research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md @@ -0,0 +1,313 @@ +# Finite precompilation of a mixed-target rule + +Status: constructive bridge under the precise native hypotheses below, +independently audited in `../transfer-audit/AUDIT.md`. This is a written +argument, not a formal proof or a completed integer-multiplication admission. +The companion finite scheduler checks actual integer flow and ordering. +The original immediate-normalization BIT interface failed hypothesis 3. +`../bit/DELAYED-COVER-BRIDGE.md` supplies the distinct delayed-cover +implementation, with a finite local-ring check and the native binding in +`../bit/BIT-P3-NATIVE-BINDING.json`. Its fixed rational cover routes are a +costed program schema, not dense coordinate gates in a plain native word. + +Substantial OpenAI assistance. Apache-2.0. The mixed-target asymptotic flow is +Jacob Alan Sussman's Theorem 1G, PR4268, with the detailed proof at commit +`563b4e6e913625637f36ba7869bf5fcd0dd4975a` of +[`wht-power-saving-lean`](https://github.com/jacobalansussman/wht-power-saving-lean). +The source, exact scheduling code and notices are preserved under `sources/`. +The contribution proposed here is clearing the finite flow into a single +uniform native supplier before applying the inherited outer theorem. + +## 1. What needs to be assumed + +Let a job of rank `s` apply a specified tensor operator to `s` selected +coordinate blocks of one array, fixing all other coordinates. A block has +an arbitrary positive tensor multiplicity `f`. A completed rank `s` job +therefore acts on `s*f` axes. All productive inputs are arbitrary. + +Fix one mixed unit with productive targets `W_k` of ranks `k`, a chronological +list of paid child ranks `r_j`, and a finite number of scalar and routing +passes. These assumptions are required, separately from the moment inequality: + +1. **An all-column native word.** At every integer column count `c`, the unit + computes exactly its independent rank `k*c` output jobs. Its paid rounds + are rank `r_j*c` jobs in the stated order. All borrowed data return to the + declared endpoint, and owned storage is explicitly initialized and erased. + Its finite operation count is uniform in `c`. +2. **Disjoint splitting and spectators.** A rank `a+b` job is a rank `a` job + followed by a rank `b` job on disjoint coordinates. The resulting programs + preserve arbitrary complete spectator fields and accept arbitrary data. +3. **Whole-job adapters.** Any job passed between two units has an explicitly + priced, permitted embedding into its destination. For the intended complex + application these are fixed monomial binary address maps and unit quadratic + phases, together with role permutations. The adapters must work at every + tensor multiplicity. Rank equality by itself is insufficient. +4. **Finite-program closure.** A finite composition of these words and + adapters is again a permitted finite supplier. Constantly many owned fields + may be supplied with their full cost and no productive output credit. + The eventual ordinary recursion must have the same arbitrary-input, + restoration, scalar and precision interface as the retained supplier. + +Put `m=max{k:W_k>0}`, `k_min=min{k:W_k>0}`, and +`r_max=max{r_j}`. Require `r_max g*S`, keeps one +external weight throughout the entire finite circuit, and lowers only its +final rank-one leaves. All rational matchers, role routes and their inverses +are fixed before choosing the odd prime and its exclusions. Every route +uses complete equal-multiplicity cover fibers and the retained, costed row +permutation primitive. This gives the same finite DAG argument in the +rational-cover program category. The BIT binding supplies the actual native +projectors; a rank count alone would not provide this implementation. + +## 2. Proposed conclusion + +Suppose the preceding hypotheses hold and the mixed balance has root +`tau` in `(0,1)`: + +``` +sum_j r_j^tau = sum_k W_k k^tau. +``` + +For every `z` with `tau=2`, a fixed number `B_N` of productive arrays, +and only rank-one paid children, whose number `P_N` satisfies + +``` +P_N < B_N * N^z. +``` + +Every productive output is the full rank-`N` job. The construction may have +an enormous finite scalar word, role inventory and owned-storage requirement. +Those quantities affect constants and the eventual input threshold. They are +not omitted and are not credited as extra output jobs. + +If this uniform supplier is admitted under the retained native, precision and +fixed-tape premises, the existing uniform recursion applies directly. A new +dynamic RAM-to-Turing-machine simulation is not being assumed here. + +## 3. The integer lockstep flow at a fixed rank + +This is the part of Theorem 1G used by the compiler. At one fixed top rank +`N`, its units, source jobs and exit jobs have integer multiplicities. +For a multi-index `a` on the target types define + +``` +c(a) = product_k k^(a_k), +u(a) = multinomial(|a|;a) * product_k W_k^(a_k). +``` + +The exact Pascal identity is + +``` +u(b) = sum_{k:b_k>0} W_k*u(b-e_k). +``` + +Let `G` be the largest `|a|` with `m*c(a)<=N`. A class is indexed by a +sequence of paid rounds `s` of length `d<=G`; its dilation is +`rho_s=product r_j`. It contains `u(a)` units at column `rho_s*c(a)` for +each `a` with `|a|=G-d` and `m*rho_s*c(a)<=N`. + +For one parent paid round, the Pascal bijection matches its job copies to +target roles of the child class, at exactly equal integer ranks. Missing +demands are top sources. Separation ensures every parent job is consumed. +The source ranks lie in `(N/m,N]`; only the deepest classes produce exit +jobs, all strictly smaller than `N` once `N` is outside the finite base range. + +Process a class in word order. At round `j`, suspend every unit of that +class, complete the entire child class fed by that round, and only then +advance the parents to round `j+1`. This forbids a unit from requiring both +an earlier and a later round of the same suspended parent. The resulting +dependency graph is finite and acyclic. Its edges carry complete array jobs, +not individual scalar values copied for free. + +These integer quantities exist before normalizing the sources to total +weight one. Let `S_s` be the number of source jobs of rank `s`, let +`S=sum_s S_s`, and let the ordered exit batches be `(e,t)` with `t` jobs +of rank `e` each. This finite integer flow is the compiler input. + +## 4. Clear every batch denominator constructively + +Induct on the integer top rank `N`. For each smaller rank `e` the compiler +has already constructed a uniform program on `B_e` arbitrary arrays, +computing full rank `e` with `P_e` paid rank-one calls. For a sufficiently +small rank use the ordinary sequential program: `B_e=1`, `P_e=e`. + +For the current flow choose an integer `a` divisible by every `B_e` needed +for an exit and every `B_(N-s)` needed for a nonzero source remainder. +The product of those finitely many positive integers is a valid choice; +their least common multiple is a smaller optional choice. Set + +``` +B_N = a*S. +``` + +Assign `a*S_s` of the input arrays to each source rank `s`. On each of those +arrays, first complete its `N-s` complementary coordinates using the +already-compiled smaller uniform program. All such batches are integral +because `a` is divisible by their program widths. This preliminary action +commutes with the intended `s`-coordinate job and fixes its input coordinates. + +Make `a` copies of the integer lockstep flow. Route its source arrays to +their exact input slots using permitted whole-array adapters. At a deepest +exit batch, `a*t` is divisible by `B_e`; replace that batch by copies of +the smaller uniform rank-`e` program. Restore its role ordering and adapters +before resuming the suspended parent class. Execute the finite DAG in the +lockstep order, and finally restore the original source-array ordering. + +Every array has now received its disjoint complementary job and source job, +hence the full rank-`N` transform. No copied scalar input or blank helper is +treated as another independent output. Every original array occurs exactly +once as a source; interior target slots are jobs on those arrays, not new +productive inputs. + +Induction removes all recursive calls: the only remaining paid children +have rank one. Clearing denominators multiplies productive arrays and paid +operations equally, so it preserves the per-array leaf count. In formulas, + +``` +P_N/B_N = (1/S) * [ + sum_s S_s * (P_(N-s)/B_(N-s)) + + sum_(ordered exit batches e,t) t * (P_e/B_e) +]. +``` + +Zero-rank terms vanish. Any plain rank-one exits are the ordinary base +program. Scalar and routing passes have their own analogous nonnegative +count and must be included in the asymptotic cost used to choose `N`. + +This construction uses full integer batches; it does not assume that +fractional pieces of a physical array can be routed at zero cost. Its exact +replication factors can be impractically large, which is acceptable for a +fixed finite supplier existence statement but must be disclosed. + +## 5. Why some fixed N has the required saving + +The independent audit sharpened this step to a direct count of paid leaves. +It does not require a running-time comparison between a RAM flow and native +tapes. Let `L(n)=P_n/B_n`, let `w_s=S_s/S`, and let `x_e` be the exit counts +normalized by the number S of source arrays. The actual integer compiler +satisfies + +``` +L(n) = sum_s w_s L(n-s) + sum_e x_e L(e), +sum_s w_s = 1, +sum_e x_e e^tau = sum_s w_s s^tau. +``` + +The last equality follows by canceling every internal matched job in the +exact tau-potential balance. The source ranks satisfy `n/m0`, concavity gives + +``` +n^z0 - sum_s w_s (n-s)^z0 >= eta * sum_s w_s s^z0. +``` + +Indeed, for `t=s/n` in `[1/m,1]`, +`1-(1-t)^z0 >= z0*t >= eta*t^z0`. For every sufficiently large n the +exit coefficient is less than `eta/2`. Every complement and exit has +smaller rank than n, so strong induction on the exact recurrence proves +`L(n)<=A*n^z0`, with finite A chosen to cover the smaller ranks. Eventually +`L(N).lean, byte-identical to + third-party/openai-math/). + + b. Modified copies of OpenAI's proof files. In each package, the folder + Work/Fourier/ (for example Work/FourierC588MHH/) holds copies + of eleven files of lean/OAI/Computability/FourierTransform/ of + openai/math and of five definitions of its Goal.lean, made the way + section 7 describes, by Shea's script mkchain_c401g5.py or by the + agents' generators that copy its output under a new suffix (for + example community/c588mhh/generators/lean-gen/mk_fourier_h.py). Each + begins with a + comment that names the upstream file and states what was changed. In + c588-repack these are Shea's own copies with the exponent changed. + + c. Files that contain upstream text. The files Challenge.lean under + community/wht-c588/overlay/Work/ and community/wht-c588mhh/overlay/ + Work/ contain the RAM cost model of + lean/ComparatorChallenges/UniformFourier.lean of openai/math, + unchanged, as Work/GCert/Data/ChallengeB2Ge8x.lean does (section 2); + their headers say what differs from that file. + + d. Files adapted from Shea's repository in community/c588mhh/overlay/ + Work/XHost/: + - HDef.lean is a copy of lean/complex588/Work/Bridge401/GNetDef.lean, + HStage.lean of Work/Bridge401/GNetStage.lean, HCert.lean of + Work/Bridge401/GNetCert.lean, HGeom.lean of the instance part of + Work/Bridge401/GGeom.lean, and HEnd.lean is adapted from + Work/Bridge401/End.lean, each with same-run hosting added (the idea + of DaysSky's pull request #442 to CrocSwap/integer-mult-bounds) and + the names changed. In Shea's tree these files are those of Nil + Mamano's submission named above (his SOURCE_MANIFEST.json records + each as taken from submissions/dft/nmamano-dft-record/ at the + verifier commit above), written by his generator gen401.py on the + layouts credited above, with the engine of this repository. + - Frames.lean adapts lemmas of Work/Bank401/Adapt.lean and + Work/Bank401/Frames.lean of the same tree, which come from the same + submission: host_adapt is bank_adapt, host_pad is bank_pad and + slot_frames is bank_frames, each with the new coordinates chosen + inside the pending set of an idle climb. + - HSchedK.lean copies the lemmas about lists of + Work/Bridge401/SchedK.lean of the same tree, and its checker + hostSchedK is modelled on the checker schedK there; HostK.lean is + modelled on the same checker. + The header of each file names its source and says what was changed. + One header is wrong in part: that of HEnd.lean says that Shea's + End.lean was written after a file Work/Bridge377/End.lean of Jacob + Sussman's. No such file of his exists; Shea's End.lean says only that + it follows a file of that name. The header is left as it was compiled + (community/c588mhh/README.txt says so). + The generators that wrote them are under + community/c588mhh/generators/lean-gen/. The same twelve network files + of Work/XHost/, byte-identical, are also in community/u8xmhh/overlay/ + Work/XHost/. + The log community/c588mhh/supporting/L2/skeptic/logs/ + Work_Bank401_Adapt.log is of his file, compiled unchanged; the file + itself is not included. + + e. Programs from Shea's repository. + - Byte-for-byte copies of his files at the commit above, unchanged and + without a notice inside them (the same files are also in + third-party/shea256-fourier-transform-below-nlogn/ at their own + paths): + research/complex-transfer-588-596/experiments/generate_global_lean.py + is copied as tools/community/route/generate_global_lean.py and + tools/community/repack/tools/generate_global_lean.py; + research/complex-transfer-588-596/experiments/bank_reprice.py is + copied as tools/community/repack/tools/shea_bank_reprice.py; + research/complex-transfer-588-596/verification/exact_moment.py is + copied as tools/community/route/exact_moment.py, + tools/community/repack/tools/exact_moment.py, + community/c588mhh/generators/design-tools/exact_moment.py and + community/u8xmhh/generators/design-tools/exact_moment.py. + - route_price.py, in four identical copies (tools/community/route/, + tools/community/repack/tools/, + community/c588mhh/generators/design-tools/ and + community/u8xmhh/generators/design-tools/), contains functions + copied from his bank_reprice.py and generate_global_lean.py (its + header says so), changed to price a local word through his route. + - The generators of tools/community/c588m-gen/ drive or adapt his + scripts in third-party/shea256-fourier-transform-below-nlogn/ + research/; each adapted file says what it changes. + - community/c588-repack/overlay/comparator/fourier.json is his + comparator configuration, unchanged. + + f. Data. The certificate of Kothe's #588 circuit, its bank schedule and + its price, as published in Shea's repository, are in + third-party/shea256-fourier-transform-below-nlogn/lean/complex588/ + artifacts/, unchanged. The packages' certificate and data modules + are derived from them (VERIFY.md, section 11, says how). + + g. Data derived from CrocSwap/integer-mult-bounds at a later state (the + U8 circuit). The certificates of community/u8x and community/u8xm (the + files under their Work/GCert/Data/ whose paths contain U8X), + and the host table and data modules of community/u8xmhh, which are + computed from the certificate of u8xm, are derived from the U8 word of + the repository CrocSwap/integer-mult-bounds + (https://github.com/CrocSwap/integer-mult-bounds), a circuit of that + community: Jeremy Kothe's pull request #869, on his #799 (which + carries Chafik Boukhalfa's frame changes of #741), on icekylinx's + gauge44 construction (#645) and on the earlier work that their + notices name. Only the word's additions and their frames are used: + not the owner maps of #870 (Kothe, with Hao Yan's #858), #890 + (Boukhalfa) and #942 (Jonathan Capalbo), nor DreamingOfClouds' bit + supplier #589. The agents rebuilt the word with that repository's + own program + research/complex-t21-owners/vendor/pr870/construction/barch/ + reproduce_barch.py (recipe U8; #869's builder, in the copy of #870's + package that #890 keeps), in a clone at commit + 407d52ff15b2217b6e22bce44728b4c3907b6515 of its main branch + (13 October 2026). The word they obtained has the canonical sha256 + 24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c, the + value pinned for it in that repository (the file + LOCAL-PINS-barch-U8.json next to the program). The logs of that run are in + community/base-logs/u8-word/. No program of that repository is + included here, and the word itself is not included: the packages hold + certificates computed from it. + That repository is published under the Apache License, Version 2.0 + (its LICENSE at that commit is the same text as the file LICENSE). + Its NOTICE file at that commit differs from the copy of section 6 (the + state of pull request #193) in one passage, which + third-party/CrocSwap-integer-mult-bounds/at-407d52ff/SOURCE.txt + describes. Complete copies of that NOTICE file and of the notice files + of the folders the program comes from + (research/complex-t21-owners/NOTICE.md and, under its vendor/pr870/, + NOTICE.md, UPSTREAM-NOTICE.md and t16/NOTICE.md), unchanged and at + their paths, are in + third-party/CrocSwap-integer-mult-bounds/at-407d52ff/; they apply to + these data. + + The new files of community/ were made on 2026-10-13 the way section 4 + describes. The credits, with links, are in README.md. + +10. Files added in the fifth revision outside community/ (package/, + scripts/, tools/lever/, tools/lever-hub/, tools/reproduce-search.sh, + tools/compare_results.py, data/, results/, research/, + notes/how-the-lever-was-found.md, notes/open-directions-4.md and the + additions to third-party/). + The packages under package/ (the sixth result, package/u8x0hq, and the + recursion lever, package/leverF, package/leverB, package/leverA, package/lever2979, package/lever) are laid over the same + clone of Ryan Shea's repository as the packages of section 9 (commit + 52394849c7ecf3412d39b925d75fc7fdb98994d8, folder lean/complex588, + Apache License, Version 2.0). His licence and notice files in + third-party/shea256-fourier-transform-below-nlogn/ apply to the material + of his repository that files of these packages copy or adapt; each such + file says so in its first lines, and the packages' README.txt list them. + Shea's tree carries Lean files of Nil Mamano's published Big O Speedrun + submission (bigospeedrun/verifier, Apache License, Version 2.0): the + gauged interface, the nine-stage network, its bank lemmas and checker, + its end theorem and the templates of the Fourier chain. The hosted + networks of these packages (Work/XHost in package/u8x0hq; Work/XHostD, + Work/XHostR and Work/XHostT in the lever packages) are adapted from those + network files, as their first lines say. + + a. Modified copies of OpenAI's statement file. Each file named + UniformFourierChallenge.lean under package/*/overlay/Work/ is a + modified copy of lean/ComparatorChallenges/UniformFourier.lean of + openai/math at the commit above: in package/u8x0hq the folders + FourierU8XM, FourierU8XMHH, FourierU8X0, FourierU8X0HH and + FourierU8X0HQ and their twins ending in Neg (10 files); + in package/leverF the folders FourierL3945F and FourierL3945FNeg (2 files); in package/leverB the folders FourierL3945H and FourierL3945HNeg (2 files); in package/leverA the folders FourierL2979H and FourierL2979HNeg (2 files); in package/lever2979 the folders FourierL2979 and FourierL2979Neg (2 files); in package/lever the folders FourierL3945 and FourierL3945Neg (2 files). Changes: the exponent + 1 - 1/(10^(13:ℕ)) is replaced by the package's exponent (in a folder + whose name ends in Neg, one unit stronger), and the seven names of + section 2 receive the package's suffix. Everything else in these files + is the upstream text, unchanged. Unlike the copies of section 9, these + files carry no comment inside them: they are kept byte for byte as they + were compiled, because scripts/build-and-check.sh derives them again + from third-party/openai-math/ (scripts/derive_challenges.sh) and + compares the two. This section is their notice. + b. Modified copies of OpenAI's proof files. In each package, the folders + Work/Fourier/ hold copies of eleven files of + lean/OAI/Computability/FourierTransform/ of openai/math and of five + definitions of its Goal.lean, made by Shea's script mkchain_c401g5.py + or by the agents' generators that copy its output under a new suffix. + Each begins with a comment that names the upstream file and states + what was changed. + c. The community's files. third-party/CrocSwap-integer-mult-bounds/ + staged544-terminal-gap-fill/ holds unmodified copies of 32 files of the + folder research/staged544-terminal-gap-fill/ of pull request #3945 of + CrocSwap/integer-mult-bounds at its head + 91f81d131252db704f945891da1ea54e29d46b8b (Dugongue's branch): the owner + data (FILL, PROFILE, ORDER, DISPATCH, PLAN, TEMPLATE, the two words and + the files of #3815 that #3945 carries as old-*), README.md, PROOF.md, + RESULT.json, SOURCES.json, LICENSE, NOTICE.md and the native lineage + notices. BLOBS.txt gives the git blob hash of each, as GitHub stores + it. That repository and its contributors' branches are published under + the Apache License, Version 2.0; the NOTICE.md and native notices of + that folder apply to these files and are quoted in substance in (g). + The files of #2979 (research/rank7-joint-endframes/ of the main branch + of CrocSwap/integer-mult-bounds at 20ecf289; Marius-Paul Dumitrean, + with the files of Mason Hale's #2917 and of #2942 that its NOTICE + names) are copied unmodified, 12 of them, into package/lever2979/ + and package/leverA/ under generators/tree/wht45/lever/p-alt/dl/ + main2979/: CLAIM.json, CREDITS.md, PINS.json, ALLOCATION-PINS.json, + the allocation files DISPATCH, FILL, ORDER, PROFILE and PROVIDERS, + and the data files PARENT-base, WORD-base and WORD-extra. + package/leverA/generators/tree/wht45/allheads/aA-data/in/alloc2979H/ + holds unmodified copies of its DISPATCH, ORDER, PROFILE and PROVIDERS + (beside the table with every head kept, FILL.json.gz, see (d)). Both + packages also hold #3945's owner/inputs/PLAN.json.gz and + TEMPLATE.json.gz under generators/tree/wht45/lever/g-heads/dl/pr3945/. + The generators check every one of these copies against its sha256 + (generators/tree.sha256) before they run; the same licence and the + notices of #2979 (for PLAN and TEMPLATE, of #3945) apply to them. + Both packages also hold generators/tree/wht43/bound-check/k-word/ + tools/build_tri_869.py, an unmodified copy of the community's word + builder construction/barch/build_tri.py (the same bytes as + research/complex-t21-owners/vendor/pr870/construction/barch/ + build_tri.py of its main branch, whose notices section 9, item g, + names); the generators do not run it. + More unmodified copies of the same folder of #3945 are in package/leverF/ + and package/leverB/, under generators/tree/wht45/lever/g-heads/dl/pr3945/ + owner/: 21 of the files above, and #3945's build_fill.py, check_gain.py + and verify.py (git blob hashes equal to GitHub's at 91f81d13); the same + licence and notices apply to them. + d. Data derived from the community's files. data/native/ holds the + canonical native words of #3945's two words (and of #3815's), the + output of #3945's own program native/run_native.py, run unchanged by + the agents. data/gcert/, data/residuals-*.json and data/t74ctl/ are + the agents' conversion of those words, and of the earlier T74 words, + into this project's certificate format (tools/lever/lower_b.py and + t74_control.py); data/t74ctl/inputs/ holds the community's T74 + inputs repackaged in the layout of #3945's package (TEMPLATE.json.gz + unmodified, and ORDER.json with the same content as the community's + T74 order). The Lean data of the lever packages (the words, the + dispatch, the tables of hosts) is generated from such conversions and + from the community's files by the generators in each package. The + tables with every head kept (the folders fill/ of the packages on + every head kept, where shipped) were made by the community's own + allocation programs (on #2979, its fill17.py and double.py; on #3945, + the hall_lp.py and build_fill.py of #3815 and #3945's offset step), + run with one added condition; each package's fill/ README says how, + and which of those programs it copies, with their notices. + e. Programs that re-implement or adapt the community's code: + - tools/lever/pricer.py re-implements (does not import) the community's + moment engine and kappa assembly (research/native-complex-moment552/ + engines/moment.py and outer.py, research/gauge44-frames-x/code/ + assemble.py). The package "native complex moment" is by Rohan Arun + with OpenAI Codex assistance, on Dugongue's #552, eumemic's #543 and + #558, and icekylinx's complex-cover notes; its outer assembly is + eumemic's, after icekylinx's #144 and Zhihao Chen's #23, with the + balanced prefix of the RaD project (hipotures). + - tools/lever/heads_fill.py and g0_staged.py re-implement the window + and family semantics of #3945's owner/verify.py (they do not import + it). + - tools/lever/lower_b.py extends this project's own lowering program + to the community's borrowed-helper words; the meaning of a warp + follows the community's native code (bw_transport.py, bw_emit.py of + #3945's native/vendor), which was read, not copied. + f. Scripts. scripts/apply-overlay.sh, build-and-check.sh and + run-comparator.sh are adapted from this project's community/scripts/; + scripts/base/, cc-jail/, bos/ and lever-run/ are the agents' scripts + as run. Those in bos/ and lever-run/ package a proof in the layout of + the entries of bigospeedrun/verifier and run that verifier's three + phases; the verifier's own code is not included, except its function + strip_comments (scripts/verifier.py of bigospeedrun/verifier, Apache + License, Version 2.0), whose logic scripts/bos/fspb_submission.py and + scripts/lever-run/isk_submission.py copy, as the line that defines it + says; the same function is in community/scripts/bos/mb_submission.py, + community/u8xmhh/scripts-as-run/build/fsb_submission.py and + package/leverF/logs/fc-engine/C3/scripts/isk_submission.py. + g. Credit for the circuits of the lever. + #3945, as its NOTICE.md and native lineage notices ask that the credit + be kept: + - #3945 (Dugongue, with substantial OpenAI Codex assistance, including + three parallel Codex agents): the terminal-width construction (26 + protected helper terminals from width 4 to width 5, with scalar and + native frames refitted), the idle-gap absorption proof, the + source-guarded recipe, the independent finite checks and the + integration. + - dataisfire, #3734: the staged544 supplier and its full source closure. + - zxv, #3682: the staged pair; #3638: the earlier T360 allocation. + - Ross Richardson, #3605: the staged entrance, cleanup and residual + checks (helpers 644 and 660 from width 8 to 7). + - Erwan Secousses / ChaloupeMusic, #3815, with the #3638 lineage: the + attained T360 owner clock and fill, and the allocation programs that + made the table with every head kept on #3945. + - hexapode (Pierre-Loic Doulcet), #3802 and #3875: the earlier complete + endpoint combination and its refinement. + - Dugongue, #3857 (general proof and evaluator work) and #3929 (the + transported-frame compiler). + - Sagar Thakrar, #3687: audit_core.py, which reimplements Arham Tahir's + coupled-carrier audit; roger-sato, #3693: the whole-word audit adapter; + roger-sato, #3642: the T530 release retimings. + - Jeremy Diviney, #3148: the coupled-carrier T740 packing cap; dcharb78, + #3133: helpers 586 and 588 lowered by coupled carrier folds. + - Marius-Paul Dumitrean (mdumitrean), #2979: joint rank-7 end frames and + five paired extractions, on Jeremy Kothe's #2957 gate rewrites; #2802 + (hostee moves and retired-lender aliases) and #2733. + - Jeremy Kothe: the frame and preload machinery, #2833 (dirt-entry + rewrite of helpers 530 and 542), #2957 (gate rewrites on Mason Hale's + #2917 words), and the source pipeline, label swap and order and fill + of #2462, #2588 and #2673; Mason Hale, #2917 (nine paired helper + extractions); Lyy-iiis, #2857 (shared kernels) and #2848; Dugongue, + #2863; philippeVV (Philippe Van Velzen), #2853, #2559 and #2679 + (evacuation, six pre-life hosts, the refit alias). + - Cinna Davis (@1337isnot1337), #2226, with OpenAI Codex assistance: + anticipatory dirty borrowing (the borrowed helpers and their warps) + and the native exact Clifford and operator machinery. + - Tekalign (@tekuuu), #2436: the four lifted targets, the joint + twelve-source construction, and the sparse native accelerator, with + the authors its SPARSE-NOTICE names. + - zxv, #2530: the eight source-partner aliases; Mason Hale, #2696: + concentrated source-partner assignment and an independent local + interpreter; themilkman216, #2621: the priority order; Vlado + Vojdanovski, #2322: generator utilities; Jeremy Kothe, #2312: the + helper width exchange; Dugongue, #2309, with Sagar Thakrar's audit + #2315. + - icekylinx, #433 and #514, and the retained native ancestry; + DreamingOfClouds (with Claude): the inherited wrapper and outer + machinery; chafreaky (Chafik Boukhalfa), #458, and its lineage. + - Josie Elliston, #1956 (bootstrap carried-cutoff repair); Sagar + Thakrar, #1964 (label and adapter checks, mutants). + - The T74 words and owner construction underneath: Rohan Arun (#1218, + #1297, #1319 and the T74 exact-fill owner construction, with OpenAI + Codex assistance), Marius-Paul Dumitrean (#1625: the pivot-566 + kernel, words, edits and rebuild scripts), Jeremy Kothe and LeverRank + (#1672), on Jeremy Kothe's k8 leaver word and seven-slot line (#1018, + #1042, #1274) with Thomas DiFiore (#1148), Jeremy Diviney (#1193) and + Chafik Boukhalfa (#1196); the outer and the assembly by Vlado + Vojdanovski (#1673), Chafik Boukhalfa (#1699, #1786) and Jeremy + Kothe (#1377, #1839). + - Rohan Arun's draft #3939 and his #3934 stack, and Chris R / + Clear1nsight's #3883, #3936 and #3941, are acknowledged by #3945 as + neighbouring work; they are not used here. + Checks of #3945 by others, which this project read and re-ran: Chris R / + Clear1nsight's audits #3969, #3988, #3994 and #4016; the exact + eight-stream operator replay of ChaloupeMusic's gist, on the operator + model of Nick Petalas (#3187) and Matarener (#3296). + #2979, from its pull request body, CREDITS.md and NOTICE ("All original + notices of the exported predecessor packages remain in force"): + - Marius-Paul Dumitrean (mdumitrean), #2979, prepared with substantial + AI assistance (Anthropic Claude, via Claude Code): the codimension-2 + census, the joint end-frame lowering of 22 restored helpers in five + groups, the five further extractions, the composition with #2957's + rewrites, producer and checks, the overlay stage, the six-class + adapters, the literal T74 allocation, the cap certificates and the + complete fresh replay; also #2930 (cap allocation, relaxation + tools), #2942 (four normal-45 extractions; its words are #2979's + parent) and #2843 (the flow model's starting point). + - Jeremy Kothe, #2957, #2948 and #2966: the fourteen declared gate + rewrites and their applier; #2894 and #2833: the preload re-synthesis + supplier, frame accounting and cleanup, source materializer. + - Mason Hale, #2917: the nine paired extractions, the T74 chronology + (ORDER and DISPATCH), the allocation checker, moment auditor, + extension stage and adapter derivation. + - Jeremy Diviney, #2908: the paired input/output extraction, its + compensation rule, the two-sided certificate and the closed-adapter + admission chain. + - Dugongue, #2969 (comparator composition and baseline), #2863 and + #2839 (packing lineage, owner engine). + - Yiyang Lu (Lyy-iiis), #2857 and #2848: shared-kernel words, staged + native and overlay tooling, the flow model and realization of the + allocation. + - Ross Richardson, #2918: the rank-seven obstruction for helper 408. + - Tekalign: the independent owner and chronology checker; icekylinx: the + exact free-operator auditor (#2833); themilkman216: the integrality + observation behind the allocation's face step. + - Gareth Davidson (bitplane), #1995 and #2013: the fixed-word + terminal-subspace bounds that frame stage 1. + - Underneath: Cinna Davis (#2226, dirty borrowing and warps), Jeremy + Kothe (#2312, width exchange), and the T74 line above. + The table with every head kept on #2979 was made by #2979's own + allocation programs, credited as above. + h. Credit for the Lean route. + - Ryan Shea: the conversion pipeline, the generators and the Lean + instantiation of Jeremy Kothe's #588 circuit (lean/complex588), which + these packages are laid over. + - Nil Mamano: the files named at the start of this section. + - Dugongue (#401): the entrance gauges and the banks of the nine-stage + network; Zhihao Chen / jacklightChen (#377, #425): its compressed + layout with banks and padding, and the written argument for mutable + sources; lydakis (#275): the bank patterns; DaysSky (#363): the + bridged layout, and the proposal, with a written proof in the + community's terms, to host helpers in idle arrays. + - Jeremy Kothe and DreamingOfClouds: the community's lemmas about where + a helper may end, on which the charge for exit frames rests. + - For package/u8x0hq: the community's U8 circuit, Jeremy Kothe's #869 on + his #799, with Chafik Boukhalfa's frame changes (#741) and + icekylinx's gauge44 construction (#645), as the community's notices + record it. + - The idea that Theorem 1G extends is Schönhage's τ-theorem for matrix + multiplication. + - OpenAI: the cost model, the statement and the step from the lengths + 2^k to every length. + i. research/. Written for this repository by the agents under my + direction. The sections cite papers by title or arXiv identifier and + the community's pull requests by number, commit and file hash; they + copy no paper text and no file of the community's repository, with + these exceptions: research/record-track/programs/a-fc/r2/tools/ + fallback_patch.py carries a modified copy (made tolerant, as its first + lines say) of the placement loop of construction/build_fill.py of + #3815 (Erwan Secousses / ChaloupeMusic; CrocSwap/integer-mult-bounds, + Apache License, Version 2.0); and research/record-track/programs/ + a-fc/r2/tools/fillmodel.py copies the window, family and width logic + of owner/verify.py of #3945 (Dugongue and the lineage its NOTICE.md + names, see (g); CrocSwap/integer-mult-bounds, Apache License, Version + 2.0), as its first lines say; research/why-the-savers-save/programs/ + helpers-narrower-ends-skeptic-rules/asm1042.json is an unmodified + copy of research/community-frontier1042-audit/ASSEMBLY.json of the + community's main branch (the community's #1042 audit, integrated by + its maintainer Douglas R. Colkitt on 13 October 2026); + research/record-track/data/a-fc/design/ + ORDER.json and DISPATCH.json hold #2979's allocation/ORDER.json and + DISPATCH.json (Mason Hale's #2917, as #2979's NOTICE says), with the + same content, re-serialised; and research/why-the-savers-save/ + programs/helpers-half-reads/bit/xcheck_base.json, the report of the + community's checker xcheck_p.py (DreamingOfClouds' line, on eumemic's + #555) on #589's word, has the same bytes as + research/community-frontier741-audit/bit/xcheck.json of the + community's main branch, integrated by Douglas R. Colkitt on 13 + October 2026 (these three: CrocSwap/integer-mult-bounds, + Apache License, Version 2.0). fallback_patch.py, and tools/ + place_patch.py, tools/hall_fc.py and tools/mkpatch_fill17.py of + programs/a-fc/, apply their changes to copies of community files that + they read by path (#3815's build_fill.py and hall_lp.py, #2979's + fill17.py); those files are not changed. The other programs of + programs/a-fc/ are mine. + j. What is mine: the mixed-target recursion (Theorem 1G and its Lean + proof in OpenAI's model); the lever (the head test, the half cut, the + full cut and its 24 + 24 split, the head lemma, the heads-first + certificate, and the tables with every head kept); the A-fc table on + #2979's words (its class solution and its tolerant placement); the Lean ports of + #3945 and #2979 (the conversion of their + words, the warp checker and its soundness, the networks of many copies + with hosting across copies, the dispatch, the generators); the Lean + engine of this project and its extensions for exit frames, mutable + sources, centre reading and hosting; the checks; the search and pricing + programs in tools/lever/ and tools/lever-hub/; and the research in + research/. tools/lever-hub/network/Gates.lean is an unmodified copy of + lean/complex588/Work/Bridge401/Gates.lean of Ryan Shea's repository + (commit 52394849c7ecf3412d39b925d75fc7fdb98994d8, Apache License, + Version 2.0; its header credits Dugongue, lydakis, jacklightChen and + DaysSky); the other files of tools/lever-hub/ are mine. + + The new files of package/, scripts/, tools/lever/, data/, results/ and + research/ were made between 2026-10-13 and 2026-10-20 the way section 4 + describes: by AI agents (Claude) under my direction. The credits, with + links, are in README.md. + +Not included in this repository and fetched by the build: Mathlib +(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its +dependencies. The comparator (https://github.com/leanprover/comparator) is a +separate tool and is not included. diff --git a/research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz b/research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..b46d44c6ee624968dd57be928b0c15d9d45f3b2c GIT binary patch literal 198063 zcmZs?2{=^Y|NkvJV_(M37{k~}veV2M%!nDr5+a16WSL|uF&G)4SrD=fLsZr%OADgV zHpY^*ETa%Ak<#`|-|zqV{eRDOJ+9Z>=l-1goO2m-=02a#`+ifqD#-Qkhnr{P;dE2z zQGDH=;Rh=zAG;}r_54TCY~I+?3z=F2S^x*(Ovd$NTT@TAvtNDQO?4`i6Wx^+KbyK1 z{QOdT-^;(1@BTdh^mixq*N0E3Kc7eceSYNEljzjn&5!^7RC_#s`RC)m-)A5HUjF;% z{=2`kYJb1KdHnke_V2gm)E^)Ie*cjA^Ub?Q@BS>_SNj~8`twWb-}~>PY@hDknAq%8 ziBA2om%9Hu@bcf;*>{)!J`eO}{|RiI-kZH2fA-zGwGZ)+%0+*#Rkr-P{B!WJ+v9z? zrDJ~)pMGEe+yDL053CQI7yoT> z!bqt(6`Xph>;5M8fx4QW$AkTB^Y^pUuPXl#-(;+P+66=h{N8-?XJB@H|7t3Dw)qd~ zraw3=ZvSfD?9D~o$(9%VEyCcS)&($e*wFU~C@6=puR(&rW32@zCWpP#nDC$t{55_w{t;5m02m{%6jmEd?I~8}6qjG!nGJgDwZI9u+M+ z`p`tQ2h_XPzn0GbDi2g(D6f7eGjQy4-XnjZ<)7Q14Eb7?{n9R%<~-}*ioX>2XTFxp zqd4pLQ65hFb;HfsBwj|CL-slL0OnqUjy70qpqJ(teEVN zF~^>!0Rm$7ANtGl-0U2&avPE7ycwydu=0=vHy}7z=U(&R1!3+NMl%RWm;z6rVzGzB zf-=tt$TR-Qmkt#`PjH}!XP8cfR`^0Y%9YvsrvLZ1Pfe%$I=CLDUg(qHl@ApA)FgtC zdzJb1BkFyB>)d1DR>K`04-4@DOF`n--e1-BqcG`LJO-6z;TM&!T2q{bpEGr+B7%$T&F~9Dprn&)(2?+{|iZfYm^3@Z@jjsmrRWsbR(1Hu5!Z$pb&}V;wT4pAVmOIfw~p0qiGf$!u^RQRx{m zH4Rq$_Vq?)M0ns*d>F8ENy7@e-(SMSs!^71c>%#ct=0el_aky(8n478!RnFGPA%8z z0cT$!*J8e!BgE}*A)wTXo!t=&*{8iP4lA))7Ai-soqHq&vy^?~L5?zl{Y@hOr=}NG@_;%8#-B#8LK=rngtml9##d%H5i^UcHX5yRNs1z24IOt5?%b@r^+x zp}n)^4JJFsk&!RvsS=7O(p0oY^|7V`EVtQEDTp8LBPiX|{v0i( zo%~05tvUOTumQL*Xz~&Rde-$_3g4NrO5f%)V^ycOTE9nkgD?y+WA#r?r^=&(28)&s z0`m4-X&r5}^NsIq@^0(Du6)w}R+8ETxqWQRo^A$MX=)B1ItCO!WFp<_d=M(A@411gCuIY4~1>G1w2u1cEa84!-MXZ-wyfU z(;=-$fN!;UhozDDM~7GMi236j960T(He#7MQ90fr{}J)QMGg+%Y7nm~IDjt(G~Q0P z^Z5!hU5_88HeU!MYmWN+ImGXP-;UqKq_u2Te0Jdil-NVdkRri@f6|X^%Y2LB(G>HZ zkw__ro6L?;8(C;xcd;$NyrgZP(>LzVF#IK%m+rHU`!`Uj2=7(y1n@WI?22qh9;O&l zz>P#c+|`R_OPCGS7VxfL&R2-1BXS1$H^14UmWTI2`m^LalffqIcchCiRY{kW4{ab% z4gNG%r8Q0zW%M$7%I}~EMWY}O&7qxqFdpK&Nfj(-9H)kNTm9%S&DQd`4SPI?eP$(6 zH2<2`KGROC%P^hq#f=U7Hqh?kqG`R31A^Qc2Y*vC)JNusUdhyu_mF2VNcknwDu*h^ zRK2>@lfg3*y-q_6S>%56=Imm(#mtf_3_Z1H&_Z{Kz6f{tw;Iys%T!z&;=cFc-24u9_wH_rK! zxgXJT53Ht?hX%OCGj2NBdLCr53#r@{Z;!bLLr|2cf(nsx>@lD5I+7zpu#@&*isQ)x zy)Y6%d?lGHAX60?sR=N21Nz%!iFhSSS#U)P5ZsOS39G#6sH8LS?Q!nf3O=+gpg~jhTLHje)n+X$l63_&tq%(;r8uqpEdE9{}KBia$+F=10JWz zAtx5{|4Xd5Cf-}~U#p`T`yV)+|LOnFMMyDIa6{Lb1DF+nGE!p2^UwFT9*mxYC~$xO z(H1v$yq!`Eo4L&yjuHNXr8Jk4} zUWQTwGuKVZ29&|V2Tg4k9kXbmrG`6P8f*>7&HgN2bpb#F?+*mv1{@0SA_Dn6otzr; z^Zm+|{j5kMz5?!De5$+^yjr)s#Q-Xss~pNB6I3!^0z0KG({r!EgwfR>k@i@@C2&mxO8L)LQtg9z*ltr?mNI6j%XCq4Y%n`E^af<^ zG%fQdaE1heFYxY5aFYOcBJ-p}M`w9`cK|Qg#f%7z7^>^j!u7W4;F{m475 zq1X3?w!fZB|8?mG=zoRe58SjZG1fdBSPBBTRxPT9mb~H_q97B{aZq;F%-HQ^U6*7B zA-`E(_}Lqv@N?Ma%Bu*uAN^o^wD6T#-o=<3Amu2w>^D9`EnUrD_@`%g*1%dB@|uRQ*8C?L_@?;u|pa^=%=c{R0XuwVf$eQ zd-99WPp%khk?icw1Lrqfb9^NkWiOV$gf`vVV1$K<@mdwvd}z`~g_>~4);PqRwnQoX zq7~Vc5HPR*QC&fJH3RprWQ#3uTmNvhPpL_C&Pa3~-b82^RhP$9eUS;b(Rqa1HoZYV zp6?iCX&57AnX{@vX{zO|hFzKXhaD3ZyYSTyqUcWa)?R}suR@du1{K*LWk&BG1nq*C z)oitsuxNm92TbQUynp^5Wp_BR!v>|zpfTJQB>9mpvo|Fd`Q%0&>EV~v-<>0z+y(e^ zd7s=O{(7*RxbL}Q%xz88=!5DCB@m^ygvW0OE|5yKW~3{C0SjFF#$nRhQooEiv>D3| zL-pHoWYKo|pPB323Dx0H9xOUqoBGxbyHGD4_kICGB|QJpF|J4vA=1%zYQOEid<_pK|?(oJFskb3_H-tq(?@K?YbzyQHP? z(5N^QA00I9;ooqXtnmS@=Y%_x zDgjp#;#A&>ODXJSAfKuP80=+itOClj4H3{%D*6b`Di1Gih)z9)>ihHnTr$1W z?J=sJCl(;C)(Y74@~&RwDyUSfIzoMZNC_2qWD%m59yFW8lhFQVPq~1NTofb$z&5xrCUf0WRD|C`?(Xi0TD?U-K?@0vXMx&buE83O%e3AZz2-f zeB3%|KAA8qbF6<48W5_bYo7O@S=BnpSjRlC%v0`*SXAsq0m_+AAY4lSZ%~Xzi^}#sxpx6Fb>9{Vg$_7Fww187WWypL|`_1os6LB+x04{Nw=P zm@4y2DN;rgkQ2JwZ<}dgfE~#w0vssS0AHXbUeWp@<|;D{3*#&E6t-B*DlPIiVDJCs z*87=DJGu`rQ2t$3HlkAge>sjzv~@LxJbH#DA$+BU9Xwz_+0 zJzIc0@1#N9xKP>s5I1yz-$C_Z+c`cnQ2VLq>idW1EAx%2=NfD737okIR*Yzojp(8I z)=dwy`R~;@tpR5w4enU8`Ff;_@&icu0jus-SiGsTROwOtBpRO#7iX2X$ARG37naE< zqv$jyyr6MlR%&pTI`AKmgVc>g_F*fh=26R}z$gN(cLC6GPHWUVO||Cyj(oY?LE6>g zVd4um;uM~O%mI^R9HexFHE}W~u7EI{%m_o9igt(4s@)z1(PetUzKRZQra9~Y^79a= za{X)K#~{E){Tf$gF=`zNz*L99M;>YynEDKf=$-VHH7Ocexy6SWHyy1kxa|%(R)cDC zB>3l9z-AV>#krLvpP-*}o?0zcA1q+`mz5z-N5rT#Y62vWiXEAazZNLZLt+vWxf!85 z0!gZe#mJ*-0z<2TLC~2)kT_~xd9Iy$%@NMt)c)ACHCe{-^thwsU5%lA^~}g+F7;Up zSimm}lGMRYJILTdRe>c}`0iQiSUh4nmhvO? z4(~04CXOz1C0H!|dx8GDt)@u)Mu;N;r`L(`- z&oXA|{9B_=8hfiX1k=0WkeB+3=tEZ>Sud&yRKzF><7evTp{&Er79nS#E;=mUG*Psp>qkqF8`)YXwe%bua2Kq5+ z(fZY7#FJ(+LRg2vj5IQxy}I$pnUKvFRUct*>cg&emIb^t<@P?R<7KLdmd)eGIn+=* zM`_-MF@s|-mv#C_*19qjzXJSWVuR@9{tQ6_PhQ(ac!4=TA)^j9_U_8g$zp=IK`!md_y?p3f>g* z4FZ&L88X%pI5`RS*Rp07&Ga0v7Ol#hc@X!?hx`mD=TpqH%9=#$T~jh>kLmn&L3DBv zj2D6IYJ;-XchMMd+(j^RlN7U!bF?rCs{FdT7iVYZYVD9H;WPaiV7jcTm@8&Zb;p_0*6H zkKHc3IrbYC$D^jBT=q55M{E;z&S?5PF@isVw;q2H#(Y)JF)E-Zd#r0k_mfaM4lpfQ;``R zVxK8QU;|>g8TAg;+C)@^QGdQ~x<5a(y49$mINUg%W)aaAoX|H`xH&wst~lR(z6g_8 zRY$yTBWJ;7gML0nVtQwO%UZ>(%4cH650}6Qd|BDJx>E!w0evK1)1s9rI_i8xEat;O zf#J5-aQv)Xx1d2os7?93n<#OlQZ>(TdHv?kuGLY;i2Gj0C8iZ7!X|e((=!8&)E7INM(Jo3lA~@Xd&ni8|x2y zqrA}dUisP|XIZVY={1B8NR|HDSw1c4gUlvLY18u1e5kLR^f@PVR$TRN`;f6gd%4_9 z6`)a&xN|JrUbo#5Xk~{6ZiDVi1G_mhakZ=3+{oY+>8K#C%buVJu!~kY{^MbR#5T)k zHR30T#KDwwm+PE5!i*c5R%mk_a!n1A{0ao^3NK~bW|V=(!U$J~f*Bz%+{fVInqy&f z_hy0hA<$hI`hw*eG6aHt2U%ANyHOFotod3ElJo}zMaB6BnTQr}F3PW0S+GW3wavI6 ztS(pM$C)6>ACvq0SAI+16ACit(%WmpS`EtqCA-tAYxSz21_i&J1+Ghtp;_YyJ)AYF z)Ng^i1qhj1O=UU>c-w=_{u69p{3BZ!!oL>irkB$b2^L=U^}sMqRSbV}Y>Rk%isLXu%$ z^_Wgt3JqxQj}Y4$wq->-{?4~&5_Q5gwGXqmbF`bw;yChB^HBeudIrgEe#bol}IRzKh`QMA6Gd zbe+ztD@s@one!{oktQ2L&()A<;hmQs2!g)3($&3CTX?3W!>Q@hDYIHE(GFV)S1YHZ z<#{*9eZT0+_w8Oi(N%$IIF8?h9C%;z&a>dhljvKl(0Altb!ZMa z{>q9#8KO6i-~B=^Q8ioZb||&hcDUk3=sD-{W!!s&on@$3>+ptdyQGYQx`WmWr}b)Q zjW9V}JiUCu_H$!SfR+CI!0Rh*n)Xr2Tw!|Ge|=pGcJBy-8f09+j%2$mRbiH@UOhYc zQa6%UY@5KhAa*YoYu@Dy=z*yWeAD$T2;$7@{iEGtZfRX&F#&Z$ht6I|%ebJz-nq!i zvU=(>>kzIKd~$f0xPUMR3r`3)3$eJ)QeQkO1^sSv`|_!D;cbK~?&n=*VK$<+|7rne-0&1o zNA|>Ojy+vZ>@Ygn%N193S4*4eTkoAn@mo9$AAVWNW(81g2s#K~mAmyPfU%#T&=w{# zZNhKTiuE}dmRoG%n9lo8QsflbrDm-5*1D@qszJy=-z64dU(4+s>V2;I`KP_-TKM9} znQnzWP`j9!|viIyP<>Xk-*RfGT zAG)z}NJ)JF zY!c3U??d@r#T3*rjW{C(&%SlFzI!Ojjr54T!9U{KmfVf5yJyqOg32m1eK>yR%xwOQ z*4fHaEDN0kf6R!A(GId*-HLe(NdNTK>_X!utSQ;4Q0lrM?&c2$(exYQ`Y_N+(3UcF zC~Yc>SJK%E*gYG^a$Z|Oyg3K7B210s73VzjI+0O`cnPo(a&fGT1Jp8IDKubHZT>RX z1z+!d7Ug~~BJq5!K*Wro3uop~L&Th~C5^w~to|CGnI*O%U z7e1bJ)Vs5x8&$tu9I=1##UdVD3Czwj~72)3iij{D7Y|0xvQAt6?ehT<=42}9V@bP((UL+@v z#=Sm!G@+KVuO;{FM86HH)b`j7iP z1oSr9(!=X)D1<%IdY+xN!VMl&9WW9i(86ORe5vF2o;uZc*iMuSZd zb5q9LlAn+%`SId|vF0$>{zAuqZsEN9n1X35Xvy+5x?@;3p7? z1C{x&&W!P~iv`Fb7;c(T89G!;tv=Ks?WTiwarPqe^;yb}g;YD(jehrdRoIwuKI|jgf7;68nBixnYlZ>bS^JF2oZ0aR)+UwqfTCRL zh!3Ah+(w&H9*M1%#T*g5~H`IMsdzVsd#bg1!dw##R->$;EI9Yc01S zP zRr&te3f;I4>9|!he(Novxr^ps`Id0?euBxjeF!0+2y8d6v^l41iyA|U(WRU#*&^Lc z)SD6CrXvrv_4-HLIWmi>D?29GJs?~ICve7^*()|qNk4L$FlwqTp!OrlsP$?bxLeTG zJL~nwwI!!-m{MR7<>vD>*UZAc^#MXG3voF(VS&2(+I-q8nVT5LAit8KvXua+#!kro z*try0tr;b_pVoS@*g$dp3b^}FwOC&d6a5~MKyIC=tZetV;kf^qM{rve;U3(UZ>hk- z)OkxBOwVP(=B4V7%QQPAkVPiTJJo@TjV=z|t=Vl?>#^v7Rk2^f^KkB2Zcb(ef4&Kd zfwoA>zd&lfY5cjoEUoLp-|+r+;*i~sNh1iFJTk5(<;*TB6m(C;XuHoodX?qBfR>-x+3I$CsWkx=S5qDq)?6n^lG7K%P4g+6tFPnS~}E9$rndu?hYh)b{xe(e+OhD~xONFWxqJKen0!MtsH+g>lj^cKI*VyJAxvobL;j?3l@dDl#hK6-DIjbp#IYiO)Q^S zSdTS|Ig&_F8KMu$2@lG-wLhu}Pcf3{kyjZIafG_3jS@mqR4l$ZL7VnR341AV zODSq9iSL{Q-tPS;TyW!zjyplcc1H>JDRB$mRLeUbIzgj8jS^-r{tHz&p+LpPC;`d| zhgHiHZ*b0iKT4n_#4V6iR1!}*3A~yZC7izyx8Sd$VsY$$hvl3Q`fB1J3_QgxkY-IN ztXTwwox=E7e#|={)rax1ST~3n3toHC&g3igmg;*7Srg@{%@d`X#rNmzrBp%g!l^HS zQ-Zm62T4rCpBdPXvpg%!265bQt$j!J>2p<~_lb@?$596IkZVz7n{LAPDzH@Ktkb?A z1XUHL&RhkUR;7m@_kHVb_YN%=(LLm1WI9&(pr6P;<6*+ZKjP!R3j5C;f6rLwaV+`Q zQ~0*h6-wHE%d@m@VQb3rANF-Yz@s;O6>NYtwFWijEPwIeO1oyRZEj|(+>F~SdUaYN z58{qs175NXnU>Dkm+0>Td1RcbEYDbHI~Oo_5ayg3%R=#Ojzc&k-!^xk6>G(G(v98t z;^u`_)5_62dkr4#o^R8e+)(_`G5zfm6!Rjd=9Z(^rl)Y`0oTd)y(jrImel25R7(=w zx_UVBdiu*J=RsU>Q29rJ0)youMPEkm_DWaq^u|lbuh};gB(S1j5?C&Q zQKzatx%%f{InvNc=z0lc{iul>KyY5%M4@9vUoGU5ZdrXq6}jmF#C-eUep7#tyPNaM zOP;bja#KReypQaNMlpmUqF>s-9NMl0pvOk*4Mxf(gZ#2#2BxDOxXO4sWy<;RED$ zd$)Q`!A5sZ$VN~Zrcz0P6asU%EVC=4#g;zY$oT#PdRsKif{(DfxBg^cYoYU5B{J&w^&1izV6OinO-+c-9PdU$Z?49z! zgtZg~s-sp@L3EmPs5M4(!Cukols25~D}H4|uP`3fyO>_YWQ?LR1#%XSlPD~|(* zac;XalG2)bMx69|Nv`!K56L<3rlre{@fS28p#b|&M*~RF9^kC={ErqxDx<2eoQ5VR z#?Oq2HL!#R48cQJ0?|b1nHlsLiR0`#dh}8nbm+9rri%wdMM#RXD(srjrz?UNkEUCX zW>afgnbPR=eaEEjAi8u%KowMAO=&n42%<+3hCeHz)ObWElTvC<5(Lh4ry({#u6l<3 zAVb8?sV#(3#0=V8aorJ`f$bXZWTGMmk11fEKGYRtp_GGyoHRZ|ge6b-`UbUQ`2FP4 zU7QwAec(3drcD>q+H;>eQOc`^32xb)+xQInr5WUZteBS7eKg zPPC|ju|?L7qu9&RXLjUgcB;~^JmEvzjJen4Xz)W4_#vldFK++vwDcoN_wuAHhBMX( zrCPY7v2XpwW7D>>wQNJgf}GaRkH?Yg3SrSySakJ2jFOZuYUO;bzS(}dy3rKPxNh^{ z;lBm5%(*>L6=0T!?bD+@f&zp>dw<)vaT3ASf-aBTI{hE^3N7fXY~`Ha>>9u69JoiP zY{Y6zFFUq9%L~1xG^}b)wT*&YyhIQknj@K6jb>3hVp#T{=k??4NNZ|lE}7(M z!uh7W>YtUt&-!waP^0eFVH)r!eyVpl{aovBRcdb6;~+|U}TJcxNuI*Z~ehqyIXn~9eU=tMV?W+hLr?oJ#)Lzd3y?B z&Mb6R>_>=0%+|~DWh|QVSbR~uju{upNg4$iz6&tC@g{xIoYX{IKL}6`jUeZrrYztz}gzpk6svAqeQ^>Is{p9UJ<4#z&O;ko4G zw1~;?SDBkS9#kz(2h-_FlUZBv<4%~D7(*%M)gRr{fx)I8)iU`s}eXY(8FFnZ3m^pK*jIf}II7 zTiB$Uy3>79lg`=%%%>?k6cNFCl_znO>d$};#xuYUojUxWH?KF8Z?p}pJU45(XeMYw zQqCKq&uyAPO91G$Q|`n|NAb_*hEf#lS9T1BWzQeQN6ewVq}ZFE%JqDAAEK089rqmB zW7x$LA{3=`ygCz(zdh*Ic=;&RINNzwNoOK@wLh1#{`mfhZ#{j&Y9<_J35`bRuY-MS&W+;iadv7sWJlh0+^!g4J3 zIS5<+<9|B;4gY6PPT3HkeCR5t{r=+@$oJl5vi>X$xb^fWd>y=hfb;sAqDBFly!-_! zIdz%ra_9)ktXPeaJcmetrDke-ab{lWQD>|fPHxmazPm<0I=afZ+T6|T`E1RYccy3q zw!V5*+koZn$Eb-!Mpuo~X%LtbI_<4$ikt47pbbSCQ!2)4$E)>0V?OA&wCwIfwv;P- z%kTDb{BjGB7>bc+nI+U#ApjP+xH!nCHRB=tvb?zm?YqZQ3+_ma>b7Q@@I z1uM(>`5Taz&(NjUYE0FfBJ41%OBf&RgbxttkUNHnP+E1=Jh7;qF@)x)2sEU$aWsT} zeb}e?#46*XA&_&4AJyd_G;U7ZckFE6Jb*u9i?Wq=YR*qg11zd)&w^1+1p*{x zfgEK4=bwTF-w1D2Vz;fCWz?QXvYXcq6Jrw^kyN_mY$3}YlMWkSG|6f(Q2 z{2!}j1Jh+yxEz|2Tm}0V`mM6>0_5Sz@I>vKkC3V_Aeki(>XEJ%V-lDMh(KQ zTg8Fn3~EB%54Y<=9uKJQutI;KSqyDoWR1)dEl@`sj6zWMoTmt3ia34@wE@1{+PgqAbkpBKnv%QCOikK9IG-2-Uq&3g`P%c*;aE#6l(+8!R}0R^*b4p1C)_FSK#s>nr z{U7e=+IttOAAd?tIyo?QdcfvjXodXtj>4D!!0G%KPWV3^E3y)PSAj$9u7YKVlGT6s zvioD~{FML(jXARUJqGs|qC9@YGI*u@ePVYqq@PdfQ z{mU)SiE$3*9@i#u9d-t*+P3P>k(ka7G+I8##6og2&~!tbtjZk7c8V?*hNfNJ2~npP z9!E%4`8o486iGoo7^IIMAtmSPHMA^k)IS4^>H5R+6RtLpVl?*M@P?cc9*MV~@Bk8Z z&E4;jZSVb?<$|Dr7Gyg|$z)Z=X)Q%}+KU!T_c7!wRjs+g#n+3>oi4a*0F-~JFzDcO zt>F;I_m#4pp^e3R0Xf8a*~yuC4LTmu7XzV8t2RJi^|VG$SWKO6%P?{=5y(8d2*?Fa zh*Vz#m-~blaXLp70K>57c7wv2G1Zf{SahPcE^Kv1y%hXd6QlG3z4aVrrhOy`0GIN&p4O#8#@B-Z&=%#4)X6TM3#{|y2At1Q(9?ty`z$rk$%MBc#g)5Ibv!}QAiF28` zxWtEmAd@>6k4PAZeB{3cuJ|0o^%@-n&JwEILI}`*bEOMv%3wQtp_el&J>@&}0frK&M?%EkxJ1{S|e?<g+H;(~N>lgpI{hDFmL=3H$x8g`s`RTx&S$2CoY!=gCj2gs}Z zFsc$4i4$}mh+&mSD&ZmqAol@yGAkQkz-Zvi0OtTViEw8PLr#&O_D7~Bmh9O=R7IvZ z|L7-Tsx}Buhd@uFUBCkSNIL&>?hhA!G!YG}B{V-p(Uq!4v-h?0v@fq9*DLZ@k&2K* zxcZR0y^em4mGuSg{^6z!Wl<^m>JoR2=G$SbC595u%Tk!IP&FC!(U-idpS@jBeHB`c zx=8Yt)I1wYAJwIX=V)5-3GQ(LJBM%${%<+f1|Pr$3}w`>9tzlHNK6I>#liI2yf06N zM}l4V9dkZ%%CK|T@q6@p@DGKTG>jwE5tp(_TdvS9^M}1iF^#}g)GFwA_4l7zU-oQmP3rrR39Lufq~rN> zEtoh_tKq||d=>Q(Ow!2h80g$^4ye%41$tkZ;}PNbg+dc+X>C`b28>;!7D)@PJM2T2 zLkS!+)4FlB*sx7J^<6o}q(Ip-z{N?(8RLBx`sVf+I-N?BEq>r%n7>Uc3;k3_Q(^*a zIg)04fTkb04}R~A)$nP2On?=7`U^*71?Eo*HT7uTvZ_Fv1XCgR*<%^SOHhvWQ0Km; z`>V+6GG83)S7zbuAV40kyGf+9Wi2{(SK5pbIXDHIn85lC&%5HkM$p|~Ta;ew537T$ zOwbCB1qPWW71~^Z?4?T;Msciht74pTpU&|gfp1@=j6!NPs*=C{bDKE1%E?~}XxMLI z1_8!cw`l&Q!@R?Q3*_6&4o&yQ;ZgZ-4s4~%b>UEjSsm)LaeFnz z`6Lt9!!127rA+kwoSQ)J_ODkZ2VbDd`IfUCCchS{QN$o<5IXZ$t2Ac3oto`c4ms%s zZGcap3-2d)i&gcHa4BDFiuk8XL)yuQJu(VbbPH1ad1L}~3#xs2JRS85LVUEvTllr( zeYB4?yCDMdoW!s5>kW#XC7--P#6Qbn=TCrYC7)A{JR==>25+G9VZc||uVX)dUlP*W zQg+%>7HHP_R~rCK8~yPC;nlYGIKZB_ocwMV=cuLs!0G(AAG3=mP?`Yf0Mr@N3gH*r zFDsV^Dwh{tEpzKlCZvJ2p?Ah{KH)sBSYGQiQ6Yo5Q-KSZpwC2HS3AwSsoJppGYNua zpej%l8wxlHOx#B1uu1wY2k5euA=DflBF-&`Q6=LH*C|NHY4e5sTXG^?^OW)ia*7$P zebk`%jVfda%b17{)*by}JS_W?D2CK16y$5o30;vH8S!0(vtc9g?ViFqHV(MN z9L8rE=S3ZAzlS#QCbf*<&X1*tR5-^y(9*F1xOkU=d*TRuPUtViAqGl25w`C-g02TM0CcZ!L&7eizO!I=sI1CIr)!l;mHfVLaTtQmYzb7#p( zRwo0;H^ND?V+eSHHS-zB-b-7{&%yAxH>F$4>)H>#Y7p*wliT+u*x)$gb)GP+q5J$j4y(5HY#V?X}E|jj+o7 zoJdt%IaN1i`GN3?n~Za_uFM%jsWXN#yAPQ^H2}7p|K-caY>3rzkJyOK&p+rtu;9*B zArvHFlA77~E#{(b+goHeYz#qt;tUN>R_2XD<`WpIm~m)N1Nbheh_EZh-r=bQ-_d(zUZRRr$|}y%r5M zc?Rz`9(HqP5go?e7XX@va@nOuaXcE`=9BGJYv>m(Bo4Wi=-f(@NC8@;fE1a}0sWtr zbSL}&g4vfY-w{nR%8kr*G;=)uq1f#Jdk#GRbNpy%f(I-iCL5<*9; zO;%JCKIG?~cY5aMG})!`ac;P8k`lW$WRVcpegWTpA+BBYWVrzTDIdO>FSeMk^!|Zc%LvY!FPQX&EFgsRwDOPt$PIoCpXNjP_PBswm>7+l2l(zaVIU z_LMciB~A{R0RPvJv>JoZ2F9ZSRG|~$0lFMFm|ZLET8&r0^jWOWG)ImAalXU64N9%{ z$9dwzHFT^S2}7gY9B=3aL12^y$)2+&Jeu>Vk#18n3G+NdKtnN*T_jGgshjBd#IN-S zc7}OOao^cKFd|e{`_+}nH2XHXOdZjYQ&n!l{xuK)N$OU3US|kU(LmFIA5DqY=M z!$E{knnSL#hNvYrH&a#Q2PXGBX5&kWZ|o(GutvQ(NWM9U@_$0E8RQhWvR>e>Fp>X| zi$vu59Q?Lp(o`?$B#p~ylgBUpAB5WFw-=|9!PJiO@UN(GbJD(+`#XrAbB@RxgqrWF z##IrWm+;Ubc<9H2&YKCtH$t^HLWasiISiDCUVE+lNfv<@Ml~jaxgQ*D;}{zlry15C^VrfA#(pm#&|VLfuMe5% zrmD(zwga@b=a`?5m-O`i!`NE@#T7jLqBz0b-4lYlYjA=SB)Ge~yCk?vaCdiiclRKH z#hnEfdCUL%zFT$gef8>9{q|JP^wH^=K0R}~dktmIYQMQ@VjkHgAORRfNm`Q?$RmvK zs2!7N`8vP?rQ?gH<1?Uh&||y-h`f=LrEG7N6f9x`35Oq-tx;#UQ#c0lMPCqP~&tJoZa}LTNfloT`MHi@Q;^V zz_TLo$(USx=4?w`JlGb&RiGOi&N6v&OZc~;Om8Pu)|zFq;+CYlK_oo}_2Ln`6d zQq8I?Q&?70<1){SoRti5qij6*;b4@Rt0KG=iPk@cyKnK^v2loJ%}B{N|H4Gv>A>8v z(U*6<`%ju1wRjQ#HIQdrg2XeNSSwn=%_1RmK^a#8ZO@a^lT$E4mw1o~)d(-~E}L{T z0`-82YE1-5o}-GV0Gi-7FzQKUSl~xp&G?fawI52+^%wYWoUnb0r>SUm0A=T*M>719?cn+VY-yd%pC+o3Kt`O=N zM>Rp-bTus6iHLMwXr2JjcGN^xF}EikG-Q>|>%ubQ4|E_VETsoKLAe{p)%)y|(}7p$ zSiW5-{yt$LsK~PENMJUJqxVD72@+G9>Ip?%bjxoJ^%N<8iwie#Qk)r~iQ8_&Z{BAPc&m#_*O<1;JvE(1N|*^ML^B;4dUD zMu92Gz4w4z0T2{kK=M#=BBgObu=E{%EDq^6&Clnq{R!p?o!>ip#h!v$v(F%tC2hab zy#(q6LGwP1W;W0f!ze7q9)I(dSnpP3$x3-4I%r#AjURzpS|uqhJ`?*|UGikoRqlc= z(+LgBr(zIS+%U>be{_l^i5Rc2pQtvb36Na3`*smKjz?eVQW#%LUPi?$O)&^w&c*VM z5-M|mU`=W$iC-uLqY6voQjAWw^pBwOzfQwg3Z%N9Nzjz#m@Ts(%l8w$5=uQvd`pD9 zO9}lpbelx8SuRQv%!}ELjqbb|P@lhg<`Qp)N;=8?j4GI>hz-fEt-pZP0xC__23mzh zlS`$LTNB9qA}Uo|AqPiR$Uhf}^hjGv$5BaO{^p1bryuL3;w*zJXKR{0K+5_=0;7=2 ze?FLQ;zE6$2}bU?LO~o|Q=B)nI=Gj4&B(y#CyrL7Z%W8tM3#^LX{;~EX{>Ejyx}>d zwijh$!PH)x?y)dc&MKTA1ADD1ASVnnce;p{L(0RtB$02kzb4|y1!1Id?aCGYM7&S%-)(?hs-nneKY=J*mwz^p7 z%wQx&b;-2Hcj9tIGb~USv(Bk1C4Lhrj^~_-K(Zrr?E6k7ml$6(HhVn~fo4a@N0n=? zN_*X+sPf4?Fm!4yvgpvH$Co~b@)t$4pp@}UWNhzP7)Z@V;$@KB2*y&2a8ZGnNFho` zMbm_DEi3C$L}@NM^oPv^Ig)o=5ntTS*Eo`Aom$Zs$$w{Z<@A#x*`#X0hHz{VIloyV z2ob2=bDMu7+m4CjjDC%zN03*OF@R&63bu(3)X@fX_dFG(^K(9KIjQeLT#XbN#=o^H zQO(1`Jjw5B9Ag5!yf}4>qGuE56acZQ9O~`R&$k4I$+*TEJ>yI8Rh|YG8sv4~u$pYRsNz}Ek7(D_KM-h-}O9C^OLy-i9*r5%PqAzssn=d)6{buYp53bP|<& z!xV0QDJQT|)7cc7_FX4YqX9xr$!q^oX<8V%mtAE^l_s-k4C8={l3mv4r?d*Lsf-h}t>tBH%4doJVgcc2X91zn-JHs*izT&zN4QQv(yV&RZTSSO4SaR=olCZ{t9mw@Wad)n#LASGyb`-CN&Q02d?y0YSh`{nsZK3BVF>EPuuCDqin^EH)dCxQIl*fEQko! z!@`?d^7HuTJb05 z_I@4lyj}5c{Mq?duyb=yw*RB%J*~z4H|WT}YNI3cQ4D3I>b!B$&bFXr+1|FGj0;Rv zaDk~RvzF#LjoY6a7L`L)wl2#z%iOZouBSv*_hjPM1x;@Q9GlVAejjDWkBujI-a^ z1>+I8O0MIdr1jH&Y4e=+Fr#}(Q|FSTwN}fzMODmC+r}T~KZvT-d%#tkc1?5IQy*1s z717J%_TbVh&z@c55Bu=VtuMe4R^V#3vp=y*?3N7h(Q#4G&3tQr#1Oce&~HQL zYQSdo&GX{j1|$r6o2h$uzIfN!5PoMNYWBAS312oX1GP`RtM0p&pY^PLYnr-Ow0Ep+ z&ziU%w28c{qPv!d^{kC+n(9{8SO2>@)4OV_Yxz*m+PS8wZDoDa+V-M}3#k2H)iyPp z8`e_~+6`UH{}&0=zU^A}so~tQp87vYqnf5wYsLrd-(Ac97YWp!=vsEFY1*`A{69&n znx=K@st4_guI2xOw5lQ-d7H6)Kk9zJU48%GAHQ=&d&9cwys5bb<$0S6;JuN1X&c=A z|5+%py#f#0*PQno|F<{hcMm83*9|iJfS#dsH`0YSONvfAs+x_`-(1@ap})Bvmc@2{ zBKg`g-gPz20{?#(-WzfCP|LWzcSqvZhxUbR!%}TKwNNx{&p2CKh@ZEe0NxXMmyF@v z|L+BVZB%B^`IK8LphXe1>q_LfHLMrx{WbrxDx$lE@_G9g;C~gobdH&}U0aacE^Q;b zTWFrQQvf;5gL05Nm60t7^LyTDH}H+^jib7vS%qw)G@xR*zwX=OY&RK#a<0H>1!s(Q z4nq&riCottJ61!bIxhRWzl*F{H|Sb6bXhy64%WAb3~xgbcq5sdF~-d?P0tkU%*=G) zzpZXi6aYVtKh-7e1>BZLgStEAaPeQQ)EDFnHubT`|Z&c*J+pgj;Z|}E#|}9 z*#w|ZW2F^|##7)HkJGJ2^sX>FE1)qZVGkdyhw?bxYK-R=HCb#6Ziw;@4ja6$0GTwCW4%3VCl(v?ihue1PpwY2SDTTvr zqYvr~kKO&ja}5aEEN`2s%Fu{Ud?MvtD_WoS4O`kY*PQa5G`ToWY->?G+!jjr2ANzK z(>jx}r-RbQHb>+S|LbaPEs}@Zgz4Va|HHkt8l37hH}vCa)-$FtblXhi5{~-2qPbA} z7SnZ<(lZUhu;lU*(e>+7$#ty_2M zH`S7Lcu$yKFs8P(=p1f4rGqplHb=A%g_ha&Wu32!+uEdtIoWnDO)k+pBwrYHJ!1zs z6D~u;^iL101P&eN`qi<`%u-X*i3z!OFzbL3x>Rp(akHqA;A@3nj+_Vyu>&6_E5BC# z@Mq@f5(l43u>@p2iak0bJ!Jj4x}U(=et)tn+Sr?DBnGK!-LXuaKdgRcZ9^9mwqarB zmCyu{+d!6 z(!$%PUFUIb(RVH0GsTDsBdRJHMza|8IAs)L51}K>Yb-90X^nn?*{lf zF!|Rx=WF5}qc>-|+Vl?xumQRYprSWH)eFS=A5pVEqF%1n7yTGa6Cc9eXlz9-poJ#2syCE!-D~tiQc!3|;u1KG1pU`sy1t?y9M%cD&r)%AEGj407t`R{t z!Z}|Z?-w0qZK6lz7Oj)L{SskKT@&B_?ZOqB>7!AtO*&I4HYsk~aXKWcn>PLzYMMZ1 z`?`Q4{n#x(K{wF->iLQ>aH>1g_M^Y72)lH#MV%%a`cxt3gd)DL?2uX$cfYQX_4uZ! z`CnVDLUV*cOkt9%YJ1)1Pg51X{85DTx~H8%ykEv1#rX_dD%`mZ%;|YQuOajIWcT#b z0!`-RC1!!mLe!wjZ#t;~y;J9o;s?j#TPbd{}34*^Y`GFJV#@g@f5-5CdXcV;?A zuL1YlWA{GYUL7v?#*9(tc>K>sQu=3+#r1MIXF$bfpmXoU^HZ0+Tl}%!`am@nhEDZ7sLTY1~E-7c0}EXr3(_xXchze zv^$eG$J=%K0qlIb8rff-=Nhi{Bt?s|=B__KQ17&6bqKv}Zg$x{E24E@3rn3q3q*+V zVYc(NP8HF;VAxQw{0?A7R zDLDnnGB19vW@l_KM8bTziawJ2BfD_KpMVJtC616S&TGz^b%THQJ49iC0A zr_9>7NaG=-y~uSYW<(7<6r%+v7>s3DSxInoAs^)#HeT3(*7he2@O~Dh0@>O}fzyTR zFf+R?I=o_m9#8Jjr>R!H3l9?Q-`t-z46(umgmQOitYZiUlCLnY)YM|MV&!d!0;pU? zy$A{LdC`3Z#T0pd^&%9z$e$wt7g0BZ(QBwRzQBR7J75zZHE%cD$G zbCCeAe2MUk`G>YIGL00^qQN(~#T>pDhKO6|%5lCuEy68~S|C$?lns8`ZOip{3;wBh zomap66Zc^+0qIJqeE$3qEXHB4La-bkaudI{V$|7^i_+$G2>$94P8!J(ND6l<3S%q{ zX6o6Q&AY_QdXgUXrwo-Zj0+SyA1o%6M{P7mUW|tRXXjEs&-s$H1P!#cgy-yXk{F@P5`s5Db(b;KE+0F}MRu?7wejdN-i?@&)Y+a!2z`3(CNFhBUyUbT+2QHI zJd*0rDbwIV@bOL3wWPa)gn1&Sq!$GDPjZr8c5u9qBPKX`sjyii*fxB-te%I?sJWBy z5@`r8t^xRc8EqH#r;Rz=5O8r^fqZqh^CDKwY4~~ugIf*5;39P=3V@FAjkO&6zO!=< z#es3ar`^&Y+)L7%V!@i#FI@%yY!!ASTfwel?NxaP>!UM%T}#-hHb~`4Lf6S&4@C<9 zy3=6Ezw5}$rs09<@yWa|@gn3R#)7=riC*(K1_1rZ$@Xgv_(>2L7!LK@yo#e1YveF; zTv8L@&aX~=1}TGl{y}yx=*mYW!HDjx=5*KDYhGgn>^$7#o_ zr;1+`wA}Doc%vI!R-?=^#eF7k)F&gx;{k`6LU?rMDXZJNKEC?-=N z4T5;>wDot{tsYCgZK$R)KmvzvBVJJ zpE)>cf9TAyTvGo$(<#E`@x{*T-$J+5jnBoMYW_%C$i>RslvV z&#l&q@d)97b`!eQr{(pDBH)%musTs;TD%N~jPJ##ltB2JP54X`sJNk6>G^zCZ68r} zbzf$c7c1sM4n9S%6sc}_2SMEaLcaPjxXDQJb-@cSSej4$%s{7(82M=~jb}vC*eku5 z2kMb*A&~_s^wmgWsSYbIU6exF9-DjK^`b^PhRr5zOYyspJPkkoQvE!+Dk1qYpA8iiTSkuVbr+vZ@%?(e%l2hr1kVePMZqr27LH4I16Jg| z>nlNDlejejeqCh@wOAeytvDF%6rmhfkvSut$!_1kc@e;AG_D~3k{%!>Pnl}*6^oF4 z^`(i3FZQPTPF8r#KFK_X0Hd{xO7p3N!!wR(_bW*VZrBz$G6f9^%NMy2&Gh^+{|HjZ zk(7i}5S>IM&J8`y$H<#gl{DD&(y%; zJ`5yg(*Q2-h>*BvHJ;m7Vm;*9jwuDIcXftZu?cy;;H@SR(LZTQm?Dj&JGp(@A0u<_ zP}j74&O2yUh&@$XWL^!C{{56*uMt4nMa5Tbu6a!JqOgi>n$vWjNj|djf|)>b_VvN! zsVFX%`;Og^gM*$ zsy(oH06_p@6ZZ0Cq<6EzBMz|*>=U-=(0LayZ;nM3t%gunZx+*DkmK4 z`z_2YxpZ|(VLAtKlI*xvQ0_TGRMghme-l74NCqDnVb@=G?3?5d;;*EMok-lahu5Zs z7RZnP6i>Ws(G7Oah3;I!dVL=V=8IKAtWboay1G_Qwtv>9;jlF+ zB_Oa03(LsMGqWfqU}XvR;KbF$w;mqO_(J3y!m=7P$w`$m>AE1CF1+&=lj!@_cGQqm zJhG6zBf*EkX!ERyN`>>o2el^boQfk<59D9wovQoOO-JrbzrKqO-AnGfzW<125;Kzl zv}u8oX>ZSE9A)w6Q2fQeeBM;-MDRSTiPkVQLK4aeWQ>qG+SFRxV(%n&z@``z|IwjzDKu=)!PB0BsD@_KUW?-Bhz3MH%iOB4 zMtsI zqQbyvH?`E@{jvf+uQ~Y@&R_I7+h?*+y?&}7CK@Ht5@k;zo+fo=Xa(}AIRvWiBSM;o zM;{#wm=d^geCQ@+WirAO9S)zPsHAhbAlvV5L= zyfSLv^%pyX2;8T=myr$PxpiJYNmE-;W2#{y&_}`~e+!bO6y+XMa?OQU3QXWAM=vIZ zI-`vjF0Cmg7fOg{@jtQ!tBAbhn1Lf2~yp)Y#@OYDr|pMNLxh zL&atOx<$s1n<%~M%?M9N!>L>9bokTA%;>MC$hd!LMWxlV#86vl7HKeIg5VYGT@xoF zV|AteO|vP9 zI6k}Ew^k#9*y>$8z$Kb@)S$9BF~^{SxQ#j$M>#w!;+=}r8kzC;*bx(CX%u-P3~!u9 zRS_~RabnKF*#S5ZQD|5TA+p2hB22PKkX1~u*?+^e#zJ1PRWpspI)daXV)*4VlDw}) zs}O{+)Szha88EOW-o8eg1(ZJ`&g_T)Uo}p2_YX@I!lLAt!Uc0EmV>j4SY$A`7fp`j zWyBim-{O}g{^Bby4gO_+K$|CtwmvMitL*SP*Cqf542V3#CVc%r=OMv?K zoTbfP!~aMZ$s%k{deDN}NDY&fJ`z9qTa+xNB=?x~m)+)QG%I&W_6`Lc%m9^sP?`rE z1kmpVFpmNA{MmoE;#a{WViYE{BU+Wd6Byn82+HX%J-6l?ot(%p@-zjIc zb{F9GDk~X2bt5v2?$KU+?yLZT^LT}jV-#K1fb5%l?1zJ+=i9<)r*JtWyNr3w?z88*zzvAN~;o7$9q+;sspu%<7 zI*rwzXD^#^t8FFdyec!XN-!juBJ|K%Zwyvnt~R!n0`EIANi(-(F7cN>(Ke5&`rL|F z@-&56BRztQlRm}xKp^yPbU=CKeg6RyJ6h&~98jF9tUKFT@avl;sI_n|Xz+))4ff!V z>yV~~@+XMwZTzyVU+d+i(GP-~uMeS&wYEOkq_8Vw)QU=?<`Mvsh_0~JFWVyF^_79^ zrKM;noK7=-KX@(!@x2uZGzo#f>nWaSqF)kZ{bXo*3KR5I#+c8)1$CL#uD<@j{zr$# z;j@$Wo;kaYM<@vwU~ttiu|Wa2!t2Iuh$YHWHliL635P0Jl$7wbD76*M-v2ae27e$| zZ?t5nUg1H~xbnzRb8V?->Z-^2O?WLLv@9#kwt`~Y{1y5-kOvpwi=VsB#e#We(;go;kfJNQ{1cLvxfLtmU^%j_ZZkoM#xA~L2o^?2HctYsuf)E6OT>XGa7 zpq?;mv|LMnT=N0M_ZLv375UYExR-``$a5JfTT#agbDY+SC*G48ORw|e7Oo!!T5bGQ zQd5C0x23nxz%J)Pw~oV5Co1jwMQDk|nDMW4VKE49udBK(f1Xn#w-@>DEWQHD#x{-7 zWUC?6?Cj_k6t(qlr2UjztVC+Eg&h1+yA1C3UThIDGN}X1S0;48DT|El8(VfPIOWa- zhMYaPMg>A1v@ZB}0T1OFxE zlp5%!P-GlUTPgnXIR!5_HL5@OJTmf&6cweMI`F+a8_JYCY*!+#R6Ai#(iVw0eN?~b zNyKxfN(IRNfHgE^0lRaOWMozlkI9e^%#sgG?jxHLJWi8_GC$7FDD+Y^X=8M3f5G49 z-~$ADfH;;H+IN6pF<8Xl`%zW?iQ@YCmnh{lNXbm0SBwig^ab2mDc}ycKW_IwY>4cl zw$RRsfN!}_;4sJhbln0cRcTmi?C3p+K5~;ON_qIKxBe9)im4CntxQ|^A!Y>$TlK|W z=jE0Zf4^Yn^eh6V7V&>-kbu%_OJ(r9Yxo2X+&xJGm|6q*KCi+p8$w?TosvZ`?rFwB z=|Pm+28+*0GeRtJk+{s3YJ;Iv_TQLgkP0rw&$=a zZ?|_%_g6^^V8jz{;WWJ!IY9X2=jS?&>%c{JbefjfqH_hRfRsSdQ4rs7FGNCwb*^(x z74pF@bkm#&8RDKA$Dj=OMN1_wDuE&>lm&#%vKiLeU^C!YkQ~&4&ElB-A@1`zg6i(k zW&84Xad*lX==Dz^SnCI7+=zg+SmqrupQMNvbe)-40vM7^0ea|;Fkk_@N+NSYR-7mO zXBfwVhcVsX%}Wum1x8rCu)Txj$bfk8NuYmgv?Y%ibKOMZDk4F41RcOZKLcL^e$Dj) z=820$KWM(xEp<_O$zQL(mtD#IfUl_$hZON0D%usiqNHu<+YFP|{OHD*&_A@Fba;F(aaj={Ju65mk8LVVv{O5gAL}Znc{QPP9lMrgH(T?>r=Ew~7 za4Vde;AX-cGfttY^2+J*Fbg`OI+munTHntR@s&F<6qc7C;)VJUud)nEY4dSzwB%A0 z7_$EZE8g-lSPa&DYsnJpSz}EEfFF@g^4utj7SJY-0QB?%c046Lt=@qrnfTD!U;`mA zrd`SxiAIRS=UZVmgL;5~Pp$$Xpp*iY(5Qr>xg3KK z#WjqynF$o6AhTa-OCX&Aj-9IsaznKE%X%NkV-=AXUNzyT-+0#~zjk?q47PQU7n9&m zO7kB;Rgr<~Usk6x5XQhDY$Nv)9qhev&3%Z=gQ_^+`w;I;tW^jWG@S)Jxbd?%bSXY zm@-k>`zWF+fM@?L+}K#x75fm>*fe|5kG2cUeJ{1o8&n>GSD6t>+7wP{=8uNZhJ&NH zJjI8Gmfn9yy7PYnzMsCo3BO&RlD%&T`@#CZ@c9uO`KPbIb3H2;%reihPYVYIX+X@S zqrr_4p~#t;Mbcby+b|sLyBBQvr3O5!ll*m$9SP8S?(V>U?xTw$-U}NQwcD&{<+_Vg znm+~SYplhS&Amhv5rzJSN9Mr5iz0_Qmw3e$gu<&U3)9ap`U-@T7r~gH5$9x})W~O^ z-#d<$rTrG;XpFvfy+WP&C^XhhhWv16h((YKXZ#Cd$$MC`v|c21SoO(tCr||*ksV!* z^i}$8Z63`>=vYcp^|v}L0@X$8_~Ukt;~OOOqCsWh8EveRM!n$~<=kTaQl!aFysQ)( zl*%;9aU9IL=g9<_ajg5z{&&Sa+n8iCq==+~A*z%Y5fNi=OVdg`S zV=s{fyZ9m=<8185wT?VEB(pg7{H&g+FHnsk*+xhK);4t4U*lpu?U8+Lx;R5w!>|Bs zVGLIXw52tON3f>}=C}uI`pv*Pfw)J}1NbhCV<`o>mEF)eCmUNv_gp!m9I?*u6 z{F$qNnoR!J#bhAq{6Q$HiCOLxIshU_MEK^ZFvsQ5Xc7F3moa|^vy@vP)&$WBf_-6c zST6?XLu)^WEP3>4ezla;$*XpMr7c}ln?y9^#8R|`+xt!tbCAR6>sR7Gm^G1uClktu z<(cv+iy6e6fY^bmW=8IZ>`DE829OfUxl4TIzC5lh^xVSt5}j=|y^&pmb}e9(fM_R) zj8;)=ic-{0YSsB7laz0jDz@X?9;o>x$@qVcRaNT>%H!C}M#&lUz4<}j08dXc+6ndK zz?;DEuV0rLiZ_9#H^k-WNK5vp-R$nP*se4hso!djuCQnArpR{ z$(0Csl;V%dVK)om4ars%_Lg+d*g_`k$<3YQFS|lNQ@Hg??}5K<6yV2%E?8d1Y5AMo zgJpY+W7S~*gH6?GtTvMXV?T@6my-QU(KAqnM;_C_>SaQ#_p&UqNMp-c%K#Bob=y!U z8d~MqkU#3QNUozFpLqBa3+GoxG0WUb_n#})fN=e+=G|1Xj%N6 z(`}}1BerEAXV;%6e!F4s2Fwq|T4WFF4HSOieimnCHPd7_nqGJ}ulXqNeazkslD18X zv|9tyl@EgUkk^^Sb5Jk3TW0?@PYy}F%v$WbncY-_^KRWSS;raFfgAo9x(>j7V26y6 z&MViCoyOQlz4SUHc5}GxyAevE*r4}UGyI8;`{3y4 ze$dNcpYb*^ENzYz@sMknd^GYa-WtT0mG+#?f4s862;0OGw4BxnG8LX}-U%V08Ln>M zH!oIdJhN}oCO742Xy>fuO~cB3rc_hX#;plgx0ij4%cJH%X7ucq#?IWKhU5Cf%rwDW z>%7#-=bp3N&&KkNcEzpKjchomVP%ijkD>39I_!%N{eOwN2(YSumpHIkD&WLpnHN;9 zm8Oxl@;Jc|wyk>9=_9VKa#n+w4Enwm;GX0aDrFV$)H|jhqYDkxJ zVd9*aJ+X_EHH%ZgHb-^)d~fayA)eQ`oo+m#@?>}RY4FosT9=BHfS4Ko+JcYb!cf>I z_n2OP)5ur! z##!l~u?b(&)=M%Ua4k{=VL*e%*C2H~) zx1r|daP^=JiQa0^J=zF??%z1bg|eC@!XjhumqdW<&xWNOoGn1c{a{m%>{Y0=R+S zM=kt$qLe0ttk?}oAY&Z?R_=EKyhIQqwUE4@ZJj#hu%l8@8pSb>-m=bBF;w{!%gEP9 zV-kNRc^lna8!1&_uQ)_Xk)=KEE#(7r%}HI^$-(bT4{Z9!y5CDM9Z4}Z{Di3?>$>(e zEiSqAjL98tf4&FRWjjO#sBT~;H2N-9ExEfY$OYD9=_MFcUaDLx^p^P|NZ|j-Q+C}= zaaDs1M}U$)l|z?Qw{R+D2kVG_!vqM`4y=5ot}}S(s>^?^t@H+chU5J5rC!9L8Mc?T z4SA=II`qwbe_130ECqLhdcWg6IwV+OcsTGxVHs45+e69YJ$ig{3Pj+MPc!tudZ|V& z{l^L?kHqz%PNsf0nSBAqduYdhnj+ohck#mE^^y<&535VCX<4EzmRhNfxqIZquX=&F zLE)U!K|D%i1{p|8ig1_dO4zW{t|jG8k0>(p^02;XBvdveg||}GZdA^F(Gx+M&UD(f zlZPwrc8oM>k=DEOsMT^e?Qhj?g24=c4?7cj9OP!dwi*$aWH+H9(Gj#P@-f8hs%N=Vby{sA;xu6j>PN$Sa z2QZ~o~_)qG`l$gxo!GsX)xNewW5(pOL@8F- zP0$oK9Uv=nBJ#TE%J?xlT9=g1FtJwAyg8{U=&|rg?yTV$-?MzwmV=Q&irHD2Pzf+dkeV(kjOP{9h_%#40@PW^*$}O8kaH2kE|;0^e5oU%w6^l7q-FyQ#W85TwB zrI_@RY`RTRQt8YFfdWEO6NLQSs@&T zmt{f37Q2bf&F3Fv!0_{Z|1Sk{ErRMGz$hv#tm&NBfmF*iKwR_pmam&ho@K zpnmauit=PneDPoRTvuCUo6%g~ z13u}Rh$?*3;5mDbIv3-KAj}P2@_ET`iguJ^u3s#h_&r7Nsd^hbL_&=0dZ@M&S|?Q8 zY*r`(Srh`ww!mIo`e#C%53-x}?&cezHRST>2HG>xN_%Ja>TA-1+;Wi(TZ!=f)R4tn zpD5)W^S=}mi7tO(;*s|ZZ>uTCfm^EK$~}L>8S4FPCTYmot-m8r_}+~oaM~O8Nb;QL zUN!&KJ^35oVB$7+q>=sBU4z0Ir^SEN#6lM-6hK4mIFHktWCOiNT==dXoD#qZPrfiF z`=$H4B>#4uT4lT3hx9L zM8c=rQrAmQ_xdLHMQVRvf_+CXFFm#wV<+<*2RBunDt?Lo`8ylLyeYV_k%Bcfw@2!y z?v~cor?l_!E)nx@FlwiSEenTfp!a_ z+(zseMg&HZ%NBF+)fskuUuNd$fyH-fdAhOm{6>TXwi>_+@`YbUc!}_E<)PWHiAO?J zc{-Vn%PhY=-5Yn}Hrp_?m3Yy4p*4a%iE0^}0Qc9zOB3F-zk5S%{VyCozOYifm(y48Z~` zgy*pSFjpnwj5j3OL<*iNf^VssC5!r6MU$?I5RQge!Vus6hi-~-^R~4~dEZE+ck}>d zg3o%py;jTPDW_=YF?HF>^&h)&nXUT+A4y+*(5d3Ps$kStoknR!mp01b--8~x_k3OJ z$4lK;jGeN${m^t3B}Gx=_Mz4y=llp<-Io-6m<62i6Gf=;@ItTW5*CQ9|% zDC+3~4?=}&78S3|*keDO_h~OnD@MQS8Na*}hEziJk|4-6KOENJ#l;buxU}-Q4#~J+ zChvRE+>$Y0ix40x=aJHXM^t)yKD@}8VI_l~0V;n(@pE+^|<^X7%q zD;}Lu(dfKMfy!^BG{wCGh2KbgaoR)A#jAoM#E1VLA$~ecB+A+vulLsHo+_7ojG zDudGTj{V#b$YC$c2k!E&88hwgwFMIn;E28$np8 z*Q9XmLpgRzJSppji2T%t0jMjlLK==SIZBx$W%|k(|%XT#9z1wbiX#|e=m9pL3*s>cay6Kx5%zaITWARd% z>2+^7Al5Uwo&^UsL`Yc5oK4az^Bo)Q-rICI%ibwZnQ4gMJTAY;*v94h=1{ zjSj0Xt$Cvz7R`OS39Yrj`(9Srm);$DM=i5k5&0aMbB3>XSTjkw&Px8B-kV7yQDilvWw4Jvl732iqc;uGL+;+ct9Fjk_@PZRP$jAn$LKU*3dSa>z7GP}?&! zpHS~K>usbusan{lNhV@vRNTzF`W*O6hU#D5^9w4uvTn0P(~dQH9R5>pG}f7IkD4BN z&FWnT&ukzFSQyu*d;aD-n5N%fuYkYr_>B^LKalS@);8MTC?Z4n$%V=nhi~qEYYzq-{S*U6 zXxc#*jnnJ-E7rj-vY*gT6M?nvvW1!5qXrn<`Y7hCEuWpL<63F52m0#JoHajgAJi2C zS@5*kxKA0?l*HjjWlXp1RzFw%N?*vQFJ-PQfqZEew|I|2*mA?jGbf|aBH2ebkg{27 zi)q)BMrx6QpO5n#B;-E(bSFcKh}!vOTD||)oUZWi-NG4l)jZXpzYMEikfTkjc@4Ba z96KUFi$il7Z~RBFdc}hzv)Er`XovPz~2B*V!~O5YbHhsG4P&z~mWVYoG64AVEr`I(gS* z{0g8*C0|4+4*hAz|GfA8M(t>_k+s8(Ac-VlN==jrN~P=-aUN^R1=8aI98{{ zNZm^AODgot2;nkN@*T^PpLrJ4HAAg3iHke?TMKk;sgl;F+~Ei2{0elNRnUS5 z@F9y&>QkF55yF}yH1NX*S_#6q2T7f87*@J)Z6YuLU(7#a6T-}1UI9|R*s}_*edq|6 zg_U2Kn+3|xhOF<~_IvH#+@{N!T`9KU-Q#zOZW|!a86iw-v>He+BJ}gf+WoD%TZ|MV z3-UYk1(M1Hsc?p?`JE}${Lg6QN~AnS=euC{-2JusehwT!;>n%TX4~7qWw)eK>{)77o)ZfKfzxzB#Ua;gPTd_iZkbGnH?n74EykwNxXSH z?qmPTHDT%R-f)m^Qg%Jak#ayN4`L?L;Pc3=RZNq&@2LwM>mZam^(*+Adi;&t0r|@s z_tU8i0lO5>F0>@N>7Yh|-; z+NAMYZa3lNCu-g!cS+bQ*v;>>Uw5ey2RxciT04!sWS#8#O5dBc{vWR1GAOQS-PR^( zAV`4V?(Xgu++BjZySux)OK^9$;O_43(!m|RCVQWI&v*aO#jI|MTGi{VF~&3In&$A? z6Y3&s<-DJ7OB_>nEB%u5I#mL&_~u>|B!~4&HrYfePz7l(i`!F`fO#= zJx{RHi|Ip`?1r}mv@zF-XxX=sMmlZ4-Tcm_qM-U~HC3D+zBdih7EC#hYR}^1o`ZMs zW3aPfyQ!?ZoQV$TGN(kWZtBP_22-;r1xEVd?q!(=n-6fYD>C=Y+jFk91ZPvr9op`UHYL^CJC(w62eSJpqOyX9zg_^PvDt zo`7g<#{zY;kx^aYa#G+JxzrJe9y!_?w$9LGcua2`^mySZ2U7f%TxScGLqq9XOFnz9|mhY%y9tA@X~cg>+78-}h`Fh}wqjO3n$yR2iiSWJaC zx3I_rE|kYzn4;YgC*)AMFNK!p=(M2fROxz9`|w+F{(4ov;Nbm{ZsYPSGKe^J6ci`?I zini&Ef_LcDkH=!@C0(k&VFAAgFdf0pZxC{;-LeQPU~P3oDcg7w8p`urwITcOhFEdP zT`O4hZxy^AMr+@RrkVQYyNP`74S9j0qxAoZjt6^$u)O!IgY;zgLiY{)t8oLiyk}#& zMiZwGZstEvUa)}TiOwShzX*au<9K&Hp#>Hjf)uede;=E~-=4W|2NTIgND&b<#sO2R zImADu=JOVf3WZmt&DO9~%TfK}$lscK& z9#&?xXXW+3Z^Uq(ThH9O5g*RFJ6T@#~06x@GcUs}8yDQsSxCa~Z#>O!iHA(F{N!J7bUqse4fJ-II9oTYbE9+J_4j5pu z5NpUipA8v)43)G%#v;o2t#>vhkb<<=K=(Ff3F&lVIf$ARV8|Gvj2EJBZP_lmTcF6D zt*+DZK(!W1h3Aej`9|}%6jt=%JE&n(0uPQLi=OHH1XH9Z4;;BG`iYa^p@(|>9}m;# zi+wOnGwt|}aY1u<$RN&mdbmP2J4Ey0Ihb6LfIX=Bub?@L8nP_zZRPG^_3YR%=t@}e z?8FcEN+rMvLiU~85JQKv{fRe0CF0hs`at6`?ZTz+$QEw+UeS)4U5fI%U;VDrt@0^q zGh!n=>Q6D@$^eM@9zm|&KM!7Vb`cnAZa0?K^B6cB`<;=h7*o_DNy`cGxZ!FIKl;ct zF+hIor~1BUNgXW+Y+u6cb5Rh zV{KEK!>7pTc=vCnv&|Z8P2T2c>bYw=%OFQ*(FeUrR~M)P)$!_WD4e}Sii20b9kx87 zjdL;?{ERe9aS(P#N-iO&JA*ps^D92@{5e`g#IoExw53w+CKXz%e-y<7r=Z@fYN^SJ zE}w>ME>rrG(X4i|&nh1TJDX8&MAWbITw2cHqkI`@EdN=c=`nG&rcyI~d znY~j34w^1Vg(F-=Bv2>$T${%Yk4PM+(EOY-l!?N-e9QEFYDBO3F4-O?Z@c1rTgs;D zC*BWK4~KhCl03P%L`Xk}M?F0ON+-9;^BH3&>5i!~C@)!LrOE?`EC*abOR^awK0TqV zuh2h;GFN6#sgXfms%#`?V)l)vtGR5MUgRmGbeuSI;)A}D^0GzKZytXqngxgF)61}v zngF9yaUEcEdZJYNprvFITM&$R3RZl6|EX7IQ-5m#5A+ZZEsOPM$J3M6FNEz)<{(^= zc^6a3Ans>qXVF0cD^4?L2QnD(`O^EaFwN${`z=-t_Hcct;>w`?pY|REL3wZtcI9KI z;9mOa+NaViGqX1KEtpw`yDH`j%%1uh%BPk1#dBxfBiWYBS^MZZDp^Ugn&tZ_C@(hl z1z1_?*O3Mt!2CnjHi|{J$`_MPLHGC5023B%m6_1)K&-*@4-7WD6Dxh8gF*smm?Z0I z|9IGF61m}xHc5>*8O*lQnp2)5@XiHm`WnAyJ1~#T~f=z<;a@ zYjxkAErAJ39U^WrVT^qVvR}RZ@p1V)jU|yg4s2+wzXlXoNq`?~xF0~M)^HpZ0f%E- z&-AiFS-!l6Vb3mPG70`xMjRoCN+WvbrVc9TxKgIpq>)@1eIWFI&5LvBgBP_r-=iRI zM!en*z;RzTg`Q^J94t_dA@A9aE}e$ODn%~xHd_7{UR{m*xKi7RdD_y>r_1PjT)o9# zD1WAMj;<9(9)DqCIx`+#AomZH7b(vWj%PbDoqLt_Wgjbr~dU`#A7A8k@VYsoy+rwEUN! zA{4`JwtIHtQVew(Pq?=z_Ng9+TrN@d)vq%nyN6vAc=Gq_+yTx46Nuv**zJa%?+XBh-zz%4HXhxUnWC&2V0U3{b;Xf9w2 z1=wtYv;8hIeVL5@x@}yF=LOr)k^JBZocq?x`(pJxgXeN9g_J<&y_nUrYrcKnJ#3wD zO`H={RnE;mnUVjeKshSk3E}Fs*q9U%8maG_>Qm=I!4`Mg3lAy>BZfu-?3}%Q5rtKJ zK{PU8>2>1hAsV?&XY1iGdi=lxs66(Fv6r~Tama+AkQ;x9?aW6CyaIK{ioqS5RNqLN z0Lx1XCbg$#f@Dq*y}?ky*`?@ULmJiaQq?vM*v14~-6P;AjxaY{hlcHyvIsnE(C;Q-w(#P(% zIbsC>|7f&#LLZRhhX04-YJ76sG&&Y;Y72@Cn`HG5?+MJ^?GTYfB#f~xM;bf53xybP z8kmr3;=w6xjf_^uBZY>@eJ;INN#j_Fu1hzAUjk$DL6BnsPVN+qX+G}Qu^1}2}2mYmqWmHU=zD+y42_=P6P3&I{q}|WanhH@W<fe0nU$w@^DMjGv4(qIF z%8rkL3}FD3vPeM$tX$I1)7Q_(=YL8VVC#c(6A!w`;>ul{4-%UcC_%cgPLd4L^{=VU zevo}8q~}tDUHjzqnhzQ^|9TzT6;5oeGla9oK5koXVH;W4^(yC1rlPPw8ms7}3i5U- z4_9QyK=Ti?Fu%;7*$zjc);^pC?s;|7+;6_#R4v+ow<1Z~<1=3qqXEnSfF2Qeu2oIJ5cfLR<8$dzA{;}=#Z2_Ls6Bv`ie#WGG z1ADWmA+EjjQgOC9xmXRihsUjZDVov*pbmuWFPM`7j(=-IZkhk?HJ^x)#<`KQnZH(G z$(e}pX{mo_BOFaV4Aw#7Ic8=KoP-y{LY-z1^*sw~VWy*4x zvTdVsDJ?53#sC?DRsmMMER{Z$1O8KVh~i+8wz_f|7U;J)Ixsh9y%GSCOAoy?ApuJe z+$@iK!2b|iDs)o#AS#%yabB6=m=$dq@BI(f@^P zG5!~_t=nQ>7r|T{2BH@CM~lVpXnfv8jLBXn8oQutg}Bff`0$vq=&~MWR)>t)k~54A zf3f!Cfe9(`Y7fEy@v}JYs4Y9Wl{!oVSPF1tC}CkeH$Hs26S!qH$Kf6zW=W5}qL25; zhSnB6M+v6`dG}1o8XGx(VgyT>aWF{}5D2^{B_Q(Oo-HFu$CpRjZy&@Rai5|r@ zxsbd}_`=M;fa8`j^*aVhBMhk=M2IS>?`P*@{InvP8)V;(7CHAb+!)w(+!v>~%Pko4 zSJq(x%8dWF^MSL-nKTNV70bW%-{rWBv)!}*g1F%qkE>_P!y(kg@^AdofEo}?|6zW1`M4 zKl^^)##gPx_c)7_9wP() zY`}(CwtM*{^C*C*vSOJfhj*}b@k$p8bi>|W5x&(awNF`J4578ID? z8|4%H57+v=wEoiC`b(ZwwE+I_I?NFk3MheSzvD3~{vMLkbEqYav`MPp#Ig#_Vg*w$ zQlxtUeu_JfYguO#Cd?^kr^+NM&a6?3bKyCfY{Xux6UenNNNsVGkcwJv2CsneBor7w z&f=QtGY;bm+wmPLf1+A;EFi{};H6zl(V#P(hz%CS+aki==uYvNil&h|RKFW!$RanX zQXC-LSQe=@5R(c3n~moR|Llf6ojRi1agL`4N_^=yL3inB1P+OO%AoC3@7S{AVp^zD zHrMGX0SSu)yS5H>TPZ%VIdGxwksjk)7mE<*Yw3jmgY}n_%`zyUAF(!LhB#s$a(vGI z{Pdv^%^PV**$f-UR7)$c*wJ_nEOszio!Y2rQ&md;h&mWx@E(JuV_&=s^ZqSe&5kGC8_4jK$pP`0pTYHuiXpVB4!8L!Y)B* z0+y|7R)~caP9h>Wiexay5YPH3j|;y)#gtB-Vt=7#^$P$QMeu=uXg^g7e>9WAcM zlXCM!xR;L6!o#s0^VQ9UM&*PfK8ecYf1^-q?M|@Evj0S(PppYJSS;fyxlUu;SKM2W zSA3F|)4|N_y&^xevph#ma`{8!yT2tw45CWu(=$b@qjlWS^3%H^j53%)$`Yh+fy5X) z2|msG?~4te%&RA;|FSd+W#Int@FjT2=;#P4g2vI~i;7XI9(1N2#xMCTis*q*g2t(` z5jhS&RWy1OiPa!%!P10t>bW3nivz}gK0*s(79$pZmQ0uCjra#qr$IwGd!RcRN4b=$ zT}9Hqe_x_Y>MSSBro1~!mmFV@zn&cIO|-lRbU}u*_%0zO6vzFZ_W?d!0?u|We zFwK)>Ulf4&)DX%Jg+v8~0FcD0_Or0*c-vIsKT2;={)p41vw}8B)W&kao~kkWV$uUv zL@>p0Dv+RT<>95PnhQu+7v#Pq1bA$zp2U&zCR$VreU1j>mLYoR1|6M;>3{g-^SxeW zihr+@@CzUIz(2Y&RG#0xmn}9b@_(Uh2mwoB8ms!e3`?QtuWf~gva+9!WKak!cq?Sl zdvF7bbev5)_5RzIvsZ^OH+~^VPj|D)cUT2NW+$+;J#kcZK*LuO48K zT3X8)IG(!kWuwz=G-@`_7~XMkv5ZyQTRh4#z#1v6FsYD*g5E0KBy-_J+`PB^d3ra* z$0ceBMbqv5x13bZYKDOZolNXTxA=Pj3GMox?I6e|M#!sANfEQqm3A3npV2jMEtk5_ z=t_W!Z7}O}qm*iS`)aG3PFLoS_8bQ6ktQsB546=AoIl&8z?Q00B-!s@A-6E5B!#w) z<^h@xg=tbKyK%D#!GZ4>hhMFM$Q9nHOh|W?*WT=O)n~1A8<>7R)}Pi30+%MImGWhQ zK!hS+@muoDUD+f7y%pY*z2Y0&%0uKSF7}>RnGdv|*-J@^W>#%EumDyt^8r59QujG0 zHb3Wtj=AAiy{Hyo0nF#K0QNWWBj`_MEUlKLrc(Pnkw8SR02tDq30>ucW|0GhMlh;J zfF@(W5A!`yy%3~N2NHDc@!;L4U{X4btMc%Lcf!{7 zczRAU2sk4CUP9D{_LTE9o*eykDDMs#|2HK}kaXjCFa9ADoc}>4`TrVVVWZ+#oX?bw z-!ekAA-)mj|5oV%E!+O90QMKy0E1oEzgOPG&fs>MDK7~K#$?J;52q|816DUGOlJb8 znrGiEhJn?Mb05S$Hz$OadeBzmQ$@<7;5y`h;HTsNRKU3ZcLgl?Uj>ZZEv$O~za6l; zC5XRof&t>*a>??NU-_gifX$6YWQk-{k|pA0!QH<7CDdOe{@CTa`wif4uev}IGXY z>-lqn&wFl4_P-waHM~I?rsRv$n}CPSvGB1`cvO#GB*roD2PdwY z&A7`GG=}Yje7G5#ge3li{j~AYt9om!#bV$io$BmL8%)sqUSL;xNRI z8DAj~M`wCH+B5jpP3zcHHD#6x>aE2W6N{u1QwNPn_dIN9Z$j|ubAj~4Ff^)k{Oi<~ zViL)f8>wHUUNzt*RVx5j-hQ6ad%j@AMmLj9Th#BV!VLFog#P zSSiH@)|g@QiR%$%RM_gk!t8+d+;S1;Zc1PJ$mWi2N^2|@XKG@j1Yu~rt;HhcpbArn z&)P^%e94<<*okumj27T4urdTi^V$2FQpr*kllsXSpd2Oo*1R#B(DAD-vu)|@YrH|% zUV8m$_XxbH(&Iimg3?-ayh)dV1~pJ{T$$Ypj4)lEKg;M|JYZV&Sf;4!@89CI`lJ|O;cB2kaby0*hZ3^BWAyu~NEV%0YcwboneHqTkR zhXMDsiLPl7OY7et7d$7K)DJhmp=>JHjrBcQCcdO?YgU!Z6KS?ini3pMS21te>4p9X6_^Qbt7<7afy zgwzQG`BOxo(*KK+fcx^7m#*+%<6XTO4r@|b3vxo27KsrvaZrWJS@F0L>Ru2*vMsFO z#Ewnjp}kQfJhZI~q8XQ%KO; z?m#SG)kM(NLcngfj_0?I5BrX>do5J>Xx3H}2n3_dN~C64*Xj~d?KjY5jMRy0WrRxWnn!?Qt0~$#Th}bya)pj<)Fs9h~5J`J9 zV5x%rOOZ3R*ibf)5mD!2Q>MW^>!(mLE2C!NaYQL7cOTbyl>7`kG#;XqU{AONliO@i zUmE@;o|m(Rwd?bK>$#&;@iX{oP)LAQk6nQA$)%ItXEMQ%S4~bl4G2zfE1A*$^{-V9 z$I|#t!)B(|)=1Q8Lwt7x=*Vd_skY$K2XQw}eRkgzz=04zI9?P&Yc3=I!xx#0l3c&8 zwCnyvL)}x@v>JG`l~#l__bgHOWu1v7F{lG!C+`8&u#XrtD#z(t^?UpYn)-;ijZo8z z;h$Sx--ChHbVcUq)Cpc4E&UH+6=exFLDc7g+1v^?(J9vy`w0p`Z5N2M134!XA`krD zxyDk07b|~3mmh{xhLTYP#xK(gzNk+297rJJ8+dQG07jRt{ z8-(2)dGGFklE!_BgiufCc1UkkRNy6kwnR<0|B#I25otCB#3b>(5md%_b2tx%;#g^y zY7T?3LEHL+Uw!J6(tgyp;uRJ5Z)WqK8rH;#^Vfg(Jx@*CkU}BVtCT`1D&CiBC}WD% zmc3sJ$^D? z)(jjIxTfAsNQRgK=#nn^cpU-Oy&2JG}Vn2Le$cuviXLbCq>hv`I3GSMYkDn_mhGNZISj zO)qxK2s(9-Siz5*PzNJNY(3>_T|LGI=UZxh6H3V5EDMa%ZHN%QiaO1RsFtHkMQB= zA+(Yg4=sWVl#j*PU=jkE(?|pj|CthV|Cth455OHNpM9=e8d+fth$oNS|1y!;|1yyR z#-gB;1j;$*vY%`I5h9Uh${m>vdp7~VF>&!ZCKy_1gOv=_!cqA@vSi+}ta&ph2|5;` zi!?+o_}6DIEE; zHnEzg8|g@!5slHN&Cg_vqxuh=F7ZNKHQB5d=VzB1nf~J@rEQi$luTB)atTRV=Hr{6 z^2BU|bv9UzElh97ivb$XHWmL*gEbbB6^!CXbFnpKeKeI>>?~N=)@$Jqfyw8T_@t%K zeYUSMAQu2X-1^st)qhaL)O6!3g}o>=inkEr;H*o{ZUv8r)*2$%X9;5hSi;!PjK=xe zb~ioHN!is0oD%8$-22f;TW2;`YPj&BEV_dR8);mfHV#wrr~Jfd(zRr`FOL@EF8PdA zZ{c?k&!cl~5hfXuK#mbElP1W$S-iR;uwWBSouCFB7H?f@8=u2MRf2Q(YEyZ4J+}rp zEmBRSC#ZLOEMbc<4}eajpxDWd`;}KxJPT*4Kq?CF&?!L4!2Cn_zA#Z{K*;p)CV;Jz z14il|m~Gx;PS|Bg2mXd4F_AY1{gywnsVPjFW-+VRMEYhYo!G!~62r0((F-S&2yoY@ zWGK}$2sfiBl`gOQQX@BF zpyBMGoLbRnXOvnLzp9sfLY7U{UDPns(d^v9SY(2xdZ??gRK&HLl6HO<4P`&M3)RP$ z+F!#vEB{kGkVO$C;S1Z43$R=sU!sTuH>YH8?x?)-z9s@EDvv(cs0=^>uI*Oo{wU;5 zBpg59T-4nJmBK+rHk2_@=~PZsk=*wa31VA!uj5QJOW_<7=q{#bz=7NTP*!!Yr?4D;8kIL2B4h<2lb>+d#3R()7qtz zD>hJ7h_KG~Y3$4Un`5U^vi{Twveu&l?rIY>Oq{1oN<}xf9eVe((kQ2^PdyLgqvSxn1U(AM7M8` znpplJeN*7-I|*7Z0a_AG>UeIGrIY-+H5f#~7vQOAgWKMzTR<4%O_sz!BL!eiYhs*f zTKZ^$RGUr%M!y99U~ zgk}A$rU(QNE#~8Fk&6l0nIpkHq&#%DKWy=KKPc(G8!Y7^AqvrDJj)*S~2T~e`Cf*;4RWURoH^E}rcTzG(G zXGUo;%L{tl(MBnD*pjhet#>MC)22>roGqK5 zLmQR$%fVNWmE|9z;B{Z+I=%DKS^}9hBkA~CEwDs>+7DB&%vtE{HkC)U8}Gf5Id6N7 zuv_-gZ0Ozr|G7gagY_gT%S^sbgu)7)+A$o+d-yh__@LO`yZFw~`J9Izai=^F6a6IQ zZOL-DTQh;QF$jX3Au45NEeri;qUqCFx_fU_4J=&^q$$CO7wJYThBjDeb%+_~&v4!B z#2&&r&?6Aw6o+f0Bn7DtVt33g5#1`|{ye^h(ZD5Qhx0hg(B}R=%BxYEn^S>U*Q1BP z-vIDKE|eig7dZ|Wj{WDg7ubjFf*mgBR*lgEF7ODo6(Y5FEKU+?&LaW?4v&nIK;bbD z=&?f&KQg_QOr6^Ip^vAn_oddu58z=LOCL8Mz#p$VAE^xQH{BmgcYGf&eBL-dZ+8(k zcV>K>;m%sz`(G41I@1H=AQR^`Q-=8qFplopFwlg8LX6_|>#!p+?X;_3Qt@Yf5x${S zghAwd$y_QySLwz0!$O6bI^Q>2hl-b+!F)t$d??4BG>30bT5j2YN%MqBQ(1hbCgm_nSYTcqCsdYx!1vLb;ats7yB68{NuCG)Tl_ z4j=M0pAY^a)q3D$zUOhD^TqF;oBmpB`G}9T z>`46i%U`$TQA&t(hYN>LL@Q<@woHh@c2vMEHw!{SRipG9wDjwo;cKlh=Xu{t7rq-@ zyiZP1<_~@j@%Z*CGL))nXkNa$?cn_!u^l=5AR&H60Y5{*oFa&0cVT7l@Tu6VUIhjG zH0FBZgphNV{o2K2nyI3VsZ0RV!vA2Wvo_LIhvCUX1CH%&V2G#878qqq3;+Y5?KHJ=OgfJ*ZH-!B| z_|TNcZ4`dtzXQ%^51xM=`e1E3M0@=%oiR7nlRC2k=>bO9{H5f+3W(TO-qG$hFU{X} z2cTMb;<4J9Nr{tr*HmMM=eUM{t#po}y)0jO)SA?b+V4g02lkslT`sg=-Qoh>e~vun z$1&bcoWwFwP;IvnU$8g+$y#4SzHC08+W|A+Cfi%3_`=$Tg*wng_D}R?WNRGb!g(o<%K*REj@IJQ)vYB#5e9$VO)wMd zlW0jKIX>((kCBm<26AV4{3L*OAB-VF4A@Ga*3S{~Z`Vb(jIBH!;TdE%2|*W0HI8gq8||EHeY;}!HU4@9x!V*FUq;MD zObBpj?wwc-pPk0BUX2W~+#`<3jYjcbtPOR(6~dx{Vw(iAKp0rx4>f z!4&KhpeC|u7be~m*hA)=yBY7~g zss*_UfagQ=<;4vN_xU~ahzI-?FYW!s3Z0YKK;YWxsVP8If+R1+U`@ySoU{}7u?N+U z>0MHJy}xB_kmw@0|7+L)Esx*#C)<9gd_cw=VXLA&VDZ8Q7SC`i>KyD=d!$?S8j$qr zv2h#nRFNXwY#&WeRT=q?QvvfHuvZ&;U1K8P2I1LS!!STGP7DG}Z!}-wq>AQaN{>w5bX#@qV;%EIpghx zuKC+@SjTv59ykDPjw^v7PdQ2@Ij1n#Tl^O{Yf~?? z3wn>Bi5Og;@)M`G4wiOYjE`%t7i7M`#2-Rp(CO{htS(sBmdyKOHLS{(7f1sACx9X2Op`%V|Ri?{(J{UFCco ziQYS!S!W-Fwi2a-BgO|KD4`d+dM7Vq$2sYQ$K56Eoal>Q7aA{Sv&OZ$a6;Ls{~lQK zGUdrrJe7T7(H$Guth#hpF%`^VFz*}xSD`gO0n2f8cnUz)u(M$NB_~Gb{!PT5Dch+t z?(o;@M}8bjrs8mSHg-r+dET4xgRsQX%cXUc8@4A1WKMDt7t_7tIw%Km2|b>7&HDD4 zctd4!K@G0(-aIj2p`SbXG#L0~l!YfD-BIiq58Sgy_)Fg@2oeUP6r9VoINs<+WnxwE zrg+BlppRS;KIN zIw+)aZU&O~F@ih2u50dfWtJ_U>gHkh+EUb4U>aj;8G#Qcn)Q@#J8)z4_>!K-(mVaw z5`9|vwa=k=#g?!_RI=>sTYM84+g6r4BL=$B2O+eS{FnzRabKoNS1hq|s2)!>wu;51 zQ^3R$+TCW{tgHMOk77iGxM~T9B0A~fGuI+1#iDm5QxL9s&V>&dUDS$0Sf}?u;R}`e zBMgtj#uVuK+1=0#v2O5&f}SDi^4c4C#?z_I*n|zwMb|?A`O@BHB&B=3>cBo8gnZwL zK2PYX0vH`|v+~VErIY6-6O=q1v0rI?3XN;`;n4e}dDg!3L_NoE^G2$1#GD8!apd4S z&Q>iSdZ@53UA?dG{s+rtWMN;L)?ax8j9TsO=mgvqQZGZ*gpVzS!kQ`u-ImwbA%t?1 zgWpR4TG8&X7}?>ql`aYxT5@e-`u?>Q!T{Y|ecv{feOsH(5Uw}7y(&Fj00$HbvXyrIMi@YcXk zX*SWXhohiXgtR0N((ts?%2v)iKBrtZweHansNs2US7S@MWEAbO>3h4Q!0{4iX3=#@mS zXQF;l4&be7hRwaG=Rz>vmGY)>8*YStiBd}}-kbfwRJY8J0e75XD;R~CPl_(-88^_A ze0%{CM90{BWTeir)xDvV@vf@5!Rx^NB6J5jR)>9YtwQBXaDLv;Bh?8jmau8>`ai8_ z`4&|sGLklp{jH+qnR*Ka8xecN3DS1n+9klkvdeM{Zl8TT1I`}w6xJ}k2_;snlBU!g zL+`gR3c=<)BRx}RZ?3W)*Fz931F`gT$H(>FBfJ6d= zkqQB&unu%DGd_+#$0tM)GwtcpTog3TjvTRPCk+N=D%N4|JA25M(eCco7W=6vFfeooR*v!-SE>Z_&HHEL^aSk(Nf zP{bgH94mQZ0Uie1HK^(X`g6C-r~w^2-*QRp^%~J5qU=3bEnS)!eX3-dB&o*pD07_i z*B#l{o7bQRT> zBBRrx0duAvD@#N#)6qVBdqDI|4Ph1VQg7)fgrQz1mHPBE*4Z$IMc*V%&`#xWe{U4K zo~c!l59%d0lcw@~fn)sO-%?)-x2TR!NE{BP=Vf*rT2YRwSgYntS#yDHK5sbGNEfZG z{EbI^`lc6m5?T6%5qI`y+S8Y;;Cjr)wGhiT{)M|928Oj}ea|2FnA~RV#h?%RicM|j ziuMdu>dp*H8ibJi=+eD9aBk1mTf4@}rz{gyZm)XBWb!gy%@6%8)Rof63cxeD+uJp* zr2dSr*{s<`hRxhsG+iSdpQ4}PpW65;L2`vMFj2Zh6;}AQbDlqY1fEx#?LTk@&E%7& zXn5)t-DFljBj-MJt;uqt=Uclcj$kLb>jp9X;F#0jq1|Y`8$cfx0bsU zbzkXw^QzB+FKGsd>7O@W%{kvcru<2^QXNmK<>FU7>#giMPYb+A99K)d{Q4Ikvj?~D zaXs%)J7h9(r>d#9+t(oKlL(OA+#00ChAEniM=2R#V!iI!{`)2RX)N88sVr56SguzwcbG1}xQS4|?;&!`a_sW@c3WCbrzZ$B} zLD>{4S4Su*Z?(^$K zLU&!;R3FHrep5Dd$|nnow=KRIX_05mtsZuMkWRhDG9?Z#FR&O{oVO3j`+)8%Ku)Ej zSGGeYq!EfFh`)`TOMA$T#AC3uf!8NXoLXkrqZB$o1?K5 zAd&7boFY4{PB1G=Kq*p{-nhxAA)z4=RN)d-ehaguP~=S25ZBVl-mM1SI3cL1hWjTq zuqp%ML#H$ujuJ1>u`(DUd*~h9X38(jl z*#VBJy>ApJ&smNYD}wb?^WK85#s%tonQlpNs`@S1#Wvj>`0;V@^uoch8IH3(iK)Gn zvtOXE4D(LZa`?YILzVz;+LI1aoj2QWq|a&W^}N;cobGVO%fVGubHIg7s1*3x+i(qK zynhMg^;wtR^kV}zW7djs&&*uU|AJfU3?Q<8@H%$t*=s*)vVO_*H;b1PHDoOlL>B(A zB7&!MDKwx!T)a#yx(l0ml$3d6Q&+Ll-2zZsbfKr0%=W0M&|6);*j&Hiy4@Le(l0hz+jE>eIk zh|%Ip38k2_FY(5_;cyfgBkrNh<2N#l!6?XFxYM^*&k11_QLI_4^5GI@ zb`v8%ML3=A6T~aRv`3Qzr@-r5E)0>Vj-N3GksqsV8F%?b=SCvol~(5cLyfRa8|7-% z1mP30c@?S54)rLEJUIQ!W=wdBGNxHI#2dB@ranszh8$G1U$yrX#!^|pL&W9GGD)dX^OVmMyBFiNbt2_RQ_ z-0d?(tLt{0iOOCoP${iNVP`B&hczCE(!Ic&dgX8gfQJc%ce8#&fwXWD?S|Q~H!4k= zVnTq>4tk(o0K`0Pw5oJZQO|R@AA+~RxlmpdD2v#}EIpkrF9{vb5Z!r{iQUrcEPBw+ zdN1WP<+-m>IKW8?Ttl436<@!l)3dj8vGN0-9%PQEX84O1PJF9x2fcj%aPldPVqW#4;v$_7nREL@_T-lP%4L8Hf4E_ri)X9n}ieJsU z0akk@d|&Kq13;lf&Z>GUu&xeF8O3Mq#Og$Z!q)9^>&j+GQg0(NCONh4*!XXvh(>Jb zqO{W+E`?KBn~uBF+JHJ%bIr+?AB^=Z`SN`WYskT$4%0`3gveDz(et!qoHC$ zFD`z`y?T-~w*dX4NW6@p`;_7fd{7s1+k9KBODIKb7DT1_0MH_T5~uY1a#IG#Q%EG;FWW4#IC&V*-#VI zQP!ag*#QyNjD6*~5#KGF;-(?mu;(8Qc{!ZIUl_ukP{FV0&>e6#u)UT#7|qEeOS{jI zqbRCfz0f+?2K}?h#)`*KTu> z)^6l9z`WI$EpOzmy%(2Y_WEP#ji|DSXaL9Y375%u)qw`x#rQ1~D6ax$OJ=;aOGpEt zqPReMLnq>bZ0B;~9c48}`##Le3cgxW^DwsoPWfBaR$yk6#g`4agk)R}orku%_+li9qgx(4hvE4KdmGJ$Pp<4G39jRS<;NvSD|kP73wwYviO7x-pW_Qvf< zV~S9VFSDR!z7@Qk*(_yg(z+cz6kMuYJpRjl!q)^gHP0{ZnhI=W|mC9A2xL)jYN?xAGg4*x#@%0M;0X^B0y z-u+S61k3?kn@zipI)#E$&IJRI|>3j97T`LZ!gQ_rgm1h0F|N6%S@u?W= zIqGv*^?K~Y9SOGWy6Y4V;MQ_OcQPjCOmIUH$4vL1C-*w!daAr}%any`%X<}|ba0cd zMj!Hn$U#*Yi`}wrvwfFQwzrIuD5DGFlF_m(&goJ=<}{Ntw~Q=sEx8>wYnHQ2?m`jA zOi2CW<8{bBU00PRvE`&+=IQDB-_=?wR>et?+sia<9nyc>tVM?J#I*a|p4iydJ4rmyO>3UukK$PmYD1-Xza9&& z{ZZ{ZOm>;-)$F$YCVZ#It)WFCt`Q|(c|~L*N+=NSN;v|&g+ykw;}()68Bi~RR@IM-giu9J2Q=?xA`_QPP6(w<33 zi8=FdW@Gi`gCw4K?$^=UVW)LD@m#Sgj*~i^N33r+zn_nIiGUZ`hv=qDhudQdi8*9# zY7cf@`zDXPfidieFQ=?4RD}@-Mo>1Fd0-Qiy*Xa1aTWfOQ$U{DFheDKIkW8=%Ry#& zc(&tu7I-g<{4NW3xLcK&mx{tIiwHbs;plFKw44*KJFN9C$pd*7!xr;4ELI2lE0h8` z9hpANtC)ShQ=KHGAidGsXZvne6|3T;w1&T0c5SIn68Bg#_njsDl@)}F;$_8_S+LqJT)s2)adRLMUWjgB_>U>u=G80S7>7nYjopgrU zmR>;_mJaI~>UuKPo*peTS$a8RcHK(JV&tKiO_@$!O{Co4Su^X?q58VVAw3~xNZTmB zEhp7{JzX{*z(izU(l0(_y&+m9Ag%`8UM)$Pxo#w1 zTfNdD^+ExHhMZTR3L=iU1Gyu-5BOXWR2fAJy=_C=j*$_!zvs>|;!f97Em9d^_>B2p zvvZfbU&L^ceTZ)QWVtnLtrg~Q%b@^IzBn`Zp|T=X6j2a_bfj4jqS*3~0l6*qkTfnH zxm^33M(SdS)Gt%x$@SXq(!|i9_GTMKs5i5%SQRI+o%ToDChos&wu*=El$GaeOST$} z-99Ph=|aoZ>?%}+NrlM?YM*CqZ7c@bksiLY^c4DXJxm}xd+Vqhy3l)5>poCv@393Z zA<;C_V@&G~Oi2yN3rGizj-E+c_gLyt<@&ahwBPOw#Z7tublpd3=Mrq&l@?BZbSQfA zajCMm$Jx&8#7i6Q&cyz_0=-1JRD;_~Xbme%Sp7k4y1v6-n;zn$S>brP;UT^^Z(ny3 z>*IYg-+ zl3r?|wwm=}kg67yAsg4^rGBP8JtE!8NS|@;=rKGCVz|gYL^pjh+*;%rc5XR%;0Y5) zPne{#4!WVp>eZ2~d($pXY>r~M-(vgnD&uh6L9AG5@_Y4UDBCRdRIw^fD(l**_Gn#! zSMbfgKV>t0CoJFbH_uYi=R1^OD;283q!JmH%^i59tE__IzO%-F7A}*}>gO!EVG5UN zo#YlSlN5L@#ggIu@^$RFAxVMP(kxQ2Osf)=_VkaJuAy|6q7p^RrKlO|DdmP0rOmjn zAp}Fwa;+n_3wm7J^bwT1&pTcC;Fro-sOOCvmguGWd>MMSD&_6dO@W?=zn$k8d2PGu zqB#=h4CBk1n{ftt1Iy7(TMU*@ZAU2;W@YWK=id8o@{{k5ZnsIxy)zZ7;c8!l$+=qNd( zjC3*?O(se%KV?&8vtG;ttJV3@((V_Q0T&o!Keka497*9iycOmPr#!Q~j3J1;M@f9M zhk#p?LAHRrTW7$!tE4DkB+uo_zLs^7`{Q{stMw@4Zt|JZ_%+ zdX$G@^$|LK_z`4`(3T$|xp?p-mW;fK3=NAXF_Vhh^HxSutMf**h)!vS4gG%Q5JI`M zc7jsYDVG_b+HXz`~^JDY={r!qrX+AiV`^mandIZHmFk~r$h-1e7swNu^!Jxh6+uY zQ9n)9aVEWiV#9fyXpD2Qk)cAJH|n+5beu`6px|(y?iRxoAMb}$>uq2hxsCm$<4hU{ z1&8xE2E?VZrK7^kHu81!YOPaZn?%`sJ&`KLYATyS>IILwj^lNl>8MkE1|Da2%LOU| z$%hJDXF-(`P5fA|r4CaBROjQ5E5#-+!f(jsH_PfA*l<#>X5=GxY@ewpZ;lqL4|!Nd zGiX&d&X*%vNiD4fTxY4M4dCY&DuJIJ)fp+R16z11%G4v+IR&27DN)Z&h={;d389d} z=b}FNllVJigs=#bHbxz+a~}JUdp7(Ht3~O{{)pAt16D`oXGZQV!KVeqZ|BKVRw7e@ zb5}|!t)^~$$Ea`lvZY;U zyj?Xgzq&a}xIN<-w=CrdxtCH=&Zv;|_S0K-${EFV=kGODXWX)sxYGr01LMfO6!eyz zl13$Zp7J<`!~6a;q@q@b9Nq%COKQ}uQ`V?Nf#{w#u5r)iixtc2pahcpPrZ_LN*k3Z z6rIPJ?^zxubJO|}prZ_Od{TqS^crYWH)A!Cb<67DH7L74ZN_y<)|03(FOB037-`O| zTUL~;CuIFPa;?{%tjCmoI<5TU%CO0cMjwEbrWAOjo>n6l5Jhw)ULsQIi@1sv4_m!O zi|7QXNDZ`9XwOp)OvcZEz>jOL1bra?JX^W2+E=}iQT$>(TAIvnAvNh$yiR$EY9|6$ zEQCUC>jmF$dHO~f+N&f6X0VGngA!4}UqLCA3cf;pzCy-dq3T!oDS2vTR%he^tAd>v zN(4_1Fv>#D4wHI9skqN&!7uY5tUT^5P=RYtI*W54>wV^?dxk$ZS1gC6)!vbr>XRR4 zGMM=%4&BWap?MhE6G%7tG3CC(SvR3%6E~@iz>wQK)V07MT12OME0iU3Fn0CfBp{o| z>B`BJ)+>b`RbNpavO$!#^?4^!M5Y=U!aSwuNLAZ#*f)>!%y?2i$WV4)a-<%tbyj_2 zMo}?Rn1SN%p@n=|5)qi9=Hs7}(NLNTriFY=qLrtp>2s!>Gl`q`{k9um_8^O6feqq|d@_hfl!fz2WZJZXZLG~@ax@xXm` zCWz~6%6cu3GvoTWYENdGfR?grNc*?e%tbZL*AJOzlh^)kEof4Hc5gw}ze`xC*-_Hu z*-iP`y#?mYl`pH7{4@h&^0RwUI98Oz@JX|rq!}8MpWTbXq~aygNi&(G861-d`jbim z*;)nPnlx8QnxQedFeQ*#-CdgEK)3D;jLDozx`5>A(J9w;TUcs*4mk|BmP0dJc)7uo9_Mm><@q|+-l?%4Lu5^qP(J_2f3^# zXA%U2OC+nWkybSM$f)Xy(uyWg*Bk+XFBZnZl&0+Y9tkn zJ@UPxoT4hEqlket7j*L+HCK&{qU32I2wX)OMU&`)PHiW3vWmI;UCKB@BcmvNGg1<3 zg5{1ys+D1!NesmFd>caygh%s3*0iMcPSk}|=VX-S;`ox9EZ|P)XtV@@J6gg}xAY_i zD8)*pJur)b(ovHYWfT=KnrphzCNWTZ98FDz7@&HtzPGLSfY`iT9nQ^9F;G&MDA|?* zBmrtZk^)j7ug>{9DWwK|m^=#s3a8+QPlhR|v>1_U15+(K3=i zlCPDWNhk@VI;Q+3#)>>wd~6*QW#oWN-2sF$Kx!FAQ8uOkV|rOL5G~IS0#Ar99t0(= zQaPhxGBq11ahX)H-vjg(s3@jsFnr04R_2gu4<$$^bajd0`x~hEl>i)IoDvFd=JjO-)0s8zPWBOK$-u%R-+$+r6$h= zJ^Sd%SB+Y6o?qBS+ptw&$i!XeVsTf0^Hrm=dg>+tX@X_}H}2?a=&q!<)?!4lkkE`p z+wjw7$W&F0+;yzD)_NIXyZo%FD05wiQ);MMFXIZP>$g?|TTA*GdGk@;I@QmH*x*`? zU|hO?Yn{QYq@R%s9%Zc)xv9p_T1{zEXe~xcsn#!u@WDgag8ERNei$^y+jt0$%wBcmf_bF9^{2HZD5bO19z4z_(!J7N@-8wHe_&K5`lkYCA~9;ni_kC$BJN5T)#)wOR6@XY8sion-Cu zZQxrnGKf<4(Aq3{P#NDb5s4q}^O;g_3w!)khy&l65r|De*zL0N!dJ#+ zQCrw!vw~u-+Z04kmAR-YS2Kd>DG;3QA8K2BizJ(^SFNB;LG)Cai>h)pBZ!^?!Rh{? zHZYF7L6mRpvT7w2o^$xaO1(q!fZEnxHbFjlMJu%_h@NUC6`r$UAfWS8BDaBYc6$i zvJocMbf^vN0Nv49cR(|0z)}6T<}PEL%$g3hfpO%9QUynfqvS+ z36*iw?%gI34prr%id@Z#^Cf@9(+0-T6RMKUS;3+dDB6rb-+1$luw2v@_E^Ip9-}s) zU3ipwHyD_Pt0NGpE$mTM@eGrU{1TK~q8Ty1 zWtn)4I(>4 zcONQ6Hdl>Wcm3ov!!4CrpOZG*FO}z7cg;1U)*YW5BgmJs#gjfKZT2{2u65V^^hRJi z-u(@{Aqnp7L3l%H!+6-Bx^A0->L@Nb+@HXE!>ykfjo45ioPuQsuK8Ij>k#i|gziOO z8SdCT#D>ah+Az)>dr}$x-Hd>{7&;iTc?gMui(H~K3 z`3#zex9XDez2gmG!0D|oZL`Nob6wKrvr+kyH8v~CgkN1n+w4=C=gODO7o+keYiw3< z2vrNsRom=w%3S%f%`xn^dO?v6%^T9dd4|SH8%AyieOa{$8A?%8w;*j6Fw{lH%{Ej4 zTVdVm*>7`*90j0BRMX}meUZ>F=<72xkV?OBcWaUa?9FUL=S_ar7vE8dz-+7R85&GDYxj14dB^g*dl^pOC}+obQot8Q>H@7 z&A<}UR;Hn-4Gbg2N0K}aqgAVy>h!i~NdV9GC~5;|Q&yvI&O54Lrx_K>DVmC3I1xzzNiM@Re4b&_T%3mr^E9JAImKD=3nwB0kQGBF zgJh!$Aypu328fU%i`X_0(fJqqH`gkBhABo7LMlMm3=koS7`6>WBmjz5kW-dbqt-g# zGZu`Htdy72HXA;Y$6D*pFwH2n&KHe=BIL|Mw}g;3dzdm7TkpddwaI(k>t@s@XIz0B z+H3^bHP*g+bZZfLWIabxl8XPDWF-YZNr14Kx%e*C&Y5wt05tcU6v z6ONFa0=ybS1W>}CGPK#lh?zsR+BD~=_pH4(14T$Dll3zccbn9{9){ISrU62Dl1gdR zB`1!tf(B89>IVzMdgj-_bK4jw!o=yvg0|U+Rjp4ix6NFboXy1dZDXJa6K4gB+GY=< zh1P=%Q;j<7tfN^tLW;wfE8(r*knA^XG0x|@+K2!5_i*yftj_0e!F zJR$if$-aw<$S5UjEhBoBi1nxd4DX=t-m_B@xA2%#D!B}g8GU_A}G86+U%z>}}xv)n|OQ?S%t zA-fqhzuA9GzN?I+bug-Ax4GswRU{xK)IfdG9$@DcLVc!?<|^53uKL}ccc@YIo6=dc zN1?#z4?ow!Y;)D`=K4d_zjZz^bOM_*Lh=uJ`0VT>xLsoyU;}oN?7~Ma?@KBK@IgM@hzOHl8u`mZ@Q_bp| zUT~JBsPR|79BQ&Rqb!c^5gW`tq6n>qFu)q6 zHPmHmMroeFK?}hf-zQ{_YLYe_*)-I<3Em1Rpm2g_6&WY|ZyMTg#L-agrWsh{#u)5o zV2u;Ugbr<+fX(6FF2%q{6E?b8SYrxDi$fa@r1YbFn=0_e{*oZbTnC_yMTEErSnLH* z=2lYD$TLgO3Zs>j`ZBhD1fNrSCT;<6A~`atzSUwZQsp~R1(2%Wk*a#Y!n)vN7+3LC ze>By$pXx}eeUid?^v`BG_OIWOKbnnO@nP4!9!=h@X7gj85{q&8KsCPb96mrBwbQC6 zVdH5C;+qp65d@iOwUYqXfhBVwK;SDSV7Px&WM5n3{b^TrQtqh!P;F~Wzb9*X3mCaC zfpvZaI(wsvL?;za0)awKYj{2t|LC;hLAX!QtY{Aoe-M$ZN>LsiLIk;=t&y%(%Kt(l zcFqz)wM$CgE$nJAiJ5uhukyWvEGcz0g znUzXNt&QvWwI98$Ci}7OaI$VC6+TIg>!9~G#Y~0(=cUPH&ek#XKl$84_pn@cBoL_U z%U(+kO)q!yxySDQU}0nb06x&gv!t*V5OQejjXA7^HhHIoLf16Sb93v^6*|V977R}_ zSTcvF^e0v15EMY`nsZCeAt;0_=d_gI{j8>9dY1K-v5i*`>>&JJ> zkKn0uq6Ml(9Qaq@ncZ}sN<~Ij*8m>9HR5OYkCD^K$m!3HoWARxRg8fCWn9=-{S#nB z`TRUPQsrc2?aP_A@A%xlnvK?_Jo+p{_oL4;^e=$Tky%_(x=ml|%(pq{ij!lyA?V7c zmB&@D0;@PZCes3jF8_G~SHV+};Py-_BU)lSRipD9AjR1>nHI`IJm_6z9RwBKOABQo z7NdI{s!>jXPO-~44Rpd4C*x2Fatdam>5wDt|5wj`9V>zq&?4BI~LzB13>A9toL z>sOO>`$=l#hWlJCssVj8$NaJU^WJXBb&9B=5)>Xh4>V=;#2VP0XZb~M2R2#dDK=EM z*Q?QD0LssGd-*){kV8Q0bIpseLfW&P7O+})0f!E|b`BkM4<(d5MC83&hX&FX?Uasc z=;mvnm1fDslupXzDtc#%@XHUGa#GN4h$rVF@K`MMlDgaXPJ5s9Du1f*N5XM#b zFS-YnGV@f^!BhuY>2uX~_w?ON(+4BI>3=kvvSh@re>|CeSk-RkA1p| zRLz`u_|iyKn^yc-^&%RTc50^u@CiQqd8f`1r;*AOF)fd1srs4MQKhskJ1taWMQG*0 zA3OQwV|e)mo;NzJFtBUVJi|LJRANOO2QduOn(hJ;mrN_8SA@=M2#w5>1vOD!P=*_Y zDYhhEz2Gq=29J9%QoiKPY>+D7kt%>x{f^WC#Y)rq?-JurpW=m%oE?nNYr zv5-aZDe(V-@a9N1)THh*tSn^&+I1&OoPy>XGF>VYmU~!oLoV8(>Y{$J*+m8rJjE^6q<;w+>+WX{GSQlfVhWj7D-3#8qQv zJiypGeh$}5mw1$Y$;)+>-6aTvnUwpElmn#vcccbG{wK2$Jj%?tU4MV_UEFFmKlU|!5**7fhJvg{ z<~f$1izhKH6t6!p$*tq{xp)%OLNWRJ${$|mQ%t^3?;26uy`T)K#9!P=jG zWc@0(-c$4f(L%Mrhcq;K9YF6HKpHtn-t8;v`XN<9m{aFGpAl6X)yleF0WVJ|{HP_7 z?X56=)wjuNLRK+~>1Er-^izU?QYbEE&1my?h>zr}K~Fs}D-rbGYy9r?0cSmYhW97WlV{fbAs z?)hM0WB&p^LF8FBRIu2`I`ec+6_KA$N%np|g&%vm1@-ri|J zT#fkkhY;0}jUC%*LEPpwa{i@NjBuY$3t5KiT>f>=(!f>InH0J&6apFsb~R(~GA&fQ zDM*gIIAk!4KkdpK&y_g6hi^aaDGWZ$oaJzC^z?F~TbY4OvvPj_ldn)J5p^;%3oiR@|Pa+yoTbIaTQGqqa%9h8 zLY_wk9;NRVJ@oh2ex_r0Fw>Y0W~!F8pX}arKl=J(e+Tw3pFU1(0(k0Yp3a#~=sa{< z$Pby~xayadHx5Ln1^tk5X33nRghNeRPg1f@$1XtZ!TdaBBB9OSNujGpj1_qRcueU= z0$&%IbBe5QM48rbTSV(*bW-r+1ZR$-ur3cBkn&aXo1xQpU zf*-Dn$>~A?TSN=x`H1@B^!gd6L?4;J0Za=e^imCCOiVE&I^9DHW$ltc{Wy51)4c1` zLkq3r9^659NjP#i8|@#iugIUxrhK(l?S97kp}zwgsPY$w`Cy{@ zh=-gbQ$iTpjGY#=M1^tHFRg0q#!d@~cX>PwESXcgc(TF}EtI|`YEr7GVsy&ilEX_2 znW6;elY?95Xz?LFv^;vZN}TnO^JmJ#;$PlpDBk629e6+GTDf=5Ln|U$5@$Zh(LDJb zDBPrWT;+95jr5yEV<0Fq+0HKWr*uDg-(~F7N;f=}>m&fgb*(iGP0=C9)}N#(VD7$t zDeU)%R1Hf~WCXcyUoI|vLTboQ0=oNg5npr%6Lq9WP#`;@<4$Nfg(IScxvyp_-4#%K z()(yGp@jt-aPOl}qTQ#td}RFKB$qImP!x=RZ0lS?H9VA%V?rJwS`lo{7DUKVri3m7 zDT>iRJ|Iu^mY5W}3#!&BOY59Ju5UwrY^|-D;$C$_evL58w)D_KA%0pvP1WEzch9}& z9$F}Gfy(dd*7+mB7&qtaAGV7*ZnDm;=Uo;Jh-ywLy+)9Xg!g<=Q zOgN1i)Ztc?zMhH{Aem-H2TSdP4AH9 zrv%H2Dle~feyRG*38j#V65~2#U@J2Sr97mNu|O-24H?VJoYjv>1?0I%&V7dZn0cT= zDGw=>Lq?;9N?GT63iX+mL-}>Y+YknMJK;t{Ob;!T6X=p9swwKpLNOj(zU8k+U7CCb z9O&m3tvoY=>a$WfwerI-Jc{hpdjFKrPugg^Ok@$N>P+tFdrg$GSLcXHrL-hPf#R&& zlrvIV2@!SoZCJz?-N8gjATxemi1I)R>_(t)Z|I6=dH2d*JnYiWN%}`OeuU;wPM~<&? zUZmUJT2i|oJ`;$a%GXm4U6dLpD!j+N_3PV|8OQlvYPnUT7!4J{D7_5;E#yh!C6{)c zg9;;8xoR~Ts|oiomD|8-Of4Xj2=T{!tTQ}zT$br7k{no+XW`}_=pykHUt=(G;vT(OqYwos-;qhf8kMGV1z zsBL{})B!snrKY3{j_a+byJZ#v_p2yV;SK~7(VXCeUAxUPp!9r>Mm^zlOR`EZ`i8DL zF@d_F#@hUGlH;@p){dt8p^pQh|FWJmtY_ZRx4a^m*2fscwv;^jkmn(!@#%{LBML2kT&0*w;bTT){ND}dzj2^U^TkeR1QpHjgyB~N&sjS z*SfzPjl+##Jt7IDfCv3zlG8nn?A>J4*P@!>_f)uXJ(9rPoD_JaUrfg*GwbdqKkYb5 zsM`ku?{CpjokHR07gM>I!WnDtChG{@hd4Zq;0y`#TG1s=z2#&2r4PJ;=-^a zW>M$3_}<-Aj5U#LaJ><%NrZ#ckD*^oABvI-2WqOuRaD=R5VFSWF3&pBr1xacX^ihC zqxv4z)Xu3l0$owKr)6yEC)2!N_PJU4x$nI`5(Lf~4~Gkvx*-qCS>u_*9eZqe>r@_e3xjb@Pu#xu6YDpbySf zUDPD|8i@(IqO8KhRD`~dgr0a(FwJQaF8ax&wOviDlYV73fps zIpJq(BJuVX8UC;ibi@#~tsh77o#ObNCeg>4(D|zyMMo(WdhopwT)Uziiw;h|n7&ix zdJlI~olg{LO?@N;XBV)eQ?DicWZLJBOA6dg?TmwQMC^lqMndtve)v*@l$`>8-K{v1W_LF^V^OzcITaIAHDX8FJt0so zqaJa2#{oh@&TSp!o}bmD%t`p~CQCi?J?M!V!D$lSwLue`>}jshWysXxoRRWAw;}en z_0vp_Z5cn(EFm%{{MYaBQEKbnUAQUqynH*dhMEM*vdJ7w>aB??U&%%34gsV4# zCFz#X%@^ipVddIjchmeV^mOxwrxAeORpT2MHC+r;IzBSB+3rO(b!ulVDtIGrU4N-^ zG}m7)^eyOqGAdwsy59Rp$o8ezdl@8Bm_^^kiIDH6WGsp-txqFZlx)5_e5pw}qJo}< z=WRU<>pK#B7|J8c4Ps()d^>uj7p7*YM`W^~YBU#ei$_WGuZn`VU`n_%ed&*_*fNPQ%@sUl`4JXu9zlHRsGm9VQh7B+CD=eysO&X z%J{8jD{uRw+!C-LQR-BM%)+ALmvOL8jiq9ZD~8~0ec0Gg!qbPuFWS~q_=>xqDf#~X zIRWwP2JtLA}@AUHot){HlJZ#3(4?6t`OykMuc<-y6FBGgK=6X$2mh&19 zDn?4z-ls**vt}H4SU)>nKc?SF(DePRA=Y|xpEeKTzFL|U!&Cg4`vS6bO*hZP{nmI` z?=kmV)9KImF>$~CQBahg^ZIrd?w7dkFVzD0mwozEP~Y9whfN+%zmwq2Glexd()MHd zBcs}0Ugbd5ypdv6>^(?@}NUd33_>E|`~Md|Z8 z{po`8p%0tz-uFSdKkxmU#x3;=49k?e#VPi~9(CP3vnJ$uSRXv*zE|$AhZNv} z*X&^BT8BYha)-6|jbCQlI@NR}1OEJK`#hdbk0;=wycwzrzz8IW>aOn;bDU+bqrb9e z7IIOi7{ET2DQfA#+^+RLRp5e5arRr^+{&gY+f<BDgKtP0xA4rvV`XHHnJONOUf1ZXdSdc{(WOF%8ml!exffi1oPD2in_5Sv1G^^^5 zy$t*Z4eK4g#H(K7lc9ycJp|rqsO*lDpkqJelj;vod;0zaiIZy|cJ@qvOuv(0?zd`S zMhFwqP)-B)i3|AvAJ}Kbk6?v|``JK5@UR(6m!Q%m0}huFQ}TgZusIw?oWl}>QaW6s zVd;`py0o(9iW@;ZACL!|>(>a8Sb}~!3d2>*#iU%E5-bwbhM+Wrb6MYlDvyVRVQsC+ zNeVsh1RK|q0l#7B&78&I;}+~B_z1>mpf?zuaiLWCF60rS@d*I17u-g~!0WU11~Q?K zoHO3XS@&@^kRgoxfWQK$IosUe9|FpfL@i+?0&Q=`J9xa$TTykX7*L(o387q2k^|SJ z39(?GnleHh-X%l>OwmWi}2XF;9LNGpk`}X1b00X?9x61$>bWj1-D7|Ww9%z&? zjqr_6Sb)uGH{uA^c#re|66TlfC#REgdMyXVW8?kx6H#C@{~93(YotwjunZZ`GUzOG zGN3ITxpKuhRj^|xDWOd+lo`xrKZ0A{6~^^$Q9EQ-CrrG|;c4WCtrS_U6cbw2u~Va? z36P4Tu$eNs-t8CEHTvq`9iI(MKp(ka4L_=eKSin$E~CRPpikeaPUA*T`}#b%dISQH zkt0^~ovQg$x+Vh5bUX}13%FKCP|PP)@j*b-!hOd~?%-SOTWo(z#5 ze}|^uVZsy;e4(Qgpy%6_YC#kN@Pd@lSN>{sm*JD=k^P0`Qc<}y!$zBbU=Prz?yqaa zKFAuthw~>+cz-?Kd><}s%DmK+c^QC}jz@vsdZ#|%QJVtxa^Pv@@`z3Nba>m6=NdiaYcRv>YL8g*IDPX+ph}hz7V_yUx0zo@ z=lU8)QXW9cg*Aer8o~S+a^-<#K){64n1>H+2GBjrh_HCqPz)?b$8k7(i&cFwg2Ze( zXi{hDT8KLZrn#5VWrjQ5EGi_zW5G5oWpe~?RP`Vh^|k}~CQHgmyzP^CyWfbJo>L7= zhOCldZQ1ksY)I;CD!}lm@qSgDqH_#ZrN2_g7lHpwU!+mEIKPJ@ z{k6XX5Es<~(|}=13qUF^0T{wGgd}Bgd`=p4%JkQ+qatZ}XiOj(^q>iy1OifWKi zs#uAEecFq)d%fn20)FZZ}IhBjxiKzu!gV((XY+CZ1OI7ybbW5g6e`S~s+>5GG zt^KK9kr=V6&{<#oQIjMp5@U{nA|yup!($|dS0si{>%FK@9nBe++gfyMSieAZ@*Hk` zzrHd>bYrNFSE$aD*xUZl>eCoR_gany4WAV#TA7`QjsD91RQRD4iZ;2DJw<}C!V>4e zfnH=01wI%-O? z*9>kiBinrHBg3t!#NgIs7aGw*EYp=hp501Zt^B2Dw0HG)n;+WD=u)XRGCYaam#j$p zIye;aJSiR&ZavK$19sj!eRzsB&IujjMA1iG@XcuTaBG{-DK4mBuOtT>!arMw?n#~#bn<%oQ3%+XbEWMXSMLd(7 zRdsl-JNKNV*sFNWVEg$y1`9ei&c@ZpnvM$J5-_ED+@_s$oB2MwDcGZVXiOA_?Lx#KB0I)~Sz0n@m-enW;!d;B*}{GAuM0+rgQp zm2_HYpXo~AKJ%>O(Z)?iIoVsAsGMaXp`oe>;q=%LPy|-54w0g=6!S^NJJR>2UjMBIid&!;wJd&8W%HWPnAlYC1J^b|LnHe2G z5Pdh#%yV!SRaQY+3v?hSm%5*G7Ellcc|EUaa-ffclc>Zw!otrvR2p3?B*5Rd;>W2X zIoO6q`&5Y`Y;;J17iCi|Q03qh3qVujk@5a)>12Ph93)zhXDSCV&+Z2b3+ZHh9SZv6 zY%r*nP0*OhHat<%x;(9zPr~5vN!HYOWV{F4b+89H3puX>p0vSr19aY#inRryJsXUU5Eu!w08iJu&9@p_ktPK>U^Y2~Lm7$!CM z%E3HqT@>-z?+%nxSzvpq4Q}|9*UJ>8dw}hwY{cnsu#B6fMtW!EVM>+e#vq<&4_e_& z6jS7{WOAU7gHqop2ZmTDf6be~zjCn5Bk?_b4UKjXzNjjrBRZ|$E8>Vw<2_xBsqx4g ze)r>MIA0S3#4z18K2Ma|#bSbOQBwrH*JD?v83qjYr03I@Nx5#(jHlLdHucsKp9?Va!*sj=c4P^5CDoJZr|(cw`UZ76W9& z3D2yRbXq9Eh_1w`bn<>ytn$qkI_&u}cy|5K*!qT|eS-iY{pi>S;lAS74+9W#j`yWp zn*3CYe^}GzS$UN3NeAKpyXV|a_xhE4RZ5V_GgPH`;+AZ)5=FH!91g5%OBf%uh8bLL!&*C z;7G>1BZJJ=QsE#eq+_n)#dk;cn>{$(9qT<9(z8T-rc*vS(~0*P$-z8p5S)XxpJ}8; z37kKD?6Y->CfOQsfb-{IOs$Wc(QV)6K+ZV`GjeDE(LyhLU5Oi#4yKuB>6L@Cw4qGQ z{q8_T)}m7#Wq7Nto!?2GSJA1CGJC&W>;bDW{$WkK&kEJF)q$J@R=L>+Qv%2C`YV_m z;Bh>PHc}1@F~$CxH$i^opz&UztS|jcqxXuya?+R)EQ9w-{yqHk<#jTq)5HbtV*)cVNiOe-;T zrqjC$xX*MYaGw#ns&VvHE{4TB-i>8wv@PCp4xXs;|=!!$%u4NsJ4 z)E`Vi>x~e0vpN{xDdQr?eyY9TQZ!@xD?=144m{(u6Ao}lf9JsbB%s{-7vIv>YlU`a z8X9fAQ+6lav@fgIj}<{@@h^qd*3|mQaCa)!3++y}BoM81v=Yd&TeEDO8?(%h6;Ew> zXtN;~Qu@3K!^--lqDpF2eofI>YtG7$s74J-zA`^F@^e)b z@XW}{bDlK{*03LYv&{y zoxv0EBvXM=mUqR_FW<9^w9A)a*QE?zK1j0Qfd)x8NvF&&A*y+Wn5eW66XQb(ZN+%7 z6WuH0=6fzv=^4HjN<`C@Cyz2}4bb{M{7M)#-HOkc=*YT*1Dmgh65da;0<@zDYuh;b zqa@=7y`>*xolvr|pqNj>{=Cdu1KFdRuEra|npz(jl^XFwRI}*BbL}z)ArUQT8B!Ed zkk3Bbc}TBdeZ3gQE=n!LaViBGZsah~rTwyO4Q7sNfw~5kWur(C7omya4{O>yD<7e{ z9H%NlJ_a*?O=fqq#eu&1>Q6YpzPRW5on&gh$KmMZV!b|y)nRC~6-i-rR#kc(HsQ0X z(j%*jF||H2+?^Vvk9H?#z#v+XW%-O{#1)=fHDur27Kb)la0tVOOJe=@kp3V1s>Zx{ zT)h2saIpPeQt&VD>RH3hnzxe?XsTN*8%Pr7`NLszj89B7Bp8YA?9O&cZBMxxBsb_ay)12cY{;D$u3eRE2 z-!urT^`@zS0b+xGLKUL^;K$VZ$e5k+fSr-+!&JB1o#9}2MxP(?XIxGBO3#f^p{6P( zWv}{7UDq>`D7Ji!yVDy}Uja zH4s*0GhlQss+Ah#Z61?aMQdCyQmmqF(3)#Ba+>w5Vn%AA$Q6yKylaGI=*m>@&d1Bh z|JG~2#b)y08K|A`fM0OW6J-i&AgRuSRpW_Lr~v%fXh-(Q{>;PvOzX-bvOmkXKa(*v z9vSb?e6&ByOAE&+qC*)r?9R2DLt=VH`}0&RH*$Os7378c zFQ4qc&iagxb3QrE`4RzWVXN|cnjyAI?|@;0m9=CRQ&$=pR*b3jk+HEN&$;YMG*B7AQhY!m@Sp;}rE#)0Ab#GSf3MI?_rF z9qD|%t3bOfT|E3!|cf*+KHS#KASxfTAJ5zdG0snlq->r-kg0 zN^Qt9S(34mz6u!AA}e8NP`_qpKtZ}U5^MF%u!G%~M&mkt%_EkHH6W?aV;#L71^OE5 z;2@e4Fy^NWt24f4WRxw<85N7xp@urGb0*~QR5Nu3=qJ=?{SJYCln0#9^tp7s1yCKq zvo{JMI2_#F9fCUqcXxMpcXxLQF2UX19fAjUcX$6z?*HC*-&gfs)vvl{r{>Jg+3ud{ z*`4k#qQHR&fah3KZOEZwZ)lq#p$-5ZPe*Uy3th6HFL-_v!uf>?h zVvU3ot5_4_Ft;nedSp5nEa>MKe*SLn*SRGGTZ%)4wzVEW+o<$-;OqlNw(a{gs)eNk z#WS1ShLd$Fww}=enYx1W%Pj%M?elkH2xwd>yKv5)r{HdC0^}4@>A4+>;b}F;@AT_9 z1uk(mfJ=p%n$|X{_W!cZg=d?d==x^wYv!I9`!NNAbfo)R+V#{@%dBlWaVf-)igv;@ zR>#v6Q#a#0$AWXeXf{9ecD7-9s7Iu8-sCo~hM$NsP*na^>hb7)n@G$R!+&Tw_l0)~ z{6bCvEPJ(lY3#0{_2c8YIujT37o9B&-5)u>emUP|B)U%iyS`7-YW{CC_M!0&m0MVZ zhP+aqdbyz_U9Mr_Ml>CL{#=|69zxfRGYLQ)6@StkZ-i-_2u<<8Xj~7r08m1km@?!ZD@-O`*%dktF|4>~-gJVKl&$ZGed>}Fp|!H@sIq7uoovNv zgboMYlN=M{EK@#~5^xfQys^0OAt`((>gUpQJz)f{p}ZSMaEr-;?buWXIh-Qufoa_u%f`XC7V2w3vQPO`AK%3dM3w3m($?lF8qSlBkpX}WDL`mFIRk$N4;OH=;@ z`i(t~je;&DLLlcvk#HKOjtqtOEWxp5A%AjlnvBh2J&RCP$JIP8StPeQXVu$SKHW0om0GPjNK#Q_jP13!NX);C4(*Z^}F@aMT@3>gaU{M(Vqx4{}{%!Za|M)WDkNSzGM@XZ(H`G}Sw;2g9$r`>Gkjr-KW#XQ23nKRKDi1KTk zb=+>pi}$pA#r@l)s9-1<%Az>Gl&M3}6`^#zk14jo^*gP|rfCv4U+_>(`;R1`~Hwc^uNyl21 zA@3V?dw5s93Dyp`FmDu+3R&~mXAA#Av~3Akn*{EIquoj~zV85RUNj)~HMn;)EZEh| zZKq0kg#Xz*C4%f0M7J*;Pu3&EVi++_ru~+jOU)R!S}brX0JkZt1_W zZk7olQF2Yf@NrI2up8Bm{EbyRY@Q~QggayD4y zDtT|GC4Y*vLvLaIc$v=2jOK<@Hy`w5J0^D;r=GeT-~^^ri|Mur73G*vXrS+xX^7FDjLuS2a;E2U&O*8x0mfCYYa`eeYcGWw568^Pn;I0h z$Fz?J0?X)VW|waBfRnq9Grg1z*yqVaovCz{94y3l%lzQJLAH_f*IPs(EEs1h?aZ^A zo=G0qIK+DhxTw5WZ--~t8)>*8q3V{B?(`3^F6)PYLxv7Z^|Pj$Xpbk0{FcI47G>1C zd8OJV^}-6W73t&kfNE~KWRhxbcJA<(nM7bmhhhD$&%$2*+mUHZcJ2VLAIu4$iJSKq zUq+Tb#(!qq`{gwy^+;Cp+ff^ZNJPLI5Lqt!z4^u7hIV*Y^N|@G;g=dArO}ham&9_O zhX1}c693^kosxC&4Bzod1w3l}E|vBjc0XHj$UVjNBx$uq)8i8tM95P|PCW@#`mc3t zDEbn>znJOeks4EUZ}MIJaHnu^(`jWY+?&hyH#DYi_|H@bHq4iBcXA{WkK|yG7_u_S zEUw+d+nVTbxU#TV%)85ZM|m%3ry>3;`i^mf1LpvAAS*{eRA3R?J*2dB`bJ5rH54cwIyZI*kdG5@3I>?B6ioMx- zzqM2^Poulna)4rwFiG}51c^kQT6#zxRROJ>9dczudlcOZqEOi;dhqO1X{|CTpihDz zmjV9*R3htf@Ib>r4WmYepVlk^>iv2XjS0u!SrH=Is#D>H;_k>w?dMiQ`yf%%%uG1O$X!C6lhb9H8(;0BXF9&-$?b*oxZ=TuxMGt-# z{YWv-eEZV;sBSML%#+0Y-|bflmP46sWd1ep^K68)01o|Fdc@Vac#Q@kCQJ)NE8U8NqOBQSh^oZ!DO0iC{_hu95Rtn*+1Br z8E@ttJUPf8!t3xY^|;I4$|21QKWj`U-{TuUODBw0D?HNaQDv+c{BV$=52vq$F+GS! zLa9y6C+YkSMe%r|ulAau+h?|OxZ$Ote2r(J!etwW zRxmR*4mneqM~Mh-H5`#+3Y;!g{b`-S3HU}iE{%teonLj(LAulpVN#3*6e3HgrYiH- zzD~9w&pDv&kjy8Pw#z~^l?B-2+l{#p5UoxXev1YjM?#}bjzc-So(W&_{H2(pzig)D z3eQCC(B@u&i!Mc;!32zXkSH;++)>t!*5w3CG*E@jn+6w**xSzEh51?%$z2EBl3a+- zy616l&9||CGtqMAMSXTeS}&>R-{`e6`wvT9oB207L`Rw3hM8A$f7hzFIc4{FsCtrY z|8iegYvm6ZrhId{E}xDt%=9V-f70h(4I1mR3O3Um!07u$PWUaV&wPPK8pzacByf0u z+C_U#dp{z?=yn!!9p8YcG2pMav?Y7^A``x5ZC;#ilc7rv?Xt6#Gqkx0g8g(=Kx7%D z3do31o40{7ye#(AJ}$fC#x2AB@utU=k0ic&;RBn3#*P`oeU}%rjR{SY3Pyth&dsfd z9)HK}5ujwr4#QU!rs@{o_@0)k#=*_|y;`bl!YRe?xqbz>UZB_4=hP;q&RX>8XpHw& z!zJV9!}3iiJZz#tb&!cyszSIPJUB^6EzooTO?!t~Dpk#A%nmajd#~(sdc8|C?VTV? zkx2RGY$ldf>bR}8+`U|v3CFaw_7vDZLn?YKAoI|kNbZSz?)P7&*L&MXPZi8=oKJttYqFwWHC`w#^wWV{3iOrAJZWo!ph`ceknPJ77wWAI;{A^QvF~TV=`pIG8cqqgo zA)j^6dM+m~t#g|a3QEC?q13Z!k3Sf|fO+l_3%w{DXYQ&{EAxfu2f`9Uw}VKEtWV!iJz52Wul&|3P|@IDvKq+`ztMfKKBQxq>|hk ze6Xn$yE{h|g@Q=g+Udc1gnnN9qm<&p+LJ%WVsRBEZd>aJ!6Ad{I>ivyTik6FX>_yog zZV|l7@iGss0v`lb3rnkI16J^17?CzJ1_#-_OHi0&vL^Cr^2 zytWaR9~5i;SRnmX5#)LN(avU$7{0?2#V_ak-ixrJ*RdcXnI!sh;iuaAelA+ni*w*7 z5`xo(sbQE*5omS$Ts-d-+RC}(N^XGLU zstj^$sp2R9cvKp@UW5{d>4lje`J}D)*rrfoq@XP&9!UXq((8`_=!JBShN~tW)Fa-` zQ&R;PC%H>&;Atc)n-)qJrr`z=1#xPTp)cCC+dC--%LJ*n6+Ou$>WbLF?_@_mio9XM zt&_c(A`+l{rP$~04hsmaJ81*)yyC>tq&umy=pw=uLHKkN)0@E z^x`u}<)AqC@})MlsZUjd_z|3I!bt6~qMG;Kf8@2d!Au1|cJ)y&LUwL^VH4dg& zh!AKU(>~$JpTG!PY9SU8H{X|qu4w9FH#O_Mecsd%_iTgnvQUz~O0<uu9^}WVGE) zT=G+EPVWL(PX4gYl=>3BI<{nJQL(yp$1BO&UKg+Kg+MT9%UH8N`%I`x-oiolpu%g* zLLjtUs!R1)2*g6QC=%2HoECL*z0IDU>8`B0*pyPJ-y zW#2KB7K)~%?aO$S-{H=%9cq)R8vhQ^Ei>fBr#&_-|NERkMK6Nf1d&YVcn z&*lv0FGeu5CL2jCTr-RrS`qGoDD$r_nd z`!Vn4oeUF7Q$7SkC%_7Ww~$oi#JJWXj87MywQL1ip{{pqn~AjM&YLv+n)iKlJ{VPA zX@>72UB=yIb5m4?R@yjH348dZCUCP>k#J#_KTr`*mrhq8^S1J+?jci3mPb_oA|U|x zD~|_?f(L4^$-4kgm>#*C8=mn|8^nFBT&Q}uaK4uo%0f)lBOV|dL=0G+wUNwmb=4l| zfBX!S%3@n;ukPYHBzvo6fbTF}S&BH!vk1gzI5h=i{G`sE%y;GA)pma$P~Cxqx0$Rl zs2~3^qbGC4wRT#&l-qUu5ZG|x`@*;8f*TK^#aYwP^=SU>^MHBHg%3<(2^C_=bZzy! zpuJZ^Fg9=J))P9>LD-w4P0e5H(<(f5_61DOY)s;y9*&Nzu!WD#Z>81KBkXLb-zRrq z3C^CrQ<@R3@cF}g-8X)&c4&fYVerwB>3JsAxr~I7Y~7)8?qOl=uWu4!KnVS9V#jxU z(u0KP9JGk%{k9j%g6;K$=+AHE1vvTsL;iA7ViugTSdvM}g!MD1qPR8FcqQI>E8(7f ztdZyhGO_28rR>;~sE~vB)aWhI(vf{(^3=ysPq8b`#vyZhzlrz_p?I|gA`WlTmIk6# z#%`?s$mp%Ew#VOHo$;bV=54|C-L~+e=b`y&g#Gy2+wJZMml68rf;ab9PWA?)~t3&O*VV;Hi3*Yzth_jYc z@KV3U&ld74%?8rJz5F)%@ntD@udW|&j^`6UgZr3)q>43nukT5Ix@(b;w-2E0rK64J zBZGQd5?&Kv2PY|h^ZmIPT<=}(`0Kf>O^c z-mwDGZkQp$O0mDD7`ZyB>|JGWNuJNOtT6ki+OihGhWD~%%M;nh=i|5=Lg|u1OAP(| zG0PPBdBw|Q^OQr;_{L0!|8oa$NV(f*LpCjca3WPNMfKCpJ#Fh-BG;Z{DK6gI?T z2kl1os(XrPNn;F;;p5)Z{61QG{Dwsyd)@_1n_usIJy$8=l|R}>a@hFChX`!qGFRU5 zimvRUn%7}LGHguNC-_&(UC?uy7h!$VZ7!)e?bzFOTmRVJ>toTsCycFH-LX7cH@h00 zmf>Fvk4TutX?X7Z?5KOdPJRsQY{wX}?ffOLn)_?=(Pja&U1p0M$7|K0gYiKcmu&^E z8^#Okij;t=li8`G5ogyeVKW@>u_VY1blQ-xzCO0Bvq}0valk+zk8x99%b1u zIWz6E0mtsKk!)o(NqHp(UR(9xn-mp*m6#lHK5Z*{@WQ3aHvCQhs1+F&9PiT6Z>I6x zX2a# z{Ic@U6M)e%3r4m0ZO)o_+3>eF1E+96p2ZN++;eK~0iTi8Bj>nS2WocKPD`js#nnT) z>TfXpBqM^icGd^QE1EGEQ63m}zrn;{6b zPJ*i#D3AlPi0p6H){$JIwo-MIJZCj$*$tm2ZqJmSH!{?Ia~~W;iZ|%_ktpIWZiU}h zu;yxnX~x0!Tvbt4*)i(PD6OL0ntsGU2{$AMC$lD@Ak%AFbWP}pwJU2(N0zr%ja1QI zsaD01trn!P6kD~iQ@2BDU>_7&mzYOAD0P!x^XzcfR{Ck>%+*FMIf+0<m${d2F1{iWM-Ce~yvUQ^eHv-@{0hE?WwR&5rl@H069 z>g~B&u_8&Rwpz;=b6EMlya_sZL(q*o?RGO>i@CjiM@{1{O|3uTN*$?{zk6dEo3DAH z`!T9Uey;JU-Q&-7Y1g=Fw_V9X8TwG4GXNR1|Q`K139rd4Filoy@H|0yaPz-4?&K z5c_FtKd(NtI-8DSXak*rH~MN?RVEIXl7|dlQmnjuyW}0QFA@&Y+84UVuN*tj9HY+- zCzeE8Q}}ooj3tWOA*`$%^5AUGc<167Idw;M5hYHd&bD6Pr1rsEh^c(q=>2fM%qs=g zdStZUY#y{EJy246icm=`R#yF$ND>{~%0NWw{pft~6L>3aSFqo#OlLFv!PvNdiwV!6 z&$p+@PDqxExc1Y(oY!PdPh3g0Y6ol!d{X+J7?6lC(s!A6ulLwY zY_V-e$7HR!y{x^BH8*#NG&9q;_319SSP4@kC;vIXA%i$pB3(d>*78DqG8B=wjrVPD z)F0MTO=-1#;CO0EUwLXu57kwGqi~=opm+! zG;dBT_mPN?E8P(i1Cwv+Vi2@JV|qx+m8upzA@hh_!e@JD#$W8k1upp`%KA zZ0RPWDht!w#7?=qY_=|X(4A0i-Go_M+xEoKW;pR#noGi7OOmx%(Dtf30l!$}#f7~d zUa-2P)6As~jZ#Ih{;OPq7kx(m!;C(^6@STt#cXaZwS=fG9FBUdD2Kpk!TYMJbyaIj zK_Jj-#q&(U;zMhEw&$JhM1qq}OQ&Y1)BK_9cD;c0p35pq^_H2ohv=YE&g5myOT>aq z1KFflZbCz0?y@m!p$gi8@j%4txF`sts!lCTyRldo&S5rVg`#6ybXp20)x3CdK9)A) z>a9FvA&O)pLl)Ly#q*A&+Ry7Bk!mhG$XKpu=P7bVNj`SW6QhfxwBRa zgtOx4SL!P-uaE5ET`g^W-`kJ>zzEb zE>UKUpmERjeitLPDzs)c!kT&^jyUO8Nsa38d$bvBkOE?EXE3u!K|Rd|W(}90R-i2! zoxDrP*W=HxE;JhNsoup+fs5a0V}5Ce*>(}v z*D&-Db_okq0P|VfDNpc!UiEw)ZGC8_CD*88F-bgeCoK^MjG9k*3D8e{gUcHq+j2o&mC*_q4;7*s>V1`v&hmIQG%GbA zxh)saWgV@6@K_+M!QNL1>a>hkgTE~|P;oAdGBmmGUp)?4n1wwn#84Gys7%mRC+n(} z^)x8D@7G={yH2Epv2rW$}TC@2ed=t{bw+TM7f`6 z7U>25KpIIvFCvAIJ56m3S3D!KLn0DEcv3*0VJVn~Fe1f?L_8A3i3*UAh{5Ioj9r3i zteHBAWJP1C1@WMM`*V!pBM(ZrCKAdz-ec{O@?yg5l6GMMiBK-^cL(zMB7xe~;Ys(t zr9cw=k3{|>@jw#6D_aW2ISyh(lsJI+SB9 z0vwToxdTrgvLBa779D^tgtsgk%_aXAe3x`+MkhQeB;ch~h&UJFG@i=xyUTW~(cgew zSwsq|!%M*|((q=XtV-OZD6aTDSck;gRe(bx2se-IAU@QN<3l_%euA@o&MB? z9UL2`B9Mm^91wt|21P)kz!~8v1fV`faY*cV;X5QI+Ib90+){cDN(6d&0ox|9jjDQg zQQfHGt!v@BE%fz-JgMS+3t=n(plYBgKt?i2lnVJu#a3~}BUI%99_TKcPJ367<8`vL z8pD&6Ggt*Dc-kzHD8|4dHaSouPG@n#I(_iF94LVaA=v>h9K4=;h=jesA{qJJaf}eB zERW}&d~%B1Oq75>`=G?M!dfYqtEqJ-7ET!WqlEjp>$SmNVV^AaxySYL!*<*dVtI_|!b7&(L*94}NJ zSE}bm4fajC<%;b(tv;ikz>!$+I9^zMZUml31ov~o>t&(sx~N_wf`Ad(Z*g7U@jIZs zSDyVDwQ3o9jm-QERdD&jPtnZ#&_TGoB`%L}fETsR5l~dqw{Lq*N$ZUv7c(UL965$n%!O&LpMcC{SD;>Zq6+>DDdbdLiQmFN_sRk$e zuQ3LwReG;u{8_8x*=7jdhiVm3{}-Alw-8Oi7@>?Ppfn<&R=l7Ute|IfK;&CrtGgSh z+d=;an8S#*nkfIUiF^uS8Hy3g8s`s$03>JyxH-$QXxRidRUKIHs zEKi}<0s9M~J%ne$c7mrdMgl^sjCgU0xLHx8a!SM+*m5lj2$LYn5$yrd%J7uF|HeXF zc$G4el~5q1G z5OqJy6fcx1oh4s{IcQEvLr+|zqYriKfAhRygfi&4pna&J!Zc+M zOGAQ$127o0@bk^3@#9@q=y@zLH?jd^-}J#wQ(EgcP;F35%P!+^V<377!RKb*V5J5w zdp&;Q`!=8ytXsS}@Uvfz;l~+F`|tB{?{Ri=6TKwe(PtyLp9u@5+^SqT&1SB5H*_S* z$Liht8Xx2%R=-6ApMCsbwdpZTfw^CDbwW+3oMsPR8|VouJ70Q|?Qf|kJJ0k^X+)#0 zf7s{?b)EB~p$zoy-bOGE!N791Im)7M6G0%)HlBO$h*_o`H+Snjc3XV!z&mln@4jRY ztGRf(?%0@=->1R%9^4wJVe6Nr->lzq&F^d|)q1ENZ&H(^N9L?vQk_V_8u^$7+MzQgPWG%FGhBUcBX(~P-Cyyn`ih;M@FC*17Y_Kkje79L&&VVfHh=jS{Aud?8Cl?S zd*%9DM8@*Lzwv%kDpoxMH#NxS=)S2X*QKn!aIG&EJv8~Evg>&H<)^S&!t8s;M#rZP zF{IX|YYwI4dk4J5to(Zb-(C^>m#vs4!ft@*-o(|8TgUXVuxBIKNq(*a!(HUMRyRH+ zYkkdxuAEae(K2`yw%a|zV`7BY z;vx&dG}{jW`1c>@+Hm6+eY%cZQs>?6r$RhD7@m|Zxa4gD%h@0`mC$YOesX~O3>|!E z{BcAd=&KBxdR^s@boRp)xAN%-4*DQ!aD}99n*XRvTaKu66s zzTh3q++)Xi%}I0#c+IJZ&rdi1Hc@l)f*_}>k$+tYb)GxBTfK~^V2fc3ynZzZ(;7PHyOq8V5DFF-xI4kWaqv%R2Z5 zzd;*<5Y2-+-&Yypk$+)ECyDZ9efF|=mH619i66;FaE{P6Ht>iYUcRPxfgC5?Z-m3j(%?plY-Oo%NZ_bPJ^~_M z|E}2awh1t_m^G#s0UkrOG1szhyq?D{O_6Xeb(cTzee20+)PpYQXe`mb%%64=%R97e zMBDMT>vUsm7%$y|c^Vu!maRR7ABmN1p$X(-!=XMqbDQ}5_X4&th8XcU(vzs&y*~I) zSRJmfqhGJBJ>)d2Bf!oCQ13wh3ATcc7m7S83gVaToh1?;+ix(ZO6{@ki;X3jkmJ4y zrMRWOO0+x_gdB%&ICo@M5*720+ZR-jf3800B~sG?on{i9WJ?B1?-DLug`gdg;d%=zV60-Jcfk(F&AgTFchrNPT z%{`9x#``ZGwL*f5gCqE`l)5|4AmkFeC-7b^_T}XuAz)fHxWBrt*i^cD0W(;J4%=H7 z;!*D7km1OTKG#>SQ|C)+Js7f@&Mw^WG z5H$taNja1=G-6BP5h#}tXpW!?Tn!GFter0@FT+X7dQX~$?nRmYCf;KG(pEEWB_lg~ zZZN)1TlniRK52Q{`p1&hMP4ZIRv7O$-T8q8&TL*s(z>YhX|)qxeq9OFG?;OvA=?@T z;UBPf%d(Mp<&c{0-mQkssvM>2H+9^Qqa0}=ua;MlBVKk?-*+eMfz1mUs)DYHU|IAU z!Y)_9Ut5~|ejW)>*&6y{b{I5EiO*HNPQ#lUi{uLv^h@@DEyfLNbLUQx7WaX zfxnyn@q8KLI24YXZ~i1;Fz@=rt8c~$LRU5RH%l1Va)*rfy3|bSU zCF(4h>g)lx^l-SVxo_KImAAH&B*vZ;^6yX^d_(vIge_=t-u^?X!PlVenv6Y=?kAug zZGND!>f;yeNMgu)PHt=wJcbbneYKF{h9a%_`ax(7p8k(2sHdR5ZXj>?!NhT0H4Ne% zL3h=yb4d}u5sV)^?A-L1KTL@u@ux4hMNY>tXtBJO?0#Nt5$^xj2%~mm0Ty-J|&kc55%CZrwH9*VM)=hk%@g=36veaFC+ zb~wgMQ?(d=6FcKwym_7VjAJ~}TMkzFpb%ZfBXaxT8%V@#!XItr{>EhHmiPD@sr?dg z^LORKXq<27;1cmJ3qk)2to^#gs`S;zWIBf{2A{u?iwEOkH1`@KULqq)+1JW{>C{qo&DyoCDx(Yv_; z9r!M=)j=Zti~?>CVI+66P4^UV<`$;!BzoE*^vq#&<%Y2^^35;%i4Q6t(=+Xc$6GtF zQ4GeF7~lW{>4fXKv_XZ-?YA2}!pX!$%FZ)V^Nfj+wc-Nd^t)L526z4?6^EO^TukVy zQOt`KMR!&+O`tV+e#agYZPu@t6+Q~}?7S)dLGgT)3U=b%-4a>7=k895Jg+#J2351Ae|tBL-cAZvGo)- zKYy3{`#{*F55wII7G};itAbf8<{`e^9ad#Uskm-M5k#>^NKFb{ z!@lin+%pUV522$Zszry$9@)KHU*7@+)a$n&>U>D}7i#{CmDm|O? zm}_I+VviG^+a;urSZ{Gpz1$gZoxaLJ zT43$hr9Xa>vDS~c&Tz(#<+^!Ikv z>q%4P<2i%6?F?LL`~xO_`leQT*D?zUU=4c@X6d-yt&AT5DJyX)Fm4rhMw1~IS~T7X zD*R(M_K8&d7J&I6wU$k2$Plo^)J&c_jbjN;k1sLyWB|vd_x2yW_~p0hR*LrqI)Md{N^eIaAz3$}NR6IV9sKGc*gtabv_@*gf93!CBBU@5O z`hF8?{pQxouC#!B`Bo;m6+~IVo{Vx2l3W9U^AjOj6t4ngqyhM0^s~74O-z*#REvn9I;LO7uJ|M?< z`nT=5N0AGrs-3GBf7{(hG%~=y+;p#b7=>0}{@5fV80ny8_!Wm373AJP)OYOG_4HQk zi-Rs5kT-;@cM!)H$XCp#&UJ;A7|IU zOxl!S0=0`vUkq9{dQ$dUw;MVgnF>?LfwVVg@3v~LgulS?eo*UrLfm}^Kj*dkgGo?P z{t}h^EY?L<(Tl*pAXWzMDSjAELy}e4$*OV!TCdRnAlQy$J-Y_|d>*KK2`PDjtvO`R z*~6PYXZh>O^%NIK_!)dIajgKwojG=-`#~PIm)7+Zx5s9CW)wPvlJDcAkaRGy37IdO zLGj2ex?7kGZC2bjoBhe-Dd-eQ@SW4VeS2|g9y~Yi745zo;d_kUJzie>WUg2+p7Wx& z)w+k9L-AemSE6j?lK!>*#4yT+_AWyASr&S%a5!2lZ6+XWla3^l2kwK15bM!YtRL%cwxi%fjQo03Iga zG`+9}^;bH+zD-E9Hs^A^2fphEN{siu5YB6BJBozkECM3OJ#u4y`Qeod^gbs7V~z;N z0T=e}$nm+U9UjT2Jg4VyoOhR14?AeL&#$_t=8mSJ_O{KgeK$Bb1wCcEq91`VrUWcM zGx12NVD3*l78`j789(}-ZZi0IS9p6qUbAsgMHG-lL|MzwqWQYaI^BmPGG@h(9XxD{ zQ{(MCz{+&cx(_IBmU!}rkCNlFL=r>AnP3|#vYZkuJxHFKw`Ga6ppgPH5S9)MUc55#g@1Pzs)`eVi`@ z<9Dz!on2Ynb!L2ow0uc9K|Cb)-POM;E$D16LQz{Cd03xqYt$VSxiV~}Z20LU(k`rF z6U{nVRW5ZVuF+4=R^-9;oIM)7>O`zR*wY`BP79!@LHiUtK&d)3jqf|VyX`@QplG+I ztck4NDreteFWtiKI<;hq85E6+deh^j>NRv#6};f>+BU2sJkpYP5yhyD$yvTY<)Ozt5OGkgaHRN&nHy_4-|G5 zF@H0@a~a^7WI!NYRrpy`RY-^=g?iJFsN6$m$MSGH|M*sX5}b2|rCF z$zP?iNM%>ZFY|Wn?QyzS#<>^f4zJxp_oxWJ3$!*uSH+-PD6`qRGkKd_-=&s{O-Z}$ zFABN7LL^roHU0A@FCnj=xN|nC+|T`cjsqT{V?nl>lWj+I6tvfd@v^!Ho*AUmuMC)` zGNC6Dx_mxzkgHpZHpK_66_LV{q%f98y4Q`E|WEm@3g}Wn*r{4XN{I!W^Hm_MNWm%X`02g9IK1+p01Gfwq6F=Oa93&!S%J`UYo|>-a`PhA z;3{B>7YNgWykmh!O*f<}-t)#&n?zKLL@2M+AE5;NS&@+1MR4NoK8dq>^?(@ao7c9H_>w8`w!GtuN6O!&n4s3zO& zCsnqmndYdvsFl!~9CJyZqZ%BUme*}K+K+x(e^LLFl|i)GOZ2eQ@n%$NHjARpG8Pte z_^7Q-Et#cQslI^o!EjK}s=SC_lS|_cM$c!cozil5u!L{Fz+Z^rmR`KwDIH(%T~=`( zDulQal9Cn0JVLks=Rwn*KtHe5#B0TEqtS3(7&Cb>^yl!(6;Jq+j3jm1jj18HFJuV^AdbqPUIf( zy>pn8#0&y|nqQRnLBu#Hh1E@0Mx8R$v;ZCT3D>1LFK{Am)Bx6h)||5Gr2nUz(7Iw_ z*ozxGL$%YUa3iY0Dbg7Cmh2+E$-!Sg-;=Ee!qcalB#BaDNc!G>eBlpz_mrSNWnSx$ zD0)JUZ89myXaxO#1*h2Xs(`s$%VZMJxdffxvZr`du3Sl!nK+`r_CpNmLlkodCCfZW z!apK=QzE@QJQU}-xw0Mv?jUfE29n>a?_S;!+K|N1Vk2BFe&z>n+V0Zt_YcGTlA=eY zy1zORQ*^mbij0*rlo%NT4cbi(FNEaC64V$UJT z!kSO4bQf_^Oc%(Cf<@21!{6gds`Zgpw!J4emOH-H>HS4#Re+830vxOS7pD}UF=IlN zPn)>Z8Q5Nxu09inzCQj$y>Z$RYeuZm1H-8v=)osd>Wq(5L1Mj-w%_&o$$s$pGC>y& zV~qZXUuZ$n$|=`onl*u^|WAfAP`AFNwumh#w%dk9VU(xi=*cKb)qF9UqDvi1VWWOST) zqEib3<@G09+kN8|pPFP|yPQdg+HW(aqA^8fj8(dGrF|;c*{UBZ#y%g-z(ZA|u2%f{ zk+(B8&z9DXYOF;$OVx~N7*5ss3)S+2jfAJw2(IvoM}->@(LKLO7 zuH<=8WFj&nIe19l&ri9UvwWh#Ye56tjOz1+5DehIoUvN{V~a6zQSq;@KBt*B#9yRBmtvZ&~z#^mn!PaQ2&MH4yHWDtS<$nabds~Ud}wt-4{SR zziP#N%vA!aukx^<@22zor?ab`h{`y9S`=D(C@bC@b$LFh(rk)6jfomyXJJdBW`HIT zJbR&(Is1jf+0x?kZz*#d!0YY)^V^(r?~|VNq+O{;quJ^0 z>hAgK@0w~{s5Zbfrgi&U1ik|YqjS==XVyH;i;xC+kM((g2kS1+sr&;~L?+#RPOahC zNyVq{H~V`M;N=ghBqe8|LAoRyNK=YtKSn z^FVQi!w-d5xWc=U=V2wn!)B=GOTDzf&mo%UhEp%OBH&$Sh-b0W!EkIOl&LsXv196L zyq-ezZjQds{6h}7W-H<)$G)K|-qH?+iOjdj6tx2dcY2S80{#=BiokY(+)Ao_^O02J z$L#TQhVojfnq?X%<4xy|P>fAx6?xcfNt)x4Q{G{d5`g26Um)oP4;9CUi6C0b7=DdD z$>rA0$BS!FqNG#df_*)~*K4(X9@E2%_UeXCFegoK$>GcK z#`MV$+JgQOf7omfjvAkzDc_8b^lMI@8x_Dc`@3bEu!3{IvMd6U!9%D-6%$4xH}zX1 zy@;NxI<8ie;4%dem;A<|NH{bSNb^(Vx(o5!kc`+4$D3i5`;s)=W@YC8Mw5&!iB@KC zhC+WgsO~4X#Q_6R!#_(SDrGsBQM6~cQxLZx^hZr<05ce13Q`ZIqIi5}XGA;AG%wO+ z_a^#xpNGq%du5>N>%VW9B$uo`9vTdf$e_(2{;!n_M?Kj{YM2Vq+SHtYW1FiJ?OFGw zg@^^UMip%$i;Umzfn+hzy{F9oV`jb(x-(E2FuSLv>LkDa99~|R(1u$YfQvWqKIA5Q zFZN(95>8$59{17I0V{NU+h&R4wY!XD8=EO$m~Cqs0uwtxl+_z&DFPo_Pq+86bi#=c zC_9uYkwL`h3nNfZ^A`=dA`&Jb{<==R}({bhbJ{U9#3fwrwMV3gj(=}Tcs-+Uo;Z*EaCusU7dx?n!(yTJQ~ z;oFc)trq$C@kZe4PifX0&9dkB^8wSrerWMIBZVU3c7ttq)S-BBwx~ale=kf@q!_DS zLF9wFO%mOtSP52KipG26lN>oKK5kyPQyWR!p+olew9RVkKtvC92sQY(%fj+V9z|Z# zudw4h%W>EBWow>WdGF%b3GBR!`Ox8-GD95EN6Zcn#0n2gqnJHWEUz2*QPVCe-?;+) zFb&w|=WJxHeHE)c<5|njVqWDP63}CcJ%&lqfxCb+MPSs3WZ7r0rA%TG`dn;U0jfsi zCq4{YTaVMkVYtdadicXWG6iV5ka>TncCF381~9?%;`X}}=!Wj>1U(az(!yhlj`$NE z3Rt1l7d9TXeBaS5`^G|>WFeNqe{8uQ+WTjj)B>g!L=W;<2}Pqe_Q@tx8rrOJfEMER z!$3l%fqjd;BdCc#USQ3Q2DW!9wVQv+4qrdr4u88%W<_A_v{t#OYd$-%b-Gj2mVMm* zDE~L<>{2Evc~e2roe2XkgEhHFZ2NZw(!V}uqz;KW<~2kp>vMWntm??{M4@g3>z{%t z-+EYvrorn<8%Z`(q|=O#T>N$$R#_~V3eHU1t0`D}L4DCg5%DV)-W?tj%{vMP)+*lP zW+KALE2a8bV5Cg zRt}K+568b z@v4fMJO&hA=auAxYimvIj+WX6W~cKq7lyYgspQJ#oeaQu`e|@&7H<}CpXLp%jI0it z%Nr;O>{Q}RLz^Tfzu1B-qJMvH`or#MNS`_=05ESxPt~aN@R~>S?{Od^{D>q`G!qH~ zfmcI^g-6d0r*nU4ucKGi9cf8o($%iv78JlP+vrGLRr+xoWBJc0qW_G70rlmdQ3f@* zd#gM9{FtuYih(2RA=MBhjxI*3xv}bRPQUZ@KK}CUMW7w+N~dh#d7sA2@rC%-@{1pU z(esC>Hhbs(hRdOIUybGo`7^f57mFkAB&Y(rH&bFT8$Og$MtAXzNBzy zGM?tGDpcT-EF@C+M~@V<`t;eW9b-o_zJ=5s<`ud(M||<(K7agRKF#ZzZHmc_>f%Es{VreDdRB+8z6X31{PS}W`B zjji3TTS#OciEDP0UDF>PY2PfzkgPR3e|P(-h9xQx>tM?;Ay!oSi~z|;n6 zc@7ixmmE*X%YdQ1fc6IT5_jv6U6d`dQwLw@%wX zFq4i1kG{H{cZ61kB$p4`tV-Bv0+0TVwr|ey8I79;ylGo$B@32~g>>JbN}8MaGlk;M zdod>(J(L~xVI{*Az2J60n>)2^8NSh8($OUJC-;5V$S6j<&Uje*qG-gXc(sWcbw}~b z8`+RYP&IL{Ve@{vL)hH_A6_0j2 ziTXt`x3@QI6S{_7Z(PcAGLO> zgh#Y2OzBKv@!7f6&`9@@7wT#y;k(?edp*5inIV=gH0uq9mPDy$tGe8rX}a|udfc(l zP-zq{ynF9aFUBW7`eej6-$h=OVkM_+AK%XJYt5IVo%fblL-ih~#}tYP#mA6RYo}A4 z=Wa{$s6B5~)8^pX(d(zdyiZKlhz|q4k4Z%``lxI#*l=!)yD=5@x=M$x-%fnX5t@}I z&yiA5Ju%1=rO{eIx{>-f0IdTgq5BxC4=CLg#DQ-Dey1n%aB`4}1iau6cKvFuixpWM zo%&Dj{+!*UI@6*kJV}v;{AmbS2a0k3pl9|zt$*2E$3igp90Wa8y@|~gj8*3wVWAQb z6xIXe^jiNrnYlnP;l{La*Ayb{eg%=lLhtv4yA24#@~b(6(@y_lV{D^G=Gd%Z_JMN8htt^n<$0G7Of zFs}5ft7+~f_c>n33`d2Y)hDVNFA*Xl5;{I2vb7J!xplM^`0o}(T{b5qT;!UGiGRC7 zD$!{Iu>3fbly^=KZv$?I_P>>I%F_M=bp>PmQ$ z%(<%s!5{gRR{HKAVD;WKKl{TOa!--{?Y6N4Lxi4r<%7EyF8BBbEgjD)Yn!enpf8m~ zusNne@ebc&x&;0r-H1;?etrndY`<)5_b0!9a$mm=agKAlNTbC~SP8{H8rMhoY6iOu zy%YHK1HgINnDUveGd}u8Wu-S2Uf=;BN^>W{gc9TlU zu;%XvmB+g&GyDs?n@Gt86d#-?dOexn-f;}G={4AejMR%#xmDj`JVdc;xck-trZqh# z0%ya+X%c19jKrV(UuWtBeDF&%^)-Sw-|}85Rc8{FGX+RVhFe@A2%$h{2C!+y<>Uk; zwEgy$!@1s5D^$5<!Dv>Aip?bHg=PG6W@th zhEG8O*;c0LFHC7K;_`cOT{J1f5-2s!z{?Y0^A*pi3+SYKe|O(f@+>9b%W65@(R{_D zJr9B3s=6EB?E?zwX`08@s)CkhF(2JJm=(-xQas&qf~x$J2?quV zh9fUv^X)}$r~C~VvK-@Wd2VZg8!oadj|hX$b3aF6X|%jq znqLgwPw}`MId8C%NEGk~n$te9z5a=C^MSf1idh2Su#ld7UKMo-)+~zVaSf*Ds2o|R zACtDlP+ZFSa%@8O0ww%6%}tMc4@&13`@7(zlf;Q)T&&R0&3OqCr!bvrLu5E!Ru3&= zx>8-q%8C)z)tI4UqW;?^r(&C>uyNHxQvBWY=&@P_enC zE0=WU%k*8m0r%-{;}JV)Mc{%#I9#snpVR}ZR?oi*+C}w$ly;4~f9fXfp?zu@xr6%t zp!mO<*{d7vZ-US(tTUZg-w$P-s@hAP(|8XtGx(bR8n*(* z;aJAd1q7cmW7r5~Yr<(D`hDu}TDK$MJD=JcU;i7El+s;8;rC)7@|wss*A8`ypT$V1 z-Qc^#+bL_U=;qSdb6L8|ChNCtalDkSz-dA^Pqlj`f7*5gWh~-eb$j62_=AH;dDWcG z`Q~+l%u*d-GfE)}+}LqrP@k8$7rF7L8=E7IYkfm}LrjI{AB6d~0TIa5u3Pq!t=9)1 zWdIL*Pmsk&?(3cMVAVX*h0K)NY6(ROX)136X@$ap-B8PJp9YkMe#}G-nY$fn?YmT;hlYfY5M==$IoEwPvtY;#CqVl#+hc+*8Sxuqz)RXUq&t3-UOGEOX!)#kp>gH^Z(`9ctsszN9B3IDLO?s1U3o-YtPfbN=o zNMqMY)!-~+x_Tr?SfBH|NF8aKHzxO!F-hNiZa{kbL7A{{-5}c31{ZxJ3&f(vt;_n6 z?%iK|Od0xYR#;5^%E5V|b-w{hZb-D;LP>FycR-aRlIkP-1kasmuC+)2%I)RP_Il;^ z&5-Dn!jK;MJK@qSSMF4yo;!l^cksy{lc6U9y45cY5za&K5jM~Q6qfQ_yy8H=zP0Ih zJ8Z&p)E(~)TZC=nW`%+bh=ShO)}MBcZ>~)E=$NO7G}^F-vPRILv>Jq;U~e_`;AbsJrx>D6-9X!jU6+*#x+B$XMl6pHtMe}i;~uoMjK3FQ90)kFgZtPY$OKhHUJu6$SZgF*P;J8ISY26-LIOKxB~D%b#rP z8tPI9E7~qf^w00ToBwt99awv+ZxBlV$YBaLg+GIM(gt#Sqm4$jy8l{W@`HI>e!Byy zW7X|h*QJHL`B-x28x2WrvfAwTPbT0g{9!MCM`q|UvBB}7pt68DW|8b~>XbvG{2qyI z>ycWhv**d3&JJ(VuGVfk8RfA;jCYIM^oK@eZ+yEeYXy9Bvfe}Dk69s0;^gp^??Pc$ zV@6yBt!&k=T3)4#9&IFiU0>xj?-dkB`lbiU@n7bGL<7E{db@r37P{D*B5Uyy`ooo3 zI|Uf$ExBBrWwl@Ueh+s6tFl}fPoPovoOe5p($yvGE3%fd2V_1WmF0I;?;}LZ^2D>~ z-$+R^40^E^Ki__q-RFHq%~Q3>kS6-BaFQXUNN4)TteND()u(HKlXY(2(b)+lv3A40 zQk~7qrC`at+2e|(Q0CIb!P5?5S&>h9#MW?6i7wdsjVIoZ2z8XEn@O{WbPVg4o+Zx#Y(DaH zVr@V{JR>$kmHy>H#^yqtEbUZT9%(9LG4v~br+)Kosv5YV-LrI>sFueVl+RX-M($wF z7DIQ+vNN27<`jf)+vj+$lGwonS&ro8yqhC-l+Ia?TQ6>&zHA7$+f6H9)86ZliBBQK ziWNLPG~%(v{Jp(LRvRMwNw0i0M?6}uJyuVU9H;Af=*Hi$*ImBoi|pb-@W|8du60)f zjmtaD+P;en5xX(gJj>v(LR9pfw9%7mJAN>c;^J!`$Hz`X2l^VUikpW2M&Ie)op<8Sr#!5uB`GD z8P@bRehTlTGf;b(^iGy{`^xw32*$twMN_5=$aXsK8tjO_+$42lxtwAMYTH!GaynRA zy4H|t=Kr3W8MEO=!%-7-RL~X*^_Q)Sx~K*aUf#t_l1PoPBF8CsF5iC2Rb=V#g5;Zk z`x`6%aGU;uCb4@nqE=hOS}A-V=*NkKdgfBJippaL5a0c8|_C%OIP*XrZ0J z&3tUiTU^i!m$!wMeDx=a(R{By`&uZ>yO8 z5lL%0pxtD`v-brLNVxQyvvZ4tVSY{(W#+!@67S9Zpr#;{Y!7VmRUXKEXL9NuHjHqa zv6bGngKEA%wlw4=3fiSthb`z{v2$SoOe}}{un1wYxYI{Oo8@Q@BOjXt*<54 zD^F)CFW8I5)(~f!Iq z#19)eTW)-)hoGTG+ER>! zV&qIZZ5MSiS$EA$@Obr6Lajz^p?y23U8JAy^l_*rfcye8Jb- zpy5`hlD7aqmSt2OTT*PK8E%teFZ^$9UMe+kQ9r@_rR<36V5tnTN$(rq$jvz z?;kNok}ct0rBUbXk7_&%HczFu^B(^ z#5NoI!z4t)-;HM4jPq0t>D&2Eirhu7y^ckl9g zVc^HewumA@-R7ufB8P~}WgiwN0)z%`T zcx4n%mjm_O_*@94xYX6_8}pWoz6`dP5ZFAyJ^3i9(>i-y~%)o@K~Lv44yfc*~?7+*17Xp!i`YJ`hY34!J|E zZGPZY8EJhqd$OW#XENMRt?z3|#Sz3GAx|+M51NV}h~RkB!-pR#E~u(AP^ys7 zn(f(dku3rT7!6b<58*|9(v?$ClU`tOmIfs5pe%p;an3C^!D--D6ImUo{f%=GghHf= zwG=&qpAL?KY)2CoAc(Juy|tGu2n;zjG8RMw&4`rklQYR0ml{-<`lvcoyx+IbdB_D_ zPU zz!gK>Pb0do?~RmC8KWVPg^J8PzkAKMG$i>|n3I;=oi!Y0<&0%b&|TDo0Z(GR%G&+&WsoceOy{)8+#pLa_>x~{IAf#NSh zxW-Qrhwj0KT1JK}GAoq=Ey|j4w=k_?>`V&qmBGjkB>F`c#SI>R!LjwDRN$Suf?IGsy?C3O#xvQsGg!3}AUscu zzU6tc%F3>{xE4g5v$PTj?YOH!5DG=X*UJv4LK=0|Q_wH7#mIfS97Wk)*C+%Mbhe9p zyNUTr%eC@Q9Zj`Vs-&W7IfzH)V!V1w7Fkz_kb4PK?**(6Jb{E89@GXetSfZ`oUAB3 ztPAi$Sh50%Zw;G?-!8;Qp3YJwal78DwkG~Em_D$#qVEXz1EdAfDr3IEm!z1Z*IRI2!{+ZYIR3)|bg?Y#F=o*x%3VhYwF36I}~({>04$O{jBzSzOu# zr5{dyh34W#f=RZmY4JzLr}@ha*K>-3$f`gJL{<&!;@W;G4j6-(AHq$3ITC4 z5jla8Be&DyxyOh4ZI;p~3uva+gRkVsuIyzH(cOp$dgAhGC1uwhoS(Q3E9Fi9zGH11$$d*%Q+sy~>^+hp9!bEY<&@DN1 z-@1SmNs2quhuy5cl9ogf(vJzG1t%*I%-L*6L`d%l!lfIeuiHQy@S42xVo%hZfY&mX zn3u!12Jb$?w3+k>K>F$~@|}81s5^vSNL8 z&OI{JJ=j z3VdxU8Ca_32Iq_~f^-g<-`C@fSg~&mb8yHTfd2Jp3t<-m)w%vY9aP1@S(rpfNi;g9 z>D}O$qxO9Gn%R|SJ%ZoR2=@lZStx!b*!}Bo2n)GYeegBn&{5Mh07qyMPO^#6Koqdv z7l}RG1Pe2t(z3i2HfHJR+Q@Ry?rgtdW=DvteiJKr2hv;A!5SN&Y{c5ZLU@SEOfB!8 zeDq}-nxb8`C+(h^Qjv$FIf8HbKZY81SyN6V1%@NnKC%S(eRW^(AD5K`I=U`|h<22! z!g7b)-QeDgQ(6inDqO>hZOE57i-?CJ`~3)#KS#9sBXhsfQ7 zktD?jqMJ~_+lj?P^z$|<_b0)v!{+z4o!0FVFH#B{T3F8A-p>E+4x#+}y3y3d5Ux~e z(kEr;b;e;%jP<&({vYS?dv*Le_OK}O_3TW#y5`kd&r!%lNEc78QjD3Wm<4bjfkQdg z)dwK^vX5wSPXBNqJ5y?-SkPN+a}NWB8s^PuQ!PRt5uuP}D1HS7)IZ`t@5q5mTu~lb zh<8PD7e%;ts}H5A?NWF}cV=9e<@83lzgMnRTPKRFkZX@2lnJ`*UymoZ`o0He0LC|x z$dF8|e|qsIERIOKhr>Yi2M38zj1)x97U5McBWBb{zDXu_z^pG!8Dx(TM58PV2;gK% z@eqywA#M`EPDsHzrT>!o%eS9Wep|C`Y~X9io)L9Fc)?NFYy%Et1tuXmPA23^4Mt#5 zh@~JIv~UDwJ^6!SmG6}_GOn}b%i}02^7%twI#<59ZCIo!?OWU8YFXM4Wn@jhb-Jj3 zCk*jI&&c`ds5<+K*y%wxa|G@k7&n1Z@6DUbn)EvI6Phw#$*_ut00io8jc(spxuz*x z^7Ws=HeN5jEJR4ofIyvDAV~+WJ?>|LdqM4d!E3?DS|Gl|t_A6%&{~qEn3mlIg{t~* zLV3-HzkuVdAOYp*Tov#W?IL{u=`lz}~&@y>T?L$K5`;D2bOo(Gcihl0_?9Y zC9wKmUAJ@0+I|#sp`9pYs)%H5AX8xg*-FOg3O3w?TpW?aUqUU~4wr>C=nF1Nl#YJ2 z?3a6G6Ks5A@94?t?~<>OFECC!-6DMPqcfUqBl1dwRwg826s<`@Vkd30m__G5uX`a` zida%F=fden?pHrWa(G_Ng>YZ1Q>nx`u46tV zk$EUXj={1qp}xceeQDW=&%j2(J)h8aQ)OWl-<@M&NkbEowMmiMATkByB0Tv4bY)s| zeeXO*@qbjaQ$7029TzcKzKCgCi0?ICmD9mM9)2-A+k&7w!qe|!74*_LRfP=d_MNXi zU?2sYkQ$E;zuDf^gIsFkfg#w2kdAOlY_T@n0O9_7eF~txYSUMRzi}E)yPy~UYo{yW z&mlDmy*H|(fON>y@%Am;&4Q`EX2Hj~O6_9&MVJrF+|;f1>;j-8JW$DTEYTtV|ja}@+hjVXB^0gs*2Uot@J z$~w1d7GV`C8YDgkVzOBifw@A4QIEa6!R$NAW>8nF}nidHh*GQXcM2s0S5vE zIngveUGl(~K;A@C^k()DLLu7%JuOQJ%}|9i&hE%xWo8Zc(_!XEsRc^mi2fxhGrikW zrxRg_{-G-{`2sZ0e|8nDnUShA6T{}`{CP=`WaCY-tI*Ot8gQZcgvef%sw4^+z}B#p zBs~WC;5|_t$+l$rVR2F2%%#hJMPgNAPJM5+wM5K>}L=&Y5=Etl_C8m^qfRq=b@o^j4KDU#TYt636%4kH31`Yy#_Mb;|p~b*e{arV!tXvZ5X?Bmyb*(Q_1QwQc zZ%t>CduE!&^-^$yFM}rdbaG(k7CJcsOUTcf6pP=XgQxPavaj{x57&rRo+KqTUB7k2 z6+_&YuutIG!$kZFlys?pm?!Wpq24SwF)LqCZejq<*@;orPc9 zn5~Jgh;h3k%BIvWh7wP_-3@4DZ68Lpf(xYeW`iX8Bks`t(jS`vJ83?d%fjr-J!Kis zKZf-W$Dp|<4IUue;(y8KZ}d3akT0QSB>DZ0AWFxua(cgo;6SOpQ(QGo+uT%y)MywO z)qX!%R77oUnC zfn?V85#JtUf-NJTGVXnnJ@d)BF}QQ;Ut^mD)%-TMKYn#UI3~X=b#1&=rOA(2*!z=E2eqpR z&fg&U{f^9k-{oXHAx@>s{>;CjgQC{p+d1TX-DYVpl9C6>HmNfwsgwcscC)4QqR-n+ zpjJUIa_g*i!ynLqkVm=4Jh2f)IktxT2R={A`bUv7{ZA6E{)=e+If0?IqVk4L5KA$> z1&ESOU3m>g*)v@Cy<>kwK&Q9lTE?Yip#Q5cU5a1OHKQ zc9XtsZac-ugKL2kb8s%-SUC5#LnoeMG#Hv8K*CK>++8IR z<->Q&uxd$A{F7G&>n}CxaHS19oE0#~gb0;2c$EP$C*r~}3|^I) znTACgJq3Ki9UPlR zmCA7Ga_kQDtgnnOGPWjI@ao@yb_H@%k$%s~N{pN7THDs>m54fa!{eO(b~80= ze`fkx=gsA}y|sT@I;@QlUjyXOG>+)sbTOIq5ghB#=;QX$oM==TXeB~7Yv5}bg)2fnzks3iKGIi5q<%yH zZb@2;m>@407LqBVw_vCd{YCx8>8u1kox#X|)k2;Lbc5XCWse$s)4oG*(k4vs+wojm z@^l&_D1O}l{h~$(yjh(EyQua}9>ud+jo6Alw+r}ExOC9rfnE*7LE5Cv4x=?T6B$t# zPfJ5ppR2xXu=erG>guI~?4K4l@Y~Z>YZl5?45m7#LP~G%XaMUPy~4z9m47q*p>RAt(RrFEb!S5Hgf8ScKE00+#waI!t@;K9h-esj>W7Z{C%UUbobPFFPrFJ zvb6Wb4ff&mKr~lw2d898LMM0l`@-8H+TQHW5-KMFMJIvR(_V*fy$jI?lJ9PtZRmz4 z>U%aj9Lz|1S z#eFAyh*G$(|IV_3&q2!(LdKXPe8py>9ZnYQ#{f44{rlY21f$IUIq0AHhonaxaNZ2T zx$@JumwsxcM1ZqpC?Af2T>1LLO`mcN^a%_mhPTu$&dM#$lVi@0^MKFsfVcZaqK{{X z&zHpjPydhMfG3B5*T>IS#?Ozb&#S(-y4SeRDZ|fqhtIpsk9Wq;L&MKwP@(Q~b@Sss z?{i=9b02gqN*}y`(C7Kt#SN|NMc%4Tq4}kf@t)TMf6{WxSI9IQl+PdM4;AiA!z>3%%}yA@y{Zwcn!RIovEb-YY^;k*aAbbP(NWVAaapjGCE-8k5yXO^Ej@$gG z^S4v5NL{+l`0RS$x4NA+ym~@Z6ubtU_x)0=Ci;y0xHX*lyrT8rgpMn%5$C+36m)u> zqX-sk2!9>+FEsSuq4YO?`~s@Pk~+M(O3>gZ2hD1MH>FveCt`u`jgQeJ{JYUb-yxQkm5Zur;E64_=x)>|olgzZ z+XW3P0N@kO;0n>Stn)(LM2Ee~0rY_c&!|h^C_CN6`Bsr zftc`xoAj3bO%8s7!MDxFZ(JMXtniBm6Z|Cs(UAk9cVEZsgr`SC5Cc4u32Ak~x)z+5 zeVSZwE134dC0tcS(CCoa%4rnyQb*pfy8e)X!4S!=F02b?EKP!HBG`K}IJax3H_g-v z>x(f~HuQWoP!F9yUe%J?)GM&Xi2rZz}*WuZiy7|!v*kaIj{dXl6(5lj?reE3*j_X2hWClQI7 z!d8UOaY2)jm2Zp1<&_E^;I3ucpfxn>H5h_%feZ$Z3%yfo$^A?8&WtbAl6SJ zxh|}g6Kz(xW-G#$w=fscae-oQ%ze#%UK+D0E(kO z-XiA4;m;o0fBdqErE$zlI=nso6Srn}OfPvU%Xy366ZaZUJlac~DL*Y8&B=JIS$lV~ zFRD2Mec=Z_^h=F;8)~fvQkCDw!QKA7!2_k6nm54vrAhb3rmKBFHPu~Cpm0R z;6)JR4PM`KsZ2xfLr{F)t-@(V;8SE@c&R!Kh&&fM(}8af3aZF~>!}mN3DD|%VQ7ZBw^-9Io-{ac8P<(>=lHOuw|S=Y6FF6 zGR$KCLKNppB=gVUXF*o8DI9brS#9Mo6=`n`)zm_cG$0sD$R3l9>56$FQahkwH)cy%Q^DAa$jzya0@#VP(K<3~Jn1HYVy4L7#!?@qjbxySY2e znm|?a!N5DaVywA3&**jK&Qk>uj0W{K6gqrSRhBX+NAxw5gj~iGQ6zm3Ldcd%+`{5n z#+0%omDU@WR!$G0fWhOB3^p*LJ733O*a;!BEJSMDL1Mv{O6?_f#UBZRan29I-+Jj$ zK;M_!VW3=2QrM%XjAEd0wo+x>CRLsan-;|;?@WlSc1UzI1APinb)}Lw4ln1WS#;e@ zsuYmH@d+Tf8U-jNVPZMrVq1U2A|qkkkwPBBiWCi8OH7Xkk~@)|S~{Fq?$Eto&(dn; za3DgjMnkRct>LBgsFdR=8>IIlnpx3^gdcZ-UI-=~N9R$(E~iW|CH0$tJ_DjaP>@|9 z1*RRFh{e^9M8(!3VuU*)(9hF525)4DA*>{j`5non}!n4 zs}0MuQY~pm8h&^{+d{34U|%R13Tu)|5eRvuP}QOBpNlE)BW8gY=ziOh=pVXz0jUAy zrucB@Lh()xUOSCTLL~^|u~vHk3sIFMYNnYHITqss2qVgaJxg~lO5lk4D|udfAbvDg z&pcduxhaVo-Hs4eeaSSq@W03oBl}R(B#A^+XSXwN;;2&5dddQ%0$ve73`X-6Y=iWS zKD<8K3Qi}ut6F}7T|gC8aZPY9uZWMB1=^-?{}G<(k@l#1P;f2mj1)awOm8E{P>cl2 z&;(|(ePTP_tWlL%VwglPNltUnG(dU>Y8@p+f@2A(U`7*}{87jmh5YeI3Z3o7l#~tk zImmaOoWZ@Yf^{Z24-sx>1d#`Qb!Lfc_JQRpp$d&D^Lz9c`7cG7Y}bF7PinoIc~S47 zfT2$WqSwgs8>}W21JoK^JD?u0-U3+= zNlcPFHjqQb7{bWyiFy!}J_;KaNCK;9;sHSN)GBeY&I|EI+oxv%$9f)WUtz!TWydD3 zmEwLnxxEuF3eqe>NS6z&XK;6&jPDCYR_IB3r7v+D3z~Mv6yrxYI-<%iDhfnSy!v($ zJB=JxN&xk94^B2rWdf4A3r`qji2p0+%UHc5)om-#Nx2iSggic4!4f#eZufJel_+~OEL|vn5wg<8BQ6%9#+4?7GeOUAGt)r zDGY{}K$g9UoS4NVWgiUoK&!=XNI;%ooG%s@6iXe-p^jXf8#=-qql6+RFENwwkge51 zR<;E)GJ4j8o*`IwJbv^@LqF3W)gj^9iSYV0aK9m!fuPz6Se`D`>5;bZZ&rnS0~vWi z><|WEdI{6U;+a&s_KCLKp`hSL@}v4mIoHM1fITj_rAYiHuoJ5YZ&d4I8%hKxGrxfz z#YB0I8KmSukn0)>n#GrAEEE$D*pxF>74&}w@`3{vvE9`bCI_>#L%Den0n_(j!69?> zl$`hq_FUO(j$GU|&dxgfd;Y&h-@}q#ktiSW6fQWk*BrPyHXWV&wvUp>MyXSZ#0)4Y zrDGKm@pH(zxuu<*6ZekDM`xrHlkkxL`&0O9j(3pVTV8gP3^3b_Koiv3Kx{CFJO10R|fW|D`!_gd?> z%GM1C%1@LkJ)=njVN$`e^H;R5MasoX{-*dLCbC$n zn;v~{-xyDOp9v}KU`e}$guIiYS#tJBWKfT-j;UzD=G@55po*x;$yjF`(_vV*@KQsg z+!1Z{Dd}!=1v6FdHTk{FDE9w8Wp>7Vmdrh&#yVkxmFgN|oLMDnXx5|!#~Qr+)^Io+ zKmk&Wu=hZFbezgp6jx6ey!^Vi=Y1Ay(kT8%TMGwo-|hv5rEvfk!yVbyrcTH&}fi->_}dNqZ%(!+!^{U zY6dV?u|h`69RkL6lDB&yQ)k_&a-twRp^d}cfu>`?4uK7}`D;?868Cidzu{A(QRO%J zo+cYCnW??~+Cjry$-)CEkkvW$*oNo42UL%WC&2D{aD~lBU68d^;IIn64pmky!B0SO zI-)-m+Y96B>n=4UVnJ#2C*o$6O)wxD$&YwTQ!0FzX&dvb^kj^>_y@NVfTb?7DqbW^ z7Eg?Ngl(ZC`+3SHG2Z6%4|)mgyp&5rm6bSwkvBUXy#bmF%vHGr`-ELVeh!rNb@b9v zydYKP%`fZE`{O_Dtw^)MW~h8+fIcx&2>hmgmk~o5Q4OQ`3Yq&16Fo51W2QInSiAh~ zF3lYK{PD{CaZo?poNlAmed{mehRDUK@oOdc1(ia68NYbqi`PUPJhirPfgSA+V_-QYEsG$E^*=Z{!c;U zl7|Cx*Nk7kWG%S~nJBiR#S^*b7J~uH>&9TJY#5cbmSm=g+3&;$8KkFe&+?*9trBNS^=T9JUOi&|^q<7YR{>xsF8(Ln7G$ zZ%RwIQm+>tW0!}Km<5O4f-tJ(bkg5*lYAI#*~E#I5$#n5E;Mg9&l7*c0iVmi5QGyT zPcr}8c6}4|{%RP7PL=u?@WKmMmM&tiW>Nl}t|3IcLIyr|jPE*k+ig~+QD;xrZV@f6 zpQmV~T}h5%z&&KT10N|r@1mpn*~{pdUyQ(SA<2U7C;NE3Cv9Gk4Fj|^l(I$nq8syg zJjZEvbzmwv!JhZLqUYI!=j3VFl6SSbDB{^!aJ8IIN57`hFmDk&Yk%`pYRaD_;qQl& zzs^_wd)kVv-VCWnQ>Bh*%-*(lSfnbn+u1K-hZZH4jW6eD=I91~)sS+|MV5(wrtvAX z?`YvOs9K3{7?7nLV?S^=g<8D0aIMm+NxfOMetuuyfnbX3E&gA}S-;FOuW@)VjZOS_ zxXj`%qY6{p>vg$xhuxx00Usps1uIUmRe&OWv~Mw@}t%JCB9`R`sY z^=sb54|5Iw1Q9OusJP5qB)xFeRwa1ZKQbU=SrammW6KG8<_yK@@bA=P0gtak6j}Z2C^X!@yY0 zIe~noF2-g}eL-3tY3!<@9MM_FAilGfNfjRaGAkjtnt{>%D92`1X3S5Xq#X+*pkzV> zcDRk8(1cqeX~TNj<+hsojI1IVon82d|YT*ALKIogx7BEZfh3Z3um(1{*~GdUl$RV6#9O zZ&8ra{%;*MjU%r|=BT=J;9-=GWd%)-&DzrGdd?6}wpw{FLNg*y7gMgueU2~9*kF<4}`NGD;bp56es@1qU>AuUzookjW)Y2tquseP9g zIQF_Vu8BLdIuC3XiMR_kO#1 z4r0Nx7zZ&&kr&>>c~Y8>rZww(9q$(=QK!}@f3&eRmB7+Cl?_@+`fF|B=Zx1^90U+R zFGZ#x*DI5gtxSqJCs6xL(O=cXOIn6QMKm)?{2Yo5grGB;yVpqgErp6PbmB-07GiZ%6^JiM zR^dvM8+iBIVVBF!4|v$5>2+jP^dyRg4fk`6XVC`+3T{yKzD)0!YyE|E&UAiU@ajP^ z^4@+r$Obv~+CgtZ&Mc@=7|Lk;_8iBGh1>HuR*hvgkST^ru`n_6vsB7P8E0HK-BTb` zm;644D~YocMa0%pBz$5{R7$OKv+TN_rZG*!xaP(&nKH7wrpol@t`x)0CF?$P5?_iD z_aWbo?BVXRioW%b`KzcPgcoKE`-u(8fpfmOcs5=TpM`#VJtP$)nGrgS*bhD;qH$7d zJZI0aAGMF3n;#X9x6PMmQi+KNhe=hJ#3b3Cy>)Oy8ZJ=$1e$9ollFTX&d~{n^dmlD z0f%!$hI??2AqEoukw33r8ROF{R+=B~4n7AhxEGxV_eyu&v-?VWB5Y`kE6DvujYO&;z z1Z>{jfHpB46Mrbtu4=ityOJg^sSI*B!UR*NdLY7U#X?FfA2)uq-~_5mIUu8?_=Hv@ zvTHQt;*-!uV$WY$F1(Qj;LT9lq-NLnG1GlbJ;%J@x--v)r}kPfdtt2!o)oK!kxE&< ziFZJxWmJb;cC4MV`hq=Yy;LUWhp0qeRQyOVu>&l3#9GT;F3{nHSL_b`^;c>&3!uyj$7s=+&N=iLy)x{JUqyvI zPS*+_*RE?wC-!hO`K9fZxAlp0V?-r@3QJ~a&pY2+r!t4Vs;htZb_(~1-IbO80NN2YVOC4U*fOdc(Q_EdP&=X|#!^Cc zBiCusi9U55dUW@^{$cH?1wGC08J>n$F*_E?Q`yi@;x|?(r;WQ+jL0Y%-`Zz%B;grw zSh0Ge?6>ZK`N^sC*i1}0VSc~PzO<8&1z~mY_p#i5#>e781A*V(`Az_5*hY3EZ%R$` zR$#W7Hv?2dcHH=_)N0?5qbu?e381v+x@n1k&B<2BBhFGSEHuqcMP5fY0(OBWLT-W} zc0CV`JED7K({Gs9nL%YYC#Q@s_UCKyHkNYvTzs8R^-yc%!VnEa+zMWhslvp^WJMze)sCn1 z`Imkwkj^v>(OH&TtgCoa$o$RG@f*yY>Re>mvC zi`_R&4!%QdsVw!;Rj=`j$k7-0ae@HtViWjfQJKk@r{lzyrvFabSk!C8K?H}$VVgB` zY7MM4ncxYdV6nR&+<8jG)b0PE8b%-6Lu>%iL$Hi#Ih(cKl4%w7*=|lDQMm+wcyP zukEDzb5J`aO5&g&9UWAw%!ipf=27oN^Dlt)PM~+#8{!c=mbq64VTb0cHA?$;P=}?3$xRhinx~TC~0`&MFm^*3rLcCuR95 zD;ZH~Sviz9`%#m7gyu1jp+D#4k|cUfbD+3HGX5q?HB_9oro-tS$Pbc6`CVw}|63%H zAhcod>v^!UE}elZ=NlT=(Z}Kxt|8b#qJmRgM?3jaEA>)`JC0IJ z`Fh;DQLDb;uqe$3BLEa&9A75c^v;ki__Q|=12`Ub0;j91i;^&V6VXKI(K1sxUe*d6 zIbL+rGv#E15JCk|Ri=KRx0q=gZ*A256Gg_v?r~&aAgrVZL@Jx&6;`d$RC=Fywv}XM zi!pwdby!GI+YqJB>caCW&88w+l)p;xXPjlLd2SKMsZm#A8;%iv$3<*Z1@o+sUkNVU z@tL$9zFnxpNdSwews?=cp1jY@tPK^v&UnBGzj|qx=4keV9nFTK8EA=`h#&0-{9n6Z zD>wmDhcBV2n3xQLGpx4%azDcIQ@URl4D+UPsCfT*mEjjXZvHB~tyjT+AJWQyd38>w zaI1M_R6W#Lv%P`SySjaUR^jgykHnmbJoX?6 zG5YhgyobR{1*wNT3IB*x^cec-CFLle`r|FH=`D@{5j)AeAJ{<0iW9I6BqBp03OSmy zDG_2p^o%4aRpZ7ELU-8jumB$ty`F$R<-jPeBkWAfc{yGyq;Rv58(2h!=I|Be)A0Qm z0SO}$N48hF=Mk1QgW8vZ0u5Y_OA)yYwRHwf0p+Tabfci1Tw|X{M~V_P4}oRbxxBG< z&<<6J0$p?)&|JEJVOV*9`m$?!HT_0!AFcRk*7$+|@=UG-rxG_@-gE)J|F zg#8$9!(1BQWPXtwm`yX!&`oIv{80Rf@F;TQ_5CZVHZ&8mps6pN>eX<3E>-Ic=5eE| z)N$gc%IR1S_G?cX=s44~j!<$FfQ!V0vp?LR+%m{8IA=5^!sqJhak0ziY}fdaG8R{9 zl<+fHTsjAN^6iCic-mlKaTV!~?pgxMBkM+v#@Uk04soYp<>y{j;mXX|B3qh92h8mI zoh8Dd_1q!EY#M-K;4{!0$R-PE(IATu3D^nrDKmy^H4pd5i|(SL)0Hn(>>QG z45*RIcF8CU1vFnn(xFKGCSNWW-vrlKk=w=%- zMyC&%MsGdqND&hZ!B%nweWs_tINBe@VG;^;>*|*Keh>M-tD5NQMOVK0>~S&QIv>VN z60JHFJ5#y0!ZVoXTw_r(;+!T5$SqIm5<#NzLQs6#=+p60g!(dZm#Xs9 z8$JvS+ooeuHgFtWwtQ~9XQFiwPlW^}`y&|6lTOtLHly@kQ3(t2k@|KCTK8<)if}G# zEnhuaM+x5axUBJUXO%xo{AR|P&`2M~G}Bh*cetLpJx1mD2V7tw7Q(6e9#`A1ulnzC}t%daOlAP+Y_e2mQyN6f-}_<;d1a>KDY67yPl zwXim-F#!a2PCHBZ+aUm`GybbM>7(l!XWzXm4a!h#m;$p7gY|%gL;%eG8k~F^aeJBKoHAMibJTz!wn!@F%vu?s_vM_Ug zKCO=Urc6iqhM@qd>f#O`$a)D#%;+E-*K8N_1boSB;zR{b){o7)uAX~B?w8CcsNT{uN9abxY3liJ@alK<@gO zh?omc_99{FWsXXv&$(r;^CKYI9C~<#oM>Nj;5{*mFyA}#>)-< z6(ktS-7S0XH#YhXNjm?Ilc=5D*MhQN%Eto_Va4v`|M=8|+Tep35l2{t1>h_4DmSZa zQ%tYQ&Yx?lor4`B9JcJ52`HBQ{%ja`8{La)Rc3ceGN&UYYdKxe5^b;qY%D zgJmJ+2Z5qXgSLK4^kl^<(e%*VoW^fn!d66qw$M`$PN3jgPo$LOF! z&jODA+)=9@oev^C`%@f316b-{&AL!zs1?iCx) zRd_OKD?fPJSZmc=K)_V;%o#z|+)bUX7KYWTBpy+89r_jjWfwuH)E4}r3Lly=W@ zV3GSXZwn2>@uYU_Xjh}`z3svMq;|d0&l#~E-?wfxrr0T-bsS{3-6CbAXq%jDHpeM7 zy#DsQH!mw;5s{!RAnfc#9Fm-y#qR-d(`k{NQ_P9t5^r0#S<|M#MHNES1vkyN$T|El zK|N1pL&$w5+c=2R`4<~$r!Kl9N+T7X=A)~#Dw$j!LC5+D-fq3x( zpOJ)3Yc_Y7s5cvw<8B7uoj-UGr}<)TRA5*)jnnnWeMz?|X-~qXasG)`tWEi@*&B@5 z1;d`i#FqzqWpPhWWA+QQx*9j>XL~%`InFU2t1!d(uhqz#ry%rbFR8NgS@ zI<7mt$>5W;-;3=cQT)AFODG*et_|vSF%mFMONmHX7#zY}E7*@A6 z=f&@UQ(d98+lrg~0R*n>4S-Y;b7*bLzQ(T50g*1v(#DMW@spso zbO0)oO@n0{E$j}$Yz33DivMka7LkDLZ?>VCI2vxPlICuBf=*CafeascD3_v_O$M@o zh6_1{fRLw)B{|bIdZ8=cfLl>Yrj;)T^vepnDsx}<6@iW;#Z>7h;49hDI_yb1KZ~+N zky|`LI9*k40sz1|d$GW|;~{Kq!_MgG&q2{!zDEG?FawW8m~=+D)Wl zK#_Bx_W4S08{M;E?oxv2zXQhqYN8p+cnH0Gj=`U%HpZC(@3HcMW%h zoFiE=3i*l_pl)>P-RQ*L=$!jaRQ-Z1VtzaYy#`AH&z%r`fA_cA`1v4?`6TnD2*&f*bw^l$ zg7qb<$D!MDfPkYMjpX|Ge@wFu_gOlYhrP?HdHa{>=Zk68GT)5*>OaC{N==pgsXkQM$dPIpvSfUu$=4-1A_2JMP|N#74NJoE^vxekkQwW z{x`<2VpJqeSwSXFbPvaw@2QNJ(a#V!=k@%HuQrUfu_zMt-IWCRyP(zEAXI^*YEO`FKgAE1O@*&VOZJkeJkU=v4o?{OR}i4woGZKY4`JXp0=V(8 z`F$iior_C5%bnRf_`#C3LmK|Q!Oa_b9zXN5&R%0=-cU(8)q!@Gs0bjS{qSqKqBkBo z=H9F?xjMHqvu!t9oWn1_K~DH~ zLOcdhslks}C)4#sTM-sasy}bH|Kl;m(ghK#3Wn!HZqp$w71!2<++$2GDJbb;UOFI~ zW5`fb%pCV_B$kT%G!l(TLhlcwO4m~4;vUmCWkY&l;p&sUu){~s=8PMBe5AO9|F(}I z_U_9U)sJOJg(Xt8mx55>_kTMV^Lz53X5$r#rA@#t;KhVX)?6aUm@k5-#OnKr9Qoh4~JRT)&}PyVF9|0w-+FGXnURoiS*+8uK3#wzbY$Tz8tU<3m|R6GHZRWBqB1*?H7;ii33t6{F>WGm2C>XeXL-H4 zj-?ha)l(1QHmMHZ|$Ao*<55Db-^(D*#LcYvJjpO^jW%oXY`NVOp9;}>JUjx zAur~&iE!MJ0^`pLoCAR^{>qI*_?{Oj7T^z3Q}5?Y`e1@dZCmLy?I??)qsa%^7ac{D zcDY(Czk9?v8jKI3CBlNBgJ6e(fxUR&1rAxs@JSK7CN9^+F)5O=zjjyy?};W61z`WI z-Oqz6F%=KbYm6+Fg5(KhH!?A71U@L=#*7CQu|r>jv0tr~<`Y+TsnYAmRV-_(X+F)+ z)?Fw;ny4WB3Uqw46z^;Fj9H*kLljHdfcS}@x3#Z$s9sRpel_t65wAP1dwx|rWt`$S zw<1>HVBRB1>-i;JFtF-I5|;1@ufj|9*%-WX!|vWI3S9C*rb|@I1Vo?`8XBzqS)cbU(Ar=HtVw0yuRFB zGk578*%EHf_pb*`I1hE3Y%cmtpR|bk60l&W9TtCqUP}}2`a9L$`Z7V2P(y`!sZ#bt zitfCkHz&wDweiqwom>R!6h9J`AO0kacOe6nQLT6XeM{Y~kF4<@S~X5D**T>pX2%KYQ}@XbZc(E**QXX^WDi+4&QA!V66x~F} zV{F2iQ()t}aF}h)J$wuiw`C~7F@&f+gI&{&f`bhhAZxKd0fy$~-U>%$f{Td?M+uXK zN;#}Ja|`2h3@`O$NOpa|Fj%L?$qYRXld>iq`T=TbuzZUjaF$-)ght4I7Wa9QcIy72 zXR)6_F7?WwL|cO3uk(hjkp`K+_u$o`%}=dQ3=kURN!h6F*aVEwWR>tw5P2iJz@kzg zwI;2j3&V_`CDlXHa8Dzc$h%SljjgRb(h*Su^WEa+&2D0;Pw(B6R-=Kh=}z#LtxUs| z=6)&wB^1&#;zH=Q2o44|;CwrT=lth1zY9vm&oGkJaqqyK=6bZgpuorXGu;77)oyFh z0X-5AWAKSRhY1w-wn_TuG)2#loXWk!g!qp+AsM>jaO;rB`eUX-?~Qq{UAsO47)GaLZ+1(T;2D?Uf^(*}F%i#r zC#<4gW^2(*ZlB>t(X-L>l3A7+j%J_;n1Gc=Ve-WL7 z!1d``W3ApkieiRKK)vdSkuUUwA99c{5oX=DyG2%j?FMgsH7Fqs_@LzUxo9@=!DPiO}=c(sxZj)qk>DS zODDX8>alz4v4QT`?gv$TlSusFNydkDZD7FrKL@}JdOQt%{v_kbx^~Zam49MADY1U| zduii}N#CP}ru`xrDdbOT7e(YHKW)e~f&DY$n%#htv?})Cy1`ku*~Q>HMdGZSk&3*z0?172R_&M4`BjRvZd_=podwwK!2kruwutr%WU+EPoRjDOm z%ASyr)(RD}agQzVh~05#OIZEST)tZcN~-m{d5h{|sXBP&YifhXY!!OMeh>Vk3LnNM z9^d`E>KiiY_@Cm;zruNp#PDH8Cw`TMG#)v}Cwu@_B|Hf z-+~v+0rTns`Thg^FpC%9+>rP=jBP{qBPzs@<$^s@RNOKq{qU0c5{0vw8Q>Dx!J|rh z7j>3=_#Jv@`J@W!+=W~jkv_N&tLd4G^fXUpZ~>3EOcXPSJCLo|TO9PnBqCt&xc2J& zX@Lt2cM>(SS{26 z(Stf*ZDqT}@GBA5b~iAGA1<+zz~EY6S+{XM{@r-{kN4JZ!<8Rbn?FX1WI^q>;CJ&L z?6|aWz13mjam^^q$mXKnM62X`+fu!hy`USW_T0b1A*;Da7m?NPglfZpG~^}>H0env zK`qAonaD_`c`n(B>C3&zpM;s2x2Oz@U;?OBy)tv&dyDqRgwl$tR3mOpZWWAE^dG0ZEq(MpcOiiwAxSh7SIIRo`4R_oGK0vmE~F1r`4&!%7nWc07e zAEFmE8IQ}z%KCX9FB@iR`H5us+2tJ*7f-U|wSW7(ONi&s{&pw&`qXUP3|il)!p~;j z_gR^j9T-rww+JMKcix?XzL9(PmF`E?lPm2x2+_k0WxuUZm13X` zrwYJsYIx9P_`M_)UuD`ea5i#0BeAz)sp|B=@R{PF*#M}uw&ypNOzemGK<$U!XBR#y zdR+1zAQ>#TdjxR|1r$1iB{p|$NZYK*Dv4H#m+ zBsGP|R#~qoREXi-R5#kfm&w^QFg8P6Cy4SpwWrD2zgpiYq)bOp%7 zIrw7~oO1woDTk%e(NMuBF!u-O3mAIMtLu=t4|I(VW&nrbavwjOD;3UIH?UxaLZ+FW zrSzjwi|KKLpfd3~AYduiq;Ef8tGZJ6Li?+?dvvWF~pC@w3{!T2?rNC_r=O z>Jdszw7)E@yXOw<8g~*7!iR~~a%SIJOO@ABFoiD`cY5#6{4lvr>=9WzcND2?C@lz| z+cDQd@F>G`WCGK)uXF-P72JM8G#-OjXEl|l=FS|Zh=wW0H%CwS@2TpRP_wHXI$yGx zXz{%#7>X4KJtCBuJUZBuSvkJstFr@Z0IbVBAOWP+6xKR8bl%4V1LFY4`tAiiike{; z(_5#dkzwAPfcfv617NHW@oZY<_-kKcmTk?ga!T_*<7XZ;#Fn3PT?pi0+z-?I2piNKi_MvU zZKxDatrh=a*f{RFPdi~JA#*%8?E<{3JpThmG2f+A_4^v!W9?Q>%{W)=9q3Fwi(eoW z&QsGP%PB12q(jXMC|6aO1MtOt3ps|95x}VxSQ&cm-=l0G z;)zb(AZTXckmCU&b}%*q?%+Xtq$*V*Bccr4^}wx`?kcYpN!4C4yK{uDIu$rb_Yoaz zD4wKMiR+9_GTwZZ(}f%n`G5hC)t@-o?_Jaa2l%W9nu?CWHV&GYW&L`x8yuztM0Sa! zX}6FGni9mR%lZ)?NA?Qd)JqD={J$AG<+Mo49TlHF7zAh|fWAQElXQPKAe_@=^kR4L zs`M#j9at+C#n5Fa8X|D{Ok#U;-QAmRJ%>HbbHXD1y6EktOT z*RcQrXIy1aSUtRasZfW8CDco$^(BH=N|w6pkfhJ~1L!Yp6lP(6Y0|eg+gu3^x$v9; zN1TQJQ_K6;w_6HU_28qL_RW%%H$E#{|I@s``uw-8Px}~r1zJh>^#5>Drb|+$eUvhB zXHTGhBorK}QS9lFHn5a2(2y}$lLp%KRRhj|A<)QxLoKDFA)JFxXG>4(TlBn*p;+GG zZ_?PSVE5i0R=s^6^Xr<@wbzPCXaLCu_L?*VvI?EfnSw#!EM!Lolg}f>Xbba+HGDmU z+Ce|5`jNd$G!6?S6Bvb)HX`MoZJ(=!SqDaW$h@XkSy&L=W34P!>np4H+#7>ZPCJ`j z$9CMbJG+@bZZA+{>X2sD9^A9u7w`i--2P{Ug3Y4&o^F>m()U4am3hb8X?H6kDxT$QrNA) zKR8EoRkZG3(tzrQcHaQAOB)8M+7(o7bQYZRH-OsD=rjUtwt$|lj2=%!_aF4K_>eDA z!$%@i$?1d-bqu7caef$N00~x-+#BfB_$W$SP(T?(_wAXS*=uF1*b#-f{fv*4lY2t< z`r2AX>)g8ajR9L`B*PXxU`N9UXCw)~B4iGtsIdxu-yXo)TVx>zQ@7jdMQqQh3ZA|@ zI_@C;I|)6g3(@q#c4t=%A1vP4Q_IArOtW|qyUu zSxvsD&Mx!AAf5L%m2vvy(9@U!!wde0yP@wvEte|dTFIdXHRrtRicp5u7I+NCDr(m+ zi2$@Z0n`tAFTAcJDAALeM~haXv?|Z;bdH0c+f{{WSi^&7?-E4o#oYR`G_XCoGub-! zALUmLbvMjj2Hk!~1=mv)d*1Kyuf5dpG?_Us`4MD?ZpE-L_GXsh5dr=Y>;_9%{?wjL z?p{k)(*wM;m(iKd5g>fEAW6N3S}ZQB)AFMvJCT!3HPXvhgx?X5|Hyoo@Tk3_W5fIO zr1#cagK6o`=FKad%`46LE4+X9{({>T+`zM(iC;g6mQ4TKD*GDp{kt?n76Ik7#lS?G^@nAoY{T zRB)bAS;WQxTi&KYjyXDuEaU!qwX@xU|h?n0!b8rM)hP)$6w}RJFhxV#6 zC7&5OJWsTsoCw;E@G801CT(%$(zv!g$j(Ik1D#(V^pMwfXknkF{viv4L;eqP@*lZ< z2!mROSb#$!0W3rd0N7I6Yj^?U^Bt7WYM_wZ{trWjlbNxyy1tr;+ zS5T!Y7J6-4$RC^tUWgwGY!Sa+!H2OKQ(AYI5AEi-k2V>;bBZT@BKmoh7>S8p94aa} zx%rz|TzXGBV^=EZ=7dRu@>6UNjJhjKyz9VxBcM;RcreYzO{r2N16UUV?wEa{xjZfzv@@vP#Z_an%wZlyRH z@-{RHusR#oQlJ|v6gS%~2#tUxQS+w}X6AzYd_RJ40cPDTFo_M|FUoW*8F|M(1MNSd zv!~KhwDMW?q?C*W3-8m6MCjM}#A+kw>p%IA!~88OZQ^%n~-%rGzeUp9^ZoSX!C z*l(yxRu(wx|8};gOK}PU0a4KjIBjwayE(Pv1hqG7^%r&fZtMc^t4HsTrz{5}!_S-^ zaP*|DCGO+b8=^i=dkdCH9Vg(TKGlwoq5kJIhi$Tv9T!h)fPrFpcWZMuWzD|5H)J;W zX%+4R@K@!9-$2?1v|nq)&nOxUlz%L-d4RIMb4Eto@@+TLHf8;HQ_C=w~ zkXz#UJxeVz7Q(I|9Mt`3B02uV3uKr~pB>ltPb3@I9PE zwDBpe+o9IFQhH=u^<{-+V5WNOEw9n2FgJqo@Wa171rtJ!c6HflUO-c!h!i=t|;qP2K|9VYs-=E(*L##}0YfGlvZGj<{G?xa)!I%A-C@ zM1VCQ{h*qspyB#`O|chAYcJ^w0^N!|JHcU8k8d&}_45;pLVUeQIxNSzb~Lf8VNVU+ z?;!d_;BNdoz!+6hq!NVQ3w|>A!}-JtYJzi)8om+0fbu(eoPk9xp8SR3*{mXw6$E2i zYT6^;M0}NTmij2)iK&7KwPkT@Nin|IE}h0WLODZUdYM}K$Ps&oQ;q{M+&w4Z) z^kggDnZ3J_nLxB9xubwe+R9s@CH@&(mI{+{9#o9^fRyc>9+i%U0|G^UxW>Nz13G~k zYT8@#VR+1%pKci$eK)r_;xvXqLiPQnKsBtRB_7bY%M;y;JEpqdbM5vXJ|wwsRTn(F zNmuAGmdXZ@G`XDfXZMagwlxgkYua`XpEkONmT8wTS+yK#wHDh8Ja3C(@!6h_hb4yV ziTnzy9;}?P7sfcNaDOvfF^=q^7Q!mjva)%ilBoD0S9+qJPiZ|5V^4b9!V{i!i;TYJ zUkTqe=d&=i8p?kCFtpKzaFmqgi;`cShJ`yeCd}cnY{ziN<^)fwZv@RpCZtR~G`tMd z-$C>$)9F1x7bJ=X4ub7q1p_a8-P2d;;f^sc$^gJ5@z5$W#4+Z1+02RRI?pScgl88x zwP76?w&TI9<|Dh$tm59`Pn;5iUpjC8^!=9#y|j1Uf`g)htUs3tLy&qLuX1kiT;geC814;E2uN#*t^*d8q` z8MjDJNb8rGPmI8N&Uq-rV+84*Kv}BA$A5lTxjO&esQRK6HX z>*J}d*dOm+{mK0O??1m6FaCbx`ummZ&li9HEO&K2SM>LvN#{Gj-R`iDr)0~ie_~HA z{Mh-lY35J$&ac1ktzY}G^Znbj(|`SHbFNe8L}&K1&drRC$q}62|ctk6+q4$;((0l2;OL3~VV43APX}Qh2xy`%j zavyj^>tI7~w-eC2>%2`|0iwM<)ZU(5tVxmW*}vXY(p|Q$C)ROxizC*dm?g-4zOoMV z_I=wXe*p6A(>D2cn`~^8!&hwhp~mG7_n)tfN`$s;Udw%cBy-9wVM)t|U;DjCuIJF3 zXt9ovlK|`7HfwR4^;jXJ!TLbuOu)GxKB-mF7k>Cqs{&dEo%YNgJoDbK|bwRNB4RRLqb)a!$1zL-322BwA{SgwW>Ge55HUEqWr|NUM!s(HMZtnxy3?fSbU z$xr1h@yFfK|E6mEsT*^B_xbU`pQ)OEj*MQscyRR7VcXxC?bfc(Yj-9*Ebm>q7y2c( z<9pZhpTP;y?Y(BtLsb%tOL~>YLS|A4J)aLwNN(@7 zdmj29_PMdpU9laPx}HA?PKayowR#?^mS9}k`(O5A*Yow@gv|C{r{|$s3C88U=kA3* zi0$|<`(S&o#q&_rgpQKl{bQkqu^nf-p5G5n_%B;Cp`)yK|Gm(**p6pi&sTyI(%O3+ zo`?R2eJHl$WpIMc^V-th|3}w9;jfS}*TK(^|N5D#@<-#I>*ddnGk>P4{t3J13jE%& z(A3zD(gZQrPPw1`HlN;3510Rc4gR#s{oblN^#|CrA5Z9NKT)+8c4aRv>g*+haMC(!OuB zB({Add2#OE*}R=W@_&Wd|NH+w_`Sz|=FzKAN1vtDJ+3pUXYB6<=e;$!Q{E=!+KK+z zfBMt^9-ORM?z}~{b@-t50{&Onu78t_-?;X2J8}}NyG)p{?T?+lQ*J2j+Nt-mzwy)m zZE*4Q{Qlkq-!6wL;JJ*q19!^bOCP&_@@_ohlh(#*t)|yG$)&I{Yof{vl{b50XCNxi z4Pw9E!IWA3Mr3a4-q=@Hl#NOoi{2w|%eXUgG{A0$y8qZT)$-^-m5ryb(OYS3i6PUh z)9p?_2$ERgD*5-~<0i|WW}WV|Z`WPBI{p`1Zvhm?^F@s&1cF0=03pF0f+V;T+}+*X z-C0}{7ALq{aCa7WcXxMRY~gM4`+rsMtM{t5YPP0lW^3nGpFZc@+ug?sL_aPZ`l@<& z6>5H5Fqhmgmf+t$|CFQeD*cRDVM#v!{lFxF4E=k#L{}pv;&ux8PpjAurk*INgu~HB z_054YoLkl|{W8E@hF{;x6}uWG5w~e6dRVZ&jl!M*(O`>p8{lHl)w@BN6D1XXHb=}vJ zLl0YxvEkd2lu=)kIr!+qx2Iz{$_=)lO$>1=_(}7$gsjZKap|r55%OjU<#5|bT9<+E za~txeuO?Fj-y=e@5BF|`@av3pToB;$)ieQIQW>ux0&NUnc?6b z&jmlMEi{KF!%7X$)jlu;oEyjnKH#3rYWbogf2L~>k?;PL=((`k&lD$3#b=cSZp#2i zKl-mgVg}2FM~3&gCR%{5rd5#FX5Yr2f^?ADeoDK*3(O zxU+>HyB9tCF6evS2uTTmpyXMDV3gSRVFm1p?%))r2YQDG{Yj?za=G&rYo?2 zsH*%)lxsrPNQlGx<*i;}sY0qUz=UDCb8lZB4<2NS)*WJo+>C`nofUER1lq+2`+RyEeO zhMZ3K=#7fv3~=FYmfAkI%+7mE!QPaPnHu7CpdNwR;^g&f7Dp@r;kT z7tQ)PN@i^8@B108vvR4oi5)SGZl!aAzLI~<9HDuf#wl&P`6DDQXjL@EE$sR*(6^c? z)U|KeEV))}lRi+)uRd2W_f z>i6f(RXaQc$p3n~z6L6#7_X_;a0*eQd+Y~1>;oX<%XFaf{)ICqdocR}puDd1sihEC zSnJE`Z)&(;bD1kDVNN9BWwl>Mq@eXrUZjsx>vBt&K=7>eD)6}Xhm}erT_%8Y&cJKb z40fG0zthb}{DSQWB9VEW#a>XhLZ5jY*{nCeTfgS0R!;eCgr21KOFVpHrB5dtWkkV; zd`<<$uzH{h73D63U^3~&cPmj1WH)o{tG%3;A;jpxvEPCur7Uf%7XMxjVeP%nR+)&6 zw8PhrYq+3WtCQmBS{_YSCPF6}^AT2p{Lknb0u2~|T+sX5INkS3Ai&DmvnKjsQkDnW ze8zK(cIfgtR;+d?tX=sw>?`5YI9L6sN040|Pn*QhF|WIt6zgcx(LQvAKa{y=&j=2Z zB_a(x3>!Vjcvo0l*i{sIk@7sZNvP0zA^J15OoAv$0*%RB~*Bf)2$Tl-Zv?_7}RZH-Mq68N-Z6+hGSr%wU;wj6vZ{Qd0mBI$ez#n^odN#do&l{VgRrl)&|9< z2L4@pABUIeGW!vWS80MmC}i`gq5ADD%1I19S~hM#IdozR*&DOGPQe*NEQHVJDs+GfdJ07eA_kb~ES5C=IbrA;`k?MUQ>f@8eeZ0w0z= z`JHk{PwUf(^0&#lS0*Zc0k57@zlENAp6~5o0-8S)o806g7&--V_^!~b?M660$%i8j zfN+D5+;k%$)Pxod;Q)lyz;nag!Q%UI8Iq3R`ArKtCxv;8th*g|iknw!Vt&sz)>mcv z9wq$~I=VlW8gHQ^eSd9pRDtGQ%<=A{D&2LWDq%MYyH_ptSR2Q3wT0l(i-cfimfgV9 z97xppxMFzxbv#qgvu5FcX&CBFwF_3PUAsE+*k^* zRod07%^B35w(77n`59TU-H_lG#$i@ng0p*Js&}InflYwZa=55oTfbH)s5?EW{1=iI<=rdLAmM_-wKlcr$R1AI3z` z_`#lHR< z0nlY3vqwHsdK?(@V-|i47lh%K7gJIG5fE*TF~IVEDq~Z@_|kd|)mo9IazmWEGW97L z?G%v}lj~jO7CyK0j{|YoWcC4{(VR2FbG{1WnHAnXJy$6Bfei1mUz!1F{@aW#{h8~B zM9Em!MG(7v*~kf(q^J#pVY8=dJGdk<0>YrB7!Pe&K=^lK*$n79Z&C2c08?mAG#LRV z>_7+n2T#QtygsK8*N(hRNTb z)eW0CpHE;p0(WcEej2Q@+p&O}gc(^%6hl$X#cY+89bWd>OYaRq9WF=TP9et=QrJwl z4RgMxMLc#_hcAve%F)2wP|a2#`5!x z{blA(#;l2DwG&49*B}W%)$IyM>8Si`0@G{JX#$9}c3v@=)5*$9p<}Uw+*Kns2n|7| z?|1ZqR|{g=Z=Qw%5jQsich++a$Ej?{^Pg()0HsEMJA~ymdadDnUgm)6IK>(6NW5rS zY!Ale8;t0PI1ve1Et$Do-$Bd*p-k?r&p@1P9a^cggVs84Ss;c>nd10MK^PG$yTi3K zJB&SYP$!}Q8`(_`@)S-Y>=-P*|3rI>^MHSFJ{02C)DoG*fpk6oMN|H{^5;!_L~!N? z@JGL=f+FengnB$_3>z!AUg*`GeLahCm(NmCeMK;E$)E|{WWRTKn}nU%&JDf1xOvN= zsvXENWS<3bgT@e0-{a{(yQ3BNg}1@&0r7&15I5)M|R4u3i^jj+o!YW zoC+t0Wg8pcM;EmfB_c$8goStZ+@4CJ3sGyZ&R@yk1T@R2{F!6OsGx7`6p>4X3CPVM ztrh5X!Q<>|ZWo}#?)+Bq>1WY9K`-L4uMzz2r@b=IorIx#%T^9@3pv0659)&-6RV_| zk*j46Z>9SdVmLmF6&l+(EhskLF}Yp^dS(y}4ldPQed$2M=vgybB~paPr*H ztyXsIP1?WIceX9SVB>C1pTl&FZY4^VYCy~Bq7Yo4b}Sa z`PXD`@&deukq+PfJ^fw^n}BiY)A4@zg9{0O{O z570s)JC?{i(y3aQJh3Zzz)d+_+}@|nSfYL3vQCxc8=#bo zNR!QhU&gP=!;NyKGU17ju|q6bRQt~MN-jfrq2G3!*lUnFnr`Pug=}Sc-H)h_aW$8z zl_%QBRY08-G{MTag!{qDfBd-Uy_7T8@fT8Bs}uXYeXWePhv3_FxOA|FcLf>{+$V0$9`+> zA^OptSRcJ(w+L7qWp`_@Irw<|2C2D>+eF^U(nfxM9P5+kqkemCcM&%-4qFZvGQ+`c zm<79McI(4Ffm4H*nD#mEHH6R>}bo-MuCa(cpv*K zZSd7b?hs!fVI}~xIkx!6OnMWAu`Ob<7U^DMSQCZ33GIfs=z@lp;2h=Z24zkVq$c)- z_&~70P}WCN5acn)p8M0u0neqT=0T<^JsojlDzLE5T-2Ojgs6}lp)SRqdXX_S%+#aZ zj6&YY0m2w@EKpa9zsJ!2x~1ZCF6vQ0MR!ovwq4kukN|_jEvWqHcd7I3g%P2Th=ua#Dk;R!} z`bUvh>Nqj|^n@%(E05h1S`Ams%c3ziyC!(l4otYa&(n$MWnAax&9s;*`;5(sl8%+>*B^#01ygUqFJo4hB{ z%qoY~E*RooiV4{&mji@xL}QOX=Zn2e<+92UX^Gm=A6tOLSQEuW0-&E~H1LX%n6jzp zBirqH-r49ViIda73jTL?v60aj7}Yn7#zEKVutupA?L#+5@L^!nDI4Xz6nzEjX7_IN36d47A%iM4UZ;~?o~43 zXqXW5*2GT^CbFoJFf!&XafV}Zg0I|2vEXBCk}QhTuw*z1ZTK_liHS2{x0Ej^uK5-- z`9ln?U=krcydqrM-(v3HQ5Oqt5@+9j{iI21 zLAUWamDoYXTR``;kBav>)=a=oo16(Pu?urUz(^Uf)7PFAr0)$df27~8XlMz{sYcgf z4=%C9Pd%%=5SzbKB9YHboUqfqx&?NpCWB&{p*;}K%gn6Hzx8&*!sv&{0d!m`BuA`E zx#=>0>;;Pl`=)cU;)2ij9%jUKj}Uq9#e8)Y1i1swbQ2UO5_lZd5ICSWdZS&#`*D}S zT{*|fKRZ_ljTUpGBG2%V)`}ezFNhJqUlf?zn}>7Q1D8VPsI=Y?5rSjaiBy8_#7PKg zdH^7|J&|eo#??y&ra}-7yIu(z4_}+i7#-pv4_XsH>2|^= zvQ}mtxHtVuJB;n8-!bALoZ|FOCOU3p&-V-nhdxB|=wVZZt_7LVzfEJ(7*6 zcmy@&9DX%_L`rEFEU1V+{A&D&RP@$cA>en?ohrGSMzj$mzn}E1_%IO72cO#9zRPAT zthq+tKrXjNACADYme2*R@-Gl@4@bM&2!C`lbtE{Kus}=K6qcpW31(k!KkWN7NSp5V z-Q`e@oV7WKuYIT#KA)NsH$QUFOtDGwK)L`%!EFyGx(UwM*8jH_@gB|(i9de4pR>8M zT&&`vE=80{wTLjeVv2t&{TJC$>b4hqf6>*GkgwKRS8Xze4P9rjy z4g+p=PMprT8qWT#6YG3cCXaz(88IoH@4$vtUFx^8iA4{0J<((O-;D*Dp&Uk=A?XOP|%$q%iMFW)` zFMqr4w}JnSofI1|#%DiuE$F9yB=1OLa>ZFdN2gJ-kG^C`plj5au>-QfI#LH14CAyZ z1mMy%ueEY)VORlU)*-U_BTRDpj{?T%L*%UYVFE~oQ+vO5Xx}-OhND=@mZ2VTp~12= zKJ209p3$i7oOKK$_5Q&^Kk0F1Y{7W zqa9u@il+Hc>4+^aI_P8U6z)=FLAHG;VcBxbm0u*wqKw^jq^_5c;zYUFxa<$ww|_hD zwYlg=Tj&tK-}71?er+y8^#0bXcv*Yo>-m@;KH^;0ndE->M`z-LF%E(&k!yj1{~t2s zNcoox4F-s@fwC@IvM#vSH4lFJk~GZ;rgaE1jlq=x;XD>ZBrRa0EZD~Kf zf^zQWG4{tl$DK+?!CByjB~~aGLV2%&`8M=#FkSxN!Mwvgqc{pE;uU0sP5&>PhWTeT zsz2#45Kld8c@|+BW!8~0@Re#0m4X<=N#JPm8X0TnrG+-f=5kHAX@{o2O&PPdA zg*lNf_|f@Uuw;&t$oOF@43}Qx4da_M)PWVewhO@qgg@kFu@ec>?{dzp`EoB(74FmR z=$%C~1T;aPI5SAV`6|&X;}=xGn0+W^{D_&{E?mIq|2d1CCQM?PIJQK3 zpz440=$IpVV&ne`D)es>xG zYjeOECNVG|HYqJ~DqWfMk2cwrT842BMsljq-d=PQr=e}s?^H61;y1bj(3m>?7gOws zIk6w@^1mZEZ!HiZYZU8v&#hSSiVeEC53HS|V;}7gI;Xp4$!=g^Eku*^*(>6!>U6*F zsxDPWm#M+6(qzTbs%O;`*j)eO`^xJsnT`RSoBG3C?)~8#cffa_cXC3-qwKldWup!7 zT=|GD5h8*F2rgv^>HpIvjH;!hnu1co0!f5ra`kVbc-9fm{ByFcKHZ%~h~!nUZX51LFS+4TOv4JVUN)XbYHt1U{K zK_VPWFXHCd_|Gohbu)Xl@-|FsbcI96?s2#>Xmx`^j&RZuwuJy96Es zUZ%I@UJvDfACvm8>`C}m2;`O+_aslhQiDAMip(S(hH3#Qv3C{83}HE`kvp~`DI3d> zFSr2Cr$fCpP&O~KOnk$-D02WiYF&39MtgYfW-5o5o*#7-sgIHqqWt4zZO=pP33w`> z#Zc0zz*)Z;n`T4=sex1`B$^^s7QQueDpc#S8}oO?7UZ3a!US8Tt2S3{#K6U2$GNje ztu3MgK76l3!~2hVo~{qN;|{OgRX)7W&$zhKUx3WvB`)#2uf5@4Z4?)~*O~Lvi@m?g zTs&Y^v)r%Uc#)Vb<|KX%#5kvVtkU7X{_h?jlA7afIyna*WvaTjjB2v&>W(jT=Om+O z?w2{9c)bT%+jH6+4j!R5BHePQ(9$(chp&dha zz7F~7mO1rdIXKv@+m#Op+7~*Uu{NO`~=SBn5Z5=FnkfpE24jkb=C#Ei{zgrzuz`T*aAhB;7@fEXSCm0GpB(6&6~w@96dmKOp3iGzb!($7XDg zTh#?mMr#G=LbpN=CT}Ucw}6h#46)>uh=P#MTQ%#o@}4;|wVK1y7iFZJe}GG zB+o5%+Lm_z`h{6wT@kRjG(9EAVNuVYa791r%WvqIjGw^I6?Z^qV9UmjbwhufRLqCU z+GD~K&l}aM2W)!uIvpqYX<_NcZ*&rWM}3%PU(o=0A)Rb1COEw^3&1G?PA$dMq$aao z1>ehldc^x$(!UC5irw02T1SV~iK?jm@HnKmwo#$pjY2xpnZn^~Tf@iZ zU(OV$l4Xxs#8V0ZJB&@_Au3H@7b9NtDo|7u3xr*gOVe9rtpS>zksr8KLF)`HwdH(+ z_hDF!iWxE)&awT^d-aBjQ`x-Y?RvUjxTV%5;u)q2WpcddqO}6MUWPg9mfm$g;SF5E z+~iBdGb&cum=1Y(1UJM+#1=kG)GF^CM%o2WetAt;v=N*|&OVZoQ;~RjesNrUq8M|S zS$o+OgD!?kZF|BHnj?BwT(HBKf)<7P2do|FBU-N%~b9>zpo%aXA02UMWqizgYk$Q%j`IJd!A=0 zO+h;(m3&B|I0wm?cAY*E#d8(x^YJL3)s=S#^6hguU6j;kz zzS72-b^_tq#gtQ-%kAFG61Ggbak{z2a>aT{()M*e+Yz4D_TJKqxdHj|sTM|IL zsnmq)TX#~Zg8r({J@sVGr7NM!7RnUUx+1gN(BR{_gg9H=Mfgd?MenflQ+YHP$+mZ< z*If1W=0;|FvQ{~p^ESr2%FXQhlKLi8aZGHmT9<<#yCE(886l&6YHj@oAf5|Dj1TkT4SitpB5N($mvu2T5 zI|;vKn&r3b;DVqyU4Mz_g6XV|j3LI5daWDI&t5(lVzpsp)ZgTnwmU!TbEd~m#M6b5?4=q z-;ORh%8RCYJT>S8eVAD90fkA{6f{&(Npmhh;&-xo%Z5S zAxmQ4T?rMEt3Udiobn9h@($fEx-IiR44bvo&_s@EOj)*h)Y7N&&9#7scBc!h9hGpX zDy<>QxyfswpN?hWr#+YjbOQPwKD}&)4-4g1L>B4l(8uf4X!|>9IlKOzcsO~Lo@kiS z!%3Q#8FX+Hw^r%*LGE9BXu=aULwDMKNY1h=2BF+pl#>8kgcOI3uWTw8L6w)MPI48C zYvZu=@Zay9$wbzS+iy>>IaK@&CUU62&GpInp)8EVi1anEG%z zv9i^K_PVsMf9_qvut-+}qRS*hbp}!B-89FSnqC4aT3 ze6oux4r>vNXtB2_nMc~qG1$S&o+JL)$C}4K8=b8^D_O!C>NxogQ_q(6V{!aa>-f{S zc0y>07vjH5SLfc;zp^>;w@A@lcEz;4NH=RYSHwv6syDbwalx-9btH{J@~i#b)`hH{ z&M5Rs50erSN}}(of95F5(HA5*ZW`+CX;vtvCxxrz(^)o+9Y)5mhqD7XqZOCrx=}2M zLfQF$jh4B7%HE&xL0Xn9;T&2T|oup8bs3Zw)RkQzE#voebSybru8CW2NoA_X# z^4;duo{up2r4g=DJn^>cp}28#XD{^Pd6B8y_NVa0dSJta$(@x>e)vI`YWCa2fV+wpmk-6mWiL6XHM*x99FD!O4 zB3t4#Ezx>p{}3&$CkpN-ikAIfWy%F~Hi7Kx)1|8jLWw@F$D9xY8q zwSWYz)yK(Gizmw#PP36M*u>MlsL7C1zVWB8xUNe&D+~;uYha-$Bm9YQ?^La357O~e zyV$%s%w;M8Gdw54%$2`XQN65ZP&3W9=L%f?osU4b3?UFY^+jnoal=Wgvr@uIt!cH3 zBdDxpK7@>wVuh#1HcG`x@z-j3$c7%KjYGy^eWV~JcFU?~jcR#1ulPf!m*X$eW2QLi ztRph}|LDn8BImv@V(GY8V6xWyf7eeQCwaT9EX8Ui$+n$)KysN|!#fFnUYo&WU=anK zmXGqSMsCi3_;mEJQMPpC)opH*6o-Wl9$G*5r#t=mS_&~UUx&hiwYs*?8kA(5oco@K zXMVA>4DFfK%R@{R#&wHmrKg~#5w@U3a(a?J4Z8O>n=-=Q-WYV^ zv41axdye9AF0xVJLP*AIjg_JkD|b!DO)~oLSGY2dR3iRD3{mxJ@0xGQ4#121?g=B= zVdJjJ<;{#|%y-+hy&V3XWELCb^?2v0bMQs`dMBQl2A|uU4KCsVZM@D+C{In{5`<+; z7UHXQ_e7ED(7da~3ho2sb1qk9(=?eQe+Y!l4$hDh{0lH^O)@<>#u@ZIXfVde>zOkh zP?8g_u0n81=H$f2h9Zu+xV*FAAn22!6rUz|4Zd>+{c zda-dE$NphnSEWQdcke=iw{0AND|5CDwgm~>BvQ-3ozYN@@l3BH?YvdXtD&Ahjv?vH zDo=t2)LdtEh;O9_qvvs#)F+A?k;e06!h7?V+Kl|AHkQRTm5!VGdVQJ|SE)(+;5cpHjxmCK?_7s{_kl)q*@L720)R0E?`&@s0*mc$Ev*tzyTgJ;4 zIHigsmln!vmQyeGLFTCnK&oSXv=_~@q>|(T8#k#&#qARxq-s-T59sQp;Md-~0 zzsT)$Etq1x9rwu&70(EgzkT+9apy^;NcG%&R@UZj0+Y0Q=eL6VU#MM37=*E!OFj=d z1WQ|@2wl^6Uccqb%w&*oF)x~VWU)ID0nY6{#Qv#E$Ykna9yi3G8UOufc?zSjFP(|h zp%jmPhwd>Bdq24^W*fd{+c(JqiY{qhuivx;UJlB9v)=WujapsP46b=NY1dc z!uwvb3u{eun02^8;ia&iU$LzUm>hBv@Kon$$|D-$kM)LSBM) zplT?iD;yJpy>>b#X+EIFkJZCgo?CH^keFu_XHO=6I`cFc+^0acbdab-n z$2u=HR9Fnf!X}ojT5;sGtsXPyTpx$lUEa30^k+mrc2^Q74A)_4whKLC0lXHq&Zbj<;%bOfQhCk}my!!x=JPcc9(N?VROo)I7mKaS>3mvAKDAet;tuumc zUN6Yvb@Ga#Gpou3_D%f=m7$^<=*afe(0t{dSnR^wYHbd&e(ox{*0?nQYPKRu|)rWl1w{ zQ@gY-=zAY+gV<1NmUeExj=b=2S=my0b;Axy0!A{IU%B4gan}7%l=L6CD9f;^cRaZ0v#s<`d1~M%Jbs6~9EOR&U`& zd|fN7;S*+SWqOd-O}28$vOmN;vUD!JhyawKg1b@ zdz$lbtAI{cUxS_lP2=v`e3@N9j?Q2Rvs{BgXS)5+cK2KM_2TPaQ6uE2Z!)%cCdAA= z^04ybKlI4`c^tLWc-wWyHqUV&y_nkRs&^*x^!WF3-8EF!ZIoZk(q%{H0sPE21h+|x z{J;1f4GP80y{0aAl2(=wtEcX-J+vfCkfU-b&hBUyR_$BW)VvJLEJA^6Iz7)x;`=pC zjUFJVWZ|3e_|e&6#Z7egLh9un?tBURt4!AZ)g(=$u|A?}M!o@XhjGY_F5w_Ulmo;q zNyf(gouUbk9!!I- zL8XKXUlGbOjmeWm+Lw^Av?HE8J1B6dv<*=xqF)dlSMkKF%;u1d$a^W0c22 zkM;fp_rP0C_17H~-+q8h&!3}D3|t~~*6&+h*)k$Vk=B(q8Pb-H8Vnl`J{G$~iagmF zf#!yW_W2ttZ)a1Cpl7R+awEF=9>eGy0zp4qGn&652$y?$WN{Cz?sna#% zf!0Re71Hk_{wK|RT!Wzg!GV2T|H@jw3kkqTTIo!7h5s6mW{ZLaR3ahO)+V+_kG-79UMg$ z1E)W~ynoD{5ycOutPTF3I&x^oZY0>~dY(}_%Rx=hT<3*2xKWwU&0qP*%uX#;d|0FP|Ee{ZBc$PwQJlsJ_{P8Kh6i3BTxtS;s9~LnJk7#;iTFQG z%+Y^N48Em2GF4PioUFf1s@zmo*9!rn3fx-m_~gQHq`E}(mf%GB%O$b}aDM*H$YI`% zaE_W&^OKDvBNE2PWH*t(T21u#>$8LEP&>xCa223x9xjGd4Ygz7#7mchN+L?QX9}Bp zkhne^EtmOq+YTPDMVZu+TrHy1%ndrMHA_2X)N6f#7hbL-5Xu;LoqKWj=Bj}@y33uT zV3y@J0texmibKfamb+oqUngZ{$^2V08}A8F;C%f<27>_ln2bhRM>Xqb6pcHbS_s|s z$bU|XM&&Q_rMIiT*Zqervl~-s)Dps4B_jtlT=RrnulSjnY*IS^+?tw=>?k*6TgHLR z|GeF#C<`}O2K)jS+jsm}Q2vTg#W2FD8O$8Z{Rtwde10|EV|Sx9^COZ7|PX+OsqiiHpJrE~6(XTyW% zJqBY&szeEQRIYDHo2HFg{R+7GBr`E30R57yDV#-P&86N4H#H68nahM0yHEeiNh4QtzklI(eEfk}81*Iln)21{imfw3|B{phot>f*<-?q>#*jpAsM~^gl4#l% zBst83i(G#DIbF)%tok!!V28?|sT>J>?cQ0^1gmszhbD2@hG{pN?=}W*A6~V@Uw4rI zhbg}q&f1r(bL-cko4KAKNt|^Rmf3!#d~HNhwjy2vd}*mu)!=*WYyhl0Zm8ufM}MGC zkLY5aY_^;;!I{V+tg5`cu3P(dbdjhbkeSC zD$8h8CfPP?B3t-Hi2cv4MnR<1?AkU$?zx?2R~?XIW&IBhBW>baZ4&;I>U^y!ET{ov z$6v{?N}%i z*k$ocrbjblr{ z3&!vFf|ssCv9*)`IE$;w%DBBsIx|=fryas@4K;ds!F-1G5uUHAzX@JqL$8m1(sqHB zG>e?t4fy}0{rQ%iUmzT>8z>P&iQ(EG6b|#iN$%xCAXXnmR>UfQwcW|2pPU|_2X%Q( z-9S%=DkLA1jkX5s2tTCl@ZqSc_g!Do(lyW2AgyKykOt<>*^o)v?#WjkF^MV8(QG`8 z`gbo5x?c91A5Q@82DYd^XR@QU{mb^)n11qE{`lP9UB~z`y%&f6SFBjG`~JM+0;gBj zt{XcpW!?N!D|NpNZVWUop4yMs(!96`uS|v%p~lNm%4FMSXM;~&o7|x@y88ti6;m*^ zHQ4uOy%hXWoQ z51N6-Be;d`2Fs~qxppe2%iR4uzpEKm+JV?LEeJ2EJh(*uPp4VbUKHOK2)3~J*^Sm^ z(`rECZ z65myE4MU;RbD7kW5V5gIaIp}PIBC=)T`I4U@A&V zRw=%-MEj%rp=>;o{?d~=zji$&S?!C2`WDYp!`(?QP=i&ufA+FGO5^LRTrd zalp0L+XRknN5Hp-HW2PQ=qG^3VpIRqi{?#bQ&RZBrY#>R{r*c3z z?5n_lZhe-L23iZI6b3|%y>5%WT1fYU`^U#^(QZy<<*vML7?l1ikK6#|6^uvGwfA)Ua63n$^bM<(3~CSCFWj~qgkXG9|L2q`a`jRMWx9hydY72#`@b|oJiT_JLE9|*!Td$yFNwpN2TpaBarJp)eGB;HGyJN`8 zX$&IrIND07>cY~QiTIfKID9hS(sJC0L3w(3i1i>6Lv#!RHNrv;J;ATO6nZa??Q$13 zvU52HPg#}Ck@oFKj(o0CF3jae3G$$)R&~fqo)A?uNE}VopP~G_22gp4al0ow{dN8u z`^ZET@YwB}7wtweNslMr2#v+Bd53uZ6T8DR67IR>XDfh6Rekxd$h7=+s2%*Ep`N=7 zB|2X%?PQcY%|cxH#bls+1XE5vxL-VE)|o9fkYDb?SSwUdSL!)_vPq`WUgq~6HXasX zXigr@G0vrTY=yjV&<5WncX7&=F6uU-T&Wd{AXf#duXll|*e|$WtO!+A#99tWG%^h} zW#-b@uv-L2bU12f%|u$vA?i=l8EEdWHYd~d9ak^RFI`h=Mp3Slk5%m^m(GgN9JG-g zdYyWsJ#UFq_}|mID#}7nHe23ZYm7#hUBCWiiJG8UA~^L1XSv?E3Oj#B9jLF8TOxKe zSf}+rHT3qc8Y=#+DO~f{zlA1=uF{giCGzE^oJ(~-X!xx5xPJfe^|a8yb4F*L4>(dR z)iJ&PV|Bj_B67j}*S|%ce|GPo_u+x`o~sx+h^oB&=qmJNd|oaM1ym9;>jCH=hF7J@ z8(RJfpgl_EOJz%_{>fLIM1+=pLKD*YbF=1Ge-+T+Uj@Xt^FIY-R{k2<g=w zlHX_cF1vxn1|WvU@EO%zf8m!G>Zcbk_+s@u!x(|@)mM#{(LW5o;)qCml(^K;iDv~x zYB`7MU+?XoN?k(UZJet&u>b4{Whp5wUbP$CtNX5--f(>F4d4`h1#`A)9%&tUy$3Wz zz!Kf=_EsEz4{18{^&I^A`%!zHv5#SV?>31&{XFX0IzawcT4Y&;t)nZ`$9snM4%TBQ+WdifQWp5DNej8e2`_ucaND?+a^4Q`YlqGZw>@xcCDXjA{|{4d8CAFQ z^>5=Y#fv)}+$ru*+)JUjySux)ySux?!5xY_6pFjMKIhx}|6A)>Yw~82OlHkYu6*`R zvNxa*Bm4qf9{*jW`T;TUaydM@?v%yd)8k`UbmCajPUQyid>?w)CqrEm9((I`A-4YT z^y6UnyGrlWF9>0%68wBGEB$v!i4JJ#H4!Nkz!zyfDwgC}%1ZA%cKBked`wtOB=7nx z++!UNZpy=l^74`O#zxm=%#&%}8Dnf$-P)``%(7tf~(1_pI zYzdxo0?@LN1=obE`(G%0n%>@%A2CH#>iulorKa_~9%)nvu6p3uJknR-6YQ*g%)5Ll z;h!95o`^PjxVvwBenGp#k;}!@M&b1-P)3sH&KZz-Dq2t3x!8Mdd|m^8iLvb*(6Szf z7t>ej_|uAn)TS;6^n5w!+i!Q(o`_V;j*yC8>Iobf ziDQU(6?q;f?NAfbh04f~t!f}K#8*a|4ol8gd?BY~^72c{L(|-ih*H|r9a8>USYc-7 z#wxx2o&SJ}BlaZ)o7KXz8piiYxPk_On5-DeCrcUkvD~vsIB5n)*_&zjI+VDmqd<^s zU5QNa_e2PRo?DWPYAIt;i0C10c067L4}v5#<=yT=u^)We{vme0LhJ7`WwmxTnDojB zdR~_kKB+}?_RS#5;9~lPhtnD@v6l}SM7fG2)gSQats!+rN*_uXWZs|7U+NYq0r|wm zqUeh5=$I_3C0`0yGAr|~+DpO_sv$X2^MZVm#(K@HM9+gcxhaC5 z!8~b%;orH6@!^>9*6VT;%rdH&8@T0^YA>|Rula^kI`JbgJ23Q<+ou`W+C2H898rI? z&nJ#&P|Z;pvrnIf8~-vxh|Jzw6@ciMGa=Bhv3@ia2 z@a7&A0f(lJS1qvA1<)-m5~Q%)Tc01u$&Vp z9(lw)G;2gXDRW#eO!i*R;k%iz!}!hAz&6NBC!So79q`M=EuelEglST}bAzp_Ufw zCi~9bUk7={w1(AM6eA!JpfJ-8o+SF1b5qdKCD$R$JxPQbO=8pw%cv{fNdP_33`zB& zbMYn&o(9wz?{1Dp_K!p@iUE)aGgj>RUSXU*d1COC*7+2K5ho{a%~_`oIqQv|t6p8O zUWRwo=fVy$ubeipz|xr9spZ(b9)N@2`80}xd67kyu0Y1_SlH%3w9dmIh#4R(gxI2b zrfC^xlR+9j&TdT~Si&Chb{wNPB0~z{{w%mtdq8@fDLFj3wcs`UtDAaY;^>X*A-!k+_10Q_)Wr zwe8QLGb#xl)xAdASKbu}LsiUd#NT2(B*KrqgcXdzRV>oZwN=}wf?Pku!y&Vho)Qvg z>{Byj1_~VOIHYDuraw^bt-Y%4ImE=0&PCT^{{(}phG!x+RuPIX*#~TX2{%DY7^lpll-14RItRvKS zQ&qrj2x&3}|CmMj4;2!22$VERL_$Z@3^;5nsS4%SAyC1y;B0hK;Wt7eaC|0gyh)tP z>`Lu0(6Ng87u1fBAL53ckwTeS3B$?q!zu~r`~FDmH!C45KM*t}HT3NrGYbBkw9oCh zdowKma)J%sh7)VE(DJoO$J$qdUQUhHc(qs3P=VT{h&pg*x~9$O_oS|Ok-JZaI`Dw4 zzewzW00>8YUrvd~i%mnoC?&Dpk~F+#xZ8sDk|FjCdV2q%1$+V4(X2&kTZ!r3dh24F zEtrbp_59Hj7-u_i%dFrhHm3^oCf7Ekn)#R&%fckHkJ!@U3?>9z138cMXR8wez4&@< zC5|krO>T;&EIRZKuzi|qttRVr)rscOxGN}d(ztY zJaJAtt95MTeTNR!2^|<)dOAnsT_CoGTs1#p?t8d$?@G;HxAso>*uplke$ApVja|8} zXx@P2zszQzeNmQV}b*2QE~!naEj_)dpz~Iv*B%6 zee&D7dRG+CHV5{XOv{P4K14!#+COx+{?L=F3koxg-8+k?P=6Xr!Yvb#~l3580W%+4* zxWsv%4a|$(ud~l#OFIblCEy--gz17W|^^Br)@iVo1stReDCHq1*5&eU<;8#=zIJZ`dVoBe9d3zD6^8p-xw>jCJ$j z)a4c0x@Pc96Jt4!{Qql=BGm?MU|=cT^Q_D;{FtE?&4ql9U}h~LNRhRX%xLSd?s=-zqBR?RzzMj&#+ zbPK0d%yX!UI|8@IR&I<}aetX^&wh(24t9>w+40xovd;pG?Wi(mT5D@<9y!*f{j<%|A9THhxs1?cTs9dJ>7=AF-yg#W7zS}yu=5P;Qpj2;Ecasln z?byzG<`M0k(rvr`egk_0?t<)*uK#C`Tw6)GgBXF{@$Kr`k|w(F6aDaKDp!x2UYD}x zP9*P@e5qqOHRF{|_Qk3gZnmT<>hHIN+sZ{B{i}DLRgx@S(zCUlllhQa?6SY2Plx`9 zQSa<56_Ja{IJK{@11k&@+QfpwI)sX_P-yDT%D30`!NI7D5v=9UaGC&2NjrjRJ(84O zTBOX_SQ2w-m(h-@Ff;Pkma z`Rm`#fPVsk`S|@rCL}2VK@AC^ff+t7Tlm{OqhG_?Fxh%xgthdEjQJEad>MjTsB7^# zKF)yOdVRGa+n|bx9wOQreX0X*0y_ObdgReic3JKVa}j3B7;> z2Vp9C-JpSUjKP%Oih=vZ*+7y{ov8ZV1GpRnOF~X37@>5G@#GR)8b?Y7L6cXVOq&lP zURkH^bdQW6aT47$D5nGIV$h45>qNzt*UVT%PSBHND2bDY0-wRDB87$w1B%ahGJ}PZ z6XReR?TA{f4s! z7+>@cC3gRZlKuZsqI;dKV6RN6`yAIe}|ZBP3O@sB-Y=k5n+>zYkht#>gfzL5jskKrA4v9@`K+h9IhH?5jq zb+kEB#WY-)x#~1pXCMVWO58l(eo5~=?GO=zVs2g^R9{OxhBMXl@echiEp+Sk#Nr*W z!Od2elv~+2`T25>nEz#K`^-}l;pcIuYwG;$cFDmvizwpVZ*yBiSN)kIALrR`5=4Pu0}X)S>8vwSOvb>O7R41W&D=h{Y1|2He1QW7+To>QV`r=UDE_3dKK4*! z*y!BG!Y!cp0lEQ&hCfj*)1) z2i1qhR}a*en9G#`q%$_DKGC1wSl?E?ZT&tAe4FrGc~vRmPkse4`#+^Sd}zaC!GC3# zt5!rCi+gn}lT;77-v>VvMtcd1y_@WlJdBSP5vs{0dZZv);ic#4@`v#MN+aKe)D$#?4p*L;!nPOiZh@jNr^e7BXeWmF%us&iv4DbgE4u?nmz<=IO#M*>IQzi(6 zF9Jlbcwk7)%@Jy`(|^ShpB4exF9yI1*?Tj6dJgHwjip|ndmXH9Yogd4N4|UPjq(Gf z6UET>ItvtWY6pO-Z3H$~y>eF4aT{l)r_-P;GQG^D=WLANTizm8G5TsOIt@CLJTo7j z=|Kys_Zb$;+h5r7{G&3z1w}G(d1%Bm|HXzlEOpfuD&<`}GoyHo11?NsEUCk*^2*7I z*zUHMGE${P!aS7zjP)x(DZMuXhaaVIqXHA9;)$n82p(2 z6Y>G)8FOsmRh>jKUE12<>?E>AWr(=Zp;p@A*|3ImMFR%j1fNhxot&?5Dqh&B)4BwPDP zM)k^wKH=|-SFUU>Eo!RqGS+IU(4MW#T11PB&14`OrLpCOF_eV)^(cKaGq;tA;R)5R z$8b}p9s_5tsw>2$hbHrI#Lf9n&Ghd1?fWymw540~LhHgK(uWNfyue9hWMhB*B5tXtLE8E%r ztzllCHwF}(Zt4@z*CThljv!|!4#2h*GOWm`z?;?L+%NzRIfg-ETQ}WGiHvV|>A-+Uyy-(0G z(nKMyo;AR{_dDs5(r=lM_t#S%;Ipt}O|f=tyQp9FZRE`nDY^56?u47@osS!R<`4?% z=8GGGl?fC{UV1BSr3s*mL%0p zRVZLnSD0r>^krS1Gm@bFmw!+>LWx$a>8&$dWK}kTOtO9G%nqSl!teI5tT+j)YQHvp zegdN$GDA!(1_&1AH#e*&(&!aDnCn50BL3!*!LQyE?O%oB%R+aqElHNl#k8HCQqJz( z7+DsullKDU)i5arzaO*A2*u5XRr66wl%3(4k4GsfB{2+2+LMRuc5p5hM$~VYN$BC| zuBd*ktN_@$@kFe%5IYuT$TUtwsjgS@xOdyi%|fHmP%1(hh}c(l$f#(+bzK^J%176q zMA&ez#_p{0anS8S4ivhXL`>F>tW+9+EEY9UB~`S_yr2l74fR7(&B!TCF13NbisR_3 zO*NN2cRz}<2MX&C_Sc9#!;^0vu2IFwgKTgO-R@MddsC=-`}vvvvaCt z)jE|m`*f#8enZLCs#Kl!ygOCA^E9ZJL}*LMe)1$VFwUfhWM-qP$xlQ018S1DngdTD zzt$h*544gedd6ID-Obyz3_2Yo*)2Aot<2lsRzk(PwQ;c{Y&Vh{)cToh4HB$UWG8Jn zMs)Za6Z85$w;PFDHbP^EZNfN}YKsI;dl0^CjWCwtz2)+Z|49z~9UpO7W%n_ts850? zPcK!c+2#L?7lr^3L`wf3M6&THDMTm9U z-sVp`j}pd1!GNV?W`QFiJx?ZSDcIK^Qc{S>mqbK0h3OGmsE?ULWjw` z#y_G%xh~j?A&`&Bo<(=|cp^fxAoNs+JZEY&y-`4Yi?(TIZhPRdZAO%@jkPlnkGSp& zpSH^rgV3?WAz^HwCM`bJyatz^=EYPX;z#8f_sqW1nU4cSuKF1{$S0Jg+p4Lw#9AJQU>*nz92rA)1)t82eXk#sQjy+MUPDj ztm1hrC=E6qbT#akQgMJ^zx}2aDv1jlqEP+9X;mbjWiPh78%vE#zCafuP&^%`SFD&> zRXXvrU)@Dk^!i3A$y540p;=yWA@Ey8a-pK+i;(?JGz9I?sm_Z~yuL(0#Jfk+v(V6= z%e;?Q-%sMtQ?K67T~LIF&$pic!aUUaZV0~}eqQU|3VyB&e(?CvFjazfeY}1a+k3=a zgA&JoK<*6x-N(yAoO{1~`X)o32F3Gt7d`gStpDh<$xRTsQ7`Ir{$j*gV(&SxBNb~c za!T5!Y%%t<3UlYB=_z$za78iH7xt}f31`B>2kI?}LzAdOVCrH%Vz#HMDZk2Az8)8N z22MrJ?V5lLJ1Mzl%bI{2viIxE%|7-$s)*3{8~O9IC)XIt+0~`6Z@o5?4W=uA4Q64y9VYw!y1Jr6tjL|Bj$tu#w z+HLa_nZMf6h;sOt3T%-cBn#oGLzrl_}P0FW#14HeKdTZum%rGt6z4y z-a4_~dE>@&o3q72MMHZulM~)FtM;gld_Rb!K5t>g-w|Q1Jwao3sZS;78_7 zX=2Z#H^%Soh0^bD{2dF^#405|sl{(yZfBr=)n?}kK5jhA<=lYcnLT^nmFM~@=PRd= zQ={(-e$V6#~H+`tBCW{DGE(RB5?d85Od)<$HOxpADe=nS{UR1*rV9@Y#ET zCHi$L(m!$PHF>U-o;&6|AvGosJFg2??E1-_4ONgw0jtP2j$IgdRHmL)ajs+$il}^~DY@}ltxjfg_Ix$U zC}}@^&o$DtXKI2K%MjbHWzQ?AZ^b07?tmN#UVfe~gwH5x-lMQlG zoFkkGA%1B4^wL-3=P$&4{FZTSAhs(J`W{_U)fj)_XZ1%7W#n+u4S|De#^#x5N}_=C ztDnTGu3W-LJ{Pu-SH9t(W6KH-J{*buBxdAL(o^eTX)w_6tE8&z1!}{?U|2$H{^L!6GgrgV%~kg zksp6_nJTWst?P(Mi}{Q80#zT^ocE{Lie!=8nFu5=FP^(|KAxUdd)TF~=t-Sa9h4hw zP_+Bf&EPlKIfT~@5yO5(ljr5aN?wohf;PsaIiljbusIv1HSe9x2*TXj2?t??S^-_V z%gg^2rf)u7qCQ-`wJV-L-C5%4B7&D32wq{lzwt@CXpgRBJYd0UEnk~=z%d_XB4cIN z&&BS(XnEZ}chF8BUWZIhnWd5b9*{(*goLdy}NjY_MU#Us_tLnHm>yKQ~qoK-!bg;wo)7^V+WSM zNh{JD^?mGw&|rLb?w({CDR|b%g~)MQUGR60?@4eOtC1 zH+hMlK<_03ygfs^4{xELA5h$<4-qfk3IA92hf#s``|0!}iN$uUEA`)Yy@fwl19UkL z3Ed>S*T_Gog+ARI3J$!ppznps|6YC3(-Pdu;qFxS+8$#(hU_sQe%Q8ztEAz)L^0Ml z^E?vdy*mBV1&PX(%5XEG1`Gv?`)ocx#n=$!)@ovG#mn8rA-BiXBhIH_)JGQj@Qzyb zq(J$ybzF2G6!xUMY5#O@XPkaK?bo`(x%1v)`?#n4U)g+UO+9LLHCp6bxhtKvby@Ci zEW7R61Z8x1_j%=Z&!v3Iq+frncXZ>pZm79-(5|^m4Q>ZcgIaW8 z)a4w#eeYn#d3!)79u_3LymIyK*}e?ivU%zf-ZFfxdAz#lcIK(t))m>pe@&T!CnB2v zNZmcSIiSP37d~&u8PX+E)>W_5nZlBAs4?aSZbG72`Q7FA zw#(-NOjpMz_vrQDMWA-8N4S*#l6|mdppxwIEL`WZNai3XdHWuo)~$b;P82~J9Zkey zAWH^wUN}wYVno+I(JaDvQ1Fp-tFqz~Hik6q*6#CVxRsMp3D}K99o3|%erKGf_;mJjd+QBV>K$+2tDm1~eg&K35(=ynFl`e!BHXD=_EtUd+ z%hyYJ^LP9&JS_Z&mzfkFhT2upH53r`yCUl{m}IVngH}_E&?+pZ0wR)UzbzGx!Z@(QFxDJwXz`>+t|4Gw{SR_ERsD3 zlA@#W1HfI(gi<6}T3!G(42j*ISd4HunS{E&+fEpU)FVL%`WoLX4`1I@xRGZ}Xo7I# zPy`{+e#TKqxKikjj0Ec&mLM8>qX2YeouG((15#3W1%W<%47t&Te3k+M$zB}TAstn< z3bs@sojRt$ryl~*ys@qjG$o;X01qGhSom5#rh7WC+Xkys+d8I{u+U&NRH(ViOjboC znbj?&)%qb##Mk^TUAu5tx znxV>&2A&~W&;fWQqvWz^{tH}t_k26f{Lzs@3=*jc&>Sd~-z^jXnE65{86wn%wDHh6 zcdt^s@wE=h4EgyP0#_(J*=z5jT34Z77_0 zuoD_`99OdvL;3aEy!fH>>M>%a>3+Wzt+TsDV#~-G7=iX zN1DTjp{qo(MapStYO?rg5{9x=iKW7vX_eYd6r{a(zMD=-Z?8jP@#Wj5>l$$Y_7kbf z22_M-C_Mm6qEgr5ipFjUUKsaSQ^tTFNGDV*oGww)7An@TBU~z(wJ{63_Ei)8Y zcA!!_fv>g?iP>S*@4qKHiEdw7Q4POuD^jbB<0p|S#7q3Rx%|c~dcS!kWD;7TV^5Js zkZewNfgQzN<9j5g!%e%4T@Ik;mJ4&cV?Jn`BfVm$EyIwVN;n>|oX~o6=KdPpt;UyD zuqi>Yr&aY*t$j6-5$V8KcggYdTtXhNa*1B5t~aC7rJpO(;c~#4c50v@RVKZ8@X($1 z=7jiGK8M`h_ijSE!-H~Lm5A}9H-B&Y&g;6d?FoM2#EAANT#Iudn3smCYAVkU;uVKs77TM~b`@E6V(dk97ZWtvDq)tZ z*FhHX)4%G7AY&O|I;jFB0qo+cWnMPP{Z)r2dZYHxPeK+_2+dQ;Ml3R2Cwnq@FkL!a6h7RB8Ctw3}NcZC|%rAFKOl6?O}7NwhOba_UggB@5~L zH?3~(;aKnQWxOWOa3i(ol>Lc5%pA%xQ=~>ftKhU_`K+UHN~T7k!Ygs1w}D#g|YSaKf3Dh`roV#7A9r84MKX34c`Pr@Z4H59=S zZAxfgAKY!4rTIOBK#6D7;D0Lvrwf*Bf!RtX5d1P6_?XY+S8<$DCaI{zDp;|nex|CG zJK+k6^J=Hggelg!`8~~?!83<0Aa|QyavjoFM=eN!;?$~#{{*__z*QEhRETH;^w=TmC(ytYg5qkm+M zT_ivXb5ZZlCvX<|$e`v?m%PE9QG0jX?LG58O+iFtX=$+&c7zOTV9W?6#=S<6EuAXc zC=N0?qZ}Vf*;uk*;;X*hFF)@Eb_PbQK|n0sao+EJ=kn?Y7CC1V3f8GPDVh`3m}U?5 zFLRQRgvkZ|6bnN1I$Bb7Msu*nRt!afXJ=pIZ&d-kB55pS*fR8LZ614=5rckE(t578 zcG$uzNiTc_76$7{jbB{Zpa+{>#EVh&5n^oMLMOq~yyV~Uw;WHelPrGnwd)Jec9P<= z{^UB4N^r7WZNDe-XA(4-wdq$1cu9U2( zk_ZHmAm|`Bz9*{?1dBDNKo8Djxjua9-NrFd{!EMwuDc0%D1Q1~VO7S%nJ1PrZ$jbD zEJ-tRbp#QtR7a@$xXzdDoK(lh?V1F0TGWfLhhtG?@XTGA(=#v*zr%iKE?o|E4$mI+e#&t^qr^6j%Q>f}1 zxQXZZkzr8UaYb1W+7%T)+;ZL$U!X{UYzfC2swbN?8Py`fAVU_+F%~$49obS^=%p%& z!ioWlKXJzyOaI>MoP!pH%ZacL08;x4ab^_(s%p03XVW;xzV5`GdKm8 z$Y09xL(t4%{j_Y{JL8p7e6tzhtAkccUm|<(#({E&L4NP8Uw&PwIOkw&4G1=v<}m)% ze61B3$IxQhvR9&=Cqg3UaS~sIz)Z|cc%ZbMvrtRTrPVZr$Sgt)p#7)#Tq{?ZpwS(Y zel6|E9>{MzuYjLJl6SZ<#NY7gjn1^ z>k&FrIczeKnL@^9C6(i}YBk4*{kDg01kx3U3 zkNfX&P+plWbSu(uK;X&~LerNdnHVT6qbTjcW+;MNX1_ovtFZC+?*RzXE1;ik>x`KX zwvqkk5H%&ogCznG=0+hgAuwmoDrEQANhSUyHC$rIA|jB74)n>;m&<`=(l92Yo}gj+)5R7MD#8)nc9z`~5z4w4Wl)lb=|Y88k4;%-Kuj-W zyw95YmNE;W$2TSP93gzf6K%53^gxAD6n-`Y(%LOUqO&81!W?u%OvHx#Rou~|*ArhF zV50b7hLUmY4l{p9l8&rj=*~k0@7PZlV9NX(aPEr%2X+RD;JX8dBCQkT*y41lEV0z= zM|zqh_E?Dw13f|go(zqVfa9q09`SPza+Yl7#sJ7ka6^0Fd(onA?)2k}xeG;u7%5Ts zO9uCK&>KL@jEaqYDLH9A(j1vVmJxnbP#hiu72)jf)eB*1p^5hN+yHC-tQrD&Q8&@< z+{A)VtaeTcHfz@P?#az%f)_hsd8q*#u6mwNGvvu9iv0cC=qiL(ipww zmX|P-q8AZ~tZjyx)& zI1YttO9(NHks(IE)cDExUPL+cmk7^BU4}8_OZkC(qRq%HHaWxoE>kq;_EqNd-dNS+ zj0MP_B;@arjJ1e^TKYFF@b}Wdm@t1lKN+43Z(!B~ za)X>wvERIsUHl`8uG2XZnEW7!l;ihU85L(C#AQl5+NCIT_E}|EDd;+BRrCYWB)!pA zf3yc7sDV4s<~`A!GC}e0edJcw>-jT&Cq* zMw24xc}BqrtdO+sfyLzj0lHYyOIa8|pylPZnec&YeaHa7CBqBT*K_u#9jqUco z!E>YPXoUWv%)BP=t*$^WCEF||@;)>zr2tECL60tsDJ~(}se2j~WI~f-xxYp-VASJ< zL7(r-2laWH4mhz802PX-ngaq|JkOaSU zqrjRKYc&W6QL(zFP~vYm99*+UxGCcY)97Gc(~HEe8dB>Tas zP>>bF8#ziCgWomnZI}$rnhYiHVJ}x)pteE_fv2f)m>TyU!bDq_Xe=?3Bbi#?n{fYT z#W=F(OW^T?V6LWhpiuK#WS`g`p1+zXfsfP-u@Y9)s3iL?j}oiqNSFDo@n?ocm+WEi z7eE#$!Xy5|&sfk{i?Zg3l2jy7I9H(mh^L5qhhciPkVfxVj;4@GPAJlzH%r*tqnCsz zp&$irJXr;C!lSwCrPM}nuA)v71+f_7T@3UlQC$wF&9j%wQLQvahz`@Ma;LY*8r>PB z#yBN7syL0IK+V{lxnt92SJxImUFfvTzJ|64{zUZsiYuD-{_L97SpKq;H_E|2DVm+WM<+g({y$V-|d;;;;WYl5^Kyv*%EA zU6l|7;Gw^a_xm>IPxQZF`YU1e?2X`W?(%Brgc?Hg0S-!_#-=pxu#!&cUvB5-;u)2d z*N~D=>7!&40j^mIp_!5=FsU?{K26KboK0@(OCpf_@{qG{JOr`5wpl02HW|gvbvC1D z8#}+iL82%l$wN;;e7}TanmwHX(0`o$TD+ky4&|VWKflC5i@PxD4(_}3D zQG8V4=pcx_cywBcxxGe%R4e^d7=?<9RFJd~tK>L>0|w%}*TyE;$MnPqeU% zj`W-(0d*?mwB$ERz%ggwZ;2BA#|fWVEO;LIB`6&(w)1rI7MSimqct|8rs2dyXK_;E z(ma^yu=GdSMZ8@S;m!TUugmPpkpj~ z)*PvNoOf{iB|U$CfeM&cHOAvgj{(6(Rrhr}5ltGF9(Ms}6gM@VZ#x&V9<5VhE`C}+ z;1@OCO8riT8K42;*^Pim;I~{Brs7ZH_@&I7Gr1LYRsIn<>Ib8C4H z?f(gu(7h`E9Kii?+BW7tDrZ*Vu=c#xQIzG9DfgqQ)CZwe=UeW%+%QYf+x@2XZ+oS* zCfEmu?7(I-6dNjBin)uvnT3%Hk|jo_)<8u_+llkH!e^G_aEQBTe>q>{x_&fP*SNoR zsU$mSUzRTZuvTG??{-5gf|Znm-@@{En@{G15cXJ0MwLclF-C#YGHm7&*${%(nKd8- zOw3ZmX$LMxW2JjTOjVDl(baFZm=hI9yAZ3u;|9YiPd5f3w#hcyol~|B?8ez$|xaj!pV+5;l3)aD#fY(5pyj~sT10~7> zXjK?Ho%u8#|#IUxjH z8pkCSc~O0Ek=^6J44eG;`$t6l`-7KrFSjaPQawRIV1(5QxEMIx5bZry8nkDCx-+^; zhum%a$R<~alb5$^W}}vB5|&quW8H(o1Gc#+Bc8t%3K@eRQJH1-qszzaTUtRb)Dix- zc8cXN>~B(*q8XvDPC@TVLigSQWSMA1KT&LGC3nikkR{Mo6QIMyD7Zr$5)m)q0GfW1LJjJc2_7(< zyJJ&)YGh(_k_~kl*rN;*ic29XkW+Scr%v^M)g`F&=|;fBSp)F75jxfVk@TUA;n#b$ zi`;5+f*Brl1uh62v0Bg~RY)EsX#j7C?vcqoy|OvH$~1WnqD)Ho2rVIrzNogBsR$)vUB^CF5Ba=wCRuYS^JN%0rJ*CW%!(RyTL{HO`BsxZpN zQyy$W91~3k&--4PVpH&oG8u;ylX3<(Pcm+w(!iCE23cD4FJHb@OleJCPHgE*OsN2| zLN8lcN-BdA0mC9X#vdL))|C?+#@oRc7=>#mILf{EiPpHyd;{~1&{U@W@l3>#I`oms zm=e&uTLWNjZsj2Tho&l02Iuwcu9FMN0)uD=1`y2Y`=DIR8InO z3cc&jLpQb~;tSs6rcaYF*7Q5~wP`nC*?d)d7zq;0lllwcK>%}Sp?cd*lM#5pt zKv+$kyFtZwcT4V0IO?e zS5Bf{H5itE6dYM1uvPZMFR?Uu@6r(h+ z{_UfqI6q(x3&AoZ$Z&eT4nBsJrK9Xjbz3}Q9uRYOt0%;8-iKam)mePh&WON^HHsN4 z)Ewbe4SSNnuYQyK9-S0EE3RD%(Z0hKom9&uGel~bGHtCxh33JO_7h{~R&gmoDg8_h zH@jauhYrK9?PvxSrzBh&U{+lw>rxpbuU}|doS06V`tcmfWJkS_lG|f4woa7JhFJz_ z-9#tuLGoF#{X(A!H`3T5VL9{PQ@>n3e9+M%5`{!b9*%mv4wz|YX|;siQop7+f2ve| z;hpzKR@6e!?FJbGEy6?CyT9(IEWF@5Gq#t&#^0z4^UQ)W17##oem_lmTZR1Eyc~sm z-BQJKl_M{NExuCMjS~x=Hc2m63pt86O+{29Lb8L7eu$$M`X81@t>iHeBO~}T$wlgv zyS`s`pcU}fgYZjrFupCGXtj%{jqD^-6B*%{WWk2@D@y?tfhm9==m04DepYS?DKWhy zNK$SX(0#{m!41GtDe3%S8(G@dbSy)ShSe&a;eNSEi>5Ye^<#ZE7*-Ojn69~#Om!NN zJ#wbO%=;QxKf~Kg?;_2mh?JvmJjZaPuaSWCh=K#KytWc85d)H)4hq2|KpAICQ4#tR zA&FxK(!^=TT;6CjbO$Du9_+ea9`-<^5A@lfDuDOY#$E zDQgXF&_s?dk6M+K?W=tLulo$zOBD0yoe&5LKLhfizw(wA5zVvYf`+;F-ztC1(AsbE zifDJ4f=>E|AL!2KO7D;m|0l#3?fr{TBVF}FVs8ul9%+qUarDzmK9K)0` z&j`yG9TbQ8;a)kraF|CVtaSQQ6kLhMFW4mp4Mu-W;#N{~aJh^7enrXz#0++Q+zj?=I+sqA+){|sP2*+ayi1llYOA1HL>?g}A zl^)v_Wk;6HhbO{3wBJ(iMT={4E;}tf^ z&8Hke<7C#S6()VgWbF`Q;>C19cfGSt&$-GdnW7Ya<%Nlb|(&k**( zQgVNkoO-%UA?64XJPci2I zIs6)qkWXPn$#Ssav1%b_eh7Y|lj0j`qCO0LceIuK$pc-TcZYu$HBhn2VErk|r7&0t-PyJ>yvTtC6d7i~pn5K$r9 z{>E*9pEi+ji;O}lKWU;?nor_FidDcQTj6r^=oq4Mn{(#vA)))8TAF77buc;xBP$s$ zjMyR>uSmOlsKi=l^93_eQ`aJb=Cg$RG0~(QF;HHubcDo;-yKF3SHn6Yj%z(6K*noW ze#9U3+)U=Wrr{Qm4zAaIp5j&MF&Ytv6=u9^vTI5(9CmE0$9sn3M3HUrtZlcU;#H#l z(TX~0AoRP02(Jq7Ih+^vu>o>}Od88)LjA_%NlyV3QpKzV8_*QYYb1&%;b{|(r6`w7 z86i6cS|~K-E)7*lx*HC>99Cfj(-*ZZsyk*5M2*{pvL{usa{#wOspm(bNP~XFLd1F;R@P zAj!}ZhB@cD&iG~L3tN8q8As~wGnuY6>CSy65MGgi< zEt>_^;tZtN0mXPf^3udY35N~S;X)7x4aZ?MKK322N={MjD`vk@k&&;`0U@XmR!zWF z>}a5+hz(Ne)aE6n(gMlHPMq-Q)h?f68%*#>cT+@;0Ii5&*YFlUqvNWFV68uB3XVhB z=QXnF6Awu;^KWvupnjDKKH=Z|`bre7xeawtflp1DNt5;vsU3?likdzOeMDRQh62rz z1ifpAwCgUA3O|fpG16Z%K?w5;pO%2?9qZ;SjL_7;uvsp^RFGmLeT1UhPR;jWAnZHq z*3={)(p<7hWbS@h1R`zm2fTyUf>yA_(WpgUsCG=7DnX{qw;#_knVT|{a^-U=VtXdO* z1m;hjdYaD2Z-+k-v@|h_pe9TRBAA$rJN48d%o%)A`mr1`1BdnaX{gX~82ziwQiZ>y z_7!c*Mig(-$;>Pt<&x0YE8o#U*hab;1>7a0&xE|I}N1!UuIMipB~4w&&V#1;3J(Lxy<0WHaeFdfW+Oig_T z@usKx-ZjG^jCex}QTp4Y%Kp#AmV1)T`t3i4>=mZ9_EIX9lzqQ2U2a9C#^CZ2OhIhV zWr?-+*nN%&Ezq25#!Nt+`fRv$hcZ^qLzpJ1h2kg8JqzIDnB&&3H3IDa#9v{`E=H~7 zme&ZGB10jx!Ngzqnd(Oz^DV#Hu5LE7Y~6$mD9hZ;p8 z6#8z(>^`*vqa~~DnZkz&T1@5^$EaiTA46g#;;j&tO<%@ZyPEqzF*HS|-ylzImD=uK zhjJhms_FBrQ|ARTtz8ipEV1uoOTqXiOypwbQZH=nrnpYL7h856->Xvb zA&kZoh4P!7^Q!3GEm0{rF}+?1GsGi?at|ft|H>|!6;o5v4Ws)}OxG>*_bU=XD7QsH zCjwgF(J4fs#uMBE*v1`n_JYxEQ8@xNX`{oiNTJbl3KpKR4}%A?2N3^| zv_0iiG96MC;SFozxDS{jK|66-Bh6W$+rLfeWO&6hxu;KU#$%=pT6l?$s{ZLmQnMS2 z=1~}*imxxkY%6;5 ze=jbfSjyhANa}2L{L|WnWpt9HqE0xywk7^8BFjTYhg<3XW}*B31V4lpmC@JQetBwH zvNUR4^rXpi<#s_dDg=)2;fhGO0kUS(0U^D)|RLnB>K%Nz!1^Jj;<>(b^bKtRuqBPKUDlO{9?JZjr$|dvG4KZb$ukGi7u5bM37~%!^CA<7|TSzb-UXR z6i{0*T{NsKrA-#>H%F;Dg$3Mt?B(HMVDZY+VzTP+x)RwQ*jb)=4b$}%kLX&X=~3w8 z*cc8{+2PcMu<<34EBRs`z_JSr#hS$Dl(qp&Vs=Jc%$`?^hdDweVAuqPP(GnKdSZyF z=;xYC(@v$(AqF2)b&EyeGZG0CBv@?AvnUIyo`eghOG*{F1^6*63Mrm5M;uox$=a1SeWIm-FXkTYC@Y3Xk+x!(eA^b3?MOezjX3H=mjXxNGddqBuScFHANMa9P!X+1)V7=c2wj;PT3 z2@Y>4irJ>nH*}$qs1qNPULT8zJkvKnirh>b0M(q?D>F>Wt92TTa1Si-vH$2U5 z*b4mrUOpZ7bWy_ws%)mDehV)hcQC_ijt!H^wAKyNd?*n2daV!VDu(ZZb(yi* zv#C;X@l?z4g&YZ49Q9kwlmp~WO{nrheyN;6?1GPrq^DS94%WwA^JDA^DJ_3V7g268 z8*uxSGxp&7Q=1HNb}{4VsH)lSHZoq|D1!go&3tt@yo+cQl_E97ntTvx#7>Py!TNomPOdPJN8*ru@h8-RTKU-u+N16Rs zKN5!zcO+H;sN-{woai`FsmhE9)+0k9A#2LvZ4rV&S3o9_C4?L$uU%V7wZiDB zw&FbwvJ*0#q7q^l=rx+QPG@t&QCrN&lmRM92gX>pbkNr>V71Y*JnX13Ghaqa9?(6~ z8_u0%f>~rYYpN`-kc#*{p*WIT81d6x*e0{LZi-!C50)|_G5g`Q7YYy-iBhMOHQpOI zmOg;`ny1a&kD4S-rHe$}`pbLs?-=D~wbZ0eGLul6fQ)Q)p&$=K5cjvu{7%ibNNOXe zq;v9`mi5To#SdFPfA2O|`t|W(q zWo2S0D2TMh(@%Cog$p1voSJ#hsoFR{X;Bc#7f~OO81_JKyIpX&6ekW!9X8ntv{{n~kXCM2Wux^kej~RNB z+T9!()Lzwwnyweo)y9wcPJKhk~tR)en+%fsF_PA8ZL2oyM>`YdIPJauBabl zxc#(AvHw7uJ*v=DdP@t>{rp0fXgUc$j?%&S`%GKVAbeBCAQ5@OK2_06wcciW(oW$vU}Ka~OWLmhBmOT2|^;xH8mdG#10hHNQW%a6gBP5VA%wW|wEi)E2t} zzvhW<-Y%F&C;&-~3E6d=kAo#j8BUFVw!?1hihw;CXFC^Z!JgDNMUiMf)ALbx3ELfT z-MyUr{N6tZ!gU&we0ko)=NM@8`XHtJTRsk5`j_wi(6-XO%B$D*#@UiuKLbK*3iK2( za0!K(UD6ntR9aj#uIWjum^E6FCve#Dyl{m#jSe!Q#5FWCZHog0)_d3o;UR?NmdU6eiXQH zMw0U!R(RR^z9bR9kg|XJJb1}J?g^U^s0M%PNB(LhR=alGiHCqOdnm>n2b&e}_95Wy zE9mVyZ9;L}x@$8b-ce3F?cda(D4sfJq9-;!LCniXp_?}IgL0v&11u8&m z;vB=Kyf17pW(aLUi*C7Axu!E0pV)<+xKnhoQM^i`yUV^iaLpep3nOWIEB&b#ien6A z51ba{eI}`h#WMh;ei94pL@d?*92f(8g&8sJ$+>=Ri?&roS_1b9JR>)=IEEo^7~7;#mx>8oUd;(7=zCD?_*+Ff@0vdmttPX zC+ztEqWD9M7gx0TA7ziB;)@^!vZytgtS6qMr))jojq(&&dMuT;kt;_SiBD7tR7cmo zj;tq|ycV(xW2p!A`r`l^VEGR^LS1rXkSRK-m1ls{G&sIZ=ffGuiu-Z~KjI^xH*cwa zbWELNtvbM~92_g)W&pFT29g-lT!Up1>QxvJ#E>UWR-0fV@*mwliQx;MyF0lw+Zz$V zU~P_5iQx3sA5^9Qjw7=An;qh>px8IZr)R^HVd(C@y@cD{ni)Fl^hy0_*PK3oew&>{ z5AbQkorVQ`FZ|anRSDw5cFl@fhR^ioIQo+vZP*xaGZ0htR6~1TTBLObXXR;IN5nD540#caHG`iGi}V;Hap+Sdw3F8Sh?M&G<3FM`6q2 z4V^epdcz3$t1@=B@s%tEa!uN{fxlO-_ZLMXZOHcp9`~hZh>O$7N9WrK7K~9(|9hY@ z^mp8*oBRkt9Ql18uSVV3gTTM<$M8+%hD(uUAvsg#ecwBl##F7_;cy`ZLD$K%r|dd3 zZ?jMm0wzD_<>PqEXhvC0YlWRDtJlKj#E=r~bbT#!_Yl~mHJd?lOa)Tqej@eKblqCs zeIE~Z?#C|Tz2uM80P;+I9rVxxi@ioQZ<+eCxiB1S;mVi^KFBCw(B=IxUZgSl^yL$+ZEh}fA>sI94WXF&5B;&M zVEiR(;*9pB*Fa!jl14TI8$AVk9*ahTiQyA(C20kxe&qHq@%Q$ie=y&8j8ASx;W1y@ zgFf!9y+h@s?=`1X1GhV-5Ma#z3?)KjV-1Vixp#f0M#uj904h2O8JYD@aiyHJ35kpl zaVt(Xq-Z{CT*C@&5|YR&qL|IO$G*dcN?*4)Z+nBd(|d`v{J54b^JGtVmg=rsUbC}Bau zaoAyK5Ac2a{1RIJoz3ScF&i4s^{Syzlwh`LzcJ_oM(_16yJ5SJrq#8P>vSOacb}wQ z@V`#nV1^}D*Gm@Dvm)adWR^~SHCM+b8syDrtRtelMv zW>|t6q#f1vO%1QaOHo=&t5Gsq3$>8unwa@gUsX{*QNz4=NOT#m=35b1jH1a4RFg&cFn;tlP6z z+Um+3lA!U;DH)l*ENPH1xn=SLF|RM#XRM%mu52m*F`8A>ADv`PZuJiqc`2}rgc{Np zp~T}s#6AK#39Z`S4OEy{cwNa84*h!-iUe#8-uZ5Xq>>Utd�T8)t@c9s$!n^02c| zHE?tlGAA3n4KCpdwt487{<>LCNEkb)JoVS2d9`W#?t=&t&$P6~zwN!vekgYlU~x~Z zP^v&bdO-7tVQpFzn39*QVh)GXP|2XVpm9AnS2Ycqc2I$?5S=Ht$1KJRxT>*!>znuO z=X6&!v1!B~!dSTp491G&k1vQaW?;dWP|xK+9qn;n0F`~V@WYv|9UK84-6q7^L6To4S>g*$7nc}O`<{#ksa@=O#e z!On7PgR@Uv(S;u0*spjS-Wxcl;(!CoEe3T(pg;*~pQq#CgamneJK)#}NHZk%)8!@$ zkq|myc_SI&0!2H2Z14%vmsCTEo2*A0>+t3I21rw5N(9m?vSqvzqKK2E|LG`FV{*dm zD!+!56j31AF%r$ZsQ=)=eD4|P&qwm{YHb90F zS8VDxwdmTL_5HoK{5ER3vEu+5>PxNb+5RtHF5o0Uu3j^5%*SNY2@wlE_Id2(ugRVy zD^O!(+ekgxN|P<}cYF*~LS=n+(;z6a*^z-i#`&OsaZh=9=?;f|qY-I(FIklTjIVSu zU!=8g8smR8?*Vd8^4TVR%mWGGmg`b$lv>y+O7=A1zCGzCj=nBn7r)NwP)uwY@;lRv z3A*UKQpawF3mH)*)juSMFc3H;5)ttpX6fRWJxxx=Q01naQ`XnT0(?NPH1;wUObciDk*#vn z8qqm_(g-qBEVsNfIhE0rG&=!PUR6srJ7Z;t5GB#%>^XJy$d$g9Jhhp`gIl7aybBS0?MjGby{lb_m6}1JFr)BqHr0%>ztsVr_C%c-O7Oy>+PY*7~;7e6s9qNVTHtih? z_Lmi70k8NsE%TPujXJ)LnsdLk8DWG6CmS_$xiX|cKDOG$50lf3eR=mleTG=KpAmT? zXv{Ji>cQy(>5m8Q1+f;RV!A#Kc4&2mk3zX+#qS;7@=psA)4twx7xC6B| z;;Zh8cB$}xyEKel=5|){Z`QJ^;rR10Kd<(IC>6RXhO8HGEWHqr=A^;s?5e=#+qXP!!8(gUq=(poK!;46KsXQycrpjg&>N$aE^yUl17$W;WEDYFz3}DQ&RhXnihPx^pFZ2 z-!Dv)S>~Ak9LehEx|h8$;soBnHu}P&Qr&B9)-P4tm-8VeOqbdaof@ulOEK7@i+p2D zPIPBbX*?$Tth}W2Q|z;i#ZG``wn;d#4B`{Sj( zu)FO${bYMs5Z}=bub`>l^MRF?w2a7aC30y1MtO{j>TNDWd=NdyR3$*0rdTk)llH{x zSW}b0^G?pVaamCatyL2LQ@SlZndCs!PMVAz!zKV1q#CMfGWA@do5ZrRC=tc?$TV}n zK*VRbtCg!}+N$mnjo^kAVg<6k>uzP9Z9JY_s=8xSkpgkl7_e>4R=PMOdE&fy28@ns zai|~q4!=smF43Mmpc7BImzWs}oNT27BQg%q#V2638(N(48+Ig<8PG_M*g5pOUAmb@ zc9cN)#morxI&mEpO>D+0y#Q8h8h&0$hu!FdIx$2kP+}kkNqqFAFsEOK;ue~jRSlAw zKX&GIP{m)-JeY-}S{QeguumbQ<&s-d2?Pob(i$uzzPl>|kZGg;dZ3f6Qz!^? z|4RFtR=n>oZ?Ej9kS ze{l3zQ;PsTbH(8XB*2bdNU(?N>kaMaA~0;^kM}gIyHc90bIJsb5kyUZ-yky~Tn6D2 zs}C;Vi8{o^Joq`2Lku}FJ$4TdA+BGFhvA#g;RQv~)~sM-WQHrb#l&6$U)Y=-V6Z*W zNxH^POHh@NT8fb=4e9Vi5Th>n(;lIUqC-6z^f|`KMDhzZzvmdIcV;6jkQrUf#+A*o zYFX%HUu7>Ind5WG**0%VVfnJ`27Ft(zj5FO-79Q|KS=du-cH5&{IE2yrb#7XG2U-k zmY3lELlepn+HqS}V_3%nrR&3{Ib~Hh%bkTsMYtvcs$Gi4RVOW9e2n}k;_=t2iR>xt z!W_1^1jt>54-DUTzZqky6mMf(-=e!?xlCC(ld;X4+`84l*uh=34^TI#gucC`#ZMldUi?ATZ;GZ?B<2XcVPX7xfls^_dAupTpEMt$tY5!|LdnN zQwtnM0i8XhVz=iI&4nKqi1EG&f%K9+8XBaIa(e|{nFj=G`+VNbFO}i(gc|>#3k7rpM5783rzx8ig7^% z|GsPUT#JJevZ$ZeMR&x(e^IIg^Gh$lxoZp>gFAbG(Fs8rEw2l5yrT3H)<+uo*%nb$ zh^A~P_BjWdsCc6b=tC%XDI47wLPQe%<#u>J{QC=mC>g^N{Y3?nxge1nEh_(JnOTuM zBDW2_3oI-zM(vfjf=&1ciJQihYB1s(TPDYc*AbdUNbg z!}@cmi+(_0FJm4yQ&{Mp^t)HNitW+9fnlH$V0^3Xi-h z1%C_d-s7o(dW2>2$9J;w^&oIHLDtV{WKzf+0aN$G?JM{!VHhCC)s8ouxUwEK-mHK% zzRr+^u|tcZy814?#zsmeb<&#2M z>b~s597=3>kwu0x+CMk$U*DliCX(luQ`+eX*KrF-s+8ce4Z; zh?_xi|DkSXEuupMM3Fs*P#1F^Czpzd6Va3gVuZ~~4dY5445F!WecLAchGqEg&Tm8A z?VaAvGion!EN9>RzI-%5DKa+ECqgXy!z0l@8ga7y;HEE%f5~9Q3BaKdq#ETkA-0egywHj&>&;b_YxN1EK7#t(l+7Pozv|DW%77*Td zl5<6-4(RG~diDXrie(5zCY6eB1!Mml z)3h~^jU;CquwwOpLCI_gW0eNJTIlQvS)(a5lmm|mEx5p#5B24L+Anir6h7&i+ti?W zinLWhqs~sZn%@c>A14(1eF`yzUb3g-Xb5X+Y%^(SyH5b_3iCV8Xy)*W9mMn)1-Kt+vud78jydWj0|6zSW4OYB+*DH@m`jgE15C+ADX0J@1lMEb`9k~xCV2- zNkuEWovECtL2H$%KWs;ht5FuYJPyxycpf{TdxR6eMf5n z7u^x}p38^!YU~j#6hIycpW)TW6+2jk5gQm`X`I)iV10d?(-S3?K~t@&Qg=!$w->*^ zW0LON4E1#+G?pQDiZDUYy5yOdA7~dDQ-gI{@w0`g%<}Zc0Bw=mE=7-Js5rO7m`UNY znCPxBPT2iFhqP)9tQhW(ST8#H1I2h?ft_nLG*JveLK$-q9%hAHjvm48cg^q(`IN%p z5zQz&qpH7ZPLYIpfefhUnd-yPU**2m_|B2VG8m6z-}PylkMk5$Nzr*}Ocs4QOsHAn zTTycNW?DHWRf1a zSe06;?9^|>v7dF2L!UB?l~ABYk;%(R+m=}K_K(rL@TjIii%w8ctRU=Fw{%!+nFa$|iEgCd2d)%Dzot zARv70CNs6w08fc2p#VQw#}>0TZV*ZSRf2w94;4-UnPtFq`J$F6Vlp3xazK<=(rEBb zbG*%g{?qUeYur|{nr?>$z1zpdMFKWYS2lu>Bq?fk62O-^6`(^w_{JKQN-oS1W6s~E znDYgnmG{tR+roM>E=99tND){8YyGr!3ZL7(*pQAqrC`&Ir(}ceDOR*m!WS$4BPOvN zKQ@C)9>s)ZvOxS-7Tu#jeWc#}GcANB@*fuKeuTv@LR+3Iu?*B~9RKelx11{2)Gv*P z?z6#4gyrY#WhNyy{kcqTYXkI`cdzg%tKlmI-em>kP}F~NNDM=zGm*}UpAcD6n>fU zXEP%|d>y!XQ_kWmlFf!o_lt=Vy!UTxd*ezuZT}?XdGEJpFxF!rravkt3AzTRn54fL zQ4+WRYo4}cZ2T0~>rHoMPyNUTQ&CN5l#&*noc6n>Q8lGW0%b zDO0d^H3lR(R*5yIg1ItFnfv@e4cNZVMZFmjH+fF5%3`OZERm4kKDf8k%`a>@wgFt9 z#!gfMCn^Juo)*FcKS`N-M~OVUgBndX$(?2`7*tp1D4PS_f>I+2>_(q_E5@|dEsOFW z+cS7;_WiP7{!9nHVGZVR*5Pk!A3i;j$*me}%R3)w)6f1vx4X|$`eKR&Xw>R9nut-o zWM3E>(~bt9*WQ^;3Y{Oe@2=e{6wV9&SoapcP)I@Q;CxPC#ZEmK`mpJ_J}DM9`SCDD zzLv(K{U+v0Oz{sV@WHpFG{5|7<7U&&dvTQ)&8sE!$SlJ2z9F$Uu;bn!@<#vmcDvPl zD9tIac|8=5t1KLCv?H1diEJDHQkMvpIZypR^)!teyHLD>`0`J6JMPC44hY{cdzN;yI>{ zw~D9rCMOM4N{rS%Zbji+wZgwYz5XFz05#+;Pe^X2bR_G4EF9CSCN%qGCHhQ; zzRHw6ahk}DOu>i%B8s{nb`tt{NP6>a3?B{j4O08R(^_4Bhs$L0Jw6~^m@$=q1wFm1 z@?zUl!5*e%-3coSka3Fp?0=7+X@>ke)8?>RupB#Z?TuB;Q+_2hP`3mfa?|Kc%dr00 zv^E2e=8O+>p_@Qc?H_P2%Ok_iHwwzy7avN4qil)F6EZnpCeYbOz_~KoKl%07Nq(BY zCyY&uvw*YW{fipGWd6FNNYRtH@_?nt#S^%%Q+ah;Ty4t?!(7gm30%fhuirJV=GNceNdIYY#MbY{1(#F$HD6%}G$Wi%8Hn)POF>$&6m z)4ve>d(Vk~*uu(5q-@?E3z)BdK1-;66&YC1_ji6^0(N_A{P!!3LfcsUU-2z1cEw6H z1S%L=RLK@UkqoK)3f%UE#NIiCvdefgG=fO_m$~MXDv610C-O36iO7wv-b;#DZ+~`F@EeS#pWS zCOtnhJaLTUP7YCJWm!ZpW$?U|M+EfJ-(D8j zu-fP~fiFFG{#%^HAEcc}*CjN-#2%zxmkYc=>sR z%T>nN%EPTJ86;32wbKWW-7dZ}9A8QgFw;5HjiXcwxAZ`JopEtb2fcMa((cvQ+jhlA z*oO;-P>%d^l{eu#|I;v_>&Nsbl~=Y;z0_}I%9o=*-p>d3!Gmi4b^DHJdRHKq4^6GE zelkI}7oRm|i=aK-F!s%N?EnfpC!@)Mp~4cgC%~T{XGBMZz1if>ilSeMt!&qM`KEKY z*>`YAo^f)k#Flra+4U0NyG8jT@}kExaXP)#^mE7F7YP?nB3oW3cN*1=d7gd2lP$Jm zJX}g?DzC{c>4=Mw1-63BKnurp)!L<_q>4u}ysn$$bpT?V#UhA{eLGp;YtF+stR9Vj zx!y`%dHy8RnGd+DJOIH%!L)u&vSRDNEWvhg>i2SFb;WWEtCzV#TOiH~3ip&mAUFG# zhq≪uasJvis6}_P<<=GI~P@?R9!$9)atzZu`=goSXOZ#D^qY)uN>Q1HOm1_a9#S ztxMdbpMturo);7vm5H~y*fS85kcg)R%cf1`ty*k(3{8JZRxForUs9JgL(6t`;E#1= z{=V{URV5g2s$0~~wvd*bL^rwj)*@z$MJw3kJSpaw$l(~%4)+!Y9(q>PdL7m)>SdDY zq&B>CVoU3Pfy^Zc-J*;xrH5wv)S6kt5}!DTDN9>|*(mmg0okFO<6E1;Vs>kg(gU{G zlU}WGBR%^8cuRnSjGXh2s|ETJBZ!=286-QDGn?7=y3Ba1?zV8AMIxZC$F(buwXTBw zlxJ!fW$0wrP4g1*z6}Cmm zd#PVUx%6B%e#tb}cgPHA)l&VxxVbt|@Y4&ii|o6VSt>);9krdE81?jw)L#bNb84%= z8I9#ghswuDygVe93sU6aQ7=RlLrlT4Z+LLxR5XRow2l-=?;F_enCY$a(cVXtuKOO>{sPe9N&myea~HW1GG= z<~4W<5YR}Rt*+c<&|qq1gbmGP9In%*#|10|jRq_OL_Howe;p273FB&$W*6x5NMEFG z#hy2+c@jQ9 z_AfKR1_pe5u7( zQK!1j_I)#O?0dPe%1%_rEY>z3d*r$6eXh=68n_6f!90%XW^(IzAFbyo=y*R9nGv?> z2)=G6AQbsQ>#O1D;&V09c|v^Vui|==E`!`&kEf?^&oQt8A^U5T*JM_s`v@Q=1*P2+ zk7ooPUHQpR@`(Eo%a7(Q#lYX%qO`Bo&okIOXS_?C=eiaZ6$l9MvyyBObh@N zxRU-`>&!c5yV4Y3A@@e!6_x7&+b{=UyDx&HS<_?c;>{5pRwyk8J+9y#zqarA;THST z@hFCUQ&2yVciw!b#y;svrrvVH&d=r0_4_mjJEg>fP=^e0UD7kT)yg$EHP0q1$3M}v zG;5@R@!baTVm`EUt0mocA)RE2%>VMh=05Vz#fn^8lfNcl<8Gq62W&f8^1Ap9Z42aY9p`qBUp&kRrhvDzy!zb^?n?+W&5g-NR z!`r%;FV7=t4(=rGs<#F~F?~j8rT=Y|BXBOCHxzdaVSKVTKG?Fj4XsZ4TnwO-SIk#% znqN{FV-~w-r<5K0=m#2oWY*uUwBOdg6R=yU<-aBuZt;z+h3V3m!63BTK0_5BwiVACu5^poOTXabg0jYBK8&7(Oy88R(B_6-4 zzv_k`8Byd*lqKXGa(v`eZfm~t^-QWDZ@(}2w236ith7&?UrcPyyfFz(>SAy9(n2PaqFT^{xNTq$N*ujW~flMXiuHCi$oeBm>%npBR%-?)DlBXvp02K&C&?@UaAwH?O^H$7bDQ8|_AUkeWJ+NU)B5<2H6 z+#c}Fy3O<oj{-jHsCkcpa>F9m8E9({z|eOyP|yHE|{s#5-Y8kkW`!_a1RvnVkRo zQ3?3xVhwR^KOJ9WXV#pMHme4_&puZCDAcj9=Ebj{cIn1y|G-hb$G0W% zZ&H09I|={oxYY%#0+oK?gW-sA5Oy=H!~t6Z+C87fPc<+7fb1CILdpzAdS}H^fa@xw zja*Pfnp@`ocB4WW4@Jk_pzImoc+9z`O*>yl>Xt__A4TFF-Bm@!!7kgg@k|oREYNw? zZ+mt)_B@a)Mk!&}y>mOji7YMZL`Mm;Q==(5xmZz&FTZ?)S<7Nn0o*1g^i?r0c@Vek z=$&LR{W7`8h@@t*)>#t~a3zjUpy8|4_TRfJN8fNwfAa(GLRM#;@CSb7sE`WrGu>pv}`p zw`{*l-&Vt&GH^T4-Ot8_VI&^Z>e7of;Q3Ed?wo0v+D&1*a4m@||jC_Iwfu`$+^ z+>d?J=IC^ORPG9c997?>>>(aNtj?JZKI{SMo`YAKg7F&0NnzG z|8TIHw!B5=Jn(EOT+n&!#iu5};x=9(5?Oddlw#N`;zkU>m{F)Bs?e+2!;SDK?Fdfo zflYONEIRu%af-O~wgBU-NO(}k_zs&SV}zCux}0jcdLw?R3w=T#OnnV znW;YG&8z&=#In=R+`jk~SA-(McD8s>=0Y6@0iS93Q3yUlS>&Av9dy!HEo_?^u0jP<|$Qa68aWq_;y z1)`IUt3Q(3%Y3Xi#GjY>Mg0!D87cHWQj)(NUvldgkF#m?PeZixu-5su_v8m1q6N|G zC=9lUljC!*8^tQ7kp0XhRz=61zRX`sZ;vVil) z;ocfKBxEW=YwbZx%*e0ppLr;A^{;qSLEjdl5bsTFIr4EC5K}OF8v3=L3rwaP0>JMp z>HInV5nC4VtFHKk%z+J_-*x`VL2+f7 zX*3}+Df4_tDx0_V3qxtkOPK*_{9tLz#`?%CGo$d#?$&Mv_ZaZ+E3csi2Dfg$LPt~* zfHaV~PgIb;52I(@HN{Y1u&HRK#u&IBqYPm8X}_+FzC`)c?qwv2>?$ zyLC7n^~4Ma;Ig57G2%~n;JSw`N-qa8#*65^uHwBTg;KD|YqWNrR`Fl1i z&qt>{NGv`FYc^@ZsxjA{axi=CSKWOc2sd%m=EA9BaTWl*E@I%r?rPqzum%ZkVpPs+ z2P}@8t4LoR({F|L14qN0MLG_sZFr@G$w_8c=Afx<>?Cen#@F5_31 z)g5Xoq?#ZkJucaK{P$xn;N9bu6rv!(y<=csDg2*mC5-OS6-o@{uRo9DY0F6w>En4# zW|AhRyAODgK3$Wi>+NI@2R9s3cBgoy!cW*39PoB$BHgi7iILt3qh)p_c7;%g)k2`% zMg=fZ>!(cyY1!N;4_NpwCN4sI>OniYF{JUSkV8C4;uXiit{_qMzQ?#fS7Z%BIHr!y zm$IS|Jw}VIeQNIb?Em4o5L=o#?1m%VX*7bHv4X{q*Af3q?`@{u)ghncranW`XPac5 z>uFR^d{6VrRBjb2-R7>@`M~F-&nNRGXdxg~_Ww}zj^ULwLD+Dx(Z<$^wXuzjZQHiZ z-E3?-8{4*R^TbY0>}--R&&%)qGuPdBcTHFKoSsuxbxoHxn>Tf&TjuOB*}aJ8MBG6~ zwMI#b+`k)rng-nu8JcY|U(cSB+YXx=H3JweCz+HxeA>{mWTgw*MM}SISCN&M24dQc zlw=c3DjG!^8=#CCzz$7*$m2=*p`8|^h1`9*&&VC5(xP6hQS(dB!!^4nGJ9_{QD}aO zW%@8^uSgPmDHLDhSg5N41NYtI%fd1+8I3`J`JSLm-7gaMhwKR#$3I@|EKDl`ZDXu% zCa8|}gh@Tmt>e3K?JvuoJEPH+&{$?~2;kDue5YsTv*%2MTFl&^I8d$-PwX@DyfkMKWN+*Amp$G4huq&G`KK4TxZq%vR>d%>N*!@nDWvESq{`ci~MkXRD% z19vCBNG3C}_>|MWL~b~|vCas9lr?0NnTlCXB2uGW7o0b`Si+vDF$?{N-Q3&s0T)c- znR-jB>%IoA_Oj`zZYiAzG6nC>ql!~X+eBjIFzm?;vymv)&s8R7T|L?qR_Fg|$A8wveB{c0z zb24`aUZfH@xS0lj_#cy>n;`6Pm719vulRSo-dQvv9UA?Kkh-^ewd4|@l*xMD3%!lp z?|SDO9ryOMZu7L)fUd1Mc4t2SaOu2idq6calhaWjelZqEfsroqWS+^5VC=-$E|Iyd zO`h%`r6rWoWyV74{_}qEfJq(2LU3(@r<^qxCxq@9!A*GY6t!XFmFC&>k5cdRar@)- z=jWr~gTd!VOV7vo=W9#PzY&Aa!>doRkKw}sA}_WdcpD4jY7jMsR`=Zi?tD4sO4g^p zevheu4o|m%8cPX8FCw@symeQ{f<(208l$O#m&-Va>{XgNe-g`?12$_lGc_)sZTi|b z0|Vr^nH-tBm5LCKDS2g@^+A#hi;nN`b_^DeX+m~S`BhewaVj=6HRhlI!`cmln$0x5 zf8Hvy#cMe7Lm6Dz-iNFQw7E{X};6#|%V5Q#TF)Iw2aGClSL7IY*mq_^$I2 z`&>6@iTS~*D{ctN@fQ2%BXtbr%HhZqYas`iptRdjYvUs2@{neMS#<(Ca`|*EexXM) zaSF_b=m>{`RQ#-5#OA7@qB#aTw!Q$OL@y|OvZ1$=?-f)2vKQRn`QqRT3d{Li8V!Mw-k#F?uxF9lH6$~gFzBEYXs(O{Op_9Gg^_;8 zCplkkssv1#x%;Kk9^7|a_Qv#)V^ajX@rLs&BL8bv=V+k-i6edKt3`AorV(cC(jG0^aMTe5tIrU;BobH%%tfC3sF zgJnq(%6hCOJ~Brs$n(x26fGUyM8vHW zc3!I(JXl1B=}k|*Dl;)Vtp*+WhE#Uew#YA)O2ZI!m$_ER4)qPNI4`DG%uYGMz58bO zEnBop7%0K)0#=6FFU4zuL!+9QP323Bq4dz)N$&Y9HW@Z-O}hCme{nDj@%MgE{QFB&`1`MGLV6+RVH7>B}59hHH&C!oDuQfFm!l+ZT{`>-TW9l>TskXeN!(Rc& zp`UCP_wWQw=!6kHO#}Jf+#GOh0=HSWmRxi%sSCwKU7+FU{5-h|HNB&e@0fOkiLT-! zQwgq&7kLitU>ydF3HW)!H3eW>0q31>W`k*|{QUkLRx4l+ors>ovK{wmg}) zAiJa@+dtfEjk&q35ztr6o#`(7lIbhW_S>=mR@Kok3IX{(E7b%$)nSV@hD<}Ae{A++ z-)d|*){pcEFcQUXgmIZwToDWjTp|&z(p&~(Y%kXFI`Cwmib!%2l?6M!iX3hFYlXY+ zkiluh4-BIu9JC_Y%yt_L&>6SV906q>j10cN0%W0gz@Ng21G@wWN2Y|Q@Z~O>jX8EfJd5G%t61Nac+z<8&SKgq&bL9qWgK2^+I9h zO-b}J&Jl}{_`9%ujJ)pQ@%4W*!0)RW;z*w5+;G)>P{OseCE9%Xk5Xwk4`mzc3Y(v} zF;|I`7pi$En+m4?N?_R8<8rlRYoQQhMU79Xr-$j`d@eCcP&7LOi1vjt1`6|sHq?&O zg6&`lfDNy4lT~S~2!zVl0>YQso46A22p%#FEu<(P{wrA#xP)-a*^8dC&R!ko2=Irp zF%);!SvQTIM+R1?d$<%J1P=uUiJY~n6TGe43#CdIBQYrw%A^S~BwSc4dHj|bQE7_~ zFg;iN9&pMFNm+(L+ucKp-d_MXbp(17*C@xEFkee8h<}d$(>yq6>Q8w@?R;Cg8d9Lw zeULArnw92Er3EWVHne>e>3Y{GTjO2&jmxhW3U3l3QON80u|b-h-PbK?h<5>YLxIK? zks|ftZ-8E%Ppt$o9xe^j@af+^&!cw8>e~APXT7sTH$iW{L>dUet@obkNVtI?VH{hm z=J+JQm)(&IVTpCY-q9(apZ^@;a}0zMv4A;UP!h!Cs|t0S-yFU+kI}TY3n;f%%pv)) z&ch`#rsl+xhb+?@a!Xm#t@&1u;2;7~gr!o8V)+Fnm2IDN-l0QnR;`#LyBVfkpj-+IjP@ytL| zPf}vF=l~)O?i7W~vE2;-{40zUm;nl7QKdjbiU=RXM|3G(s0#Xznh!q zIxP7;Uc>Q<7$bD3hIqSVWGd=UrQ4Y$+Bv$_`qjhQ%fsS2oXD$N>_ZGPALS8Dyi9Ji zVlL=T?}f0F`=11-^GYU{Q>G|3eNVV=?j`5;I{TW*<&>3C^Yz>s*&>R-T$*z&H(cXe zl1%36P|z$&U1Zkv19UgMdp2CjI%{v^%L0*5WQZS%714W<-=<~DnzAu%H21^`6w}auH)t)8f?2vR+mk}E88jaHE5vpE4ZcG=Gf&A9m+v5D2 zgB9P@Uotbe9E6ir1jp)lhe8Y9$1{_GVr$XWPQv+_CQm zK^Zr1lM`xNwr{*oPdDY5Um2uD_6fWNux;>%tei;&3+)!U<(0OnU{8VV%ay}dBt6Fi zo{`m@XYYP$%@6_&?#W&M+#*40>Mt{&w>1G>%PKja$FZm`Hdh{tcN>;OOIv>~UZM-_ zecv8^{kz{g<{o<-x|3a;cR(#Pe_lX39lQuL4(|XA=QnyjiKXoTgyX@6x7b2DvcaF@ zVeeaaY}tB_S3i#$#17s^jvLnA9hO~ocHT$)k!m`(NB4bK+CHBRg@JZ=2>VaK5zpc0 ztGVI^gO~Ra-{$L937sUpbb^rmOU4cEl)Vqej{e|K`nF>`-)8OhPc9kx@yoQqhU?c4 zg~a|%Pjz(rkK4Zd_V=msYX@@DMS5&DtfIfQmTWE?-|ZvT4RRQpo@At6rh|R__*B3- ziOxm(-JMx5gx7D}U4>718!gr(*LS9NFDBeRO@9hhwP(8Q&mwoZ65 zq}6^>LD)@Bh!l8f=Dx4u>1SXOz@#^u(|4I)+IBxSd|ZE=kCsjPM8;y^XA>?@f6NmM zsAH6ivkc_m*C>xot(0$em{hHAKQ@@$yss2$PZxk3R<+9;rfk>!3G{^bA8j&FI%-}3 z)?F{JTrhqPDL=ax`Hzfn?Rt>TOB}MJ_yEQA?|7I%9{JS|XFM85cdX5ScHAx(9058r zM$4HsavKFN2o1n@rM#BorP}Oqcd>!`?W;K^z@rb_MFoFu31ZWyo?8G>$ovOZL3!Ie zTfO5~&8<~)hNJ67Rx|>q!H9Q@GN)}>dx^Ddz{aP2=BxcvlR|X!3lCkf2`#={2W$xk zjSf&?oawRJcOt@v<*K*+bK^COy5lA%(>*Q(f1^2yaESX&4sX2eq9>tQ%H-eJXjXv3 zLw7fo9eQYd6y$xXY9h0y4^M~sY3BX6;4OZLGa50tWtta{zr#1R5z>|M7d`%fh=k1@o3D2@oZ|9CEcL*$(6yCf1OHF8!_}}zyRPVG zrdQYYM#(Arq6kvWhZBbgpNWr;{6cA?RI(fjti3DtOrjunnyk=-Z9`&NPbb|AFst_=aLxO%f@)@XSJ$_X`)&DUbx zeVlXA^H!xCkzJ(Bxbi)B0=J#cK><%j(vP*kKO<9%vF+~}pQVj{M))Dd>)rWEe*f&Y zKkPIJO%^U-JKr}#Cz@kBif}D9olUySFMB9K!AN8-=LLnO-PA}6YA-$n2C zLeeR7c(NS4*u%POyluYf7b&o%k7S!)?k9AawvTKBf-bm-W+ zVQV+I8hAbT@gn>k@T%?*^|5JG@pYIjcD(qE_4+4hpP``Yk+4~G`*N-paOaLaoW0$W z5pWXKImB1l^G?s5;WzuZY`K4Vxlv=%HS$=|zExb^QgIGC^9}`i*cvFS1T<@{``I5S zogrTOcRSi9aK^Z3ZXcby{M$XErDi^3-qCvjI{sjrS&MwzMl77;yJ!YkjgnY_Cj)NR zI82^iNOY{Ibhx90phq6h2js`!dI+N5zn<7dVM2?+0QZ~MUGj9eTV~Bo*38!`-@%L1V52auWWpd~qb~(5{vf(L_w(mZ23EMleNq4Bn zx6gXF+2_bC%dL{+$R&DGi{*_a`$?BgxbS%Xo5B*sC>Fe_etITQ7 zQiI7z`r@{W@nhZ{DakkRSfR<^mhK?G!_jOD^wO=X6N+Dg!Ewp%# z5x49#xR?}{oQ}AMCmWXTxJm?vHfr__EL&h!3U?ya{f`b3_FcE^Kh~%Uq^1Q3x!#@u z8^J5-20foVr2aYru}w4v6=+s;`=?A78f<w7xy(p&b?&PENjiS3W8fS1^we-F7I zuMVF#Edigo4ef_7M6nKEUW>0h#sUAnDr0*-7k)Uyy~PT>Nv@BS`h9uHEB)x!N6P(d z*GH;Zge>C63;wcDm+F3}$^125@|T6CH0wJ}#jkN%WiPRIzOqizWR1ex2vz;~|H07I zNFJ)GdSR;Ri@jf$bw<$CQ`RX>Q!5Usj^OMnwpI9isIYy{{wY2{s&ckTVBz5MpM&1Uh)5jnfW2~<@g1m_R)mx+}`A#fT*5HVSqCizfpKn`i^2J(eh2T--P|=BZe?<2We96C>Rm^<#9hzsI z1rQKf;^J1xWtT^q$tyz*zd0y(a(+gZ+dpt5$rv8n6=VDAJl+zI>dx0`9&A{o?Tb_T zk1IRDqY5>cTRNHg;j-}6Z)CNTGZ&8D{=sDS*Znu6zKR@Jvs_w74Zoq8oMYJJm$m4M z!6&)upqa`U*yLmI+P{>~4u8QDBy`!|Sc&T?P{eh7XS^xp;gHh8ifzQB8hKtW6h9hK zsTv-;fhc?7DnLtSBeLjxj6d3s+OwVa&AJ(u%7|q}gOI#)5;tM_BIfpkzgnnjDXAMU zi}z=KRjX~_1%9L%b(-TKW4&g6JDowoh~~t5j~5T{B7Q#&x^ID*CnAyz@FRYI3A%s! zDiBKs1pPJTvpdyYAR>_r_(S}T`|I8Vc0LzRGC+>_oja)hrnsa=CqRk#T`H))&R$RZ zUIS|W>p1TK4dQpBp!-y)c_L)V03zb|pul@*4*DX)OK=1@Fz=``(|Y@d5L{-wGw3q>!%?3Abat zqXf>FUrR?$3J42gy-@_tgq}+!)=ZdKuw2IlFmEl99+Vj}O$Ficp9}(?K=xz;^XYMkK zpcKt$Uphadb|9Kt2gQHP0#3gDvgnt<7nK=rUCb!k!k2IFCCYzFd{!*RCL3u_Hz}FF z&~V~9KzQkrU zLVVLQoU%Ed71!VYiO(0PO0}#c5Ee}tcvPL`~1(DI)^Rhp{~^J%m3yxq`ZG!0k*f?y5gY*kmKj*k{+nKP3$ z%Ki2-q?A@mYrVab8E|jBeJI&2lJ*=+W0}6XQb#vEY92A$=8Jszp|(7r_$5>n_`Doinq&U6?4Cy6YA$&a9R&!jphSDv4#D#lqR?P~*bGxK?V z74SLn^YhK%^KJX%HY?}VAkL}GBhlgK$h5!Jz7u1jYqZd8?tTr31n4E#J_7B{I~*MF zCs#N#hMl-eo3(caVPu8KZ%W^A91FqG1b%vO`qKt)V7ca)760)?qos#I;#&{L3ZT4u zIX8k^(TmyeAQ7+DtS^In@E=-@d9`i0P~%t;l+C!1ZOz&WkUWpEkrG>2vld9G(M4(P zp)y#oYJlPT5h%o{An$N=YL-)Em^;?{Z)vTAn9AS8?)*AqKJE-JxQpb`+tUte+&I$~ zF@rR+weAD^V6etyYOvpPwKsCh)Ws(I0Ss)vmV41a`RAFZ0SzNyO%%Y`yX@XbqgI2o zsn6-a_p8b0Mzejgn6w&HF(%yU$^1DgDC{jEg}ceMoQ6~Dv1Fril$&0fT4Z%)q@9_DywMLAX>I*Tt-H<#rusATAp~eVE)g&` z@{jD!lQEn_!DD{_QPR~wJl@W_&I(qOX+l75YPhp;iV$7Iq;)3CLQ-Uj21MM_VX>U|{=8#zy%2a@D{eWEnmj8XWPx)w)9Ud)AYW9RjO zaLksa42#YAlmg+HvxJ?|&C?aTsn4tnrCRygcG(&$Lt==n1K4NAG;v?<1rbHY?XI}! zjIU7ah6C@i1=GxVtFi}(AB(PoP}#O{T75~7Vg5>5r3KL$r-C^B&T<^quU{(hu-JqT zsr#A{41XIPVX?Ct6dhgtRy(z+J5lA z=2qXa&M-NoDKgVkwDg-_zGL%l@5A+W_80G8Rl-F7;qkzKSWkWNz&bk&IfDMHZ_NK8 zFQJ$6nUFYjHmPxEG%g`8Q;wW@=1hmpiHZNv{w?PFU;UQ&clk_K6+N&;-@Y_e?8hh? zVjr7u$~{e77jUMUmP+e_qaA7JF#XiKf4uMy`8<%SHGb&<7E%wl7;u79gzL||`vkf4 z*JR+gb=9{xc8k94q=DXl&PWB>iEws8xSwx2);smR30kqRU76KXFw(yC6@~*ln>7E` z6+Q#4S<}O+NaZg1JC?N53Gf2WLM7GAfj%g#Ylh7=+2UH zpXv#E$InijiBSvb4cvpyjKjk&T+?4YJP=T0sU!V}s#@;(Lo$+trU;Py2mfWGY_Q1erA#IYsn|2;;E;QIE5ZWu0 zZX06;Uy0bD1iPjK<=EYp^8``6D0Y?Tn^h)wFdX?;NQmEne`tEvArvakZ|IKAspRQ= zussDP(*Mj%3u|tqHPHKdm6h1`uv_@s$isz|*WiS|FK4ajxIid7l7{lzE-rEtN5XD9 z--CY3pZ}F0j-_=DoSt4IkzXGZ4CZkemS|C8yh4wUdjQ~rG68g47{f7M+O}&s6Wl`k}=I-wtQTd=&qmZ0B!D-{>aERP%&7@>Pc1{tI> zy=QA@||iyC?USE=R$Ck!773n6^zaWf=NCd-F2+!W2Wchtp_fSkx;yxF_TA@ zFyV1*GC;--?H)0$W|8?drdI0^>_u8`pg+l>4&kfWUz(n*ifE5q`M&&2g&BGTj{rAk zQ6RQFv?$tozGMI|pe$Z8!T=$rkY9dIHjoBmO@(6#&;-pgBb^B6?}%j0qSBE`b(660 z({4~!6rKx}!`3PXW04r$=xS!HH(_aEc%mAU3R$x2(5>fGqUXFo z%DgO{*?hv4YOgLB!Iui+_Z-%_SgR{BdaUtQR zXRJ6CisULf?F{b_3lzIVRClw^5!lOkp%H2&&GchO=1 zEuaQ;5ui($8w+ofOrQ*xrco$oNoXE#8)r>i9`qair^Sj`Gm)f;-abaB!AFvL@s`|B z9KN@I-?5fow3*{Bse$|HYQFtSvOV(vrQA~;0VmNYT^8( zph6P0@{%TX3A9qOw(#4@rf{Tq5Bc^Z{tB4BR-{X;n2A@w0ZkKVx+OOP&`lw8@`&+; z2u%A~WnsYRo|X994*P<q;V&}DcWf4Rjv^r<}H~g3R-UaMqJ2I`#tX8?OAj}9^DvrE{Q524##L3q`*xWBM z%FzeLtV<|oG_0daJj6Q(qjK1;#IIC7feV!HA7}_UR1*Be#t&g;eQe6kvz|~XO_XGqM(mar^W?c?Dn2;8>9Rb@1E* z>&I2>b1*(2HXVbhDkBG9tc1~YrDq9TWkXO#QHXyV+(IhSq(+1=W|0huG-an#;yQC3 zSP8?V`HV~paB)6!+_P|=EVE|HhP4E^WL*d;&yy)POe?$x<}oJR2W1*#!cR^*p}YA{ zcpxi&1pN9@=3sRSK0dFo)-XQinPgiC76^}e`=F?MIdD@}?hsvXUBDxmbqe@)dsd|> zoWOOH6q5k!SSM`=6K*E6*Q=5tZ|qayCuG$~ASkrQK<@itsf74#dLuTldLQB!>}p?q z0=TAM%ISl-u#Fe(cUZ;vZzO%HsHPB;;cDa8(jzeE;-rq%2_@2`(mRZ;{uJiO1h|57 zo@-%+1MbyBXa$immJ9J)XI_HBu!{Vy$aK;F+RRQbK~JV$7cIHa*n4`!ySiekvHq>( z=Q=VeYfsC&7|HOIRKMxOYY7pzzyE+xl@#uEfnNzlNeTsSNn`hx<87E3sBS!v%ibY4 z6cq78mGpH}r=vqLGSqi4IWtnhK)Ls!u&$7xxTnfggRk?ODqw#wxN`zOIwaE4p*`+y z{Z1j;-`Z|k&hX`u&|aV(lV#iuj*XXToG894%k)t&OL~1tkzdPxLw8sLnrg{@jXWT~e5Mr%w#;-af3umFrXX&ekYP@E z+|9Wg12?@@Y8f$oRwxA`eKxf6GDssmaCu}CZT~tBF)yZG8=(jiLV&}~5*x0lB~#_x+}FG0*qT zxCEkVHb{MK(;<98*phUJw*l%oa4vh0vYweRwifdr#(954R8vT9mijCtL7*9kKpqB6 z7og@RJCcOy`Ul0)34+md zbJ2V5jzL2Amzt4#E4__^H;#W)ZW(<~4A7_2?+3`i|D|IIHXi-<$AUPJ1}_Aid!1GU z^iqAr;y7SM-a5lynAiU3Cd`_EIX0Df>ezTRwWtRQttcpP6vxw7wg1?fB5WewXH%)9CaTSg8lu>1$e=wT>Y1>dyxKe2+>)0n?rg zq-o)ta(}b6*USK^r*2jifyn`|Fx@}ZFK=^5x6awA`a4>VY&j37(Uwt$9Yx`Q2yH@& z@@Z7g8!jlls4(KBUhp_lC#WVThMkW(HJaJ{VKKQ`Fpl-^#xUepvy_|=`q+;A=z51Y zpO}LPHZG}NyQKZ%orWMOpIzrQ9k@p4*pr1h_(-8+ZLm|f5h?)|@AIiO|ftXz==;$^_)ERK0PzM=H z@F+w(Wqx1SRabY)%kU9mO#2HT|9G>R>w_d5cn45-PzmeMJ z%~|jX2JS^V53OZT5Sc3!b_57&`$Ec=0_Ryhu7hYNyH0xr$>Br0K;I#NR zZ(*1Bna`K7Q0Aqg(CozM^57bdV!TzhHKedXClK z%SaHtQn$@wef9(n;nE0(k+REV3&0pSn2y(0jrRMsdV81ZOKWQ?2O)tM>CNF5Cu|ZO zyRe0Ejx9&9o?4rM+@$e0nEFw1bT_UuJ14{V=ew4*_(A506ZE4oF?qP2@j6xN;Bq60 zzv8IE=)Quvp(OBb%nho3$hn|D%p3O>ETeT{Oi}hk!>F!pOw|<53G8LHBX@EPKMY%_ zIC);H!)zN*_PafD9T>Dq*yp=lNa!k%QLlgJsgW8eR+OwPHX$?XPkL=4n(OvoMrAH) zm8o3T`hM%GDG|Q?8Z>)$U-nGNk@vfkS?)wcKm91OW<+v)Qv%#e_RHN$-E>x);5;_Z z$DEhgs33dt0|bknQAlD`USl8}>qTniI1?L#ph_1r|M?ZqkAJ(F1Xxy>KB(npkSFeA zpw*|b758H>V=@N~z1+V1!K@bRcyK+yB$mjDk}ZVPG#?w_ibraeXkxMjN62A4{?wwU|_AQ@$SKpG~*F4u2 ztKrrgATG4}5@Si%D&5o!^H0&One>7V2i&8z&L9V6FS2<)4;OM0knUu^$z2M!onvE*_ndCiqqO5 z=a48Fy*L%3&ancqg}R!h6?GvC`Vc*f;>24+NFrh@4Axc|@mio_HbEr8(*_26G58Cv zCsNJf_s1V2vlC$LV`o6(S#>Wka>p^TDYFgF_FlXU#ii_$NY5~s7Dm`Z*!r|F_$;Gw zXN=Y#xGz{~^}WYD)4?%aYGDMfsTyzMF+E5pNfS7Ekk6Evi-BlH!hh`2*Sq0TGR648 zz25&Gn2SxZv4|5`OeN1^l;FVN+a`s40rnj9!dE1LNdUyO1)Q<765qO+I-c$9Q$7SR zg2L65^#g+wICG5LTo;?|jAzfm$MVzfYdBbYjp_y>bM(u9_U`Keka zp#jh7PtwDo#LMSH zDdT^)g_PQpJ1;cNyKyg0YqG;TmzZI71Ha1xU);iJiNT*DDw@e^Y59Q65a{7p1cF_s z+N9t!+|+fRV0r`^-ynCkGJKhXs;CrmmQ0SJB(z9u3Jshi^~ur6cGK?aapNB-q@au@ z3iLQ1WtgX5_S?lL`JfObzex=#1^H^>ayxVM%r+{Se%C&V2iC3DkWbBR{)YK(#yfHV zl7pJ2UZ3IZ9R7xnf^Pd9riF!2`1@3iY0Ace!ef=s9*#&bZWV#veeL{q@dBtBg1ZCF zs3hJ=*4~>6R2~kMuQcGNUI9F3ht9L+t5wI>iFX6xpvF%oEYn_Kf9Gqe zhF=w)+Jc^K)b97s>s85Z58O51tJ_EHF?n*O{+ZS5$hf!jn>}o2P=CgicIPsMG4X(p z5-EYcBw?e6WEW2Uxmhm^^9^!6&pC^!uNF1zf^IcxK}NFab-b!@06Yr`nJw-c>B$Mw z&Ivd)pRM~HEfRj9?mE`Bye<7s)sl8E5uB%}_kdB*Q!y4Gqi9bp559T#uVnNtDG85Z z(7tSpIh(F&DnVFgXjm8|q#gYW`*&_!q@6*B%q8X)D2Qo@RqqB0-i<&hijhR!2-D-_ z^e_iWii0yz;cdWq)5a`a&OA6@aOe&(W}89!G74a@TM>We5!JK#xRR*w(}>(R4B^*n zh;CR*Ac{T|mcZVRDpc%X43Mj)P!%FwSySFmj%Z@s0mYu0IpYmkxsU$J1Iv~WE{6RC z$7-`olT_r1s}St7{0!*lm^b0B{{Fd zh#|ngeQvl=x^Vk@_)hx==P+~(bsY?m6IAA5n0G7|%p`&rYn=4aNJo^c}ak@ND1Zn-FEp%nK8ChXu0Z!Exi`e z;f7}Ah?peGX=Q15Z1#Ao5H{qU4?cGXv_6!=Td!iI{#85XIZPU1#aT)M_i%gNXxKpcPL{V; z9`7Ok%-K>U&+2W+!T<{Uj8OJ{{;c^T17sfX_06X?LYJDoW~)JpC2lC#R6l$P|Na`F z|IBF&17p_0>qSF;L3PZfh|>KHb8~6GT?9k6S5$~kXvvDa?WmUj<7(Ys8gj8E4yS?w zW)^G#@Z|GNgf8Cp8bMGx1+IG1kM%wlO3YCMt$z_~@*T~n+i~9?I-!5i!}KBErbw^t}driuNo6gH%=QP>)BH@{apW?nQhx3 zLW5x`FCJ^c1V4m)8|2Lrk3<#MU>uBYOohXd(`(!qcd_i@M*)NFF!!lYhjjx;OMjDp z(I3#&XwGhoI%nNXgMXtn1hca2e}tsEhOqcI@!G#osCh-zZ1Dt_W&=;$*Sqm#DU^-m zKsKO$%0{3>P#l6&q;Z7tE8W&{kw+ma`&Ev895ZPj2!{;gAh_Q=kR^6=gEcMQcnzbP zXV_|$8)3?N&{Io85TXzDL^cIb5TgMN^Yx_TIXaK?6qLUbrQ-rFpdD&)Vk8xgDtoEd)Mo}j-MfUs{w z`uk-YP~mgH)Ba>Z0)Lt2QgoP6#0sw}fiCX`6L$jrgJeMs3&%5gM>hqJD2q*Au*P$j zY#g1T)XhU+_=8tuYZw|x11(U3lCHhC_N`br1nyv90NGV!rxr-RfMSsw_Z_&d==e2N zkdO8mZwt1&5A=#0h9hQF1f#S)0KaV(y7rKkC<+d0`A$O0B(p<`PZ-Zy#&r^IvvItKTjEEuAo7z&Mh^FfoM( z1^GPA`g*FvBCH}oT`6P7n1UP7#X;~D2Oo>-2_FSPxakB@;gKz1AR#+mgBke9;D12O zq6JAoSvyH_*adrmsm-r?l~Qy4;D^|x)wxcJ6E~IUlM=(@VX0DB#HnLkOqqbaPd79t zDJbzY0U^!7p5Z$)GlK=k0pQUk0EO&ardVm-$)n(OWl)Me4tPc|5W?A0AA1_jVs~<4 zwNngY0auAJ&Qrs5Y0zw@y#2*S9YgGf8E-~PeuqrTqhmiBLbd;DiE3Us{nE z+5svGe*4e^_Omcj9kyg1%#eM|`WBIw(av5e?; zneC>p6uA;>d ztgduOR^r;kA!p#1scl)`l)!7rbUi~E93r2O?BuVm!&S!r3I70jYJW!um(@U51&j#| zqcD-y!{%$a?2~y`y-(1s%<} z{tsJ5gXORH9_Pa%r#;gJG-CC{j~!_oEQ7dBh@rViiAi6qRGCSp#8*kMwmzeoZYwL* zZYGts0chSt@R!Fh8z-k4KL1Rh5I&xe=?v*LS0t)M5j-e}*N{{j!qvh9R=T3P;_12+ zhcx!%0FUgTP{nlHV2y3dLOetIBbTe(nKH9k51Y(J@7t>| zn{Q>lNWkHaVjVPFj)RTV$O(g( zDsdwhVd=ZpD_+B_Do8QG*a1~3X#ynR-!di4(pXe3PztnIf5sG=`Vu2k;BSfywB2zW zBmAr8bW1#d@L;pi6%srVIFj=Rn(eko@3xO6_&nF`?a^c*)m*?(JR>wXHoy}V5LCzj zEpWkMLBHSYrKL4D?N?Oqi(NYCTIP3<MCE@3T|j%Bv|t=YYK3cBEaEDq`@4=Kd?d0 zLhA^ZqA}tmhT;@cPNl<;0QBWG2;xY51+om*1)~< z!2qlb?t-w@tyzQeF+Ob7N2Ouj;qQ(o)2%#%qRt-7 zFHGY3Z6(oGM~t4!!C+B!$uu>1uyLHw!N53#eijno=zUP}pgSCA8%{&0A#X1#ZMU}9 zX0oUy%;C-}YxXNzq&HUN}Ev=~*vtjX;A^dDGhbmOeD4DtO@!PBn;-`$wigrK5;M&OblD>*NqRMQsVmrG~ zxHbOb!`b36TLZt-MgXQ8F-U^_tQsgpk}?1-?5GqM#p#yq<_ekVco!7%c(D z8mUCtOKNPL_^x;=LSL=lOFo4(xfc=aESiu_Mp|vT)2IGVz)LG?<2wh*95`*uK$Gw$ z0+^vnv*FJJp#A5Y1rMeJRSwg%aK!PKE$;JWi~B*Zs9`t~AZ#eCcKz{eT_ZCkq@AEJ zPJ4iuq&<9pdKT*ieu<|@$1|p%V1bnO73nqTf5xEWI76u z=Wu_T>L#8dHZfNzB3xmsB3$QPSog3^b(!uqYolPXNWdR z^xmQyeT3-Ii7p{V?;?YU5;7?moqMgb@4feRU;8?Hd#8`# z{K+C+0htig|57#;TZ?+r1{|YkGZBs8Kh3 zcw_e9u#NFfDp>W8eQX|I%@cHmTv7JNJr|XFby`lxILUE6bgAui;%AaGxhp@Un_FRB z18nNWZ@sJgPx9&%1Sn$7xCj3>MSOb)1Y{=OQ~gs~I>@M#`}xUF`WS1upBAMM1b=|y zp#O#9IzW{H_LbKWLEs0eScdwDAWs>n=S5{tdKGc-p<+1QokshpmQ9g2R^C;vZ@bP6 z&^_-|eo;P^Ed&-iJM&JZNMf%`c}kunGX#8&*oO#=eGmGKZA*WWO_akUIPP}#D{o9< zw zT(}Fs+@vePj{fP=XD~p{YNV656jsO^NzW?nj{e&sTB!?f(c6p zU0Oae|9sRN=hlO}nIF%tl~2LzK;!M@p6CTZioP}Fmv)g25}*x=yL#%-Z?Y>}e=9Zs zRI?4VpipR~rSbMqfKxZHS|=)lK(d`88gyCj@C$sk@~N<9r-XTFF%8rJ(R9j9bG@%g zYWB3sCv4P~W4+jBW@C@2MVK+Dm3^N9Lm4t&f`ke%SFETF^?&#CK3TwC1m9E@J+j+H zaDMYuam|W->@%w9t*@x4ZWV`v;nSc)rEDS7?bxImq)Xn`b7Ft>LssIp1PkOngTXsP zzF&q-sbqhw{+r7@{}#a$(w$Pyk_s&?L<=h^x+Dx3{ryNm(dLi$n>YlfRoARdGq-MH zYw7{UxGDZ_8K~Ri=+T|zIZS48xDD@}>RH>h^f;?&Y11G?CRi19ep;5VPCUfhM@&IB z!aKFY>#G81aR6`-xO3g)-19++ZM_kujlt#6vwu+jHa^8hQy6hJ| zh31lSsGcTwJxL^MEBP^<_J_9b4^tbu@F%}W^lJ`dn+3Imec?_a?P)_%7o}RhT|xbH zlzW97Z{k=}m&K9fRt}ZXtFNksKP|O3@Uh=D(l2%}m$XovYznTmB_D8q&&j zdnFhA#tX_2w=Sc!VXA9cN{yRK_M-%Aqf9z7$Crt|M;Vnx_2$3%H|ZI%bqq`Mz>wsm;gG%{M%G3I`lT}t%;Zzi;j~O1=fBy19r`O zd<&$N4#!mCTQ0_?KpU1$=J%u&paOkCO81Q=Qu?fGVEJPYBI;7+l{8s0`cj_XfOENi znJDbQJI1y;nFqFl`8x>YM`?KKU0fm+i2%`82ZS5Z8<9GJL!D_AK+%OGZevt4`!MD% z(UU@LLB4=YTX;5JKCpL|yF&pt$-(!xjx6s3y2p`PButxAa*>5j+K#@qia!3f^}3I- zHKx;@?@5z97B2n2i<8w&!5|YrBo;33pJ=DB^XY;5v{f!3a~?Nmk}=m!xzuAf+HLDXV?mk$NDDfR=`?%w{uwa4>4aP8Lr;o7k&lKA>tXalFlKDsNMdqnbG zl0u`QE1ssoB8flkuB4wQyT?B8T~xWLkcKoF%%_$~(pF*(pHIL19`#k!(mFmw#;lJg zqRwjC&MtSfL(X-5viQ+9e@#h!HMk|ugJgmYe*%q<>s;L~0(dIRZVev<%g&cXz%>njVN5Igz;w2p;&)F4qvCmz zJwnLFrlwVbl%6sJeUZAh6=sSf(BbFRiB#?{Ox(49fixW=!adTEx1*j~mR-E ze02Fp3aL?Vpr`Rr1HqXeo@5_9EEMA)XKru^w~Tn-A2CVOT-g0TyBI>{x++UMJpwJ8?c5h(KzLWnKidWV z%PXL@`ab%{?B7^gt1c$KmUJS3?Y@ChaX0o{A7#@9HCYlfNecsfd1(DK%epIBC27%j zT!w$YH|$DsG}FpU!WIf;v@bs(O?_{bU|Q@?ImPsgy}E|6NJ@k;UkPGXHoUfUBi&=nol%DY?Z*IqV5de1V~ZVN;U<%ellSFvV+Uv&9G;W4gb%-x?wRteVLf*xB&BL$Z}E{(%Zav1vzpHa_OMpcV()U zvkG4Mi$@1j!Z2heW&#@J8m-Mw@uaiFI<(<}k>kk4A)n(}S5R2n@;=QW~cZR&Kti7BEW+>l2_jW}oAp zyX6CEa-USr4|v6yX?;_9l^&r@l1D5|7RpOqAk{K>8@c%&SwROld(=t_2d=ggJoU5H zdBMXENIL+56nFsp$lF=L@Df7B+gimqheg+K-CV;vwJXMNjy|vdB7NwF%pkG*hj211 zPWh}ckv3`U2UoImdm&4Al*e>Tjh&>)mK>D>EUH5Zs%^M1cYO1{)KO_R6kD2 z`%iVk?xDI=XO6VuiaFaI$K@|>>G|G1>fM|dUs=3)yfTEt3v|F(@l^Tj0={^9WMOgu zy6|CeuIbF$st%wi&ghMeQHoQt{yt6!$mitawbdKhRZ+zo^}4=}r~sjMHr(r^kkcpz zOeJL1eXZdCZRLuC$Ct##=;M=kfd4?nlS9+DrUigs4sFU1}RAXUS) zwlpxCop&lGJb|BW_kDD zELl&!)rdL9*baFs-3|`hEAwgm5Z>lOWfj1wb>=p+Y=&KX2POS9CNtQ>j^a z2KAvXVpYa{=Jw=a^E?J>)uDWovQW;Gxs1{VmBg~Kq4h#rTsGj_S}ZM*2CQ!ji0M{Altm0+WyY76yltxtUT#_n&PobRIiH?OufxMwl_i%7%P9YUc#-vX8Q=XWCtI6ogt^?`Lw|Sa0ygkp4>VBp*Q?hO*=CvuW)Wx`4qj%@Qo+1p&w2d zNeAQ4e^klfL8@r|e^R@~7mqC*^X=)e_^u{>ud_+uh`e2&JEZ^X`0S_dUpRV43APy&Gm2ljV&jF}-7E3;Zjg}oVwNnNc=k9aw1YD|Q<6G7mB4RMFvYF@?NmT+d}kZY{lhk)8L87S$2@-D~zv7n8K`Trxs|6*;{}_UvD9`Kqg!lu0}@LdiXR z^tEb}ci3q7QJ?bZ__+Y19&YgQ59QhDl!$oeuRO;D7K@Ac1P>J*$>{iJ30ly9cu1<@ zMRkuA4mSJx20qdy3!<#_46;NsrH?Wwkrndo*AV4;yj5}19N9z1H%5$@0b=!1%5+6B zL3g%cw7Q9zHz1qVLkTilgt;k3#c@tPK0ae75%JR^#s2QVf#;q^Z?7m&G*EaOhRD`O z`0BN8ZkO3QnS}^B(Tej@kfJoy3zf!r$kmVnT`k-|OVHtO0@#ut`h8y9NG6zc;bH0& zlR2{h8}Y!~$2*(f`QLpiG(%x816;-`5ep~mQB4+@^bcSt!gO$5)Y zRlob!-)P5fB?*S^1;23!N+R`=JRlSSFZC1yPL+HpOm#^~f20(KDZC)0ad?=yQ;+N8 zS(w0Y|Ch9`@^c5w{Xl0jwVufNJ;_N9Rrr-V;K>x2K?e3@Bixrax%>z7M}GnaoIGeG zjHJdo7FzYFOJk~55i*10q7fMLJ>dn+^RooF8Ypzv{XSUUG9}2Vreng58Haq5#m)$L z`EOapIY6F=I24Ba%s{%Me^mg1+tcOxj&E{GsZstNQL?kb+MV&_K&l#rskE10fn+JC z9}Xc4#@MwOfB4$3B^)sT%=@+asHU)u8|*c&%xMLX2>#K!T-13gREYsx(|uKS@y6y4 ziTlN)|19t~KEJXme>2ZfG{V(w2=ty4D-Zp9*Pf$e8|A8FaRJ_W4?huYp_PZ&#azu5 zbxJ)aOQ|LL9E-+(yQ9|M^pAsN%PG|xR1L&?H3_rnJBw1F?qe}Ib1yNa?<(HsL8qid zGrYsWH|Z+=JLZr`o*8mcvutq&aR2I_4&4+d*5TpT;eqJz5F1SGuf`uFW$*4a>sUm7 zWYji!XMY}Lxui&``YPy z?6&o+&lYtOxFfw^;|46k)Hu5Il-kzMNFy})clN{iiG?Vns_ql`=PEd7cWb6fX30vL z>XfOyJr(Szy^j~LA56GWLzf$zKh{Tec6P_Kk<_$uG)5;V-q>cv?>r&jQcu_>QIMK? zxHaB;OrTLP3&zZWO-&~Z8OL-}SVu@~3Mi0QPshlF(F}8<6q)kU5YPyOakV>$@x3x6 z%1V(Mm${pWH8DJv|2-Mw9Xm?~5LZ*S$mHSm6jx7A=2qXcP=qGR$mMqGktnu$}&BR0GTvBxv;9yvHLrg%!on1v_b45oAz>7 z@K2kd#If@)bWHJgaZ~nRrjYXBhkh{xMTuIy!&4$B9`eRQ5qrx2;GNzG!x?o`b2%fk@&Y^ld#v|s{Es8z!gVxTxUrQt-{X~0PPOaK9KjxE8~UU zc<2p|RqBSQ8qQ8q1|w!c8u)R*DCBKE+xi6Nf9mwUs;iB_UBus4aG$>j;osY=$ z4+6}o@nnsm_>3=@07JTwk7<(Zr|^w-7IiEzpKe#>w;V^n>P#={ z?7sf1U1AKR=L!b(az%57c~S5r4gjw&i@Vu(s#wR zP4om4Rxk$yM=%|SNrvyLqxtI@4C4iSyOj+MV|C$KCUDwzUR;f(Vt)#zBd^u;=BgPNG4-*M6VBcA%-UCrAzf9)kF#QkZy^p z{v@W|_QrB#TG=ICt2FA)pv7U-*!e+}%epcV5BrhT_aHz?WL|j-7D*&4GOhxA^jBhe zJdvP!+QFx)x`O8qvxHMepuh6l6g$U3nt+%tutox9*$ovQu{QAlk53QqkuNGru$ohs zjoYTQ4u&vgC@#aYu|`?OAZv3;@LfcGEo|%xa>$yk!MT&)ij$LMrH9CvTFd>kMVJRh ze97}tvLhTnW*j>P5$!}a!r1QKoXz#8)iZlBd-WQeTY-uO_G~b+PWjF>rUEh-Hfp7)b>2+0Y zlFqI%7X={O!4eFRmH6t!>Js9~#xMK2(tf1q(+Yd*GXOP-JJsVH%mA=s>jzt1mWEh{ zKz1fl_;h1VqHKEFa6rvT)M1mH5OnS=^y9oV55-O~gfAqq|K5tCB?z}gGLi`Sj-TRa zcw?-Xei+n=HH9w-FV#YJr{D@H5q(yd9sjBi$p^vtu!lN`ji|3 zI{)?*M65fFrPm(;`JS#-sEj<9npm@FXxA3p#q-v(e(4JL-#P;rGN4$;h}h77Ppozm zm*t(C0z;~*nd`%+6+Q!JG+Jjb!KMPH!V}>k88H{hHkKcQlFufxIhCWKnBFs9jgda> zy+;{KUI6V)>J!K_-mO-yzS_Jm+!bstnE6I|DS6chH zb!HcGPwRMEi)k`8E;C8Wt8~(PP5P7JFUdaX<@x(XiC60ms(OX46%kI9C3e;dP9F2^ zhXcfaE~JbtCXbQ2IHY3GqAH`TE9yP$JCsMQiTD9HSjbC8(yk5&h#4_M;N>f?m8FDl z>4H_5uo3=%pGf9})-j6zhIV{T7pffQ)*p%!3aSbX_!<&NZ{PKTKW(rYhvIF0s7_gfMCV;AsgjODN zg8776b!Q^p046{XBm<1g9i`j{u^+-I^ak|VaIky6iJY6!JG)wv^@d~5>8Zz=^cgd@LjYI zLb2~p4lY&Ao}uq}vZ*ZrwIFL`&~m!FF>cu^S?B`vc~wv!^tn7^2Vo-s$2AC_k#Q_* z|Jo&IMiTSy^dvW9%-af|?1ve$g)x&$PKN=FM^4I!TOETJI5y1)>hvEE9+n6qrC(Ik+#E_kZ zuoo=RuKWvA*k%l4WT*h;!ygf+nI_w|cX^bRCMOVrBnEEX@q-s4hZ*{BBOKXm`z7t4 zCu~(*fel-%GWye==(JDmL-;C7=ynuYb>0-H5=uH}+~4osF8iI`h06KGeq;UP`BKOp zjyS#75QzzybmzY35{dD$ATwcuEZ4=Ztu}5TR_KndjQf#RI}^w8RNq3#F&jm!eg$Oo zs`7B$IaKTk^9+qQ7S5KkrqwQ^AmHsc7h2fxG5_EhY!UtP590@YRp)eODhtZYdrOq% zdXj0Nr$iII@I|@{YN%0N!u_dPh0qT+6SvXQR&B6Z=3x7Mlmchq5);W)&S!;IY7t3W zyaxpTx81WY@TmIBIT;{6bffV-xF2Nf3Pxr#lA{u~ii+C{eu`FtPvWgK6CxTPpwIr= z>^_lq%yxj{PPCwoMWuhT8sjL>Dj~%H=QFX|lY56hM7|sSE`m4wflI&&m|7a-`-A9I z9)vZg?CUkuUfy0|mLerG{HHn3WaKWo?D^XweaB-Yg*PDSrX!ythyl3sJA}j-<{OLd zW~$_&@~@!Hy!@=cidt0~-#@c(=n&Zg8%^ zRU)gYlxkYl&zPc_4n?Zk+H#Z$mPWm%%l@WQa(X#SZV(pAS@xpXN-3=#gHyY39^_BOI^%=mb$-HR?9i+uPMQG07-PI z*-NEK`6&eFd^q1IGNG^sYhBMzJt{P!wg(%i-pMMD38afHu?hrIuQ`m(<*)@N&Tljr zlU-44u8;cdy&jur&(okZ!KPA)M7lE; z`XYO@eucy+bFrZ5H82!qZLvXuywC#Jt7<0*QRJp7J5%XXLysg%n{v zO(G3bfa3roiRUwJPO7=-l(4MP{wz1%fIPa`AWd*!eR615tBc8&+tv8Mo$CmPS|8O9 zj@OlMl^%`1rkI3~;E_j6`j5t69G3LIRjyV@(=o3+b}4e8>*HkA<2LFd-zHyVdo^J* zD7#X*#E;Qa6ndS&C0$OUT+M8G%#xlV?(*-mUjC;`?b8Yuh1LoAS{*x4iY1E_p;nl9 zZ2Ge-&unhV;Sjcrj;}1QMYGr$Bs}8U2SSbiTBP4(u;0IaSRPw!)t}Zp694emX!^m; z%DbhrC)oLQcT>~xr{$D?9gxoPk9oB|w}B5(KZvP2yYZuCknMnsm$a*o&y=OOyj@8= zweeupz;_`vR(bGS+}s`FR1E(HisR#P5LQlFBzegBGM2K+_&M27?s*8^Tk%mZI#2FL zt#u?`o9+2L^mOoD1-Kzyq8r5~M`nPgB7Y) zpv)_-fLn#G5iN&N684rQwhsp16|jqblqC<+n65F0cg&`axkAjkvKLyo>jv~fDH!Dp zM7k!J2J}QDI1(>jdZ*g7!{D(aE?#)|by8WW`QMyaK5h5K|NIeOD5 zd)d;XOs#a2jL5%dmTV-I_+i#M1?vo?Uo_rnhETY!Q0=6J(kK3Je(;!RRXk|mee{qb z##QjgU+T2;;I!U=LPmv$Idny%ie|LcxvDq+9Zo-c=hXrE^)r*4haTwi;9bS2dEkgCB+iAZ{k2HB$zZ!@?+uL|ouK>BG`c17sar(X zsh-=#BRSpn<^rFA23e*Itl z6Y4LrPaBGLha%SphS#EoC|jONDr#FVCD47mdRdfH^gI!<)o^j+kw2*$ljODd+gq4; zd9@RFD1|g7R}$J0!zSSF{iYJ$H92iolq38dJroSq>eYaW)*;00$`NPO}aC$|-~iU|J>z30BAar*^DEwCq{RBtuw zS;lkTt{2GQ7wJ((KhJ(=uJq8bKVK61jucNbGY>-V>n0w+G~AnxYnA%65D~TYR?c*W2$r~S9f|AJCpzJn z=L$b@a?NF%=aqaFkA`E`emK9LW)4uk%OU@Q7tXjpj((DMDwx35)#Hfx@JDv&T%_06 zwNV)Tlk(+iQWYrhJ@!W7=H6}7%jYz`T{2&wJ#M+0Q0g#j|8RA(H2y(;EEFU?WCQsj z!xXu*dDGWrVkr}v0V<`=Uw(o6b?M@pa-#0z-^uJUZ()gxsyAOe9{2ugTi^;lTkUVww{IEP8k+H3uATIT;YgI3RPEWCvzi6Igyd6f!>Fjkb)VU*sJop1*xm^E5TAdviu{!856vHHN-r96Ar zRbS~MadIAZ06%rCbL#2Hi>*VRT*NHc502pem2H(MnIhe+$_!7j9)B3?p#K)%AT+kx zW>i`OV8^aXlL2*8Rh#-lAVcX=%fj~`Bz61j@v`yLHT;Y3J#R)7kCkll9}kobvB22` z9AO!R^Z(5uW_YZ^-)$!r+}dk0+}g>hU8pr>@%9<=J7Urf!yzt&%GDg{XjrB@hwp?p z^{D-Q!^fAywr}SE9X#$=h{*e!tG?yVo4u3e`@fezwwLd30;R$GnaCh>Dx!!M7ZZ>$g#*q)`^9@!7^m(<`_~amd=ND+V0k*;{eWywS zwaL@I{P#rWNE;pbG{!*Y$eJ4^)kovk&H>8{z!uWc3d9y#l`bOE>HB=f)cMPynyE9J zb(g`KG)jiG0#Lbiz_7lD8o6HWJC`!_8iY-^b~nsC%u~De`T9DIi+*dKE~2Gwv4wnO zG05Z{O@=1A6e-fb>BTS%Ld%c1nLf&-5;=1fC&_#)5@Hu_v32kjGQ z<~-696!?Xc`E9L*cEi>8MHfT+YjkGo95;4t;13t(pNW^`f;gE(j>$n=ok$DJ=_Xtal9}a{Kh}gd*@OsJ>w1KyE$&dUrgKmvqrc-ixH*kzfbdCDmTY zeEW9|5K&F(6CZs-;Ua2So)}5pn*T19uDh&s?&v}7pFIV%i}a7;|E~C5a5i5{B!F52 z^YN^X&8uTHz#55JA&J*aAy>p3Y#18E;U1hc;tK$0wiPUWK~>!v>#$^Un|&`Ha=*7N*SU1J`or!1-_?(Dt@}F?1zGo)nN|kC F{{d=+q^JM@ literal 0 HcmV?d00001 diff --git a/research/direct-mixed-flow/vendor/higher-moment-README.md b/research/direct-mixed-flow/vendor/higher-moment-README.md new file mode 100644 index 0000000000..0a736ca89e --- /dev/null +++ b/research/direct-mixed-flow/vendor/higher-moment-README.md @@ -0,0 +1,416 @@ +# Higher-moment strictification: tensor power 150 and a smaller uniform rank + +**Submission authorized by the user on 2026-10-21.** + +The complete p7 mixed supplier in [PR4416](https://github.com/CrocSwap/integer-mult-bounds/pull/4416) +has productive ranks down to 5 and paid ranks up to 48. Its chronological +product, paid target completion and disjoint splitting overcome that overlap. +This package improves the charged tail estimate in that construction, then +generalizes the logarithmic compiler bound of +[PR4411](https://github.com/CrocSwap/integer-mult-bounds/pull/4411). +At the same proposed conditional **κ = 0.00268647**, the results are: + +| Quantity | PR4416 | This package | +| --- | ---: | ---: | +| Chronological tensor power | 6,240 | **150** | +| Product ambient rank | `121^6240` | **`121^150`** | +| Independent productive fields before uniform compilation | `7688^6240` | **`7688^150`** | +| Maximum paid rank after splitting | `10^6240` | **`10^150`** | +| Minimum productive rank after paid completion | `11^6240` | **`15^150`** | +| Sufficient uniform ambient rank | `2^16201843136005340321` | **`2^349300000000`** | + +The tensor exponent decreases by **41.6×**; the exponent of the sufficient +uniform rank decreases by about **46.38 million×**. These are comparisons of +specified finite constructions and sufficient bounds. They are not runtime +speedups, practical template sizes or corresponding estimates for every +precision/storage constant. The winning uniform word is not materialized. +The selected frontier is unchanged. + +There are three connected deliverables: a general higher-moment splitting +bound, an exact smaller paid native construction, and a uniform-rank proof +compatible with the complete consumer. This is the larger scope chosen after +the H completion obstruction; no numerical measure of scientific significance +is asserted. + +## 1. Boundary contract and expansion decision + +Retain PR4359/PR4416's all-column native contract: a finite chronological word +computes specified transforms on distinct arbitrary productive fields; paid +positions act on the actual current physical owners. Whole-job normalizers +are restored, complete spectators are preserved, and owned centers are +initialized, retained until safe erasure and never credited as new inputs. +At every positive column multiplicity, ranks multiply by that multiplicity. +Matching only rank numbers is insufficient without these native hypotheses. + +The source product algorithm runs one U copy for every productive role of V, +then substitutes V into each common chronological paid position of those U +copies. Fields may contain correlated data but have distinct physical slots. +Never combine two different paid positions of the same suspended U copy. +The targets and paid ranks are products; their moments multiply. This is a +finite chronological substitution of algorithms. Read +[the pinned product proof](vendor/p7-TENSOR.md), especially §§1–3 and 6. + +After the product finishes, normalize each complete rank-K output job by its +permitted whole-job conjugation. When K= 1, +u >= C, sigma = t+u >= 1, +J = c^v, L = b^v. +``` + +The bases c,b and the power v are integers, so L and J are exact integer +ranks. All moments here are finite sums over the actual rank inventory. + +For any original paid rank R>J, write R=qJ+r with 0<=r= 1`; this is why sigma must be at +least one. Keeping the original P_t^v as an overcount for all unsplit calls +gives total original-paid charge at most + +``` +P_t^v + 2 P_(t+u)^v / J^u. +``` + +For a completion D=L−K with 0=1 and logarithm power p=1/q. +Its proof only needs the logarithmic factor to be increasing. The same +argument works for **any real p>0**, including p>1, which is useful when +the separated unit's ambient rank m is itself large. + +Assume the finite source/exit compiler in +[FINITE-PRECOMPILATION.md](vendor/FINITE-PRECOMPILATION.md). Write +`L(n)=P_n/B_n`, with ordinary base `L(n)=n` for `0<=n=m its exact +integer-batch construction gives + +``` +L(n) = sum_s w_s L(n−s) + sum_e x_e L(e), +sum_s w_s = 1, n/m < s <= n, +sum_e x_e e^t <= sum_s w_s s^t, +e <= r_max (n/m)^theta < n, +theta = log(r_max)/log(k_min) < 1. +``` + +Choose `theta < theta_bar=a/b < 1` and p>0 with + +``` +2^(b−a) r_max^b <= m^a, +theta_bar^p < eta = t m^(t−1), +m^(1−t) < 2^p. +``` + +Then **`L(n) <= n^t (1+log2(n))^p` for every integer n>=1**; define the +right side to be zero at n=0. + +For 2<=n=m put `A(n)=(1+log2(n))^p`. The shifted logarithm +condition gives `A(e) <= theta_bar^p A(n)` for every exit, hence + +``` +sum_e x_e e^t A(e) <= theta_bar^p A(n) sum_s w_s s^t. +``` + +For y=s/n>1/m, concavity of x^t gives +`1−(1−y)^t >= t y >= eta y^t`. Since A is increasing, the source complement +capacity obeys + +``` +n^t A(n) − sum_s w_s (n−s)^t A(n−s) + >= eta A(n) sum_s w_s s^t, +``` + +with zero-rank complements treated separately. The strict inequality +`theta_bar^p < eta` closes strong induction. This uses no concavity of A +and introduces no unknown multiplicative constant. + +This is available for every separated unit with the stated t-superpotential. +Choose rational theta_bar sufficiently close to one: since r_max max((1−t)*log2(m), log(eta)/log(theta_bar)) +``` + +satisfies the other two conditions. Thus the leaf-count estimate has the +general form `L(n) <= n^t (1+log2(n))^p` with an effective fixed p. At fixed +p, a target gap z−t requires a sufficient H of order +`(p/(z−t))*log(p/(z−t))`. This concerns normalized rank-one leaf counts in +the finite compiler; it does not bound full word size or physical runtime. + +The compiler's integral batch replication, arbitrary original arrays, +whole-job routing and finite owned-bank allocation are unchanged. With +N=2^H and desired uniform exponent z>t, the final sufficient condition is + +``` +(1+H)^p < 2^((z−t)H). +``` + +For the new p7 unit, take `theta_bar=6/7`, `p=13`. Exact tests give + +``` +10^7 < 15^6, +2*(10^150)^7 <= (121^150)^6, +eta > 0.144386809622024146828684313913 > (6/7)^13, +(121^150)^C < 6.907234273066686405887998346943 < 2^13. +``` + +The smaller logarithmic power 12 fails the stated eta condition. Let +`z−t = 1/700000000`, exactly the uniform-saving slack already used by +PR4416's outer point. The rank **N=2^349300000000** satisfies + +``` +349300000001^13 < 2^499. +``` + +The preceding grid point H=348600000000 fails its corresponding comparison +with 2^498. This is the first successful multiple of 700,000,000 for this +majorant: the function `(z−t)H ln(2) − p ln(1+H)` is strictly convex, starts +at zero with negative derivative, and has just one positive zero. This +does not certify a minimum native program. + +To separate the two contributions, retaining the older power majorant on +the new v=150 unit already gives `H0=37443877100` and +`H1=140829080288374101`. That is about a 115× reduction in the exponent +from the changed tail/rank separation alone. The logarithmic majorant then +reduces that exponent by a further factor of about 403,175. + +## 5. Complete consumer and finite constants + +The complex uniform saving is **376107/140000000**, approximately +0.00268647857142857. This is exactly PR4416's uniform endpoint; neither +its tested saving nor its outer parameters change. Put + +``` +kappa = 0.00268647, d=(0.00268648−kappa)/7 = 1/700000000, +uniform = kappa+6d, b_outer = kappa+5d, +a_outer = kappa+4d, q_outer = kappa+3d, +epsilon=1−d, beta=1−3d, r0=d/10, stop=layout=d, +ordinary_BIT_saving=0.0027. +``` + +The checker replays the byte-pinned PR4405/PR4416 parameter ledger and +requires exact equality with all saved p7 parameters, nine rows, 54 checks +and three extra guards. It separately executes only the historical +`check_ledger.py` ledger function and its comparison constants as another +oracle: all nine rows agree and all 63 predicates remain strict. Its derived +grid/backoff is recorded explicitly; the old m=73 admission code is not run. +The minimum nine-row saving minus κ is exactly +`524529867/122500000000000000`. + +Mutations close epsilon, remove layout funding, raise unfunded κ, close +the uniform gap, underfund BIT, add an old per-axis scan or make group width +equal to global dimension. Each must fail its relevant ledger. + +The newly compiled word supplies its **own** finite constants. If U counts +actual raw p7 instances, allocate U distinct owned centers. Let W be the +final productive width, P the paid rank-one count, and R the full native +record/normalizer count including completion, splits and compiler routes. +As in the pinned closure argument, use + +``` +G = 2490856*U + 8*R, Z = W+U, +E = 64*(Z+N+P+G+1)^3, +B_constant = P+E, C0 = 32*N*B_constant^2. +``` + +Pay actual coordinate movement separately. Retain every owned center until +its creating unit erases it; centers are excluded from productive W. +The fixed-word recurrence and eventual constant absorption have the source +form, with these newly expanded counts substituted. Numerical full-word +counts, denominator heights and practical precision thresholds are not +computed here. Neither a smaller N nor a favorable moment supplies an +independent proof of the inherited physical/analytic premises. + +## 6. Reproduction, provenance and coverage + +Python 3.12, standard library only, from the repository root: + +```sh +python3.12 -B research/higher-moment-strictification/verify.py +python3.12 -B scripts/research_package.py --package research/higher-moment-strictification --check-only +python3.12 -B scripts/research_package.py --package research/higher-moment-strictification +``` + +To generate a fresh receipt, use `verify.py --out /absolute/new/path.json`. +The saved [RESULT.json](RESULT.json) records all intervals, finite parameters, +integer comparisons, ledgers, controls and source/verifier hashes. + +Logarithms use 80 exact terms of the binary-reduced atanh series with the +geometric tail. Exponentials use 64 terms after binary scaling into [0,1/2], +outward rounding at precision 2^−192, twice the next term for the remaining +tail, and outward repeated squaring. Negative arguments use reciprocal +intervals. Every decision uses fractions or integers, with no floating-point +acceptance test. A separate exact small product/pad/split example checks +the inventory and preserved surplus, and a sublinear-tail counterexample +guards the theorem's exponent restriction. + +Canonical base is `12fa8c5c844be21bfefb38a19503fbd867a11244`, priority revision +7. [SOURCES.json](SOURCES.json) pins the orientation metadata. The 15 unchanged +exports in [VENDOR.json](VENDOR.json) include complete source paths, commit +IDs, Git blob names and SHA256 hashes; the verifier authenticates both hashes +without requiring Git. Pending commits are represented by self-contained +exports, not implied publication ancestry. Source exports remain unchanged. + +The PR4426 invoice oracle is compiled from its authenticated source bytes, +with only ROOT and PHASES rebound to the exported file locations. Its literal +controller, supplier-receipt and port-recipe checks remain intact. The two +ledger oracles retain predecessor code and attribution; they are arithmetic +cross-checks, not fresh native supplier admission. + +Local validation used Python 3.12.8 on macOS arm64. The registered replay, +metadata/pin check and committed-byte preflight passed. A separate Git-free +copy passed `python3.12 -I -O -B verify.py` in 0.333 seconds; changed-source +and changed-receipt controls rejected. The optional full source-history +preflight could not run because this checkout is shallow. All pending-source +inputs are self-contained exports; standalone replay does not need those +foreign Git objects. No Lean, Docker, native all-size or historical suite was +run. These checks authenticate the stated result, not independent scientific +acceptance. + +Overlap at 18:19 UTC covered 536 open PR bodies and 3,279 discussion/comment +records with complete reported pagination, plus local notes. The newer +#4420/#4428/#4429 checks cover earlier strictification proof/arithmetic and +slightly smaller sufficient powers; #4426 supplies the invoice replay reused +here. No remote closed-PR-body or arbitrary code-diff search was performed. +The task metadata records the changed scope and remaining direct-compiler +question. Submission was authorized after local review; no Discussion claim was posted. + +## Open next questions + +1. **A direct compiler for overlapping ranks.** A finite acyclic integer + schedule would remove strictification altogether. Start by replacing the + Pascal matching step when a paid rank exceeds a target rank, retaining + arbitrary inputs, complements and chronological suspension. No such + termination/matching proof is supplied by the mixed moment alone. +2. **Full finite-word size and precision.** Derive compressed upper bounds + for the compiler's batch denominators, widths, scalar passes and owned + instances at the specified rank. Ambient rank is only one size parameter; + this remains the main barrier to assessing practical constants. +3. **Independent scientific review.** Check the higher-moment inequality, + the p>1 induction and the native product/adapters at their actual callers. + The unchanged raw supplier's internal paid bill and all-column/physical + premises remain separate inherited obligations. Another search of nearby + c,b,u,v values would not resolve those obligations. + +Prepared by zxv with substantial OpenAI Codex assistance in discovery, +implementation and writing. No subagents or independent human review were +used for this new work. New material is Apache-2.0. Native/controller lineage: +zxv's PR4359 and its retained contributors. Product/padding and p7 controller: +@1337isnot1337's PR4412/PR4414/PR4416. Integer mixed flow: Jacob Alan +Sussman, Theorem 1G. Logarithmic-majorant predecessor: zxv's PR4411. +Invoice replay: Ryanson Jonathan / @pinterbanget, PR4426, with Claude Code +assistance and Apache-2.0. The retained supplier and outer sources preserve +their original contributor credit and notices. diff --git a/research/direct-mixed-flow/vendor/higher-moment-RESULT.json b/research/direct-mixed-flow/vendor/higher-moment-RESULT.json new file mode 100644 index 0000000000..e66b39c674 --- /dev/null +++ b/research/direct-mixed-flow/vendor/higher-moment-RESULT.json @@ -0,0 +1,384 @@ +{ + "finite_controls": { + "rank_one_surplus": 13, + "sublinear_tail_counterexample": { + "J": 1, + "R": 100, + "actual_charge": 100, + "invalid_upper": { + "lower": "73.245553203367586639977870888654", + "upper": "73.245553203367586639977870888655" + }, + "sigma": "3/4", + "t": "1/2" + }, + "toy_paid": { + "1": 5, + "4": 9 + }, + "toy_targets": { + "10": 2, + "25": 1, + "9": 1 + } + }, + "invoice_oracle": { + "laurent_monomials": 14, + "main_targets": { + "121": 224, + "25": 448, + "41": 448, + "57": 448 + }, + "new_kappa_claimed": false, + "paid": { + "1": 37305, + "16": 448, + "2": 10695, + "3": 3360, + "32": 448, + "4": 1530, + "48": 448, + "5": 300, + "8": 1464 + }, + "paid_idles": { + "16": 448, + "32": 448, + "48": 448, + "8": 1344 + }, + "rank_one": [ + 131723, + 131115 + ], + "status": "PASS_PR4416_INVOICE_REBUILD", + "targets": { + "121": 224, + "25": 448, + "41": 448, + "5": 420, + "57": 448, + "6": 270, + "7": 840, + "8": 1395, + "9": 3195 + } + }, + "kappa": "268647/100000000", + "outer": { + "ledger": { + "functional_checks": { + "fixed_halo_explicit_metadata_branch": "13475000001/175000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000", + "new_semantic_group_guard": "3/700000000" + }, + "margins": { + "boundary_algebraic_matrix": "329093274529867/122500000000000000", + "fused_gaussian": "329093273589601/122500000000000000", + "global_coordinate_router": "1880533/700000000", + "group_bit_router": "1316373794358401/490000000000000000", + "group_scans": "349999999/350000000", + "main_transform": "329093099529867/122500000000000000", + "microbox_face_corrections": "13475000001/175000000", + "polynomial_products": "699999999/700000000", + "sparse_union_movement": "50094718274529867/122500000000000000" + }, + "parameters": { + "a": "1880533/700000000", + "b": "940267/350000000", + "beta": "699999997/700000000", + "bit_saving": "27/10000", + "cap_xi": "111344718099529867/122500000000000000", + "complex_uniform_saving": "376107/140000000", + "d": "1/700000000", + "epsilon": "699999999/700000000", + "kappa": "268647/100000000", + "lambda_": "39892541/40000000", + "lambda_prime": "174529867/175000000", + "layout": "1/700000000", + "q": "470133/175000000", + "r0": "1/7000000000", + "stop": "1/700000000", + "tested_saving": "33581/12500000" + }, + "strict_checks": { + "actual_bit_above_effective": "9467/700000000", + "actual_logarithmic_gamma_guard": "1/700000000", + "actual_logarithmic_group_guard": "11155282162970133/61250000000000000", + "alpha_logarithm_absorption": "1/7000000000", + "boundary_algebraic_matrix_above_kappa": "699529867/122500000000000000", + "cap_above_band": "50094718099529867/122500000000000000", + "cap_below_cell": "11155281725470133/122500000000000000", + "cap_below_phase_cell_power": "133655281900470133/122500000000000000", + "complex_above_effective": "1/700000000", + "complex_below_one_over_32": "9997233/350000000", + "complex_endpoint": "1/350000000", + "epsilon_below_one": "1/700000000", + "epsilon_positive": "699999999/700000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "698589601/122500000000000000", + "gaussian_above_main": "87029867/61250000000000000", + "global_coordinate_router_above_kappa": "1/175000000", + "global_gamma_power_slack": "9/7000000000", + "group_below_dimension": "1/350000000", + "group_bit_router_above_kappa": "3494358401/490000000000000000", + "group_gauge_power_slack": "11155282154220133/61250000000000000", + "group_key_fits_record": "1/350000000", + "group_positive": "699999997/700000000", + "group_scans_above_kappa": "698119469/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "477749790400418148631/500000000000000000000000", + "lambda_above_internal": "1/1400000000", + "lambda_above_sigma": "3/1400000000", + "lambda_above_tau": "1/1400000000", + "lambda_prime_above_lambda": "1/1400000000", + "lambda_prime_above_leaf": "699059733/245000000000000000", + "leaf_saving_above_effective": "349059733/245000000000000000", + "main_transform_above_kappa": "524529867/122500000000000000", + "membership_arithmetic_fits_record": "1/700000000", + "microbox_face_corrections_above_kappa": "2155924779/28000000", + "microbox_halo_volume": "55300000003/700000000", + "new_complex_uniform_saving_above_b": "1/700000000", + "new_semantic_guard_with_C1_one": "1/700000000", + "polynomial_products_above_kappa": "69811947/70000000", + "positive_layout_slack": "1/700000000", + "q_below_effective": "1/700000000", + "q_below_internal": "1/700000000", + "q_below_leaf": "699059733/245000000000000000", + "q_positive": "470133/175000000", + "short_record_fallback": "349059733/350000000", + "source_axis_superpolynomial": "1/700000000", + "sparse_union_movement_above_kappa": "49765625699529867/122500000000000000", + "stop_below_one": "699999999/700000000", + "stop_positive": "1/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000", + "union_tag_work_per_visit_fits_record": "3/700000000" + } + }, + "legacy_63_checks": { + "actual_bit_above_effective": "9467/700000000", + "actual_logarithmic_gamma_guard": "1/700000000", + "actual_logarithmic_group_guard": "11155282162970133/61250000000000000", + "alpha_logarithm_absorption": "1/7000000000", + "boundary_algebraic_matrix_above_kappa": "699529867/122500000000000000", + "cap_above_band": "50094718099529867/122500000000000000", + "cap_below_cell": "11155281725470133/122500000000000000", + "cap_below_phase_cell_power": "133655281900470133/122500000000000000", + "complex_above_effective": "1/700000000", + "complex_below_one_over_32": "9997233/350000000", + "complex_endpoint": "1/350000000", + "epsilon_below_one": "1/700000000", + "epsilon_positive": "699999999/700000000", + "fused_gaussian_above_kappa": "698589601/122500000000000000", + "gaussian_above_main": "87029867/61250000000000000", + "global_coordinate_router_above_kappa": "1/175000000", + "global_gamma_power_slack": "9/7000000000", + "group_below_dimension": "1/350000000", + "group_bit_router_above_kappa": "3494358401/490000000000000000", + "group_gauge_power_slack": "11155282154220133/61250000000000000", + "group_key_fits_record": "1/350000000", + "group_positive": "699999997/700000000", + "group_scans_above_kappa": "698119469/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_online_final": "477749790400418148631/500000000000000000000000", + "improvement_over_pkg_k2": "1008477392794717479267911225169191627777122102965890395790280701170194526587548469132116575062403/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1699": "1008828268656645435748941712936355250934431507/1000000000000000000000000000000000000000000000000", + "improvement_over_pr1712": "5044141343283227178741362020680007884145727138632283638941299969772687285461029288600736779707649/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1758": "1006724491197700948453466314800026327686526580209199320247542619067215757027414399369818327775017/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1786": "10067152118499510912194521335000000000000000000000000000000001999999800001/10000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1828": "2013430087748910957328658012158594846003377122994839409079344959674400000000000000000000000004006719019826502178085342683975683/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1839": "5033575219372277393321645030396487115008442807487098522698362399185677258698371805868475000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1875": "5033575219372277393321645030396487115008442807487098522698362399185677258698371805868471719335776838627743415457068895139647759399172939286143496816535216421325187363046885361425772909502231218314437622205930116079297234806627210590217190600996553729143901162562581526621534715086055386213403722175000000001001679754956625544521335670993920703/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1876": "503357521937227739332164503039648711500844280748709852269836239918567725869837180586847171933577683862774341545706889513964775939917293928614349681653521642132518736304688536142577290950223121831443762220593011607929723480662721059021719060099655372914390116256258152662153471508605538621340372217196657216794137380775174500330086462142358142864921147118845386980694114022172311249292673931726844600000000000000000001001679754956625544521335670993920702577/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_pr1897": "1006715043874455478664329006079297423001688561497419704539672479837135451739674361173694343867155367725548683091413779027929551879834587857228699363307043284265037472609377072285154581900446243662887524441186023215859446961325442118043438120199310745828780232512516305324306943017211077242680744434393314433588274761550349000660172924284716285729842294237690773961388228044344622498585347863453689118814253082419197486359454032147189198319033143866021423837056207677317517847011467076188001061138620310116832610271556685687769184940440093096226243113127523863162928128796969576356494654526264864467/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "improvement_over_previous_local_final": "477749790400418148631/500000000000000000000000", + "improvement_over_previous_package": "10086500976855635663689448641223998986170598784229341400200650717283025923262102542077285802551153/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "lambda_above_internal": "1/1400000000", + "lambda_above_sigma": "3/1400000000", + "lambda_above_tau": "1/1400000000", + "lambda_prime_above_lambda": "1/1400000000", + "lambda_prime_above_leaf": "699059733/245000000000000000", + "leaf_saving_above_effective": "349059733/245000000000000000", + "main_transform_above_kappa": "524529867/122500000000000000", + "membership_arithmetic_fits_record": "1/700000000", + "microbox_face_corrections_above_kappa": "2155924779/28000000", + "microbox_halo_volume": "55300000003/700000000", + "polynomial_products_above_kappa": "69811947/70000000", + "positive_layout_slack": "1/700000000", + "q_below_effective": "1/700000000", + "q_below_internal": "1/700000000", + "q_below_leaf": "699059733/245000000000000000", + "q_positive": "470133/175000000", + "short_record_fallback": "349059733/350000000", + "source_axis_superpolynomial": "1/700000000", + "sparse_union_movement_above_kappa": "49765625699529867/122500000000000000", + "stop_below_one": "699999999/700000000", + "stop_positive": "1/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000", + "union_tag_work_per_visit_fits_record": "3/700000000" + }, + "legacy_backoff": "21/5000000000", + "legacy_grid": 10000000000, + "minimum_margin_minus_kappa": "524529867/122500000000000000", + "rejected_controls": { + "closed_epsilon": [ + "actual_logarithmic_gamma_guard", + "epsilon_below_one", + "gaussian_above_main", + "global_gamma_power_slack", + "new_semantic_guard_with_C1_one", + "source_axis_superpolynomial" + ], + "closed_uniform_gap": [ + "new_complex_uniform_saving_above_b" + ], + "group_equals_dimension": [ + "group_below_dimension", + "group_key_fits_record", + "membership_arithmetic_fits_record" + ], + "insufficient_BIT": [ + "actual_bit_above_effective" + ], + "missing_layout": [ + "positive_layout_slack" + ], + "old_per_axis_scan": [ + "old_per_axis_scan_above_kappa" + ], + "unfunded_kappa": [ + "boundary_algebraic_matrix_above_kappa", + "fused_gaussian_above_kappa", + "global_coordinate_router_above_kappa", + "group_bit_router_above_kappa", + "main_transform_above_kappa" + ] + } + }, + "predecessor_H": 16201843136005340321, + "rank_exponent_reduction_factor": "16201843136005340321/349300000000", + "rejected_mutations": [ + { + "failed_at": "complete charged normalized moment", + "mutation": "too_short_product" + }, + { + "failed_at": "tail moment exponent at least one", + "mutation": "sublinear_tail" + }, + { + "failed_at": "strict finite ranks", + "mutation": "lost_separation" + } + ], + "schema": "higher-moment-native-strictification/1", + "scope": "Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.", + "source_sha256": { + "research/higher-moment-strictification/vendor/FINITE-PRECOMPILATION.md": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "research/higher-moment-strictification/vendor/FINITE-TEMPLATE-CLOSURE.md": "3f8508c63862dd83968bd30df91b08ba5afcee1e10db15ca546cdff0caef95d9", + "research/higher-moment-strictification/vendor/LOG-MAJORANT.md": "3b74b9b22258bd265a025a7e6f06f199e1625f3f0b735b972e6e91047eeb8e45", + "research/higher-moment-strictification/vendor/check_ledger.py": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98", + "research/higher-moment-strictification/vendor/invoice-review/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "research/higher-moment-strictification/vendor/invoice-review/vendor/NOTICE.md": "da983933f88516f311b2bb8750802e4bd03a537eacc0bde351cfb36b77a93f15", + "research/higher-moment-strictification/vendor/invoice-review/vendor/P7-FACTOR.json": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "research/higher-moment-strictification/vendor/invoice-review/vendor/RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab", + "research/higher-moment-strictification/vendor/invoice-review/vendor/SUPPLIER-RESULT.json": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6", + "research/higher-moment-strictification/vendor/invoice-review/verify.py": "a72b0c0da8beedbdd1a65e83009295c31fcd30664e85aeb1b620235042cbf0b5", + "research/higher-moment-strictification/vendor/outer_endpoint.py": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "research/higher-moment-strictification/vendor/p7-ENDPOINT.md": "e7056020bb9757d45fdf1a8eea9e811040ce72d53bc16e7f90f72a5e712fa3e9", + "research/higher-moment-strictification/vendor/p7-NATIVE.md": "26bf9312cdb496b1113c9ddd8aa0fa922ed9e480005703212942af358394183d", + "research/higher-moment-strictification/vendor/p7-RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab", + "research/higher-moment-strictification/vendor/p7-TENSOR.md": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + "status": "PASS_HIGHER_MOMENT_STRICTIFICATION", + "strictification": { + "alpha": { + "lower": "0.999999984403907977028692329024", + "upper": "0.999999984403907977028692329025" + }, + "ambient": "121^150", + "cutoff_base": 10, + "delta": { + "lower": "0.877942785206780917722562601792", + "upper": "0.877942785206780917722562601793" + }, + "floor_base": 15, + "gamma": { + "lower": "0.903981539721477814868265523050", + "upper": "0.903981539721477814868265523051" + }, + "materialized_product_or_uniform_word": false, + "maximum_paid": "10^150", + "minimum_target": "15^150", + "normalized_paid_upper": "1000000635204363556136250491144161837938214611877310981113991233610194892493163042995932145748443566398677069212449817849347590568236176459579539001979969712918643865874634198553766207360874447748594152802372160823515706917812863624324588309448164247279181670682524587922166460943924036141865870233593287572765694512062966529681268238027148629402289227769948550454004579273122673115283917084645472692704053780372399331749927451738974321744119172945600769747/1000001500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "old_rank_one_bound_lower": { + "lower": "2.524485503105612497245887828271", + "upper": "2.524485503105612497245887828272" + }, + "old_rank_one_gamma": { + "lower": "0.998191712473006243732169576257", + "upper": "0.998191712473006243732169576258" + }, + "paid_moment_exponent": "16216419/12500000", + "productive_fields_before_uniform_compiler": "7688^150", + "rank_one_surplus": "131723^150-131115^150", + "rational_upper_limits": [ + "99999999/100000000", + "181/200", + "439/500" + ], + "strict_moment_gap": { + "lower": "0.000000864794339252354870976549", + "upper": "0.000000864794339252354870976550" + }, + "tail_offset_u": "3/10", + "tensor_power": 150, + "tested_saving": "33581/12500000" + }, + "tail_only_power_majorant": { + "H0": 37443877100, + "H1": 140829080288374101, + "N": "2^140829080288374101", + "scope": "Tail transformation alone, retaining the older power majorant.", + "theta_upper": "6/7" + }, + "tensor_power_reduction_factor": "208/5", + "uniform_rank": { + "H": 349300000000, + "N": "2^349300000000", + "eta": { + "lower": "0.144386809622024146828684313913", + "upper": "0.144386809622024146828684313914" + }, + "eta_minus_theta_to_p": { + "lower": "0.009586237698168518342122636732", + "upper": "0.009586237698168518342122636733" + }, + "gap": "1/700000000", + "grid_step": 700000000, + "integer_test": { + "left_base": 349300000001, + "left_exponent": 13, + "right_base": 2, + "right_exponent": 499 + }, + "logarithm_power": 13, + "m_to_saving": { + "lower": "6.907234273066686405887998346942", + "upper": "6.907234273066686405887998346943" + }, + "previous_grid_point_rejected": true, + "smaller_logarithmic_power_rejected": true, + "t": "12466419/12500000", + "theta_upper": "6/7", + "uniform_saving": "376107/140000000" + }, + "verifier_sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" +} diff --git a/research/direct-mixed-flow/vendor/p7-NATIVE.md b/research/direct-mixed-flow/vendor/p7-NATIVE.md new file mode 100644 index 0000000000..394d9a03c1 --- /dev/null +++ b/research/direct-mixed-flow/vendor/p7-NATIVE.md @@ -0,0 +1,180 @@ +# Complete all-fresh p7 native controller + +This package extends PR4359's exact local construction at +`da637c87c89482bc4c86be36bd0071b3d400dbed`. It uses the newly regenerated p7/keep232127 +Laurent word, the authenticated THREE-base full-identity native supplier, +and the source whole-job helper normalizers. The new checks establish finite +physical contacts and complete inventories. The native all-column semantics, +permitted scalar/routing primitives, uniform compiler and outer analytic +transfer remain explicit inherited premises. + +## 1. Literal word and actual arbitrary inputs + +The selected p7 controller has 15 chronological native calls, seven main pairs, +and 112 ports in each side of a pair. Its right scalar program runs first, +then its literal LOCAL/IDLE/ADD/SIGNED_SWAP program, then its left scalar +program. An independent exact Laurent interpreter replays this entire order +and checks every coefficient of the resulting diagonal operator on all 14 +formal input roles. Changing one backward local orientation to forward must +fail that equality. + +`factor_receipt.py` authenticates the exact original factor generator and its +two imported dependencies, regenerates only mask 232127, and compares every +serialized coefficient, boundary word, diagonal monomial and literal event +with `P7-FACTOR.json`. The independent Laurent replay then checks the complete +word separately. This is one admitted mask, not an exhaustive p7 census or +an optimality claim. + +There are 1,568 independent main input arrays. Each of the 15 native calls +also gets 408 distinct fresh arbitrary helper fields, named by stage and +native helper role. The total is 6,120 additional independent inputs. A +helper is never a copy, a main idle field or another stage's helper. The +source native word accepts every persistent input arbitrarily, returns each +helper autonomously, and has no external cleanup bank. Its one owned center +is initialized and erased and receives no productive credit. + +Apply helper normalizers only around a whole local native invocation. Their +actual endpoint widths are 5,6,7,8,9 with counts 28,18,56,93,213 per invocation. +The source gate authenticates the underlying word, both orientations, +helper boundaries and arbitrary-input receipt. It also restores the original +eight rank-eight center jobs per invocation; their former 3+5 split is +unnecessary before the new tensor strictification. The exact midpoint and +absolute phase remain checked against the original native receipt. + +## 2. Native owner maps at ambient rank 121 + +The old source utility used a fixed 73-axis container. Its owner formula has +a dimension-independent extension, which is checked here at every one of +15 stages and 112 ports rather than assuming that the old container extends. + +For port normal q, let b_1,...,b_8 be the actual first eight orthogonal axes +from its pinned initial idle recipe. The checker establishes + +``` +b_i dot b_j = delta_ij, b_i dot q = 0. +``` + +At stage s>0, let e_i be the fresh coordinate axes in positions +`9+8*(s-1),...,9+8*s-1`. Put `v_i=b_i+e_i` over F2 and define + +``` +G_s(x) = x + sum_i (v_i dot x)*v_i. +``` + +The v_i are mutually orthogonal isotropic vectors. Hence G_s is orthogonal +and involutive, swaps each b_i with its corresponding fresh e_i, and fixes q. +Stage zero uses the identity. The checker verifies the complete 121-column +matrix and its involution, orthogonality and q action in every stage/port. +All coordinates outside the original nine-axis block and that stage's fresh +eight-axis block are fixed. This supplies a legal full-field coordinate map. + +Write C_a for the source Gaussian factor on a nonzero binary axis a. Its +Fourier multiplier is a Z4 phase. The phase polynomial of a product of C_a +factors has linear terms modulo4 and quadratic coefficients modulo2; +higher parity terms vanish modulo4. A physical translation adds an even +linear phase. Every C_a product and translation has multiplier one at +Fourier address zero, so its constant phase is independently fixed to zero. +Comparing the stored linear and quadratic parts therefore proves the full +phase, rather than merely the polar rank. + +Let `F_s` denote the positive product on the first `9+8*s` axes and let + +``` +D_0 = F_0*C_q^(-1), +D_s = product of positive factors on fresh block s (s>0). +``` + +For each forward/backward native call the checker constructs the four +entry/exit coordinate-and-translation maps between its actual main references +and a shared spectator frame. It verifies both map directions, the exact +raw diagonal difference D_s, and the cross operator D_s*C_q^(-1) for a +forward call or D_s*C_q for a backward call. Thus the raw local contracts are + +``` +forward: D_s * [[1,0],[C_q^(-1),1]], +backward: D_s * [[1,-C_q],[0,1]]. +``` + +These are raw-input operator equalities, so they remain valid after the +controller's earlier scalar basis changes and on arbitrary correlated data. +The exact audit covers all 6,720 main contacts (15*112*4), with inverse maps. +The all-column lift replaces each coordinate by its common column block; +this is the inherited native generator substitution, not an assertion that +tensor powers distribute over addition of matrices. + +## 3. Endpoint targets and all full idle jobs + +Every literal diagonal Laurent monomial has Q exponent +1 or -1 and stage +exponents zero or one. For each of all 1,568 main outputs, the checker builds +its actual positive target axes, proves their binary independence, and checks +the full Gaussian phase after the specified translation. The 784 endpoints +that require a nonzero translation reject its omission. + +The main target profile is `{25:448,41:448,57:448,121:224}`. The exponent +factorization alone is not used as physical admission: each target has the +separate 121-dimensional axis/phase check above. + +The controller retains twelve complete idle windows. All are paid at their +literal event on both main sides and every port: + +| Window index | Pair | Stages | Rank | Physical fields | +| --- | --- | --- | --- | --- | +|0|1|0,1|16|224| +|1|1|2|8|224| +|2|2|0,1,2,3|32|224| +|3|2|4|8|224| +|4|3|0,1,2,3,4,5|48|224| +|5|3|6|8|224| +|7|4|8|8|224| +|9|5|10|8|224| +|11|6|12|8|224| +|15|3|9,10,11,12,13,14|48|224| +|16|4|11,12,13,14|32|224| +|17|5|13,14|16|224| + +A Counter equality checks a bijection between this paid inventory and the +literal IDLE events; no omitted or duplicated metadata window can alter the +bill. Every emitted recipe retains its pair, stage list, port and both +physical owner names. + +For an initial window, begin with the source's exact rank16 axis list and +translation and append its later disjoint fresh blocks. For every other +window, use precisely its listed fresh blocks with zero translation. The +checker proves rank, independence and the complete phase identity against +the product of its D_s operators. A whole-job coordinate conjugation sends +these independent axes to a canonical rank-r call. Helpers are all fresh, +so there is no partially completed borrowed idle input and no helper/bridge +chronology to assume. The entire original idle operator runs at its original +literal event. + +## 4. Complete bill and new fixed constants + +The final raw inventory is + +``` +T = {5:420,6:270,7:840,8:1395,9:3195,25:448,41:448,57:448,121:224}, +P = {1:37305,2:10695,3:3360,4:1530,5:300,8:1464,16:448,32:448,48:448}. +``` + +There are 7,688 independent productive fields and 55,998 paid calls. Target +rank mass 131,723 minus paid rank mass 131,115 gives exact surplus 608. Maximum +paid rank 48 exceeds minimum target 5, so this raw word requires the separate +tensor construction, target completion and paid-call splitting before the +original compiler applies. + +The scalar bill includes the 15 oriented native words, every boundary ADD +and SCALE, every boundary swap as three additions plus one negation, all +literal bridges and all seven terminal signed swaps. Its conservative allowance +is 2,490,856. Every coefficient in the boundary word is a unit. Coordinate +routes, inverse routes and phase translations are additional finite movement +operations and must be counted in the newly expanded word. No old p3 movement, +prefix-growth, row-stock or precision constant is reused. + +Give every instantiated raw unit its own owned center for as long as that +unit is suspended. In every product or uniform compilation, retain all actual +scalar operations, native calls, whole-job routes and inverse routes, with +all owned initialization and erasure. The new full-word counts determine +replacement precision and storage constants. The finite construction is +specified algorithmically; its enormous final tensor/uniform word has not +been materialized. This is a conditional supplier construction, not an +unconditional integer-multiplication theorem. diff --git a/research/direct-mixed-flow/vendor/p7-RESULT.json b/research/direct-mixed-flow/vendor/p7-RESULT.json new file mode 100644 index 0000000000..ebb30a9b3b --- /dev/null +++ b/research/direct-mixed-flow/vendor/p7-RESULT.json @@ -0,0 +1,296 @@ +{ + "endpoint": { + "compiler": { + "H0": 4307773805920, + "H1": 16201843136005340321, + "N_encoding": "2^16201843136005340321", + "delta": "1/1400000000", + "exit_coefficient_log2_upper": "26640", + "final_strict_power_gap": "1/1400000000", + "h": "1/26", + "materialized_tensor_rule_or_uniform_word": false, + "negative_log2_eta_upper": "147931769/1250000", + "paid_max_bound_encoding": "10^6240", + "rank_one_induction": "131723^n > 131115^n; target padding adds equal paid and target rank, and splitting preserves rank", + "t": "12466419/12500000", + "target_max_encoding": "121^6240", + "target_min_encoding": "11^6240", + "tensor_power": 6240, + "theta_upper": "25/26", + "z": "139623893/140000000", + "z0": "1396238929/1400000000" + }, + "gain_over_PR4359": "38647/100000000", + "gain_over_PR4405": "19069/50000000", + "gain_over_PR4414": "33/5000000", + "gain_over_allfresh_p3": "5223/25000000", + "kappa": "268647/100000000", + "ledger_source_sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "minimum_outer_margin": "524529867/122500000000000000", + "negative_controls": { + "closed_epsilon": { + "actual_logarithmic_gamma_guard": "0", + "epsilon_below_one": "0", + "gaussian_above_main": "-1410399/122500000000000000", + "global_gamma_power_slack": "-1/7000000000", + "new_semantic_guard_with_C1_one": "0", + "source_axis_superpolynomial": "0" + }, + "closed_uniform_gap": { + "new_complex_uniform_saving_above_b": "0" + }, + "insufficient_BIT": { + "actual_bit_above_effective": "-270533/700000000" + }, + "unfunded_outer_point": { + "boundary_algebraic_matrix_above_kappa": "-525470133/122500000000000000", + "fused_gaussian_above_kappa": "-526410399/122500000000000000", + "global_coordinate_router_above_kappa": "-3/700000000", + "group_bit_router_above_kappa": "-1405641599/490000000000000000", + "main_transform_above_kappa": "-700470133/122500000000000000" + } + }, + "outer": { + "functional_checks": { + "fixed_halo_explicit_metadata_branch": "13475000001/175000000", + "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000", + "new_semantic_group_guard": "3/700000000" + }, + "margins": { + "boundary_algebraic_matrix": "329093274529867/122500000000000000", + "fused_gaussian": "329093273589601/122500000000000000", + "global_coordinate_router": "1880533/700000000", + "group_bit_router": "1316373794358401/490000000000000000", + "group_scans": "349999999/350000000", + "main_transform": "329093099529867/122500000000000000", + "microbox_face_corrections": "13475000001/175000000", + "polynomial_products": "699999999/700000000", + "sparse_union_movement": "50094718274529867/122500000000000000" + }, + "parameters": { + "a": "1880533/700000000", + "b": "940267/350000000", + "beta": "699999997/700000000", + "bit_saving": "27/10000", + "cap_xi": "111344718099529867/122500000000000000", + "complex_uniform_saving": "376107/140000000", + "d": "1/700000000", + "epsilon": "699999999/700000000", + "kappa": "268647/100000000", + "lambda_": "39892541/40000000", + "lambda_prime": "174529867/175000000", + "layout": "1/700000000", + "q": "470133/175000000", + "r0": "1/7000000000", + "stop": "1/700000000", + "tested_saving": "33581/12500000" + }, + "strict_checks": { + "actual_bit_above_effective": "9467/700000000", + "actual_logarithmic_gamma_guard": "1/700000000", + "actual_logarithmic_group_guard": "11155282162970133/61250000000000000", + "alpha_logarithm_absorption": "1/7000000000", + "boundary_algebraic_matrix_above_kappa": "699529867/122500000000000000", + "cap_above_band": "50094718099529867/122500000000000000", + "cap_below_cell": "11155281725470133/122500000000000000", + "cap_below_phase_cell_power": "133655281900470133/122500000000000000", + "complex_above_effective": "1/700000000", + "complex_below_one_over_32": "9997233/350000000", + "complex_endpoint": "1/350000000", + "epsilon_below_one": "1/700000000", + "epsilon_positive": "699999999/700000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "698589601/122500000000000000", + "gaussian_above_main": "87029867/61250000000000000", + "global_coordinate_router_above_kappa": "1/175000000", + "global_gamma_power_slack": "9/7000000000", + "group_below_dimension": "1/350000000", + "group_bit_router_above_kappa": "3494358401/490000000000000000", + "group_gauge_power_slack": "11155282154220133/61250000000000000", + "group_key_fits_record": "1/350000000", + "group_positive": "699999997/700000000", + "group_scans_above_kappa": "698119469/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "477749790400418148631/500000000000000000000000", + "lambda_above_internal": "1/1400000000", + "lambda_above_sigma": "3/1400000000", + "lambda_above_tau": "1/1400000000", + "lambda_prime_above_lambda": "1/1400000000", + "lambda_prime_above_leaf": "699059733/245000000000000000", + "leaf_saving_above_effective": "349059733/245000000000000000", + "main_transform_above_kappa": "524529867/122500000000000000", + "membership_arithmetic_fits_record": "1/700000000", + "microbox_face_corrections_above_kappa": "2155924779/28000000", + "microbox_halo_volume": "55300000003/700000000", + "new_complex_uniform_saving_above_b": "1/700000000", + "new_semantic_guard_with_C1_one": "1/700000000", + "polynomial_products_above_kappa": "69811947/70000000", + "positive_layout_slack": "1/700000000", + "q_below_effective": "1/700000000", + "q_below_internal": "1/700000000", + "q_below_leaf": "699059733/245000000000000000", + "q_positive": "470133/175000000", + "short_record_fallback": "349059733/350000000", + "source_axis_superpolynomial": "1/700000000", + "sparse_union_movement_above_kappa": "49765625699529867/122500000000000000", + "stop_below_one": "699999999/700000000", + "stop_positive": "1/700000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/700000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/700000000", + "union_tag_work_per_visit_fits_record": "3/700000000" + } + }, + "schema": "native-p7-padding-strictification-outer-endpoint/1", + "scope": "Source-bound native p7 geometry, a finite tensor recipe with target padding, exact moment and outer inequalities, and a specified finite uniform rank. Native tensor closure and the PR4359 inherited precision, storage, analytic, fixed-tape and recovery hypotheses are written premises, not a full formal theorem certificate.", + "status": "PASS_CONDITIONAL_P7_OUTER_POINT", + "strictification_source_sha256": "1f3c2a38b34d9dad7266be212ca5d0225827d8e05bda4831e6c25c5713f624f0", + "tested_saving": "33581/12500000" + }, + "independent_interval_crosscheck": true, + "scope": "Conditional native construction and exact finite arithmetic. The finite word and inherited physical, precision, analytic and fixed-tape proofs are not formally verified or materialized by this checker.", + "source_files": 23, + "status": "PASS_SOURCE_BOUND_CONDITIONAL_P7_PAID_PADDING_IMPROVEMENT", + "strictification": { + "alpha_interval": { + "lower": "0.99999998440390797702869232902431332", + "upper": "0.99999998440390797702869232902431333" + }, + "alpha_upper": "99999999/100000000", + "completion_decay_block_length": 2, + "controls": { + "one_decay_block_rejected": true, + "undamped_completion_rejected": true, + "unpadded_rank_one_tail_rejected": true + }, + "cutoff_base": 10, + "cutoff_encoding": "10^6240", + "decay_block_count": 16, + "decay_block_length": 390, + "delta_interval": { + "lower": "0.64382470915163933966321257464784307", + "upper": "0.64382470915163933966321257464784308" + }, + "delta_upper": "2/3", + "exponent": 6240, + "gamma_interval": { + "lower": "0.99819171247300624373216957625759087", + "upper": "0.99819171247300624373216957625759088" + }, + "gamma_upper": "4991/5000", + "materialized_tensor_or_completed_word": false, + "native_inventory": { + "artifact_hash_encoding": "Uncompressed UTF-8 JSON, sort_keys=True, separators=(comma,colon)", + "artifact_sha256": "12784fff6a13e3752ea6e80018e0484c5766a8adf2e88a7e71c80cf2bb68f398", + "contacts": 6720, + "dimension": 121, + "factor_receipt_sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "fresh_helper_fields": 6120, + "keep": 232127, + "limits": "Finite exact physical controller admission; inherited all-column local word, tensor strictification, new full-word precision/stock and outer transfer remain written proof obligations.", + "main_fields": 1568, + "native_scalar_allowance": 2490856, + "native_source_gate": "PASS_ACTUAL_ARBITRARY_HELPERS_AND_COMPLETE_PHASE_CORRECT_IDLE_JOBS", + "negative_controls": { + "omitted_endpoint_translation_rejected": 784, + "wrong_native_orientation_rejected": true + }, + "p": 7, + "paid": { + "1": 37305, + "16": 448, + "2": 10695, + "3": 3360, + "32": 448, + "4": 1530, + "48": 448, + "5": 300, + "8": 1464 + }, + "paid_calls": 55998, + "productive_fields": 7688, + "rank_margin": 608, + "scalar_allowance": 2490856, + "schema": "source-bound-p7-all-fresh-complete-native-controller/1", + "source_sha256": { + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "research/kappa-rebuild/bit/complex_controller_factor.py": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497", + "research/kappa-rebuild/bit/mixed_productive_bit.py": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e", + "research/kappa-rebuild/complex/fresh-certificates/THREE-base-HELPER-BOUNDARIES.json.gz": "f90517e395bde58c72cacd5d3481c4ea31d459fe4535384ac16547ac40460555", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39", + "research/kappa-rebuild/complex/full_identity_rebuild.py": "9af2ffbb0038c92e2a7d281081b0daaeadce75b11b566e5427845dc1af91e33d", + "research/kappa-rebuild/controller/P3-NATIVE-COVER.json.gz": "facfc6d6ecde151afb7e6a167776f3fdaac1c816e785a21a39f7f0bfd9140f3f", + "research/kappa-rebuild/controller/p3_native_cover.py": "fae71fcbbd20b9ee73b049cf6f43ea1d048217fb15feb6055a007e47da3363fe", + "research/kappa-rebuild/transfer-audit/p3_cover_audit.py": "a0fe9a26f77556e83b31b0c91fea909d6f3d8209d0f9f7ad4e5bc1375d33615e", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902" + }, + "status": "PASS_EXACT_LAURENT_ALL_MAIN_CONTACTS_ENDPOINTS_AND_FULL_IDLE_PHASES", + "targets": { + "121": 224, + "25": 448, + "41": 448, + "5": 420, + "57": 448, + "6": 270, + "7": 840, + "8": 1395, + "9": 3195 + }, + "whole_idle_profile": { + "16": 448, + "32": 448, + "48": 448, + "8": 1344 + } + }, + "new_max_target_encoding": "121^6240", + "new_min_target_encoding": "11^6240", + "normalized_moment_upper_rational": "10240625039/10240638976", + "paid": { + "1": 37305, + "16": 448, + "2": 10695, + "3": 3360, + "32": 448, + "4": 1530, + "48": 448, + "5": 300, + "8": 1464 + }, + "paid_rank_one_moment": 131115, + "productive_fields": 7688, + "rank_one_surplus_encoding": "131723^6240-131115^6240", + "schema": "p7-paid-target-completion-tensor-certificate/1", + "scope": "Exact moment bounds for the documented chronological native product, paid target completion and disjoint splitting. Native all-column, precision, storage, analytic and fixed-tape premises remain separate; no full multiplication theorem is formally verified.", + "source_sha256": { + "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + "status": "PASS_EXACT_P7_TARGET_COMPLETION_STRICTIFICATION", + "strict_moment_verified": true, + "strictification_gap": { + "lower": "0.00000136095023295546357907266586564", + "upper": "0.00000136095023295546357907266586565" + }, + "strictification_gap_rational": "13937/10240638976", + "target_floor_base": 11, + "target_floor_encoding": "11^6240", + "target_rank_one_moment": 131723, + "targets": { + "121": 224, + "25": 448, + "41": 448, + "5": 420, + "57": 448, + "6": 270, + "7": 840, + "8": 1395, + "9": 3195 + }, + "tested_saving": "33581/12500000", + "theta_upper": "25/26" + } +} diff --git a/research/direct-mixed-flow/vendor/theorem-1g.md b/research/direct-mixed-flow/vendor/theorem-1g.md new file mode 100644 index 0000000000..36d2399f35 --- /dev/null +++ b/research/direct-mixed-flow/vendor/theorem-1g.md @@ -0,0 +1,264 @@ +# Theorem 1G: mixed jobs with grouped paid blocks + +This note holds the proof behind the recursion lever of the record track: an extension of the τ-theorem (in the +form argued in [../../existence-routes/](../../existence-routes/), "Theorem 1") from paid moves of rank 1 to paid +blocks of any rank. It was written on 14 October 2026 by an AI agent working for me, in a simple model of jobs, and +it is reproduced here with its notation, cleaned of internal file names. + +**Status.** *Argued by hand, not checked.* Two independent AI skeptics tried to refute it on 14 October: one +re-derived the logic and simulated the construction with its own code, the other built the construction explicitly +(units, random matching inside the prescribed classes, a generic deadlock test) and checked the hypotheses of the +induction on the actual flows. Neither found an error. No person and no proof checker has read this text. A Lean +form of the theorem inside OpenAI's model was built on 19 October as part of the lever record (section 6); its +status is the record's: *proved in Lean*, as part of each of the five lever packages (in `package/leverF` and `package/leverB`, the modules under `Work/Mixed/` and `Work/MixedCost/`), with the official comparator accepting each result and three skeptics upholding each. + +Labels used inside the proof: [argued] (an argument given here in full, by hand; no proof checker has read it), +[computed] (a program, named in section 4), [what-if] (a price that rests on an unchecked step), [open]. + +## 0. The job model + +This is the model of the τ-theorem's proof, recalled so that this note can be read alone. + +- A **job of size s** is: apply the Walsh-Hadamard transform H on s chosen address bits of a register holding + 2^ν entries (ν ≥ s), that is, a batch of 2^(ν-s) independent transforms of size 2^s. Its cost is counted per entry: + T(s) is the number of full passes over the register (one per single-bit Hadamard leaf, one per free pass). A pass + over a fraction w of the entries costs w. +- A **rule** (a mixed unit) at block m: a word, correct for every number f of digit columns, with W_k registers + carrying a **rank-k target** (k of the m rows transformed, the other m - k untouched), paid blocks, and F free + register-passes. Applied at column c it turns jobs of the target sizes kc into jobs of the paid sizes r_j c. +- **Split**: a job of size a + b is the job of size a followed by the job of size b (Hadamards on disjoint bits + commute), at cost T(a) + T(b). A **plain leaf** of size s costs s passes. +- **Φ_τ** of a set of jobs (weighted by fractions of entries) is the sum of weight times size^τ. +- **τ** of a rule is the root in (0, 1) of Σ_j r_j^τ = Σ_k W_k k^τ (the *balance*). With every r_j = 1 this is the + τ-theorem's M = Σ_k W_k k^τ. + +The community's recursion is this model with one target size: a paid block is a recursive call on a whole register, +and the W arrays of the next level are W slices of that one call's batch. A rule with targets of two sizes needs jobs +of two sizes at once, which no single call's batch provides; that is what the construction below supplies. + +## 1. Re-check of the rank-1 case (the τ-theorem) + +- **Step 1 (multinomial flow).** With p_k = W_k/M and u(a) = multinomial(|a|; a) Π p_k^(a_k), Pascal's rule gives + u(b) = Σ over k with b_k ≥ 1 of p_k u(b - e_k) for b ≠ 0, so M u(b) = Σ_k W_k u(b - e_k). The region + R = {a : m c(a) ≤ L} is down-closed. A frontier point b (not in R, with some b - e_k in R) has size + c(b) = k c(b - e_k) ≤ kL/m ≤ L and c(b) > L/m. Confirmed [argued]. An exact re-run found 0 unbalanced sizes, + Φ(sources) = M to 10 digits, and sources in (L/3, L] [computed]. +- **Step 2 (Φ conservation).** Each unit is Φ-neutral at τ, so Φ(sources) = Φ(leaves) = M. Confirmed. +- **Step 3 (free passes).** The sum of u over generation j is (W/M)^j, so the sum of u is at most M/(M - W), and the + free passes come to F/(M - W) per unit of leaf Φ. The passes spent re-grouping portions (one per class level) cost + O(1) per register used by a unit, so they fold into F. +- **Lemma 2 (lockstep).** Process(g, λ) issues move k of all units in the class. The outputs plus (λ/M) Source at + generation g equal (λ/M) J at generation g, which is exactly what the child consumes. At level g there are + M^(g_max - g) calls with λ = M^-(g_max - g), so the sources used add up to Source exactly [argued]. The literal + simulation was re-run on 1+4 in 10 at L = 12, 30, 54, on 1+1 in 4 at L = 30, and on 7+38 in 88 at L = 12 + (7,833 classes): every class was fed exactly, the sources used equal Source, and the leaves equal M u(0) + [computed]. +- **Step 5 (top split and constant).** Every rest has size s - c(a) < (1 - 1/m)s. The induction closes with + C' = (A + c0)/(1 - (1 - 1/m)^τ). A sharper constant is C' = (A + c0)/η_m with + η_m = min over t in [1/m, 1] of (1 - (1-t)^τ)/t^τ, which is at least 1 - (1-1/m)^τ (Lemma A below). +- **Rounding.** The number of fluid portions is the number of lockstep classes, at most M^(g_max+1) = n^O(ln M/ln k_min). + That is polynomial in n, not the number of lattice points, and still far below 2^(n/2) batch entries, so dyadic + rounding costs a relative 2^-Ω(n). The claim stands; only the count in the earlier text was wrong. +- **A hypothesis that both theorems need and the earlier text did not state.** Each unit must be a correct word at + every column count f that occurs: products of target ranks in the rank-1 case, and products of target and paid ranks + in Theorem 1G. The community's engine also asserts m^2 > 2 max(r)^2; what that halving constraint asks of a new + recursion was not examined here. + +## 2. Lemma A: the top-split induction with leftovers (the exact condition) + +**Setting.** T(n) is the per-entry cost of the best schedule for a job of size n (with at least n/2 batch bits). A +*flow for n* consists of: +- source weights w(s) ≥ 0 on sizes 1 ≤ s ≤ n, with Σ w = 1; +- exit weights x(e) ≥ 0 on sizes e < n: jobs the flow leaves over, each completed by a separate call of the whole + procedure; +- an internal cost I ≤ A Φ̂ (free passes, re-grouping, plain size-1 leaves), where Φ̂ = Σ_s w(s) s^τ; +- a deadlock-free order, given that each exit call returns a completed job. + +The schedule splits the top job into portions w(s), each portion being s + (n - s). The s-parts feed the flow, and +the (n - s)-parts and the exits are done recursively. So + + T(n) ≤ c0 + I + Σ_e x(e) T(e) + Σ_s w(s) T(n - s). + +**Lemma A** [argued]. Let ψ ≥ 1 be nondecreasing, and let β > 0 and n0 be such that for every n ≥ n0 there is a flow +with + + (E) Σ_e x(e) e^τ ψ(e) + ψ(n) Σ_s w(s) (n - s)^τ ≤ ψ(n) (n^τ - β Φ̂). + +Then T(n) ≤ C n^τ ψ(n) for all n, with C = max{ max_{n L gives ρ_s c(b) > r_j L/m. Some b - e_k lies in R(ρ_s), so ρ_s c(b) ≤ kL/m ≤ L. ∎ + +**Lemma D (exits)** [argued]. Outputs leave the tree only at generation 0 (d = G). There each class has at most one +unit (at column ρ_s, present when m ρ_s ≤ L), and its P outputs have sizes ρ_s r_j. Φ(exits) = Φ(sources) exactly. +Every exit has size e ≤ r_max · r_max^G ≤ r_max (L/m)^θ with θ = ln r_max / ln k_min < 1, so ln e ≤ θ ln L. Exits of +size 1 are plain leaves. +*Proof.* By Lemma B, outputs at generation ≥ 1 are all consumed. Every unit is Φ-neutral at τ, and every consumed job +was produced or sourced, so Φ(exits) = Φ(sources). G ≤ log_(k_min)(L/m) because c(a) ≥ k_min^|a|, which gives +ρ_s ≤ r_max^G ≤ (L/m)^θ. Finally r_max ≤ m^θ (since r_max = k_min^θ ≤ m^θ), which gives ln e ≤ θ ln L. ∎ + +**Lemma E (number of units)** [argued]. units ≤ Φ(sources) / (W k_min^τ (1 - k_min^-τ)), with no log factor. +*Proof.* A unit at depth d sits at column ≥ c(a) ≥ k_min^(G-d), and its input Φ is +Σ_k W_k (k · col)^τ ≥ W k_min^τ k_min^(τ(G-d)). The total input Φ at each depth is at most Φ(sources), since Φ only +moves down through the tree or leaves it. Summing the geometric series over G - d gives the bound. ∎ + +**Lemma F (order: no deadlock)** [argued]. Procedure Process(s), called with the parent's round-j outputs pending: +1. the class's inputs are exactly those outputs plus top sources (Lemmas B and C); +2. for j = 1..P: issue round j of every unit of s, running the word's free steps between moves as the word says; if + d(s) = G, complete each exit job by a top call Do(e); otherwise call Process(s.j); +3. return. +A round j+1 is issued only after Process(s.j) has returned, which means every unit that consumed a round-j job has +finished. A unit starts only after all its inputs exist. So this is a straight-line program. Its recursion depth is +G + 1, and every exit call is a smaller instance (e < n). ∎ + +A careless order does deadlock: if a unit took one input from round 1 of unit A and another from round 2 of A, while +A's round 2 waits for that very unit, nothing can start. Lockstep classes, in which each child class takes only the +outputs of one round, rule this out. + +**Theorem 1G** [argued, job model]. Under (S): T(n) ≤ C n^τ (ln n)^κ for all n ≥ 3, where +κ = ⌈ln(2/η_m) / ln(1/θ)⌉ (κ = 0 when r_max = 1) and C depends only on the rule. So T(n) = O(n^(τ+δ)) for every +δ > 0. +*Proof.* Take L = n. The flow is the tree normalised to source weight 1. The sources lie in (n/m, n] (Lemma C), so +K = m. The internal cost I ≤ A Φ̂ with A = (F + O(W))/(W k_min^τ (1 - k_min^-τ)) (Lemma E, plus one size-1 leaf per +unit of leaf Φ). The exits satisfy Φ(exits) = Φ̂ and ln e ≤ θ ln n (Lemma D). The order is valid (Lemma F). Lemma A3 +applies with ψ = max(1, ln)^κ and β = η_m/2. The batch-bit and dyadic-portion arrangements are as in section 1: the +number of classes is at most Σ_d P^d = n^O(ln P / ln k_min). ∎ + +*Remarks.* +- With every r_j = 1 the tree is the rank-1 construction (ρ = 1, exits = leaves), and κ = 0 recovers O(n^τ). +- Exact O(n^τ) for grouped rules, with no log factor, would need a flow with Φ(exits) ≤ (η - β) Φ̂ (Lemma A2). This + tree has Φ(exits) = Φ̂, so by A4 it cannot give that [open]. +- The log factor costs nothing in the exponent: every saving below 1 - τ is reached with a fixed constant. OpenAI's + goal is a big-O statement, so an existential constant is allowed. +- Without (S): Lemma B needs r_j ≤ k for the pairs that meet, and Lemma D needs r_max < k_min. The case r_max ≥ k_min + is open. An example (targets {3:1, 2:4}, paid {1:6, 2:2}) has a fluid linear programme whose optimum was still rising + at n = 480. + +## 4. Numerical checks [computed] + +Every program named here is in [../programs/theorem-1g/](../programs/theorem-1g/) and its output in +[../data/theorem-1g/](../data/theorem-1g/). All were re-run on 19 October 2026 for this revision, on an Apple +M4 Mac mini with Python 3.9, in under a minute each and under 300 MB; every output was identical to the one made on +14 October. + +Three test rules, plus a control: +- A: targets {4:1, 3:2}, rounds 1,1,1,1,2,2 (τ 0.746375; θ 0.631, κ 3); +- B: targets {7:1, 4:1}, rounds 1,1,1,1,2,2,2 (τ 0.928234). This is the truncation of the pure rule {7:2} with paid + {1:4, 2:3} plus a rank-3 idle block; +- C: targets {5:1, 4:3}, rounds 1×6, 2×2, 3×2 (τ 0.930659; θ 0.792, κ 4); +- D: the rank-1 control 1+4 in 10. + +1. **Literal lockstep** (`tree_flow.py`): explicit round sequences, each round in word order. A, B and C were run at + L = 40 and 150 (up to 259 classes). Every class was exactly fed (no surplus, no deficit), the sources used equal the + merged count, and the exits match the merged count by size. +2. **Merged exact checks** at L = 10^3, 10^5, 10^7 (up to 1.6e10 classes, counted with multiplicity): 0 unbalanced + points; all sources in (L/m, L]; Φ(exits)/Φ(sources) = 1.000000000000; the largest exit at or below the bound + r_max (L/m)^θ (16,384 ≤ 21,761 for A at L = 10^7, 2,048 ≤ 2,391 for B, 177,147 ≤ 295,508 for C); the unit count + within the bound of Lemma E. +3. **Cost of the whole schedule** (`recur.py`; F = 0, L = n, exits by recursive calls), T(n)/n^τ: + + | rule | n = 50 | n = 400 | n = 3,200 | n = 6,400 | + |---|---|---|---|---| + | A | 1.612 | 1.896 | 2.034 | 2.052 | + | B | 1.144 | 1.197 | 1.218 | 1.229 | + | C | 1.177 | 1.192 | 1.249 | 1.246 | + | D (rank-1 control) | 1.162 | 1.180 | 1.183 | 1.183 | + + The grouped rules grow slowly, far below (ln n)^κ; A's local slope over the last doubling is 0.759 against + τ = 0.746 and falling. The control is flat, as the rank-1 theorem says. +4. **Re-check of the rank-1 theorem** (`recheck_t1.py`, which imports the τ-theorem's own programs from + [../../existence-routes/programs/tau-theorem-and-laser/](../../existence-routes/programs/tau-theorem-and-laser/)). +5. **The community's circuit T74, as a what-if** (`hub_whatif.py`). Control: the balance with one job size reproduces + the community's figure for T74, 1.6797550e-3 (1.6797549561e-3). The mixed price, assuming every idle block of T74 + is a head or a tail on its own array, is 1.8169468e-3 (+8.17 %), separated (8 < 25). **This assumption turned out + to be false**: only 11,010 of the 22,748 idle blocks are heads and none is a tail (the README of this section, + section 4.5), so this figure is **refuted** as a price of T74. It stays here as the test it was. + +The skeptics' own programs, written from this text without reusing its code: +- `indep_tree.py` rebuilds the merged tree independently (toy rule A and the T74 mixed rule up to L = 10^8): + 0 unbalanced points, Φ ratio 1, exits within the bound. `partial.py` prices partial truncation, which showed that + the result depends on how many idle blocks really are heads. +- `explicit_sim.py` builds explicit unit objects, matches outputs to inputs at random inside the prescribed classes, + and runs a generic topological sort of start, issue and finish events as a deadlock test independent of Lemma F; + Φ is tracked to 50 digits. Every lockstep run is deadlock-free with Φ(exits) = Φ(sources); a deliberately careless + matching across classes deadlocks, as it should. +- `cost_fit.py` and `check_E.py` compute the actual flows up to n = 12,800 and check hypothesis (E) of Lemma A3 at + every n there, the unit bound of Lemma E and the exit bound; for the T74 rule `check_E.py` checks every n up to + 20,000 and every 997th n up to 3,000,000. No violation anywhere. They also + confirm Lemma A4: (E) with ψ = 1 fails at every n, as predicted. + +## 5. What the new recursion needs that the community's uniform recursion does not have + +The community's recursion is one call per job: a call of size s slices its own batch into W rank-m arrays at column +s/m, and each paid block is an independent recursive call; no call ever needs a job of another size. Theorem 1G needs: +1. **Several sizes at once.** A unit at column c takes rank-73 arrays of size 73c and smaller ones (rank 49 for the + half cut, rank 25 for the full cut) in a fixed ratio. These come from different producers' outputs, never from one + call's batch. +2. **Fluid portions.** Classes are fractional portions of batches, which needs a portion and relabel step in the cost + model and dyadic rounding with at least n/2 batch bits (the class count is polynomial in n). +3. **A class tree in lockstep**, ordered as in Lemma F. +4. **A top split** of the top job into frontier portions of sizes in (n/m, n] plus rests, done recursively. +5. **Exit calls.** Jobs of size ρ_s r_j are completed by fresh top calls. +6. **Mixed-target words.** The word with the head blocks removed or shortened must be proved correct for the reduced + targets at every column count f that occurs. +7. **Hypothesis (S).** On the circuits of the record track it holds with room: for the half cut every paid rank is at + most 48 and the smaller job is 49; for the full cut every paid rank is at most 24 and the smaller job is 25. +8. **The structure of the circuit.** Each block that is cut must be the first operation on its array, acting on that + array alone (the truncation lemma of [../../existence-routes/](../../existence-routes/)). This is the head test + of the README, section 4.5. + +## 6. The Lean form + +On 19 October the recursion was written in Lean inside OpenAI's RAM model as part of the lever record. Two things +changed against the plan in section 5: + +- **No log factor.** The Lean cost bound does not use Lemma A3. It applies Lemma D at a rate point z1 and argues that + for every exponent z above z1 the exits' share of the sources' Φ shrinks by a factor at most 2 (E m/n)^(z - z1), + where E = r_max^(G+1) bounds the exits; since E m/n tends to 0, Lemma A closes with ψ = 1 for all large n, and a + finite maximum covers the small ones. The statement is: if the balance holds at z1, then for every z in (z1, 1] there + is a constant C with cost ≤ C · 2^n · (n + 1)^z. The constants exist but are astronomically large; only their + existence is used, which OpenAI's big-O goal allows. Lemma A4 is not contradicted: it concerns the exponent τ itself. +- **The program.** Units are coded as sequences of roles (the Pascal bijection of Lemma B as arithmetic on codes); + each paid block of a class becomes one child call whose answers are read back ("Hadamards on disjoint bits + commute"); the leaf class hands its exits to one fresh top call; the order is the lockstep order of Lemma F, by + induction over the word. + +Status of this Lean form: *proved in Lean*, as part of each of the five lever packages (in `package/leverF` and `package/leverB`, the modules under `Work/Mixed/` and `Work/MixedCost/`), with the official comparator accepting each result and three skeptics upholding each. Its module and theorem names are listed in the lever package +(package/leverB/). diff --git a/research/direct-mixed-flow/vendor/tree_flow.py b/research/direct-mixed-flow/vendor/tree_flow.py new file mode 100644 index 0000000000..31a9c1ae4d --- /dev/null +++ b/research/direct-mixed-flow/vendor/tree_flow.py @@ -0,0 +1,167 @@ +# tree_flow.py (bound-check/rl-prove, 14 Oct 2026). The DILATED LOCKSTEP TREE of PROOF.md section 3 (Theorem 1G), +# for a mixed rule with GROUPED paid blocks: targets {k: W_k} (k in K), rounds r_1..r_P (P_r rounds of rank r), and +# the separation hypothesis r_max < k_min. Exact integers / fractions. +# u(a) = multinomial(|a|; a) prod_k W_k^a_k (a in N^K), c(a) = prod_k k^a_k, m = max K, +# R(rho) = {a : m rho c(a) <= L}, G = max{|a| : a in R(1)}. +# Class s (a round sequence of length d <= G, rho_s = product of its ranks): u(a) units at column rho_s c(a) for +# every a in R(rho_s) with |a| = G - d. Round j of class s feeds class s+(j) only. +# Checks (merged by (d, rho) with path multiplicities N(d, rho)): +# (1) exact balance: at every point b in R(rho') the child's demand equals the parent's round output; +# (2) every other demand is a SOURCE of size in (r_j L/m, L] (root: (L/m, L]); +# (3) exits only at generation 0: P jobs of sizes rho*r_j per class, all <= r_max * (L/m)^theta, theta = ln r_max/ln k_min; +# (4) Phi conservation at tau_c: Phi(sources) = Phi(exits); (5) unit count <= Phi(sources)/(W k_min^tau (1-k_min^-tau)). +# Literal lockstep simulation (lockstep_literal): explicit recursion over round sequences, a pool of issued jobs per +# class, every class must find all its inputs issued (parent round j + sources) and consume every job it is given. +import sys +from fractions import Fraction as Fr +from math import factorial, log, prod +from itertools import product as iprod + +def tau_c(Wt, P): + lo, hi = 0.0, 1.0 + for _ in range(200): + mid = (lo + hi) / 2 + if sum(w * k ** mid for k, w in Wt.items()) > sum(p * r ** mid for r, p in P.items()): hi = mid + else: lo = mid + return (lo + hi) / 2 + +def lattice(Wt, L, rho): + """points a in R(rho), as tuples over sorted K, grouped by |a|""" + K = sorted(Wt); m = max(K) + pts = {} + def rec(i, a, c): + if i == len(K): + pts.setdefault(sum(a), []).append(tuple(a)); return + k = K[i]; e = 0; cc = c + while m * rho * cc <= L: + rec(i + 1, a + [e], cc); e += 1; cc *= k + rec(0, [], 1) + return pts + +def mult(a): + return factorial(sum(a)) // prod(factorial(x) for x in a) + +class Tree: + def __init__(self, Wt, P, L): + self.Wt, self.P, self.L = dict(Wt), dict(P), L + self.K = sorted(Wt); self.m = max(self.K) + assert max(P) < min(self.K), "separation r_max < k_min fails" + self.Wv = [Wt[k] for k in self.K] + self.lat = {} + self.G = max(lattice(Wt, L, 1)) + def R(self, rho): + if rho not in self.lat: self.lat[rho] = lattice(self.Wt, self.L, rho) + return self.lat[rho] + def u(self, a): return mult(a) * prod(w ** x for w, x in zip(self.Wv, a)) + def c(self, a): return prod(k ** x for k, x in zip(self.K, a)) + def inR(self, a, rho): return self.m * rho * self.c(a) <= self.L + def units(self, d, rho): + return {a: self.u(a) for a in self.R(rho).get(self.G - d, [])} + def demand(self, d, rho): + need = {} + for a, ua in self.units(d, rho).items(): + for i, k in enumerate(self.K): + b = list(a); b[i] += 1; b = tuple(b) + need[b] = need.get(b, 0) + self.Wt[k] * ua + return need + +def check(Wt, P, L, tau=None): + T = Tree(Wt, P, L); tau = tau_c(Wt, P) if tau is None else tau + G, m, kmin, rmax = T.G, T.m, min(T.K), max(P) + theta = log(rmax) / log(kmin) if rmax > 1 else 0.0 + N = {(0, 1): 1} + src_w, src_phi, ex_w, ex_phi, units, bad = 0, 0.0, 0, 0.0, 0, [] + src_sizes, ex_sizes = set(), {} + # root + for b, x in T.demand(0, 1).items(): + s = T.c(b) + if T.inR(b, 1): bad.append(('root demand inside R(1)', b)) + if not (L / m < s <= L): bad.append(('root source size', s)) + src_w += x; src_phi += x * s ** tau; src_sizes.add(s) + for d in range(0, G + 1): + layer = {k: v for k, v in N.items() if k[0] == d} + for (_, rho), n in layer.items(): + us = T.units(d, rho) + units += n * sum(us.values()) + if d == G: # generation 0: exits + for a, ua in us.items(): + assert a == tuple(0 for _ in T.K) + for r, pr in P.items(): + e = rho * r + ex_w += n * pr * ua; ex_phi += n * pr * ua * e ** tau + ex_sizes[e] = ex_sizes.get(e, 0) + n * pr * ua + continue + for r, pr in P.items(): # children via a round of rank r + rc = rho * r + N[(d + 1, rc)] = N.get((d + 1, rc), 0) + n * pr + need = T.demand(d + 1, rc) + supply = {a: ua for a, ua in us.items()} # parent round output at point a, size rc*c(a) + for b in set(need) | set(supply): + sup = supply.get(b, 0); dem = need.get(b, 0) + if T.inR(b, rho): + if sup != dem: bad.append(('unbalanced', d, rho, r, b, sup, dem)) + else: + if sup: bad.append(('supply outside R', b)) + s = rc * T.c(b) + if dem and not (r * L / m < s <= L): bad.append(('source size', s, r)) + src_w += n * pr * dem; src_phi += n * pr * dem * s ** tau + if dem: src_sizes.add(s) + emax = max(ex_sizes) + bound = rmax * (L / m) ** theta if rmax > 1 else 1 + ubound = src_phi / (sum(Wt.values()) * kmin ** tau * (1 - kmin ** -tau)) + return dict(L=L, G=G, tau=tau, unbalanced_or_bad=len(bad), bad=bad[:3], sources=src_w, Phi_src=src_phi, + exits=ex_w, Phi_exit=ex_phi, Phi_ratio=ex_phi / src_phi, src_size_range=(min(src_sizes), max(src_sizes)), + exit_max=emax, exit_bound=bound, units=units, unit_bound=ubound, classes=sum(N.values()), + ex_sizes=ex_sizes, src_sizes=sorted(src_sizes)) + +def lockstep_literal(Wt, P_list, L): + """Explicit recursion over round sequences (P_list = ranks of rounds 1..P in word order).""" + Pd = {} + for r in P_list: Pd[r] = Pd.get(r, 0) + 1 + T = Tree(Wt, Pd, L); G = T.G + st = dict(classes=0, src=0, exits={}, issued_before_start=True) + def process(path, rho, fluid): + d = len(path); st['classes'] += 1 + us = T.units(d, rho) + need = T.demand(d, rho) + # fluid = parent's round output (points in R(parent rho)); top it up with sources, then it must equal need + for b, x in need.items(): + have = fluid.get(b, 0) + if have > x: raise AssertionError(('surplus', path, b, have, x)) + if have < x: st['src'] += x - have # source from the top split (always available) + for b in fluid: + if b not in need and fluid[b]: raise AssertionError(('unconsumed', path, b)) + for j, r in enumerate(P_list): # rounds in word order; round j+1 only after round j completes + out = dict(us) # one job of rank r per unit, at point a, size rho*r*c(a) + if d == G: + for a, ua in out.items(): + e = rho * r; st['exits'][e] = st['exits'].get(e, 0) + ua # handled by a new top call Do(e) + else: + process(path + (j,), rho * r, out) + process((), 1, {}) + return st, T + +if __name__ == "__main__": + rules = [("A: targets {4:1,3:2}, rounds [1,1,1,1,2,2]", {4: 1, 3: 2}, [1, 1, 1, 1, 2, 2]), + ("B: pure {7:2}+idle 3 -> targets {7:1,4:1}, rounds [1,1,1,1,2,2,2]", {7: 1, 4: 1}, [1, 1, 1, 1, 2, 2, 2]), + ("C: targets {5:1,4:3}, rounds [1]*6+[2]*2+[3]*2", {5: 1, 4: 3}, [1] * 6 + [2] * 2 + [3] * 2)] + print("(A) literal lockstep (explicit round sequences):", flush=True) + for name, Wt, rl in rules: + for L in (40, 150): + Pd = {} + for r in rl: Pd[r] = Pd.get(r, 0) + 1 + ref = check(Wt, Pd, L) + st, T = lockstep_literal(Wt, rl, L) + ok = (st['src'] == ref['sources'] and st['exits'] == ref['ex_sizes']) + print(f" {name}, L={L}: G={T.G}, classes {st['classes']}, every class exactly fed, sources {st['src']} " + f"(= merged count: {ok}), exits by size {dict(sorted(st['exits'].items()))}", flush=True) + print("(B) merged checks at larger L:", flush=True) + for name, Wt, rl in rules: + Pd = {} + for r in rl: Pd[r] = Pd.get(r, 0) + 1 + for L in (1000, 10 ** 5, 10 ** 7): + ch = check(Wt, Pd, L) + print(f" {name}, L={L}: tau_c={ch['tau']:.6f} G={ch['G']} classes={ch['classes']} bad={ch['unbalanced_or_bad']} " + f"sources in {ch['src_size_range']} (L/m={L/max(Wt):.1f}); Phi_exit/Phi_src={ch['Phi_ratio']:.12f}; " + f"max exit {ch['exit_max']} <= bound {ch['exit_bound']:.1f}; units {float(ch['units']):.4g} <= " + f"bound {ch['unit_bound']:.4g}", flush=True) diff --git a/research/direct-mixed-flow/verify.py b/research/direct-mixed-flow/verify.py new file mode 100644 index 0000000000..df9ca12ad0 --- /dev/null +++ b/research/direct-mixed-flow/verify.py @@ -0,0 +1,274 @@ +#!/usr/bin/env python3 +"""Partial direct compiler, nested integer batches and exact size controls. + +The near-root direct exponent theorem remains open. No floating-point result +is used by this verifier. zxv with OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha1, sha256 +import json +import gzip +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def source(path): + env = {'__file__': str(path), '__name__': 'pinned_or_local_library'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + return env + + +FLOW = source(HERE/'flow.py') +Flow = FLOW['Flow'] + + +def authenticate(): + result = {} + prefix = Path('research/direct-mixed-flow/vendor') + for row in json.loads((HERE/'VENDOR.json').read_text())['files']: + raw = (HERE/'vendor'/Path(row['path']).relative_to(prefix)).read_bytes() + digest = sha256(raw).hexdigest() + need(digest == row['sha256'], 'changed source: '+row['path']) + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'changed Git source blob') + result[row['path']] = digest + return result + + +def bigint_record(n): + return {'bits': n.bit_length(), + 'unsigned_big_endian_sha256': sha256(n.to_bytes((n.bit_length()+7)//8, 'big')).hexdigest()} + + +def ratio_interval(n, d): + scale = 10**18 + low = n*scale//d + return {'lower': str(Q(low, scale)), 'upper': str(Q(low+1, scale))} + + +def compile_counts(targets, paid, maximum, force_unit_replication=False): + m, W, calls = max(targets), sum(targets.values()), sum(paid.values()) + surplus = sum(k*v for k, v in targets.items())-sum(k*v for k, v in paid.items()) + need(surplus > 0, 'positive raw rank-one surplus') + widths = [1]*(maximum+1) + leaves = list(range(maximum+1)) + units = [0]*(maximum+1) + columns = [0]*(maximum+1) + slots = [0]*(maximum+1) + largest_sources = 1 + for n in range(m, maximum+1): + f = Flow(targets, paid, n).merged() + a = 1 if force_unit_replication else widths[n-1] + widths[n] = a*f['source_count'] + leaves[n] = 0 + units[n] = a*f['units'] + columns[n] = a*f['column_mass'] + slots[n] = a*(f['source_count']+sum(f['exits'].values())+(W+calls)*f['units']) + for histogram, complement in [(f['sources'], True), (f['exits'], False)]: + for rank, count in histogram.items(): + e = n-rank if complement else rank + need(0 <= e < n, 'all recursive ranks strictly decrease') + need(a % widths[e] == 0, 'whole integer subprogram batches') + copies = count*(a//widths[e]) + for records in (leaves, units, columns, slots): + records[n] += copies*records[e] + need(widths[n] % widths[n-1] == 0, 'nested divisibility') + need(widths[n]*n-leaves[n] == surplus*columns[n], 'whole-word rank-one identity') + need(units[n] <= columns[n] <= widths[n]*n//surplus, 'owned-unit upper bound') + need(slots[n] <= 2*(W+calls)*units[n], 'all compiler routing slots counted') + largest_sources = max(largest_sources, f['source_count']) + f = Flow(targets, paid, maximum).merged() + Cmax = W*(W+calls+1)**(f['height']+1) + need(largest_sources <= Cmax and widths[maximum] <= Cmax**maximum, + 'single-exponential width envelope') + n = maximum + return {'n': n, 'productive_width': bigint_record(widths[n]), + 'paid_rank_one_leaves': bigint_record(leaves[n]), + 'raw_instances': bigint_record(units[n]), + 'column_mass': bigint_record(columns[n]), + 'routing_slots': bigint_record(slots[n]), + 'leaves_per_array': ratio_interval(leaves[n], widths[n]), + 'width_exponent_envelope': Cmax.bit_length()*n, + 'source_count_upper': Cmax, 'rank_one_surplus': surplus, + 'paid_above_99_percent_linear': leaves[n] > 99*widths[n]*n//100, + 'nested_batch_checks': maximum-m+1}, (widths, leaves, units, columns, slots) + + +def finite_flows(): + rules = [ + ('separated-control', {3:2, 4:1}, {1:4, 2:2}, [1,1,1,1,2,2]), + ('strict-overlap', {2:1, 5:1}, {1:2, 4:1}, [1,1,4]), + ('source-open-equality', {2:4, 3:1}, {1:6, 2:2}, [1]*6+[2]*2), + ] + old = source(HERE/'vendor/tree_flow.py') + rows = [] + for label, targets, paid, word in rules: + for n in (20, 40, 80): + f = Flow(targets, paid, n) + merged, literal = f.merged(), f.literal(word) + need(merged['sources'] == literal['sources'] and merged['exits'] == literal['exits'], + 'literal and merged whole-job flow agree') + if label == 'separated-control': + predecessor, _ = old['lockstep_literal'](targets, word, n) + need(merged['source_count'] == predecessor['src'] and + merged['exits'] == predecessor['exits'], 'unchanged separated predecessor') + need(not merged['boundary_exits'], 'separated case has no premature exits') + rows.append({'rule': label, 'targets': targets, 'paid': paid, + 'flow': merged, 'literal_classes': literal['classes']}) + strict = Flow({2:1, 5:1}, {1:2, 4:1}, 20).merged() + mass = lambda h: sum(k*v for k, v in h.items()) + without_boundary = strict['exits']-strict['boundary_exits'] + need(strict['boundary_exits'] and + mass(strict['sources'])-mass(without_boundary) > + strict['rank_one_surplus']*strict['column_mass'], 'omitted boundary exits undercharge') + return rows + + +def inherited_rank_size_bound(): + old = json.loads((HERE/'vendor/higher-moment-RESULT.json').read_text()) + p7 = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['strictification'] + T = {int(k): v for k, v in p7['targets'].items()} + P = {int(k): v for k, v in p7['paid'].items()} + v = old['strictification']['tensor_power'] + H = old['uniform_rank']['H'] + need((v, H) == (150, 349300000000), 'unchanged sufficient ambient rank') + W = sum(T.values())**v + paid_mass_upper = sum(k*n for k, n in P.items())**v+W*15**v + need(W < 2**1950, 'productive field exponent envelope') + need(paid_mass_upper < 2**2701 and W+paid_mass_upper+1 < 2**2702, + 'every padded/split paid call counted by its positive rank mass') + D = 1950+2702*(H+1) + need(sum(k*n for k, n in T.items())-sum(k*n for k, n in P.items()) == 608, + 'underlying raw p7 rank-one surplus') + native_bytes = gzip.decompress((HERE/'vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz').read_bytes()) + native = json.loads(native_bytes) + factor_bytes = (HERE/'vendor/P7-FACTOR.json').read_bytes() + factor = json.loads(factor_bytes) + need(sha256(factor_bytes).hexdigest() == p7['native_inventory']['factor_receipt_sha256'], + 'actual p7 factor receipt') + need(set(native) == {'forward', 'backward'} and + all(len(w) == 22633 for w in native.values()), 'actual raw native record counts') + # Macro description allowance: 15 exact local words, both serialized + # orientations as an overcount, literal controller, source scalar + # allowance, every productive/paid/contact/helper/idle slot, with 32 + # records per extra routing/ownership slot and literal payload bits. + ni = p7['native_inventory'] + slots = (ni['productive_fields']+ni['paid_calls']+ni['contacts']+ + ni['fresh_helper_fields']+ni['main_fields']+sum(ni['whole_idle_profile'].values())) + raw_allowance = (15*8*len(native_bytes)+8*len(factor_bytes)+ + 32*(ni['scalar_allowance']+slots+15*max(map(len,native.values())))) + need(raw_allowance < 2**40, 'complete raw macro/serialized-input allowance') + W0, P0 = sum(T.values()), sum(P.values()) + Uproduct = sum(W0**(v-1-i)*P0**i for i in range(v)) + need(Uproduct < 2**2392, 'chronological product raw-instance count') + strict_surplus = (sum(k*n for k,n in T.items())**v- + sum(k*n for k,n in P.items())**v) + need(strict_surplus > 0 and strict_surplus % 608 == 0 + and strict_surplus//608 >= Uproduct, 'expanded product raw-column identity') + product_allowance = (2**40+32*v*(W0+P0+1))*Uproduct+32*v*P0**v + completed_allowance = product_allowance+32*(paid_mass_upper+W+P0**v) + # Include each dense binary chart/quadratic phase descriptor and role + # indices in the fixed completed-unit allowance, not just opcodes. + ambient = 121**v + serialized_unit_upper = completed_allowance*64*ambient**2 + need(serialized_unit_upper < 2**5000, 'fixed completed-unit description allowance') + need(2**5000+32*(W+paid_mass_upper)+1 < 2**5001, 'compiled record coefficient') + need(2*D*(H+1) > 7*H+30049, 'explicit closure exponent absorption') + return {'kappa': old['kappa'], 'H': H, 'N': '2^'+str(H), 'D': D, + 'width_bound': 'B_N < 2^(D * 2^H)', + 'paid_leaf_bound': 'P_N < B_N * 2^H', + 'raw_p7_instance_bound': 'U_raw <= (B_N * 2^H - P_N)/608', + 'owned_p7_center_bound': 'one per raw instance; <= B_N * 2^H / 608', + 'routing_macro_record_bound': + 'R <= (A + 32*(W+P) + 1) * B_N * N; A < 2^5000', + 'raw_native_record_counts': {k:len(w) for k,w in native.items()}, + 'raw_macro_and_payload_allowance': raw_allowance, + 'raw_macro_allowance_upper': '2^40', + 'completed_unit_description_upper': '2^5000', + 'compiled_record_upper': 'R < 2^(D*2^H + H + 5001)', + 'source_precision_E_upper': 'E < 2^(3*D*2^H + 3*H + 15021)', + 'source_C0_upper': 'C0 < 2^(8*D*2^H)', + 'routing_slot_bound': 'slots <= 2*(W+P)*V, V completed-unit instances', + 'physical_scope': 'Encoded whole-job adapter/move records. Their permitted physical implementation and tariffs remain inherited, separately priced premises.', + 'winning_uniform_word_materialized': False} + + +def verify(): + inputs = authenticate() + flows = finite_flows() + toy = [] + for T, P in [({2:1, 5:1}, {1:2, 4:1}), ({2:4, 3:1}, {1:6, 2:2})]: + row, _ = compile_counts(T, P, 100) + toy.append(row) + p7 = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['strictification'] + T, P = ({int(k): v for k, v in p7[key].items()} for key in ('targets', 'paid')) + direct, counts = compile_counts(T, P, 1000) + B, paid = counts[0][1000], counts[1][1000] + need(paid > 990*B, 'exact direct rank-1000 saving is below target') + kappa = Q('0.00268647') + # ln(2)>2/3 by its first atanh term. 1000>2^9 implies ln(1000)>6. + # exp(x)>1+x then gives 1000^kappa > 1+6*kappa > 100/99. + need(1000 > 2**9 and 1+6*kappa > Q(100,99), 'exact target comparison') + direct['target_failure'] = {'kappa': str(kappa), + 'proved': 'L(1000) > 990 > 1000^(1-kappa)', + 'scope': 'This particular finite rank fails; no asymptotic impossibility claim.'} + rejected = [] + try: + compile_counts({2:1, 5:1}, {1:2, 4:1}, 10, force_unit_replication=True) + except ValueError as e: + need(str(e) == 'whole integer subprogram batches', 'correct missing-batch rejection') + rejected.append(str(e)) + else: + raise ValueError('unit-replication mutant accepted') + try: + Flow({2:1, 5:1}, {1:1, 5:1}, 20) + except ValueError as e: + need(str(e) == 'finite direct-flow rank contract', 'nondecreasing exit rejected') + rejected.append(str(e)) + else: + raise ValueError('nondecreasing-exit mutant accepted') + return {'schema': 'partial-direct-mixed-flow-and-finite-size/1', + 'status': 'PASS_PARTIAL_DIRECT_FLOW_AND_SIZE_BOUNDS', + 'direct_exponent_theorem_established': False, + 'finite_flows': flows, 'exact_toy_compilations': toy, + 'exact_p7_direct_compilation': direct, + 'existing_supplier_size_bounds': inherited_rank_size_bound(), + 'rejected_mutations': rejected, 'source_sha256': inputs, + 'new_code_sha256': {f: sha256((HERE/f).read_bytes()).hexdigest() + for f in ('flow.py', 'verify.py')}, + 'scope': 'New finite matching/scheduling and batching/size bounds. The direct near-root exponent is open. Existing conditional endpoint and native/physical hypotheses remain inherited; no new kappa.'} + + +def normalize(x): + if isinstance(x, dict): + return {str(k): normalize(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [normalize(v) for v in x] + return x + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = normalize(verify()) + if args.out: + need(not args.out.exists(), 'new output path required') + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt') + print(json.dumps({'status': result['status'], 'direct_exponent_theorem': False, + 'p7_width_bits_at_1000': result['exact_p7_direct_compilation']['productive_width']['bits'], + 'target_failure': result['exact_p7_direct_compilation']['target_failure']['proved']})) + + +if __name__ == '__main__': + main() diff --git a/research/joint-helper-lattice/CONTROLLER.json b/research/joint-helper-lattice/CONTROLLER.json new file mode 100644 index 0000000000..49a2f06758 --- /dev/null +++ b/research/joint-helper-lattice/CONTROLLER.json @@ -0,0 +1,5224 @@ +{ + "ambient_rank": 145, + "boundaries": { + "left": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "1", + "0", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "left_program": [ + [ + "SWAP", + 30, + 31 + ], + [ + "SWAP", + 29, + 30 + ], + [ + "SWAP", + 28, + 30 + ], + [ + "SWAP", + 27, + 29 + ], + [ + "SWAP", + 26, + 28 + ], + [ + "SWAP", + 25, + 30 + ], + [ + "SWAP", + 24, + 25 + ], + [ + "SWAP", + 23, + 26 + ], + [ + "SWAP", + 22, + 30 + ], + [ + "SWAP", + 20, + 26 + ], + [ + "SWAP", + 19, + 22 + ], + [ + "SWAP", + 18, + 29 + ], + [ + "SWAP", + 17, + 23 + ], + [ + "SWAP", + 16, + 27 + ], + [ + "SCALE", + 15, + "-1" + ], + [ + "SWAP", + 15, + 31 + ], + [ + "ADD", + 12, + 14, + "1" + ], + [ + "ADD", + 10, + 14, + "-1" + ], + [ + "ADD", + 8, + 14, + "1" + ], + [ + "ADD", + 6, + 14, + "-1" + ], + [ + "ADD", + 4, + 14, + "1" + ], + [ + "ADD", + 2, + 14, + "-1" + ], + [ + "ADD", + 0, + 14, + "1" + ], + [ + "SWAP", + 14, + 15 + ], + [ + "ADD", + 31, + 13, + "1" + ], + [ + "SWAP", + 13, + 30 + ], + [ + "ADD", + 10, + 12, + "1" + ], + [ + "ADD", + 8, + 12, + "-1" + ], + [ + "ADD", + 6, + 12, + "1" + ], + [ + "ADD", + 4, + 12, + "-1" + ], + [ + "ADD", + 2, + 12, + "1" + ], + [ + "ADD", + 0, + 12, + "-1" + ], + [ + "SWAP", + 12, + 14 + ], + [ + "ADD", + 31, + 11, + "-1" + ], + [ + "ADD", + 30, + 11, + "-1" + ], + [ + "SCALE", + 11, + "-1" + ], + [ + "SWAP", + 11, + 29 + ], + [ + "ADD", + 8, + 10, + "1" + ], + [ + "ADD", + 6, + 10, + "-1" + ], + [ + "ADD", + 4, + 10, + "1" + ], + [ + "ADD", + 2, + 10, + "-1" + ], + [ + "ADD", + 0, + 10, + "1" + ], + [ + "SWAP", + 10, + 13 + ], + [ + "ADD", + 31, + 9, + "1" + ], + [ + "ADD", + 30, + 9, + "1" + ], + [ + "ADD", + 29, + 9, + "1" + ], + [ + "SWAP", + 9, + 28 + ], + [ + "ADD", + 6, + 8, + "1" + ], + [ + "ADD", + 4, + 8, + "-1" + ], + [ + "ADD", + 2, + 8, + "1" + ], + [ + "ADD", + 0, + 8, + "-1" + ], + [ + "SWAP", + 8, + 12 + ], + [ + "ADD", + 31, + 7, + "-1" + ], + [ + "ADD", + 30, + 7, + "-1" + ], + [ + "ADD", + 29, + 7, + "-1" + ], + [ + "ADD", + 28, + 7, + "-1" + ], + [ + "SCALE", + 7, + "-1" + ], + [ + "SWAP", + 7, + 27 + ], + [ + "ADD", + 4, + 6, + "1" + ], + [ + "ADD", + 2, + 6, + "-1" + ], + [ + "ADD", + 0, + 6, + "1" + ], + [ + "SWAP", + 6, + 11 + ], + [ + "ADD", + 31, + 5, + "1" + ], + [ + "ADD", + 30, + 5, + "1" + ], + [ + "ADD", + 29, + 5, + "1" + ], + [ + "ADD", + 28, + 5, + "1" + ], + [ + "ADD", + 27, + 5, + "1" + ], + [ + "SWAP", + 5, + 26 + ], + [ + "ADD", + 2, + 4, + "1" + ], + [ + "ADD", + 0, + 4, + "-1" + ], + [ + "SWAP", + 4, + 10 + ], + [ + "ADD", + 31, + 3, + "-1" + ], + [ + "ADD", + 30, + 3, + "-1" + ], + [ + "ADD", + 29, + 3, + "-1" + ], + [ + "ADD", + 28, + 3, + "-1" + ], + [ + "ADD", + 27, + 3, + "-1" + ], + [ + "ADD", + 26, + 3, + "-1" + ], + [ + "SCALE", + 3, + "-1" + ], + [ + "SWAP", + 3, + 25 + ], + [ + "ADD", + 0, + 2, + "1" + ], + [ + "SWAP", + 2, + 9 + ], + [ + "ADD", + 31, + 1, + "1" + ], + [ + "ADD", + 30, + 1, + "1" + ], + [ + "ADD", + 29, + 1, + "1" + ], + [ + "ADD", + 28, + 1, + "1" + ], + [ + "ADD", + 27, + 1, + "1" + ], + [ + "ADD", + 26, + 1, + "1" + ], + [ + "ADD", + 25, + 1, + "1" + ], + [ + "SWAP", + 1, + 24 + ], + [ + "SWAP", + 0, + 8 + ] + ], + "right": [ + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "-1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "1", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0", + "0" + ] + ], + "right_program": [ + [ + "ADD", + 30, + 31, + "-1" + ], + [ + "ADD", + 29, + 31, + "-1" + ], + [ + "ADD", + 28, + 31, + "-1" + ], + [ + "ADD", + 27, + 31, + "-1" + ], + [ + "SCALE", + 31, + "-1" + ], + [ + "ADD", + 31, + 30, + "-1" + ], + [ + "ADD", + 29, + 30, + "-1" + ], + [ + "ADD", + 28, + 30, + "-1" + ], + [ + "ADD", + 27, + 30, + "-1" + ], + [ + "ADD", + 31, + 29, + "-1" + ], + [ + "ADD", + 28, + 29, + "-1" + ], + [ + "ADD", + 27, + 29, + "-1" + ], + [ + "SCALE", + 29, + "-1" + ], + [ + "ADD", + 31, + 28, + "-1" + ], + [ + "ADD", + 27, + 28, + "-1" + ], + [ + "SWAP", + 28, + 29 + ], + [ + "ADD", + 31, + 27, + "-1" + ], + [ + "SCALE", + 27, + "-1" + ], + [ + "SWAP", + 27, + 29 + ], + [ + "ADD", + 31, + 26, + "1" + ], + [ + "SWAP", + 26, + 29 + ], + [ + "ADD", + 29, + 25, + "-1" + ], + [ + "ADD", + 24, + 25, + "-1" + ], + [ + "SWAP", + 25, + 28 + ], + [ + "ADD", + 28, + 24, + "1" + ], + [ + "SWAP", + 23, + 29 + ], + [ + "SWAP", + 22, + 25 + ], + [ + "SWAP", + 20, + 23 + ], + [ + "SWAP", + 19, + 25 + ], + [ + "SWAP", + 18, + 27 + ], + [ + "SWAP", + 17, + 29 + ], + [ + "SWAP", + 16, + 31 + ], + [ + "ADD", + 14, + 15, + "-1" + ], + [ + "SWAP", + 15, + 30 + ], + [ + "ADD", + 13, + 14, + "-1" + ], + [ + "SWAP", + 14, + 30 + ], + [ + "ADD", + 12, + 13, + "-1" + ], + [ + "SWAP", + 13, + 22 + ], + [ + "ADD", + 11, + 12, + "-1" + ], + [ + "SWAP", + 12, + 30 + ], + [ + "ADD", + 10, + 11, + "-1" + ], + [ + "SWAP", + 11, + 18 + ], + [ + "ADD", + 9, + 10, + "-1" + ], + [ + "SWAP", + 10, + 22 + ], + [ + "ADD", + 8, + 9, + "-1" + ], + [ + "SWAP", + 9, + 26 + ], + [ + "SWAP", + 8, + 30 + ], + [ + "SWAP", + 7, + 16 + ], + [ + "SWAP", + 6, + 18 + ], + [ + "SWAP", + 5, + 20 + ], + [ + "SWAP", + 4, + 22 + ], + [ + "SWAP", + 3, + 24 + ], + [ + "SWAP", + 2, + 26 + ], + [ + "SWAP", + 1, + 28 + ], + [ + "SWAP", + 0, + 30 + ] + ] + }, + "diagonal": [ + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + -1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + -1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ], + [ + 1, + 1, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 1, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 0, + 1, + 1 + ] + ], + "invoice": { + "main": { + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "owned_streams_reused_sequentially": 1, + "paid": { + "1": 46446, + "2": 12834, + "3": 4032, + "4": 1836, + "5": 360, + "8": 144, + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + }, + "paid_calls": 69012, + "productive_fields": 10928, + "rank_surplus": 752, + "raw_scalar_record_bound": 1000000000, + "targets": { + "5": 504, + "6": 324, + "7": 1008, + "8": 1674, + "9": 3834, + "17": 448, + "25": 448, + "33": 448, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "73": 224, + "145": 224 + }, + "thick_calls": 18, + "thick_stages": [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ], + "thin_queries": 1680, + "whole_idle": { + "16": 448, + "24": 448, + "32": 448, + "40": 448, + "48": 448, + "56": 448, + "64": 448, + "72": 224 + } + }, + "keep_mask": 35047648968703, + "kind": "complex", + "pairs": 16, + "physical_events": [ + [ + "LOCAL", + 0, + 0, + false + ], + [ + "LOCAL", + 1, + 0, + true + ], + [ + "IDLE", + 1, + [ + 0, + 1 + ] + ], + [ + "ADD", + 0, + 2, + 1 + ], + [ + "ADD", + 3, + 1, + -1 + ], + [ + "QUERY_SHEAR", + 2, + 0, + false + ], + [ + "ADD", + 0, + 2, + -1 + ], + [ + "ADD", + 3, + 1, + 1 + ], + [ + "LOCAL", + 3, + 1, + true + ], + [ + "IDLE", + 2, + [ + 0, + 1, + 3 + ] + ], + [ + "ADD", + 2, + 4, + 1 + ], + [ + "ADD", + 5, + 3, + -1 + ], + [ + "QUERY_SHEAR", + 4, + 1, + false + ], + [ + "ADD", + 2, + 4, + -1 + ], + [ + "ADD", + 5, + 3, + 1 + ], + [ + "LOCAL", + 5, + 2, + true + ], + [ + "IDLE", + 3, + [ + 0, + 1, + 3, + 5 + ] + ], + [ + "ADD", + 4, + 6, + 1 + ], + [ + "ADD", + 7, + 5, + -1 + ], + [ + "QUERY_SHEAR", + 6, + 2, + false + ], + [ + "ADD", + 4, + 6, + -1 + ], + [ + "ADD", + 7, + 5, + 1 + ], + [ + "LOCAL", + 7, + 3, + true + ], + [ + "IDLE", + 4, + [ + 0, + 1, + 3, + 5, + 7 + ] + ], + [ + "ADD", + 6, + 8, + 1 + ], + [ + "ADD", + 9, + 7, + -1 + ], + [ + "QUERY_SHEAR", + 8, + 3, + false + ], + [ + "ADD", + 6, + 8, + -1 + ], + [ + "ADD", + 9, + 7, + 1 + ], + [ + "LOCAL", + 9, + 4, + true + ], + [ + "IDLE", + 5, + [ + 0, + 1, + 3, + 5, + 7, + 9 + ] + ], + [ + "ADD", + 8, + 10, + 1 + ], + [ + "ADD", + 11, + 9, + -1 + ], + [ + "QUERY_SHEAR", + 10, + 4, + false + ], + [ + "ADD", + 8, + 10, + -1 + ], + [ + "ADD", + 11, + 9, + 1 + ], + [ + "LOCAL", + 11, + 5, + true + ], + [ + "IDLE", + 6, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11 + ] + ], + [ + "ADD", + 10, + 12, + 1 + ], + [ + "ADD", + 13, + 11, + -1 + ], + [ + "QUERY_SHEAR", + 12, + 5, + false + ], + [ + "ADD", + 10, + 12, + -1 + ], + [ + "ADD", + 13, + 11, + 1 + ], + [ + "LOCAL", + 13, + 6, + true + ], + [ + "IDLE", + 7, + [ + 0, + 1, + 3, + 5, + 7, + 9, + 11, + 13 + ] + ], + [ + "ADD", + 12, + 14, + 1 + ], + [ + "ADD", + 15, + 13, + -1 + ], + [ + "QUERY_SHEAR", + 14, + 6, + false + ], + [ + "ADD", + 12, + 14, + -1 + ], + [ + "ADD", + 15, + 13, + 1 + ], + [ + "LOCAL", + 15, + 7, + true + ], + [ + "ADD", + 14, + 16, + 1 + ], + [ + "ADD", + 17, + 15, + -1 + ], + [ + "QUERY_SHEAR", + 16, + 7, + false + ], + [ + "ADD", + 14, + 16, + -1 + ], + [ + "ADD", + 17, + 15, + 1 + ], + [ + "LOCAL", + 17, + 8, + true + ], + [ + "ADD", + 16, + 18, + 1 + ], + [ + "ADD", + 19, + 17, + -1 + ], + [ + "QUERY_SHEAR", + 18, + 8, + false + ], + [ + "ADD", + 16, + 18, + -1 + ], + [ + "ADD", + 19, + 17, + 1 + ], + [ + "LOCAL", + 19, + 9, + true + ], + [ + "ADD", + 18, + 20, + 1 + ], + [ + "ADD", + 21, + 19, + -1 + ], + [ + "QUERY_SHEAR", + 20, + 9, + false + ], + [ + "ADD", + 18, + 20, + -1 + ], + [ + "ADD", + 21, + 19, + 1 + ], + [ + "LOCAL", + 21, + 10, + true + ], + [ + "ADD", + 20, + 22, + 1 + ], + [ + "ADD", + 23, + 21, + -1 + ], + [ + "QUERY_SHEAR", + 22, + 10, + false + ], + [ + "ADD", + 20, + 22, + -1 + ], + [ + "ADD", + 23, + 21, + 1 + ], + [ + "LOCAL", + 23, + 11, + true + ], + [ + "ADD", + 22, + 24, + 1 + ], + [ + "ADD", + 25, + 23, + -1 + ], + [ + "QUERY_SHEAR", + 24, + 11, + false + ], + [ + "ADD", + 22, + 24, + -1 + ], + [ + "ADD", + 25, + 23, + 1 + ], + [ + "LOCAL", + 25, + 12, + true + ], + [ + "ADD", + 24, + 26, + 1 + ], + [ + "ADD", + 27, + 25, + -1 + ], + [ + "QUERY_SHEAR", + 26, + 12, + false + ], + [ + "ADD", + 24, + 26, + -1 + ], + [ + "ADD", + 27, + 25, + 1 + ], + [ + "LOCAL", + 27, + 13, + true + ], + [ + "ADD", + 26, + 28, + 1 + ], + [ + "ADD", + 29, + 27, + -1 + ], + [ + "QUERY_SHEAR", + 28, + 13, + false + ], + [ + "ADD", + 26, + 28, + -1 + ], + [ + "ADD", + 29, + 27, + 1 + ], + [ + "LOCAL", + 29, + 14, + true + ], + [ + "ADD", + 28, + 30, + 1 + ], + [ + "ADD", + 31, + 29, + -1 + ], + [ + "QUERY_SHEAR", + 30, + 14, + false + ], + [ + "ADD", + 28, + 30, + -1 + ], + [ + "ADD", + 31, + 29, + 1 + ], + [ + "LOCAL", + 31, + 15, + true + ], + [ + "LOCAL", + 32, + 15, + false + ], + [ + "IDLE", + 7, + [ + 17, + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 8, + [ + 19, + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 9, + [ + 21, + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 10, + [ + 23, + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 11, + [ + 25, + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 12, + [ + 27, + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 13, + [ + 29, + 31, + 32 + ] + ], + [ + "IDLE", + 14, + [ + 31, + 32 + ] + ], + [ + "ADD", + 30, + 28, + 1 + ], + [ + "ADD", + 29, + 31, + -1 + ], + [ + "ADD", + 28, + 26, + 1 + ], + [ + "ADD", + 27, + 29, + -1 + ], + [ + "ADD", + 26, + 24, + 1 + ], + [ + "ADD", + 25, + 27, + -1 + ], + [ + "ADD", + 24, + 22, + 1 + ], + [ + "ADD", + 23, + 25, + -1 + ], + [ + "ADD", + 22, + 20, + 1 + ], + [ + "ADD", + 21, + 23, + -1 + ], + [ + "ADD", + 20, + 18, + 1 + ], + [ + "ADD", + 19, + 21, + -1 + ], + [ + "ADD", + 18, + 16, + 1 + ], + [ + "ADD", + 17, + 19, + -1 + ], + [ + "ADD", + 16, + 14, + 1 + ], + [ + "ADD", + 15, + 17, + -1 + ], + [ + "ADD", + 14, + 12, + 1 + ], + [ + "ADD", + 13, + 15, + -1 + ], + [ + "ADD", + 12, + 10, + 1 + ], + [ + "ADD", + 11, + 13, + -1 + ], + [ + "ADD", + 10, + 8, + 1 + ], + [ + "ADD", + 9, + 11, + -1 + ], + [ + "ADD", + 8, + 6, + 1 + ], + [ + "ADD", + 7, + 9, + -1 + ], + [ + "ADD", + 6, + 4, + 1 + ], + [ + "ADD", + 5, + 7, + -1 + ], + [ + "ADD", + 4, + 2, + 1 + ], + [ + "ADD", + 3, + 5, + -1 + ], + [ + "ADD", + 2, + 0, + 1 + ], + [ + "ADD", + 1, + 3, + -1 + ], + [ + "SIGNED_SWAP", + 0, + 1 + ], + [ + "SIGNED_SWAP", + 2, + 3 + ], + [ + "SIGNED_SWAP", + 4, + 5 + ], + [ + "SIGNED_SWAP", + 6, + 7 + ], + [ + "SIGNED_SWAP", + 8, + 9 + ], + [ + "SIGNED_SWAP", + 10, + 11 + ], + [ + "SIGNED_SWAP", + 12, + 13 + ], + [ + "SIGNED_SWAP", + 14, + 15 + ], + [ + "SIGNED_SWAP", + 16, + 17 + ], + [ + "SIGNED_SWAP", + 18, + 19 + ], + [ + "SIGNED_SWAP", + 20, + 21 + ], + [ + "SIGNED_SWAP", + 22, + 23 + ], + [ + "SIGNED_SWAP", + 24, + 25 + ], + [ + "SIGNED_SWAP", + 26, + 27 + ], + [ + "SIGNED_SWAP", + 28, + 29 + ], + [ + "SIGNED_SWAP", + 30, + 31 + ] + ], + "prefix_pairs": 7 +} diff --git a/research/joint-helper-lattice/DISCOVERY.json b/research/joint-helper-lattice/DISCOVERY.json new file mode 100644 index 0000000000..53f7d1028f --- /dev/null +++ b/research/joint-helper-lattice/DISCOVERY.json @@ -0,0 +1,10886 @@ +{ + "changes": [ + { + "new": [ + 51 + ], + "old": [], + "ordinal": 449, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 451, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 453, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 455, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 482, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 483, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 502, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 503, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 504, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 525, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 526, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 527, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 548, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 549, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 550, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 551, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 578, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 580, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 594, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 595, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 598, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 599, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 600, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 601, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 606, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 607, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 608, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 609, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 614, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 615, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 616, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 617, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 622, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 623, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 624, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 625, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 626, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 627, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 627, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 628, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 629, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 630, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 631, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 632, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 633, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 1997, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2002, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2151, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2156, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2305, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2310, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4007, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4008, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4013, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4014, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 9, + 17, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 4019, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 4025, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 8, + 16, + 33, + 65, + 128, + 256 + ], + "old": [ + 4, + 10, + 16, + 35, + 65, + 128, + 256 + ], + "ordinal": 4043, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "old": [ + 1, + 14, + 16, + 34, + 68, + 128, + 256 + ], + "ordinal": 4049, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 5, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 6, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 7, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 8, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 9, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 10, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 17, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 18, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 21, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 22, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 25, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 26, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 29, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 30, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 33, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 34, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 37, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 38, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 41, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 42, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 44, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 45, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 47, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 49, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 50, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 97, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 98, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 99, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 100, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 101, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 102, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 103, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 104, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 105, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 106, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 107, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 108, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 109, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 110, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 111, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 112, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 113, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 114, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 135, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 136, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 137, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 138, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 139, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 140, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 141, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 142, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 143, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 144, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 145, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 146, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 147, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 148, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 149, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 150, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 151, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 152, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 153, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 154, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 171, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 172, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 173, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 174, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 175, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 176, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 177, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 178, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 179, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 180, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 181, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 182, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 183, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 184, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 185, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 186, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 199, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 200, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 201, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 202, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 203, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 204, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 205, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 206, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 207, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 208, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 209, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 210, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 211, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 212, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 213, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 214, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 234, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 235, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 236, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 237, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 238, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 239, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 240, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 241, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 242, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 243, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 244, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 245, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 246, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 247, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 248, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 249, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 80, + 144, + 256 + ], + "old": [ + 45, + 80, + 144, + 256 + ], + "ordinal": 332, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 208, + 336 + ], + "old": [ + 5, + 11, + 35, + 208, + 336 + ], + "ordinal": 335, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 400 + ], + "old": [ + 5, + 11, + 35, + 80, + 400 + ], + "ordinal": 336, + "phase": "B" + }, + { + "new": [ + 7, + 16, + 42, + 64, + 128, + 256 + ], + "old": [ + 16, + 45, + 64, + 128, + 256 + ], + "ordinal": 337, + "phase": "B" + }, + { + "new": [ + 7, + 9, + 16, + 35, + 64, + 128, + 256 + ], + "old": [ + 14, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 338, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 16, + 33, + 192, + 320 + ], + "old": [ + 5, + 11, + 16, + 35, + 192, + 320 + ], + "ordinal": 339, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 128, + 272 + ], + "old": [ + 5, + 11, + 35, + 80, + 128, + 272 + ], + "ordinal": 340, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 144, + 256 + ], + "old": [ + 5, + 11, + 35, + 80, + 144, + 256 + ], + "ordinal": 341, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 137, + 286 + ], + "old": [ + 25, + 45, + 73, + 137, + 263 + ], + "ordinal": 353, + "phase": "B" + }, + { + "new": [ + 45, + 87, + 137, + 265 + ], + "old": [ + 25, + 45, + 78, + 137, + 265 + ], + "ordinal": 355, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 146, + 261 + ], + "old": [ + 2, + 45, + 80, + 144, + 261 + ], + "ordinal": 374, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 194, + 265 + ], + "old": [ + 5, + 40, + 82, + 144, + 265 + ], + "ordinal": 376, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 388, + "phase": "B" + }, + { + "new": [ + 45, + 400 + ], + "old": [ + 45, + 76, + 400 + ], + "ordinal": 389, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 400 + ], + "old": [ + 9, + 36, + 69, + 400 + ], + "ordinal": 394, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 146, + 272 + ], + "old": [ + 9, + 36, + 69, + 146, + 272 + ], + "ordinal": 397, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 130, + 274 + ], + "old": [ + 9, + 36, + 69, + 130, + 274 + ], + "ordinal": 398, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 144, + 274 + ], + "old": [ + 5, + 40, + 73, + 144, + 274 + ], + "ordinal": 399, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 410, + "phase": "B" + }, + { + "new": [ + 45, + 475 + ], + "old": [ + 45, + 76, + 407 + ], + "ordinal": 411, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 469 + ], + "old": [ + 14, + 35, + 66, + 407 + ], + "ordinal": 416, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 130, + 341 + ], + "old": [ + 14, + 35, + 66, + 130, + 279 + ], + "ordinal": 419, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 215, + 258 + ], + "old": [ + 14, + 35, + 66, + 149, + 258 + ], + "ordinal": 420, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 199, + 268 + ], + "old": [ + 28, + 45, + 76, + 139, + 268 + ], + "ordinal": 421, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 217, + 256 + ], + "old": [ + 5, + 40, + 219, + 256 + ], + "ordinal": 440, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 393 + ], + "old": [ + 21, + 45, + 69, + 398 + ], + "ordinal": 441, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 66, + 130, + 258 + ], + "old": [ + 45, + 69, + 133, + 261 + ], + "ordinal": 442, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 130, + 258 + ], + "old": [ + 21, + 45, + 69, + 133, + 261 + ], + "ordinal": 443, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 393 + ], + "old": [ + 5, + 16, + 40, + 64, + 395 + ], + "ordinal": 444, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 89, + 128, + 256 + ], + "old": [ + 5, + 40, + 91, + 128, + 256 + ], + "ordinal": 445, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 25, + 40, + 64, + 128, + 256 + ], + "old": [ + 5, + 27, + 40, + 64, + 128, + 256 + ], + "ordinal": 446, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 33, + 66, + 130, + 258 + ], + "old": [ + 11, + 21, + 38, + 69, + 133, + 261 + ], + "ordinal": 447, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 128, + 265 + ], + "old": [ + 5, + 16, + 40, + 64, + 128, + 267 + ], + "ordinal": 448, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 137, + 256 + ], + "old": [ + 5, + 16, + 40, + 64, + 139, + 256 + ], + "ordinal": 449, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 194, + 258 + ], + "old": [ + 5, + 25, + 40, + 194, + 258 + ], + "ordinal": 461, + "phase": "B" + }, + { + "new": [ + 21, + 45, + 66, + 386 + ], + "old": [ + 12, + 21, + 33, + 66, + 386 + ], + "ordinal": 462, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 137, + 336 + ], + "old": [ + 5, + 40, + 82, + 137, + 258 + ], + "ordinal": 483, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 137, + 274 + ], + "old": [ + 2, + 45, + 80, + 137, + 272 + ], + "ordinal": 485, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 387 + ], + "old": [ + 4, + 17, + 34, + 64, + 395 + ], + "ordinal": 530, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 388 + ], + "old": [ + 11, + 17, + 34, + 68, + 388 + ], + "ordinal": 532, + "phase": "B" + }, + { + "new": [ + 12, + 21, + 38, + 71, + 132, + 260 + ], + "old": [ + 21, + 38, + 75, + 132, + 260 + ], + "ordinal": 556, + "phase": "B" + }, + { + "new": [ + 11, + 18, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 51, + 64, + 132, + 260 + ], + "ordinal": 558, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 385 + ], + "old": [ + 10, + 20, + 38, + 65, + 385 + ], + "ordinal": 583, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 390 + ], + "old": [ + 1, + 10, + 20, + 64, + 422 + ], + "ordinal": 585, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 38, + 64, + 129, + 257 + ], + "old": [ + 30, + 38, + 64, + 129, + 257 + ], + "ordinal": 608, + "phase": "B" + }, + { + "new": [ + 11, + 21, + 33, + 71, + 129, + 257 + ], + "old": [ + 11, + 21, + 102, + 129, + 257 + ], + "ordinal": 610, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 394 + ], + "old": [ + 6, + 24, + 32, + 64, + 395 + ], + "ordinal": 632, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 416 + ], + "old": [ + 6, + 11, + 19, + 96, + 416 + ], + "ordinal": 634, + "phase": "B" + }, + { + "new": [ + 7, + 25, + 33, + 75, + 129, + 257 + ], + "old": [ + 30, + 38, + 75, + 134, + 262 + ], + "ordinal": 658, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 64, + 160, + 288 + ], + "old": [ + 11, + 21, + 64, + 160, + 288 + ], + "ordinal": 660, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [ + 3, + 48, + 72, + 413 + ], + "ordinal": 685, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 392 + ], + "old": [ + 3, + 21, + 37, + 72, + 392 + ], + "ordinal": 687, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 401 + ], + "old": [ + 3, + 8, + 48, + 64, + 405 + ], + "ordinal": 689, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 33, + 64, + 136, + 264 + ], + "old": [ + 21, + 38, + 64, + 136, + 264 + ], + "ordinal": 711, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 51, + 82, + 131, + 259 + ], + "old": [ + 11, + 51, + 85, + 131, + 259 + ], + "ordinal": 713, + "phase": "B" + }, + { + "new": [ + 4, + 51, + 82, + 136, + 264 + ], + "old": [ + 4, + 51, + 136, + 264 + ], + "ordinal": 759, + "phase": "B" + }, + { + "new": [ + 30, + 32, + 76, + 129, + 257 + ], + "old": [ + 30, + 32, + 129, + 257 + ], + "ordinal": 769, + "phase": "B" + }, + { + "new": [ + 13, + 19, + 33, + 455 + ], + "old": [ + 13, + 19, + 33, + 65, + 390 + ], + "ordinal": 770, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 70, + 129, + 257 + ], + "old": [ + 30, + 32, + 70, + 129, + 257 + ], + "ordinal": 779, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 129, + 262 + ], + "old": [ + 10, + 20, + 65, + 161, + 262 + ], + "ordinal": 784, + "phase": "B" + }, + { + "new": [ + 15, + 17, + 37, + 67, + 129, + 257 + ], + "old": [ + 30, + 37, + 67, + 129, + 257 + ], + "ordinal": 840, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 34, + 68, + 129, + 257 + ], + "old": [ + 8, + 22, + 102, + 129, + 257 + ], + "ordinal": 841, + "phase": "B" + }, + { + "new": [ + 2, + 28, + 40, + 76, + 129, + 257 + ], + "old": [ + 2, + 28, + 100, + 129, + 257 + ], + "ordinal": 842, + "phase": "B" + }, + { + "new": [ + 5, + 27, + 42, + 73, + 129, + 257 + ], + "old": [ + 30, + 47, + 73, + 129, + 257 + ], + "ordinal": 843, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 848, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 849, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 850, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 851, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 872, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 873, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 874, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 875, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 880, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 881, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 882, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 883, + "phase": "B" + }, + { + "new": [], + "old": [ + 2, + 5, + 40, + 80, + 409 + ], + "ordinal": 928, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 949, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 951, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 1052, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 1053, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 1054, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 1055, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 1101, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 1102, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 1103, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 1104, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 1121, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 1122, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 1123, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 1124, + "phase": "B" + }, + { + "new": [ + 3, + 12, + 21, + 37, + 68, + 132, + 260 + ], + "old": [ + 15, + 21, + 38, + 68, + 132, + 260 + ], + "ordinal": 1185, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 67, + 128, + 256 + ], + "old": [ + 4, + 17, + 34, + 75, + 128, + 256 + ], + "ordinal": 1186, + "phase": "B" + }, + { + "new": [ + 4, + 11, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 51, + 64, + 128, + 256 + ], + "ordinal": 1187, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 17, + 34, + 64, + 132, + 260 + ], + "ordinal": 1188, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 128, + 259 + ], + "old": [ + 4, + 17, + 34, + 64, + 128, + 267 + ], + "ordinal": 1194, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 132, + 256 + ], + "old": [ + 11, + 17, + 34, + 68, + 132, + 256 + ], + "ordinal": 1196, + "phase": "B" + }, + { + "new": [ + 1, + 12, + 18, + 38, + 64, + 128, + 256 + ], + "old": [ + 1, + 30, + 38, + 64, + 128, + 256 + ], + "ordinal": 1201, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 64, + 129, + 257 + ], + "old": [ + 10, + 20, + 38, + 64, + 129, + 257 + ], + "ordinal": 1202, + "phase": "B" + }, + { + "new": [ + 6, + 11, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 11, + 21, + 39, + 65, + 129, + 257 + ], + "ordinal": 1203, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 102, + 128, + 256 + ], + "ordinal": 1204, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 30, + 32, + 70, + 128, + 256 + ], + "ordinal": 1205, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 129, + 256 + ], + "old": [ + 10, + 20, + 38, + 65, + 129, + 256 + ], + "ordinal": 1210, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 1, + 10, + 20, + 64, + 128, + 294 + ], + "ordinal": 1212, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 10, + 20, + 33, + 65, + 128, + 262 + ], + "ordinal": 1213, + "phase": "B" + }, + { + "new": [ + 7, + 10, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 13, + 19, + 38, + 70, + 134, + 262 + ], + "ordinal": 1217, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 74, + 128, + 256 + ], + "old": [ + 6, + 24, + 32, + 75, + 128, + 256 + ], + "ordinal": 1218, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 11, + 21, + 32, + 64, + 128, + 256 + ], + "ordinal": 1219, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 6, + 11, + 19, + 64, + 160, + 288 + ], + "ordinal": 1220, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 1, + 12, + 18, + 70, + 160, + 288 + ], + "ordinal": 1221, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 128, + 266 + ], + "old": [ + 6, + 24, + 32, + 64, + 128, + 267 + ], + "ordinal": 1226, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 11, + 19, + 96, + 160, + 256 + ], + "ordinal": 1228, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 10, + 18, + 96, + 161, + 256 + ], + "ordinal": 1229, + "phase": "B" + }, + { + "new": [ + 7, + 8, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 8, + 21, + 38, + 64, + 128, + 256 + ], + "ordinal": 1233, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 64, + 136, + 264 + ], + "old": [ + 3, + 21, + 37, + 64, + 136, + 264 + ], + "ordinal": 1234, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 17, + 34, + 67, + 131, + 259 + ], + "old": [ + 11, + 22, + 37, + 67, + 131, + 259 + ], + "ordinal": 1235, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 81, + 128, + 256 + ], + "old": [ + 3, + 8, + 48, + 85, + 128, + 256 + ], + "ordinal": 1236, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 136, + 256 + ], + "old": [ + 3, + 21, + 37, + 72, + 136, + 256 + ], + "ordinal": 1242, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 128, + 273 + ], + "old": [ + 3, + 8, + 48, + 64, + 128, + 277 + ], + "ordinal": 1244, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1417, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1418, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1433, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1434, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1437, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1438, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1445, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1446, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 0, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 1, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 2, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 3, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 4, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 5, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 6, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 7, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 8, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 9, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 10, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 11, + "phase": "cleanup_tail" + }, + { + "new": [ + 2, + 5, + 24, + 40, + 72, + 385 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 12, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 20, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 21, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 22, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 23, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 24, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 25, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 26, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 27, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 28, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 29, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 30, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 31, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 32, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 33, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 34, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 35, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 36, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 37, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 38, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 39, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 47, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 48, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 49, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 50, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 51, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 52, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 55, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 56, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 60, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 61, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 62, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 63, + "phase": "cleanup_tail" + }, + { + "new": [ + 3, + 12, + 17, + 33, + 64, + 388 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 67, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 73, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 74, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 75, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 76, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 85, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 88, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 94, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 95, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 96, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 97, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 98, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 99, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 100, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 101, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 102, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 103, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 104, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 105, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 106, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 107, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 108, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 109, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 110, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 111, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 116, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 117, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 121, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 122, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 123, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 124, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 125, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 126, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 127, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 128, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 129, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 130, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 131, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 132, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 133, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 134, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 135, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 136, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 137, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 138, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 139, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 140, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 141, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 142, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 143, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 144, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 145, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 146, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 147, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 148, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 149, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 150, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 151, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 152, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 153, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 154, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 155, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 156, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 157, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 158, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 159, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 160, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 161, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 162, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 163, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 164, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 165, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 166, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 167, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 168, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 169, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 170, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 171, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 172, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 173, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 174, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 175, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 176, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 177, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 178, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 179, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 180, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 181, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 182, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 183, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 188, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 189, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 191, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 192, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 193, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 194, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 195, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 196, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 197, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 198, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 199, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 200, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 201, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 202, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 204, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 205, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 206, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 207, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 208, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 209, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 226, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 228, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 230, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 249, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 251, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 265, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 267, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 299, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 304, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 320, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 331, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 363, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 395, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 408, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 412, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 424, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 428, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 448, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 449, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 450, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 451, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 452, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 453, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 454, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 455, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 482, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 483, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 496, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 497, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 503, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 504, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 507, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 508, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 526, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 527, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 550, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 551, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 566, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 567, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 568, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 569, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 574, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 575, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 576, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 577, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 580, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 582, + "phase": "exit" + } + ], + "log": [ + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.001075597945600748, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006404789164662361, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006386309396475554, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005889208987355232, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000636169919744134, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006324949208647013, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.01074653910472989, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006191260181367397, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005904210265725851, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005857199430465698, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005849860608577728, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006328618619590998, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006294939666986465, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006302008405327797, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005877329967916012, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000590289942920208, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006303780246526003, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006298108492046595, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006195418536663055, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006841688882559538, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006465218029916286, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006277388893067837, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005882920231670141, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006315950304269791, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006366858724504709, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005855481140315533, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005937719251960516, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006369180046021938, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006377371028065681, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586268026381731, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006332618650048971, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006257679779082537, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005849250592291355, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005888910964131355, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005945321172475815, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005879260133951902, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005923090502619743, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006292159669101238, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005877669900655746, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000592509051784873, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005896689835935831, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005870978347957134, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006910338997840881, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005820540245622396, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006245570257306099, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005984250456094742, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006365531589835882, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006284690462052822, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005876009818166494, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006361349951475859, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005852370522916317, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006305361166596413, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005846978165209293, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006745990831404924, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005877090152353048, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006306229624897242, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006269770674407482, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000637667952105403, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006279710214585066, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005855760537087917, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006291440222412348, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005854519549757242, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006271519232541323, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005840531084686518, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006309140007942915, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005870680324733257, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006304038688540459, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005886279977858067, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000638019060716033, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006365550216287374, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005845869891345501, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006315300706773996, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586286187171936, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005884871352463961, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006310341414064169, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005902270786464214, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.002707120031118393, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006361750420182943, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005890568718314171, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005862549878656864, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006373829673975706, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005868400912731886, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586383044719696, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005930899642407894, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005855520721524954, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006308129522949457, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006310890894383192, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005876431241631508, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006608550902456045, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006281349342316389, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005921840202063322, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005838889628648758, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007187989540398121, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005906580481678247, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005960490088909864, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005959039553999901, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005850319284945726, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005865979474037886, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006297028157860041, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005901618860661983, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005843169055879116, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005854018963873386, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005893418565392494, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005946510937064886, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006296269129961729, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005865739658474922, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000586255919188261, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005932447966188192, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005939060356467962, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005937861278653145, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000588906928896904, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005843418184667826, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0005870410241186619, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006217740010470152, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006238999776542187, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006359750404953957, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006392451468855143, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000669943168759346, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006323710549622774, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006138479802757502, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006138591561466455, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006473229732364416, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007065420504659414, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007806401699781418, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007903361693024635, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007443451322615147, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007032470311969519, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000755043001845479, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.000780660891905427, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007481130305677652, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0008334990125149488, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0007098079659044743, + "status": 0, + "variables": 2 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 0.0, + "seconds": 0.0006818929687142372, + "status": 0, + "variables": 2 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0021314399782568216, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.001980497967451811, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019613991025835276, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.001956850988790393, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019325779285281897, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019336049444973469, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.0019299481064081192, + "status": 0, + "variables": 374 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1, + "previous": 5.53365780699012, + "seconds": 0.001986332004889846, + "status": 0, + "variables": 374 + }, + { + "best": 13.129143554949362, + "bound": 13.129143554949362, + "constraints": 6, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 13.129143554949362, + "seconds": 0.0007041699718683958, + "status": 0, + "variables": 7 + }, + { + "best": 13.129143554949362, + "bound": 13.129143554949362, + "constraints": 6, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 13.129143554949362, + "seconds": 0.0006857099942862988, + "status": 0, + "variables": 7 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.6408980239648372, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.518841665936634, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5807887772098184, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5805281768552959, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5855261508841068, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.6540732628200203, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5800754020456225, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 378, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.007595666917040944, + "status": 0, + "variables": 817 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5755825641099364, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 378, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.00785870710387826, + "status": 0, + "variables": 817 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5494221800472587, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5762166669592261, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5391419599764049, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5634573090355843, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5678934010211378, + "status": 0, + "variables": 6517 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 750, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 5.53365780699012, + "seconds": 0.5686389121692628, + "status": 0, + "variables": 6517 + }, + { + "best": 0.0, + "bound": 0.0, + "constraints": 6, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 2, + "previous": 0.0, + "seconds": 0.0007262879516929388, + "status": 0, + "variables": 7 + }, + { + "best": 15.034699473516357, + "bound": 15.034699473516358, + "constraints": 11, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 15.034699473516357, + "seconds": 0.0009872689843177795, + "status": 0, + "variables": 13 + }, + { + "best": 15.034699473516357, + "bound": 15.034699473516358, + "constraints": 11, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 15.034699473516357, + "seconds": 0.0009186109527945518, + "status": 0, + "variables": 13 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1127, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 5.53365780699012, + "seconds": 0.5781218349002302, + "status": 0, + "variables": 6960 + }, + { + "best": 5.53365780699012, + "bound": 5.53365780699012, + "constraints": 1127, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 3, + "previous": 5.53365780699012, + "seconds": 0.5941225439310074, + "status": 0, + "variables": 6960 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008034992963075638, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008022414986044168, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.007987846154719591, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008007899858057499, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.06002827896736562, + "status": 0, + "variables": 312 + }, + { + "best": -22.13463122796048, + "bound": -22.13463122796048, + "constraints": 174, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 10, + "previous": -22.13463122796048, + "seconds": 0.008030876982957125, + "status": 0, + "variables": 312 + }, + { + "best": -13.848534080955442, + "bound": -13.848534080955442, + "constraints": 104, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 16, + "previous": -13.848534080955442, + "seconds": 0.0012454588431864977, + "status": 0, + "variables": 98 + }, + { + "best": 72.27751861391584, + "bound": 72.27751861391584, + "constraints": 21559, + "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)", + "nodes": 1631, + "previous": 159.47331231171188, + "seconds": 1.9969544738996774, + "status": 0, + "variables": 34903 + } + ], + "saving": 0.003001235, + "source": "322e0ec764aa7ef7801383feb1f656e460dd8bed" +} diff --git a/research/joint-helper-lattice/FRONTIER.json b/research/joint-helper-lattice/FRONTIER.json new file mode 100644 index 0000000000..9e05b4e025 --- /dev/null +++ b/research/joint-helper-lattice/FRONTIER.json @@ -0,0 +1,187 @@ +{ + "checked_at": "2026-10-21T23:33:26.343365+00:00", + "coverage": "Latest 30 open PRs sorted by updated time; prior snapshots covered the active kappa chain.", + "comparison": "No higher kappa than the submitted 0.00302015 found in the checked claims.", + "pull_requests": [ + { + "number": 1764, + "title": "Research: rank-two interface candidate for paired frame transitions", + "head": "92a6b7fef74a7f1e3efb911a366ce32e2d026397", + "updated_at": "2026-10-21T23:33:24Z" + }, + { + "number": 1930, + "title": "Construction: three-stage persistent prefix shear chain (no new kappa)", + "head": "f4bfa47d0a050b3ecf0cdf198d077093661014ef", + "updated_at": "2026-10-21T23:33:20Z" + }, + { + "number": 2216, + "title": "QQ16: add an F0-B1 selected-state shear", + "head": "b384a72e79054fc9589048c2f9eb9fa85fab65ce", + "updated_at": "2026-10-21T23:33:17Z" + }, + { + "number": 2249, + "title": "Research: high-arity connector toggle cost floor", + "head": "2d3a99a0887236ff340596b1295604b9a3a39b07", + "updated_at": "2026-10-21T23:32:58Z" + }, + { + "number": 4469, + "title": "Independently check #4438: within-cell gauge column transfer (C = 3 least, equality at p = 2; no new \u03ba)", + "head": "baf56b163de5981ade5afa28f75bbd7e019f8b65", + "updated_at": "2026-10-21T23:32:55Z" + }, + { + "number": 4467, + "title": "research: #4436 direct-flow leaf walk \u2014 exact \u221aG regime to depth 60, predicted saturation keeps the refined-induction cap below s* (no new \u03ba)", + "head": "43cc0fa102706dbddf97a76f7b4f34363e086071", + "updated_at": "2026-10-21T23:30:29Z" + }, + { + "number": 2134, + "title": "Six-source one-TRIO path misses full paired coverage at 14 calls", + "head": "7d9b18640c410dc3da19aef0a66291c5ab9b2ec1", + "updated_at": "2026-10-21T23:27:39Z" + }, + { + "number": 1900, + "title": "Construction: five plane queries for selected P111 bit decoder (no new kappa)", + "head": "2f7c02ddcc7c086baa57f0db28c0a4ebdc465496", + "updated_at": "2026-10-21T23:27:31Z" + }, + { + "number": 1865, + "title": "Research: nonconsecutive commuting C3 fanout schedule", + "head": "e7d290e9d56eb1a7a8622572272af8e0aef161b9", + "updated_at": "2026-10-21T23:27:23Z" + }, + { + "number": 1836, + "title": "Research: higher-rank paired boundary at a single ADD gate", + "head": "9a7cb3c6c74b9745084f859c5fc8142ebb775cea", + "updated_at": "2026-10-21T23:27:03Z" + }, + { + "number": 4468, + "title": "Independently check #4437: the ideal column majorant holds (and is attained) across g = 2 steps (no new \u03ba)", + "head": "b5f7fbbb4a4a778f78da69ee1a5d965a6af081ad", + "updated_at": "2026-10-21T23:26:49Z" + }, + { + "number": 4465, + "title": "research: refined-induction ceiling on #4436's direct flow grows with lockstep depth (log-gap g, no new \u03ba)", + "head": "36d9c475d4bbc99e93952e0ad86a802e1bc581e8", + "updated_at": "2026-10-21T23:16:29Z" + }, + { + "number": 4466, + "title": "Independently check #4464's stage-zero commutation; the recorded translations are forced: t_i = [c_i \u2261 3 mod 4] (no new \u03ba)", + "head": "496a7d6bd053b7019935529ce5b5c3eb3dc664ed", + "updated_at": "2026-10-21T23:13:54Z" + }, + { + "number": 4440, + "title": "Conditional \u03ba = 0.00296 via query-thinned productive controllers (+10.18%)", + "head": "9123d75afea5096d25eb98b2b6080cbbe0d91c01", + "updated_at": "2026-10-21T23:13:42Z" + }, + { + "number": 4441, + "title": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", + "head": "149af87f1101dc7a72f2fe57294f9bacf8d053ba", + "updated_at": "2026-10-21T23:13:04Z" + }, + { + "number": 4446, + "title": "Independent retimed p17 certificate: conditional kappa = 0.003001053", + "head": "e2bde8f5b9bfa2e8d51f959656d84ebcc2af81b7", + "updated_at": "2026-10-21T23:12:34Z" + }, + { + "number": 4447, + "title": "Conditional kappa = 0.00300123 via a missing three-dimensional contact span", + "head": "02b51f341013c607dc480248c94c216b8260d8af", + "updated_at": "2026-10-21T23:11:49Z" + }, + { + "number": 4464, + "title": "research: certify the actual stage-zero Gaussian commutation premise", + "head": "82c7db427100033aa1275ecdb16ebc2e2ef10b91", + "updated_at": "2026-10-21T23:06:01Z" + }, + { + "number": 4459, + "title": "research: #4436 boundary exits \u2014 exact mirror identity, rigorous share bound 0.321, and a correction (leaf exits dominate)", + "head": "488a75a9e95e14448b6301719249f876f3999931", + "updated_at": "2026-10-21T23:05:07Z" + }, + { + "number": 4463, + "title": "Add a source-bound baseline for the selected productive-helper schema", + "head": "108509ac7a441617e3783fbd991bdf249fd23e64", + "updated_at": "2026-10-21T22:58:53Z" + }, + { + "number": 4462, + "title": "Transfer the \u03b4 halo exponents 11, 24, 26, 26, 6 across cells; robust to the 'rounded' reading (no new \u03ba)", + "head": "c8fd7f81696d5b8b838c996cc384e76ab378dae3", + "updated_at": "2026-10-21T22:57:39Z" + }, + { + "number": 4460, + "title": "Independently check #4451/#4452: within-cell halo exponents 11, 24, 26, 26, 6 under delta (no new \u03ba)", + "head": "6aaf48105c2100d0dcf47b5b1ff5a85c37ddef52", + "updated_at": "2026-10-21T22:52:22Z" + }, + { + "number": 4457, + "title": "Independently execute #4440's controllers and #4447's native word on lifted operators and physical frames; check #4359's delayed cover (no new \u03ba)", + "head": "dd40f88a4d45a0ae2487eb24f935516f749cefef", + "updated_at": "2026-10-21T22:44:27Z" + }, + { + "number": 4456, + "title": "Independently check #4436's direct overlapping flow: all 9 recorded flows reproduced, exact potential identity to rank 1000, L(1000) matches (no new \u03ba)", + "head": "bbef80cd12c66afa31cb347c7393fafc873a0c88", + "updated_at": "2026-10-21T22:42:02Z" + }, + { + "number": 4455, + "title": "Independently check the p17 chain #4440, #4441, #4446, #4447, #4453 (kappa 0.00296..0.0030012): invoices, strictification, roots and compiler ranks hold (no new \u03ba)", + "head": "e02ca27f9a30b9aeb5e2eb701bf2eb0a27d4e193", + "updated_at": "2026-10-21T22:28:06Z" + }, + { + "number": 4454, + "title": "Extend the rank dual to four planes: COPY floor 16 over every field on 361,706 of 367,290 plane quadruples; 5,584 open (no new \u03ba)", + "head": "6eea96234209fcf9cb3901d9c298d81ae3b3d808", + "updated_at": "2026-10-21T22:19:14Z" + }, + { + "number": 4453, + "title": "Conditional \u03ba = 0.00300120 (71.9\u00d7 smaller uniform-rank exponent)", + "head": "de6869e2e4d9c6f630bac5de4a919d99a2cb884b", + "updated_at": "2026-10-21T21:38:35Z" + }, + { + "number": 4452, + "title": "Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new \u03ba)", + "head": "af68f5973a572305af174b3c49c440592172134d", + "updated_at": "2026-10-21T21:36:09Z" + }, + { + "number": 4451, + "title": "The published 4\u03b7 weight error meets the 1/(16p^2) ratio budget (no new \u03ba)", + "head": "be243a2818f0de3421c118dd21601aafe8e839dd", + "updated_at": "2026-10-21T21:21:26Z" + }, + { + "number": 4448, + "title": "Independently reconstruct PR4441 helper tariffs and complete p17 invoice", + "head": "6d535abed7b60d4a99dc54903011a72ec367e901", + "updated_at": "2026-10-21T21:21:23Z" + } + ] +} diff --git a/research/joint-helper-lattice/NATIVE.json.gz b/research/joint-helper-lattice/NATIVE.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..0910f74138decf498e7fc445cc2daff4390169d6 GIT binary patch literal 35042 zcmX6@Wk8eP+a{Ed2I=l@BqSA;4gu-z?uOAJIXVPEq@)|9M#tz-Lb^qIFa~U}cfbF; zZ~O3^^E~I==Q>y1j7d0X|NSs9PkW~`=#?^RJNvZItNa8If-*Ap0S^AG*Ux;)pGR>F z2q?EG6ORA;m&5ybp2=i{mS?ZByl2I*!%$L?b67Pse1CQK7WgIq5Auo8V-s;u&nXG4(jY40(&57KY}x`&1L!0*nEl!_QbU{@CMGVB=mMH z9C7)y)`83ofggjzLy^aoVfS}1m=+QNCXx?@KUKnJkw@_sVaQc2!Nb1Iu&vwjeosRVZ0>i??5O>Fn%Hem6 zeekQjtxW*(wi0;J2fr-#=!4D5Ur`o!%p!*^!h&HtYe&fYu?x9Sh27mf6j0?W<9oK z`^x%|mpi!@$U6Cu&Ay_Mqpe5ywa4SmNOz{+Xs?_#m9$-u*%7TD%hWP!h^%o=f9AtWdwEflh^w@n77M%iL+(KZK?@us>L*PfS>)Z=@*8Q^p#?5f# z*{nt6a5(gO3xL{xS^NGdMC7)=>;XLV-^W;rIWr!vc{Wee~@|nXpMw zy-hi?om{PkJ9vOR5^}$BkJ#*!X^;;?TzbqtyMH?CxCje^9jL@yLSr9!xb^fMTjv5x zNEEF`@thG?wm3)7Dy|MD$Kc^T0OXm6MP9~aF(drA0SUd1KY|@~Ag`8_jxCBC z(mb{Rh|9IL$CIu5(3+s9Z25JzFvQbZ1JQaEH4S5UX_+70buZvA1_@_S(0xCL=Iw)C_e6zNcX8%fnBbZjl(kl#SW~V`?ssvE zjP)*ej4!<(eE~zd$G-ZDf|nezDpopyg%|Oqx>RYaC1qcx1S+LguCB28K=H2^FG_0e zPKTG(FREv&?z@jymp_NH_p@>ef%3Y!o~{;8;sQQKNyam;pqmYnNrOrXl2|;P#_tJo zy_*xPtn;Wi;!dbEud*@e>Itotodt)K-SDEuGN~Dt${(^Kz60}nz1wqH8qywC-S59H zl3aw)nFomMF5cd)rX-Q?Py)Z2w|Ltn15z7`SLZllaIN0v5!ZuHe;R{NSA~+tPu*(3 zr(&L3{&aP=-14SDj?FS?B#j2Pb-H2K)4LrD1Ia`{#&eN~%#2%7kbqWCV1>T)l+ns{DW`?Sdr20>{>SlkQiA2g^ zrO|r2%sY_c?pw@yG(+U?-AcVPDy^B(HIwn--u8 zCpQ11&Pu(>CXyf%f9uZF+;Im9(qf@(>Dudg7q=f!26J<2`)tExmQ_en!;Ze8*8ITU zw{_n_i>nLO?WtH^*p9T8OJy(gXM?1E`W_;79Hup55iU!8coeWPF$tj&%-Yt|X} zb+?KKkVyOJ@it$(z2iOK=^2*6W4*Tc$x{L4L>i9PO+SB-U_tXRdn*t2kO6jB>qqQu zEYDz|6(-VQ7@*kVGURlA5;ghHgpU@jiR*KAxfk=N)MvKF*#qCAwLB*vQhd$#IzbH- zTSBr#prdqg$r5$0f>{HsXs%4qhr20lai2lXI1#qN+=O?5R7J3fz@|X*nuaAoR?A5) zfT{P3J=gVk?x>oKAkXX(qua6Dh@;?7W~sG7?{j~h<$QX|Ikl4kVVZV^MIg|agjknn z;~}EDM5d&}&#uzUKVJyT(BbY{6Z&9n@SDj_&bR1Cr;_K5-WUZgVM=P&6U9}D5 zZ3B3&1!SN%EYN?RSgi{$OKi)q%`8E{I4kIi@K`(#|7CdN8ok6l ze&}MvW0Yjf*xJS>^RXB0c7(Y4U#IZcFbN}d3KL*IoZ(QJEy<1kg4+t;={zMTV7W8c zsgY~o%Y4TjcRJSOkGzYP#E_hG^bmu9%TrCn6dfqm@(zo8I3sgxjZiFHx}mcF-yn>_AwR~*|1hjnVj({aSl zo0Bb<8Y>d=j!6u=a&$YedMzHRzISgB1-s$BZ>g!SqTh-;(Cz1=vh9}9-VWPUzTeMCChiowB@+(tMV7LJeD?dB) zZ@b%Z4R+C5RZP`a#<)I4j2`ltPR)C-h=RA%UG#-%b(9HHt9X>-bl$cX-5V0+{cf+% zUQBUg%)0C#cZBgb710tO8Jnx1Rs+W2&6cjRpSs4|CpOMTr zZ$nq5_rdO?qLeiIk}L|~ZEA^FZ-_BIZPrI;sVWwTVYkOoSq|eTOSg+j)<{j*{3@w|TdtRLvP;2MC&WiUJ!0Q)^Z@aY}3s~eZEee+&%4ySS=Ea9pTf2GA z=7x^2ZV*LI^qpL64?0>Hf@Dlwt;1_#JzID;tcqfwX`qh+_Ao+YH zAi~?7ZLENmI(>UhKX>~{4EOwS573&o80iUYb0dM_ocDHO1Yl{lOShBh6LzXKONdcX z*w&X1t)>tyiy0&ld7Xs>6X~zB3E|3MNAly(D`RvNnsxi1cjDmVobDqOFr>{%E|PFJ z0Vk%zt98)`q#K6FtRvr)?A%@4yu# zNe7P-Pmh`K!Kd#S*ZhY(p`8loBHo05iF9B$*b_c{Wr!gIQ zPB)yKX=Q%THD6knb7jf9@jzAv)dlFaB#cjf4< zd@sT_z{-9X!5ZY3nuiBovPJzd9b7HhT$@-sNIxP#JuYYpZ zdTyy;?r?#f_>@FBo{vE&-RN5qH1coNUp17*_TABT9(Pjc>9xu8gDSQ2tLBOY?;qJp zL@R@orz0xk&jWuPl$|AN4|pyF|( zxxGq~UE^S8w5o_(UwzXuEdzClZ<+dy*oyUgvc=7A3QHll4!S;wf4MPpTv~dSXS7jh z;><{9wa_ygNk%L zAqtN0A6ycuemg}Jb)QL!-i>$8U(iY>?({Wl!ZT$vHIMfaeSobGuit!@Gex;_f^|#?zs$ zXXbyi53I-Iol7axX{sN}6%VIv&%9g*;N@>pvwv*LkPcJB^>hKVn^{-nCtU-}EqO1PoFVT5q*<@w{PUgdU*8!vcET~dBtv*`mQ(sAMkW~08 z70TJmqkBoX-9=i%UH`MC(l6rZ?+{w8*5OlPc<8>caZJ&vWN!_2d-O|NDy4M-ee6Ji z_gBn>_5fTCOzG!TU(71M6tX4b?m1cFC%+;c-LP~Omyu#kCfVSB2ZQMN=H|Z(5DK)U zJc{gMz5FejA0*=7V;;nfB4ZJtylBwDU!y{Y#XY=X&GIn+5_v$<=UEM483;QtbU=fc zY`8Sy=OhMQl;JCRoxbUd(o(9lwUV-~ZF6jjb+dP=+(&KKh0z0rS0rusk9o7du|IG* z)IW~2OCNd`h=A&~@e_)SsTn1ffmi(|MJE!Vq#8G!JQQ=h(AXJ)ck57*{4uG*JM%Rr zgC&zsk>?E?MMl}Z!w?&*v3yw57dkl@kBcgoZ;v`YaceL}*VPYfy<24jG`y! zotSh0B~bF!Z%s2l4nmlT5Ob2HnZv?fq0DqjyLpo5(KZUfV?UGmdKHIM)Gz?+3G^fHsu;jGke6vq(7%isMidckYy)tbF<0QFKS(4qJc* zZNLR^?D;H5)R9cC(nGHMWWg$c@WPE!J5iqEMB<3)$ZYV1ByZyT7Kgn{7xtOE%e&Oj z?~u-h1qz-fW3X0Y!86&H);kP=EcwdkDYi;%Fs0@`k_=|tBBh+|9gd!c4j!)GGg5&U z<8T9pOIdfciXN@1UqQtutnzc;cbK6a-YK!ctIeAqPO|UT`PKIUWGII7NnxG64W7f) zJ}I0}JRGsE=~Xl77XHVwyZ{JkT6QHA<7z50+wt|$*#tIXZ(1+TfTqr$OMcw>fk~*i zX;kG_*BUrACaGP3%dC#0^(9pWhM_zg|LAa(5-zvUI}q8c&4XeJt1tR4$y- z@l`J0;krvt>K*{lUle`@N7+3~hs9rltk$|E##3I&cDXzzA3XePX>;211P;-{lnl@< zGE?P1S?lkFNY;PpSU2Gm;hgidb1Dk4G#Q9z(oMsrf268_wAh>Y|7g6v-gtFsmfDkh zqI`Nan8MwNYl(69!%79?&Nfn3B!VQ!?1M8)f_?9fk}!oycMlKRMl-#u4_&P{O$?K%x0H?)2$+S&xR6uAq<8nZcK=Ct#arwsAM!eo&SzbEWZ z>yxv1Uk9>x{;1RGp38uL7mfI{(_D^_Vp$8^HZyYGj!ePj_+{WO7_w|BU&v3cnwt=? zKl{%^PWMUKI^zzZqpoHGqgQclH}zH}WsQ=?|5^=*<$p0zKUc>-o$c~6?l3f0yzhFM z3(cv%rrAK!%&}#fCAX%WU!v~giq4wix~n2bCOA5W2E4xqS2?sovF(n?cY!}6mYaVa z*^sxexA_?~)l1c%0o0$VTr|4H9zv4+XcM6x~DL0Zt3udZUP?Ag-L9iY-u+A!!pXeAl0K7M6m{W(ayfq1}EYy6aMtaf}v9oxg_As*4rSyAaE=N4Y0lsLK6$ z{P%;%oh25$MwCi>)hehnRV0+$83I4n+B4kR6LiaFG&ijo`=Ayv{kw%-;wu()Wgnf! zUHMZ_?gOtBIt09K?4*3y?m4knw0EK(^rMV3gSqt01Lj0el9%DB!MhNzEXLH!)MhVj z2EBv$g+yQ8&#(c^#kXOmM+J@?U*g~UC|)(r@)6F5x`?r6gqE{O9ESDcX?y9t=zlC{ zCO~gR_N?e806uHPIfY9P+1~G(Mrj<6G!&aC}mHBl7w?F{p5n()8faJ}w z%6h5(clD%C-c?zzuqRfh>aCuXq~`y&_68cCIRw^8f9~Ab(;$!^@OzCaF+%vBw`7P)8`Hg+yAQ@cX*8!Z=k(U*H{J=9vi2c5B8R-2!)9((y zc30Z7lcefjSD#Z_D<9ltyS*|m(|>n7kLZm$!}#_7_nXkxE+@YzGV531ZYEL&yyWG{ z@RNJiZwQVw-2JZ(%U^9`wkXCot1m)ym~0-_h|2mJ(!{#k^`s)_A5>;?F=GnS2FN&Z~3XZDJ`OEEz0y!`!S85-14|W9UEKjo6}^7*UPU zn%o~%$ckOeZP$h2iP!>tU4F-_*qU({YJ?tWehS|wRfL@rudTKIqpraw>e4L%mpX(ZsQ7V&9sl7?)Xw4)#*js8T{c3fbtbnYEo8LGiV zHok|kO8xWiGYEfV^7zFrcV9>de^pqZa!Bx2il;>OR#M9H_gVy|y(89@an`WZ(LYkc z5`lC00w6!`h=WIt@=WOTa=ArUro~ zPv!*J9+IWUk)2Yt{wt2O?*{MV=Z+Nt<=>*1++W|U{xGilJ{|%d7~iUfh?-^GnJvvS zx<*aXs#g~Yj`)1ct4o1pz1B?{(!3y@X3?hD&*vFcuU9fYcv!31Jg4CCL=i3VbA{t5 z8znlju^%_)<=91Bz0xgV{7_XpzE8@*<*Lib%cD1N~F{u|; z5eu1+^(klL%vU+Id96nWRu?JA=;UUV32T$ij9MQ~cq8HzNimFO8eE7+vl@p>IgVq{ zA&zqi_Q83nkh?CIjr1Px1Mq~WdvrGNN;!yNlxaLKe@m{3`eK`US5Ho*7_u?N-Jjgd zg$wXPg+FnUy3Ju+OJkLUPm`XwJH#h@Sab3P&0&B8wD|arH+<0NiB&S2!OF)Pr~wRy znxv%|3ndvy$J}~%vNkJY<};wVEk+#4oTjd>6zn2uUwCrFldPz6bR4qR>$gS=+Uq|C zlZ_2u^}iqAX&y+}WA<97&`>@Gd?0pPVbE%3JrNuWmIxJ*v~L+6a-(Q@Q7PiX3CCI< zbIbYv8IN`X2is(ZugWB`$~uTFHX*ZrOopT4OIri}dUev_!^>y3FxCmn$jDxJirF&$ z8mJA>ik7*gI*twkEV6{R9~?F+Rq~N4yJQN?YuXRTh3rp1r#mw`V`=;c(|x|^U0+!; z%#XZuqUMSbwvypaHW82+Tp=Aj7!?}zg}qKYPo-3NG*$xatrJB(c#8kqV^*Lgf>M-E zI&KdP%l?ROm*8T(86VL5UaBL)_GoX{{A}ASw|4;2k+H_7jSOv}AHC*CP1uw2biFF% z&%k{&^Kw0kQcti^5219vxV9o<8^`|qL~9k!d`3^Ww3%TAZkso+H^3uaEm*8=clC?P zeduPuYb1KDQt&=V!mRf|r0ebf&VBFifWKGz_uUw)wW}feD9j5feL6Qetfh?2Dth;= z!9{%?UXUZD#C<`NEA<$aQuean6usul^st2PHu!ht;p6w@KSA5f!xJAf@>$s>^VK^5YzLGI8_M2lH&;G+A` z-A^z*t*M6^tqk{&q<5Z7Il)^{D8!qH+LtmS9x&LRM*wG&s$vT;4859&JqP!-l=+29>B_ve&r@!g^h zqk?lYb?@5BihPCH^4O0z=S?ngXKlSyr=Tw`JzdZDbFEX=(!!p~xtG^sL zSrPZpe>AOje)mOX*N3~_cu~(#el3w^hXOmNTd^`6K{od#CXG_tJP=R*t|6caB17iNs+K`2`Ck{BH*MAaps zrDANZ4yE13|iJ9N{~BCh6a5|$Oi_Se<8HWfZ|unHmV^+&t?*d zeEqcdKZVh8pA57%NN5SB|CkN0HUV(t1XiYmg#cP+Un)veA(1|Hzcb2ewQp)qxxFvXz1q^Hzy+5wo;K7?d@ zG>X7Q=RKujU;}6uP3RXDy15F}=1JA>2_=R0OOL64x#1=mwJk2=^>oVR92$IE$&Y;C zJo6aL6Ov;XrC`kui1iYwc|U_=qa5Jj&a?rTzGsk1EGP)ZktJ;k_bD`nm0xiLkbaPur~wkw1UxeHicLm{CiYA;PrmyJlxJSI^$iD4i5)~CozCc-5m*Va3q z2aQ`Qen=Tl_aXwzQo0u6THndw*EZ%tLOw+QVDi945{N@xrq!?5e2}&zk)Y0UA=5Q> zQShFo+_;M5Z8UsT;i?qwNX${ zN1IwY3eGH_^RVLlKH*;5OgO!IjPTC}O>W+za& zC^{EFv{Yc(gp#O|zS#E)?a3^V*&MMEC6HqW3PXDd%Rqu8{N2CeS+k-X&_RB65Roj{PYOze-xg(eZq4?oJ9+5`>M=G`Yl(_E5<5@i6E zL(ved5A1XLMz}3=*#FUzb6tG4>yNg#0W6{w<1O0zL3Hv6(kg?_^S)nr1*);W<3CqD z7rq8dBFhJ!(=#5`-GwC#uACRqM)%TA)od?ORSn`x z9`an>x*l9{rSQ>2)kwE?0Ap(Kvwb&PMi0nQy;Dnx(zfLm(@S>BPA0R!l1*10L5xnA zmC~A3tIJ!X>K_)2NWH9B!qt?oQEyRhriTEjDtYie!7ag?{QMD@j+e!_hRId#oo-?D zmB@Y4k1f2!0om#zyVyd8yDG=}dz{}4Ye6!hi*{J}IfjCIs-GJM#BZfgm&>~$*;dEdt2Up2BLi-sx+(<(vtFN5Kz>Z&KH>+@9Z<@0H|RU zI+*`3)c^Uky<_i}GDE1S!E3w@%M~N4-h4=XuDH!3DAv~8?qS1L*hmH|iQirT(+EME z)bi=f>jQ;NwTXM4pt`j1*ME_GInVR{UE$}^Q$jble>`N4ogDm&D^tG=ycd%os&h^Y zH#^r*o)%XVD+Q1UzE<1F{zpF3jJ5~mZ4}P;;zT98u4eUKSl8muAjN1wP0hWP&qONv zh7=y)q`FYTMq_bX^D$=bw@{UDJGV9b5+l9grr{Fr%1+lBuznq7XVOHn6Hn}9m%dT$ zp!W}Lkw{X?fyp$8VNEaz;f8#xE#Z$euly7EU;flWDn&!w=`jO-o^X1hX!~PNdUAN+ ztQ>=APjcHmaC35Uprh9R6CIV^p5h}d{O!>5UBF*?-3$CcA_Q-UcU_rbdJ@eSe=;ULqHNnxadt1e2K_INIeCkUW85kwHeU{=&6sy|%~UKtes0)}d{3w* zOK#5Em7Fv!-RH1qAmyINN#{+rlFi6Fnb)kzD1m)Sq=MI6A;}f?9Z{k)r=Mw=bK3iC zTeCv!iKj)gzp`44Sa5=9{(>VHe1QI86KqE-0Ec^0>+HS1`5H=1dw)cpj&%+vEd3~t zrc33r7z6ZnyXW~hIWVUsTf6Zzr^U%;e9v$n-OX{LyRmTX_1y94_d~tBuCRA=4=V7G z4s5#W!uYKsb;vrcNu=(`eU_x#0mvNNzrvAmcYK{7D}v)OwP*V(PLwmPsUnkYze8Rl zOd?NUXvaMNI5IIm%BuL*21Q@vmD4C&ktdY)GJe; zgi00X6jMoG|pZe&RJL zb};dH$aN$`z_?y{RZWKJ(2AT;PYXsz`8HzE+0=}mW$L}8(eH2S@Mfu`GiQ3JeA6b-*E}1WqHOGeRf2jI*NkCB zH`Ag#fA^nBOm=UV9BX^B5>Jt*b+!>elsiB?2(G63@~dfL#i4Hyn}>pz>9Ut}_kY6D zP+Wpdt#iJs`^dhnJ|N(BR-nEE>U47sos2{CRq#*nRk}pq)lMCf$&)OUw;M z$gr~XExC*Jhsmo#Oc>Eh!s>$`AUF7pfw1nsiNIvlrJt+M1*@D9LTxp>57i)3}yWWV}KIvm| zR}!bZ?A+^AeyBH2yuq@YkfdWb;u?R|Jh}I;zEGB6|D=>1ybd zA8{i)?>au0+9Nzp`0hex&Y^PHvXh>~V8-?9mjDyMu#$Q5M4gAm?+y=4_taU&p?4|V zwj%j59GSFCZcUWe?dpVU-T@po_t9QVvXV(hSDA|r+I&1d9Ox23HZ&|Gtd5T) z8S+m=6~BZ%K&@`N_5!;;E4aP`inUR>=}runnkhvBv~XGc?2T9 z-Hb5gL(r6%KSq18AA%X~jZr`@r zSlyXS8PUgMKmZ_IE^1TPPVTe@n`6F7%y9o3j>Hgnk+G*b$^cOvHj#F_w#6*Ksg{|2{Z>9+{H zl`3Q942qiUSNsSr%=Upztkoj;ks|muW#zfUqE|AaMZE)FXFXvK-ZGrL9=7f>tP4Fo zr!Y-{X}0Mh&r>C9E7r@wtPL%K6tj@C;m1=L6rSmFmwq*V!I-;2L7S=}su?8))oCkg zaMk0jl7lxZ;Pni|ZtQ0KnfLvBl4RU^w;o)q__(*U8JR0B5Vy4ZpIM0mqy17y4URJ#Ul+$vyZh{RZS4!l;PD4 zR=cXq5-ewz8M9>k^X&Jzu=H>hTmXg@|t{ea`$_wKah;U284=T0h|GUUfTEc?`vUkgsU!M*#ym|aT&Icfr8f-!{%l$ z@3^M~;7Sk1{3-&}gcHnbw%oqD#vjZ8^_=+vuWkoiUy9mM7d7!|jcc{7FXTS3T0w_C zds^okf&_Btn?i|mHryJMrFOn!vzO-=UhY(ci(HQU8hf@K9MlsHE@p^ePiljd*F(`u z8qG=$gs5b;fnTTfMuTnrbf}|MASGPatr@4%SwkO2+Gd`Ht&id-$^K@;-hdaizi=F| zGa?c4Q$aP`|B=aYIfZgYLq3`Qy5+iv7@dOl`$`& zY~uG7Uoru;T0QgnmZ}M@)sI~YxnVI@ziG9#JEO+XafW;bH0#Ox*qsfrcqA?0yiLF8 zn4Y3-;LX+O1h8B78CMl2ynIO-V--B~p9~q5xg{6|aRb#lFi|$QFqB{BN)Ttq)P9IP zx;9jK{2Rz6GK41ecJHj|b=)n%p}$O!fT;T}b=K&IA$(sxV@(YH5xz?8)cdkv!Cm`w z){>YfZ@x?+j^r~dI!3Jw*`M5Y_EZI(Te^c(iyQC%o@>Ti6C4&J2S7dB1M>wWV@#U8ET5zlZxq zop=j-nBWJ9^Ye7hOD!C0b&sT*3&EWE2)Tef;_Gr%5En=XO#b7`GK&&yL|8WX?^CVW z7@7Vneul;~epB`XaU;7$7OQj>#J8!=gV*n`f{JY`KG}jlbrNvPw^7}FHn(5v^6GU* z*~J`bNcHM1%JH?jpk(j`LMN;NZ%v($sPO%l7i7&zw@o$0kuCbIM6$sjXjH$3@D!M@ zg=3%bkIG~^+ne}8Ua!oJujXEvN`DBcZV=3_xLk=VMIzi=W@E%SQc|uh&47{`3wL-a z)1>{JWx^Fb1|>bK+p>ZuL#xqH+sBfLHUAzR0Xf|d+FA42pIzD0?+gUUrw8+OgIsD} zo+w!a`Os%epv;HaZ#^n|AG2XiVxw6dhCMCydYd7jYK)VdtVDZ^nZyPP?bf>Sp=`-T zb}Pp2;ViLG{w>j&%t*}g;R-3Xy*CVAy3#VK!RPyob{-j@VoQ$g-?FkFFY%EJLX{rFeVqQK!NB9xe+XW51H#i$+ z=s;ilBt6leGNq;~Zq)tU>bozEtoDtdWt}LWeVe8Qf^56&gKfcgY=*aCZWXO$-ub3Q zd6Pw^;s@ShHR>}HcIqif43`=9I(t@P|7`eUpRSTjsF~1~l)h=0Jhs!rmfYpqs8K3PtTo6O8rmOtE#>qI}uJOddtXCL;r1MdOb}q_{KSYFHJEE*q85ExaLOZR)u8#alV|ah^H-W_XF-qnBFwNq-t9@I8{KMo}lm$Fq z7$Uh;GgnzozT!21BQUGwsQ>2wM-a3rL`R%!>oh*{aWm4b0`UftC&LgkMv=s~v3d?` zmC>{(;PQb`>25uhKM;Bqo@Y90C(CyoX`kCBLe1Y0g$gTT6+Ygs1YEFwAuOf+?$auL z#-I9KK8Q=y9kQ1>NtqQAwV=iYC(SH$N+RSgk7_coPuWf+(3{wc7q11g;2-te{g==b zQI4DW7j)WiiX34z_q|F-M+emj8dwN;QCGs)%$a@sYr=yjPjq{?aGlH`4j#tWzmMUe zi|<~-d}GYF+RonKcB%F^WA`b)1@8jJ=aj=lPp2W;S>(^#t-Mi)M?$^AJ zvYe?++MZRtO6DV?R%mr1XDuv?a%+3}t-7w^p1HOFp}aPaH1P_T<(}oP4K!zX@LlH8 zM_$Z!?+}D5j{YvKV^fx(B!-I!aWT7AYf?N4T^lfLl2DD+R7k?T+|!mR3`U00ymN}W zttRb&3m$TGcxng7QsqOe-1cF7LE|Q)wE%kkWNHg93^=UOPRtYSLVBBMLYy{Gv;ex_ zIgtHf7E~F$7>OVOCLdwSXVR7b=QJ`FKWZ?nK~~g5XUA>$d@m13i|mY6yqfnCSJ76E z9@s#@di2|g>eZcKd`#X#`nKtMX2yQjtgn8M(}|rNG*^Xro}!Y7$JkZZzdG&k`ex@o z^hhREAvgED?kx;jO=X*fp8>lnRP~P@)-(;U3KaT{j2{e|Ul zbP&JkZ4T!DZGwAH?)4C66QKJ`qD{4ZHT7zdqyc+^~-gz)Lv-{WK ziLL@9Sxy&aS?ap*f5D^IGzw+>yu-|k99E5~%<5ar2wI&l`0?xWf?`b`7xmuOmnH4) zOYhOnAg|@c=fBg7gdPVhULb2r5D%^Y&Oh3 zeq+Ec>nZm6B9~WL;A`|{Dd3B_k#i1<$m`unIXSw zlOTfs%HdmPqu$A?&W~Z&&%q9{!3KT$k-(-K***t}JYrPmsUI^P?oKB3)|S|PjiC>9 z66z@ie>HQu)e(()C_LGYS6--?)G)4k1F4JRydGNY+7}M6#fT@`KiO$`Wo61Q(Z@J7 zK|1X&y}3{##6$0Joae#CN$Su2Unap%%rg@VV_vzpR z{TI!BULVLex4nwZjcG$G4%t=mVTx`snsQ@fXUCU+JxdFL9n=(J3~zr1PdeqTGBXaZV?$ zg`b>4bSIaZfG^u})oPc#&<=aJR8@Bb-6d$CwT(ZbUR7yklG9lA@f9oR#U+V@`!q8U zym!7u2>=#WNnZyZw@W%;FxY4YFen4Y7)qd+?wp!m+sRzse{WH&Iq&+uLj`sFv(<}k zX&}Ujxg??kGCdeM^N$(%P;;zmN9{$w=TaL@ud?em0he`;V?t3Ji=0u4Ein%@8_^wE z_7veQlMe+iQBvT6FJUdg;~+$7jhz5j(hu|#t9XQST<@budNl1E>~_@;Vw4q72>M@g zvJ-+*5qFz=S5()%%aOk%zUBZlla_AYR~}4&0!~AG$s5(Cm^G84ypCJ%+8)ugwnKR7 zwjw%~=VAZZrqrPx3xNz<-JB^U(^55`U-Ds|eJ=KN8o~%Yn(8kS+xLD0xyGyv-YjhH zXtuHiS!sRg5Hr?ikLAHEVrp!A!yKa8uWyqFWi}iL!}K-iHLfzPj{s+gNc<%pjcICw zxZ`9vM|iO%hsQUqQtaSbCA-zCv!0v>YW!;GFXH-Ufk&GqNekVn=;~&EH)kz>Rn$WJ zZ|m9qYPJc@+g>>;BB>rCi7$LmN{6NZHuWrrx6jB1azC!6dK?5##ad3SQ7mR1 z^weEmVMJIIP>^DBs`X;D2iFV^M4;MYWWt!6q}c$|t!dN;!3|Whqn^7mEOp| zmKC&i3dq_kUyhb#+lqI?G<|tLb7!}HOZuNmBFUkZJWH^%zTYAAXcBdx4f3-q^ej>e zTQsdP2*IK$h`TZVmow)L3}WyQ+Foon3DZi=ZXmMY{%FuIHk$+Q;s+<+qUS9pK)?82 zK_%*c=DT@h7NNp0O3CeypNR8-5EDhj?=KkhLJrNZx+zs-X zcnOrYjoK9JRpsvX_yZETN?=j?v>MtT`}%>!xv5saH|Bl*k4b`j^zyLET#ug%x!mIV zp4AyL9Kf?6x_C86QT|xLr%7;`%;>KU%6|pYya9kuDGGwjb0x9(^OGH%N#TG4uGs?J z_Hz2`h+{4-CODq7@$K|0LG=*7R>+lVFX=w{$w#X3yHrSgRyP`@ zVFuV1Ql@@u>%BqViI*u%4oa>a6#RJNN>{vV1v4%+y}k7UZtX+ z^^!Y90DC69F0*&B{%aoQ_7q`?G+3@v95$UDeFNoh*eefm)Z$p%GUUhEkJ;EkE|Q;C2^K76gy_74#7W;v<& z?$P-jv8oZbbA>@wfNynt?q8AriS8}fxcu}7elMHlPmQV+EXyQJ)BVg# z{Y2n4Z(Jj@!h`IK7b6m={1SF9-K5a$v<0407RQ4ZQGxTIy&B~ML*({n*;O_JPFyRx z3{9T5wU1`l0KNq)jirmzd7j-E_Hs|4A-A({ZH81jx*)c{X<_~j%fT{fMEuK?CGDeG zx*j%ETf~spy3j8LI!2N(5!TeEI%z@LzLq`vN%W=aR|3L^#%&+|5H+nX*y=crt$xC& ziP*L=`kD#-I2_d~-vgI0;SsD?lk?8w+AF~4h#s@`lwtdmjeq{nUu)D--A?eWoli$O z_fAIz))2X*%Q#`1=PjQW+qMPV5kIkLw1$7ASWQ($m+;)Nq=i;Yv%!@pvs^1Q$yj)C zZGyCgm<5t%fS(`SrnqUML-!#lb8;U-d!EIaJKcHeK4kY}Yj`Br8Bv3{Sd_gGVuUU( z?vc-a4y}8CN+Fd)Yq%ZiGx5R3V=ltmH&PVMiV(z*Si9ZJWJ34HM5Fe#MuZ{$whbR( z_F`3o!&Zn|20Oa+%`z@^XycJAbu>x#S;k+!tE=(}P0Y%m_#KSeh>Qc{KHv23_W4$E za$3TpnNzrohc2vosaii^{ckm55_i)0NiMAA$1$g;JLO8m+7>wC!B*aRboJgV-QC_) z*R8r{Zi|bXdzDNi`c2$}iD47{VTmX6%Nw~6mk$$(P;td8>1MirBxLqzTC|oRBJ5&| z;6JDrTfgb*uKmmz4G;cfBZ?X(T6=Y}zv%W&i_B37w>hU8N^&W8?8r zt4S!5oxrTMiDE!8}k_{4N5ujh;1Z&2mV!OykSN5|$#1@{JRhU)MlmHL9Ar<-d| z(J2LXRFg|43Q8C_#^6HKx;sWcE+fUq#_kuav#XWSKOFjG(qh)S7!rPXvTlstCN0=Q zrO=}xiR{3aJ|9ak2Iee8;iL!_Pe0gXNN5R$ z#xcas<{THxPB$N4rHk5aL;7kFDN&#;-`SAWZ!~ zWy$1(^N!D2^)6gp@D4j%z;382Dasn6s0d(-_ajuQxt6AnC-E^MG#T}?^pRHoTgBx! zS^jh;WzQs7`OASQmEj~oE7}t2syk99dU<7aYqm!14X7-}c-sFrO8xe!>>T46Ha}&} zt$ROVdi}=+=Ng6WRGYQ*oz5DR<|te-&1+Fil}ignhs0?!cY{qfSi;^_e8i;6I@iX?=e2K7!k zP}!i&c5UGLJ{@#L6BZ?1$s#$MSVP+02kLTowc4QAueB@>Jxwzk`{WIT>5k%uxag$X2$}K=DDi;P=)^pb4!m( zMzt$}1ljU2-5UepvG84(%(cH3>H6)D$R8eN?`6P4mMSBv$SpIwf zYx@;7u|H7}vy}_G>-pyVf^oEMcsS}sdYZa@Md!tyWx=08(3P}j`;rNW6>nsjzReN6<<5Ehw-s^Tq?ZmTd8#YkQsg+ zES&FEzv)Wtd9wUp$l4( zGClIf>oIseJH1V;q(-fkRFc%6xt=VjV%RNukogat6 z0I*V;$YXS;3J}Y|rSt$Un@}LtO2&#NWf^GC<6OLg%Y^>Of(S{Y_lQT>Un1!EBiwMe zUg!R5^O7H@Ia$;n>%UXq4^a5Pcb@m(7pR!1X=x25aFT^JwWS< zjwXTIKeM9jh%Q>r)C`w0r5u{{p9cWul8DsT+5gCDW(=<|5g&qugKjY{)lS|`r=9|1 zy2SjlbaF%f6#n~O%y-!r%vfe{@QuHtd<3^Bw?Fz_;ueWHzJ16YYSH!gdPG8TTk{(zt83|F~%*t^t392jIeT?UObhVfdJV1cZ|C#K&I*$4+|2Tav&^0zp+cdZf zxSbect-4MUNe<3TCcZC;P7RhqwJ86W{W8B#ibs0`CZt1Sr-HIjOhzG~#^;5aKSC*O z+B&;)$;1sqOYPKUJb!z_Y1Zn=W~?$#*kV_$S{I}~7-YKXXBz+3b+xzFNT#`RN#d)i zXOu=YEgOOIgz$?@0@sddMOlVJ-Q^`NZxw{Xw6z2u);jE;5|y}e(;B6pC2g2vq)MiIWrOInGDdUn8m=cc|=4J#zi2gl!E%&}U3>EWsjMHxFMiwgSC+`3xY zw@d%L_6*j;QN+B&x5M;{%B$jEYRCWeJSjlRIucwqLlv>j!1%uP(UtwNL);Z!F7%cY z{+Z-1u?wL>PO+*%D?9%aNLn3h-70(YjsAhLC;p)T-aPQ#2Z<+8M=Yg&cTW^21FMnd zGsG!8;v&m?LEi6qpn}b6<)QhH@Hrr(D``@tP3%fx2Fgek zeUOe0duldg4%IpTQhvz%+(?bZYS(YY)TzSf_yHA~Ivc$o-3;30ldcB|By(c0EoxYL zWg{ifBP!{@b#q&ErrU;6)khZQI@PmafI8Sl{bJ5iSeTdY9A)ejJSw`umyUWQ$ zvVuDcsiU~2sgb1Zld-g>Q&dAKoMgEt1LyxkW!O_Uhecab%n$`{Exz` zi1GqmKfjwEAEP4L90FCi-7w!~T3_bu9ebLm&WeWVnD_pXrjcf~5$)Fz*V39NrX31- zkcmt|_@DZ5JbWvq9|G{N)i5(@k}Kq8UYtT*y7z1|2>So@)ofb_8>+&f@i$HYGP2`H zrgXp0QQ91;vKHReOuHY7+>A0lx_d<7M7cLHWs~Y9GJn@=mMTY4u)QbNM$M~`ddMe# z_-P6<^1T#1%+Oivd41c#-wpR#*n`o_+@$Qg4)v;7&l%~G`LP`r4RKU5R}7Ac<1?~x zWx5<@Co%UgD+wdknalll-!-i0zm;v7EHqAryT&A+?JBsrurW*}sIYhH!OBR~Lpr*M z3$+Y6kKb9QVf{w5nBdgG8o^n`>e=R$`-40Fr>nSyY{c3?yKc&>;kc&F!-djg(^C>_ zvH!8I2&;eg1TOSLqfrRs@? zx$5?#vT7tKd{ui#-}-CH2*A~e`kBH?AbBM6CU-*o?T=%mt%)0K;rX(S*ei>8&9$IE z$8xNx|3ks^Nyy(1wesWbVMV_M=LHM=u@_u5YbM8#_0$kvs1lU!hF#l1Iv03*cgIba zy;M)U25MLGw;wrTZO$@sm}1tJ-AqaFNrTWL&08}}1U#B}gW7PN2;FyoUDYkF z;2nPDy6|vv48zn4&sRv8DcwsV4gauOy7#W|L>y+aL{=I9;%Q00P0ay}pX^#|#>ujz zh4)M&{yuw;P07;vrVqr$eU|WTliOXgcWUVD{aD4h6S z07Rm$d@sgC(v5do(TN33ym$x>^hY>jG02*u2>TVx!(Kxr{t7Q!qwr})7GwdUnHBZU zTAaGnTopz53Lj@&y!ymTxTA}G<(RKk#;tzEJ~)3*mZeJuy>og8kfClHmfTO39pY|% zPvT#QbkUL3`WKj*6HO29(xK2QV9St}IM!Pbb{F&i8Ho1ozW>eiAt+!Y zAOBo>$6E`{OkN13ByVNB^YGN>Cp`#$9$8Z^oXRd+A>kJOqrAhCS@tlczh{gv=vpYe z@lPTO)7r06f;}yluj8663aNZ0hV}aI?_8lWbr-L;Ghb)kTKioZwzB>a2LflG6J zV&nQlwIriHQwi3O?BcBIS+ePasYR#a3-nn|Ck}er5dmfUX0Jz%W0r>Hx^NsWr4CjM zB^z3DmT_THY@$hI>~(*mYQVNtMi@yuv`}5OeVkd$BJS>k2^mOl8wxv63vm$oZsZMn z1zlU@Hs<>*nfSyAItsVtm&aa+cLv>}X3V$c9#>U58h;&LFgjN|aRNvvM46a+OQP$s z%(T%)V38M*z3Y#fCuDY!M{{qZuhZauUsB(l+B`PT##eh?SW|^t?30)(yBs3f$F!ip zuJLWF@3&}+5wEd1{fKSxbz%acnReUE3A7B|!>MxQdPHgP)1;H2_Q#G z4MMPI!W`oh=EcV}Z48sp#dL@xWJTlUA!2R2e~CB3YScB)Yo4?l4bSIORm8`NGIipJ zbko9TM<%3{k>KP~KHd|y&@FERe%h)}G+E7h1QGIWfMxjZTItVW1Cr6FVV(j4C_{yR zm1mxtMQN%FSBuscX%~C2(DG&__U~Q7ka_Moi(x)HMrRbc5vi@ILhT#E9q7_gHRPq- zDkKazfocoB#J@FBm9a?Kml`!l{L`H)`&lcluC>Q*zskeef1%qeJkBHci{xXD(ZhU^ zq2E7jo^Q&jutK%ByUpMtRfGao-USDDBCE}E;7A*Y<0r7@erH_DOaS8I_&N#gH?&&y zM#Db+Zc4I=C&|SknWa8v^fao|;d&Dbr(c#nA7-X*#WfOQC#@21Hg!;)kXZ<-*Sat; z8lt-0O%>nP1aB}w*jWqz*^y`XN)_G4k)2na&BS;zATHaooHF$Z!pT45c1PGKJRsxU zv9?jtQtT$?1tafLKT$rBO>Q_JyJ^ppNQORi1S~rU{$=StGZLq7N><|W130Nb(x?8%@+a2V zu9F3sXbpx3aNh}j^`|}LBa{NZ2m7ojy9ZAKw4`;dfK!I>WEJ&9bCXyS@^9&v^`Lqm zf(VNiT7rbZ?^moBzifX|tJsDYHfo6W1f@7tn>G9=6P~gEOsKr(U^-%I|FL5^y@7>Y z!;2s25lJ;vL)orBAQPJ^Oryf{O_oNDsJidCH1j*w!D$q0JCMZuAs@|3<(uCMd~!cc z{0A;j(F~R&3wp1-*Z6o{KI^_gMrE@JH=mp$?)0bKhy~Pq055G_)=7TsfOcSuc6Ng^ zkN-t`X)D^^FZHSE>HRA1uz{zmIYmHcE$mYe#473={YPMKbfrmz!|6xy3-V{h5wq*% z*6HGLCWY&VV)2w6?^us4@4~KkWz0b4oHnIr->F~Mh~6Uu%g(c}J}=N;84wK%W+xKdh;=DmUD-GTJX5@sWn>rQM0I1n;1U zgte7Ks@P2=r(Bu5^e}m;8`IEzgEl#2?72~gk-U}Bce#DL zjl{59PR<4lQ*=&pdbF`lbDXN@?BKqL-%m_MB4T4|n-YY$cxW0~N|Y3>0h|35!_^h2 zhy+9uq4b!o+O@qTr;?VEI)nbvFzzAVftdMoVU=vT%xU8!Dh=kIr<(^0(b8UAzb}_; zznx}rpM4>K1mTRte%#aX={;4R%>>JX8rg?MqrB9QJ){Dc;o(dpS{*diO`tl41*jv>LF5H9NxzLMtdHaK2Et*elG#o6qLOrvQr$Cz)0oF-5< z=QK%>jtSH)5876;EM~uEN-nJHp(&gP4iGGF)z;VLK+(mjV0%?dKq4h_JqS6Gvj)^L zzh(D*378U2r{I-RQh0sLZdPAeTBpHTRkq4<{Uqg|&NFjC_bqxCRu!Urewt4_xKQrvoYO})K0r*7}Y zHTiTxa?7+RuE$rmn?|vy-;->;)wn;dfJ~I80m=#%lF{#o*;YH|df?Mt__t~9&{GYQ1)Hkf_!&jjHvt20B+*-bGPA2`qBu&+NtnXTraTj{9k4zJ= z35br@&(n}hbpETkylF=|#Z|XR4r=x@TjnM5QG`N?5tTBDW6Jfex=~ot?Fhd_F~;<@ zI{N7;9~3K2tnFtro2zoIxmtxROyir8J`~Fra*eWOg(4xesDP7JKW468l|FjoR%{ zMCk&oo_1|^6B$-LH%Avbx}Asa=*&D~Trp>NV5K~?O()?;Iy{4kN5V+_Q*5zYyIMoS zRFTHwYzK3~x;TttYV0wG_yhA`i@DaB?j&}zBZ0yoBGawRUXX$ON4-@5r<^~fLJq)@ z&PBgHK%FdqfYlY$nzeUVb+}XX0{6?F(^JMueemi1x$V*(&{wwoXQs%`7n8JM#eA+d zDy^)jCF%ac&0d4Jkgs*Pn>bll$|F(T9ho^uyZxGU$yxT2+`nBVI~@lyv*VU~^R~0t=>N+xrpvSmEU*tuKtI^VYU)NtaI1JdQ*P)6vkv(+ zGbh}8XR{r__s88=0_Q}uNa|vDS5p&;Z?AfOmCq@nytx(9g(V1fHhgLwy}<-mmc{a2 zX`Wbyx_&|zSXIX=({&Uy_nDCHHuiNFNsRubO_e-feqo)UJZk?>=hyTd!(#G{3EP6{ zXQ+LTQ?;PkipA4S=?B9fD_jdJ;_HBB8k+V5OMgpl$X;x>9Ml`=TLdefjJtxJY$=8; z!F%H0K+KeWc-u2#ns(&<%R-zDGnZDEInb9i2&K=qnhm4D!BhB;1z%~hRg>fT3L{tN zV=nK4^5mN=-ku{Fw9HjFX zT4WaB-J==Yr%T}XiR}fxh4Xv$SiMdb6UHGc9}A&jzhnTdB&Vvs4!+QjWx_$r(-Are zmy~TK_;=?VRQp=Sm@?HU@fb05skrKbnb*TCH`zhg$e%V`c@3ZFM`6v={Ro?96Orny zROmbO|JBmSR>3amb$T;yjXGF1y*;t}om%?HPng~9VUTMw$K=&Zi}nk`ZD5eQrN<6+NeSpp2yf z^y>b+6Jb*bI5OzvoLS0FT3@Q#Fk>v#o0W(;oTW0fFFrem8uj>74gwL(P?R*yxZS8) zKN&l*)#nvA6eORDgfJV|vapybN#4&C+1dyZcFT9x(rqW&#*W*UUS_y5h_ zSjYL)*(mj$@KZ_bp&RlH=?xB?K}b(zmZ!3@s^^>A7wdDI74?;;7H-Rk!$p?nY+HI3 zNx#qH$#V*mU2?lbR~NRAg;4YceDC#?6p@yVntC$;MwTO+OUAzvE&covX1rh*sV zj<1i1Nb5~6_px@lxyIa(ko|AZdDo8iI-m_cl0oR13HyK#0N?%XF&tjViEX`?-1ou& z=0gpw3M^|FB1tdu;a-{32T3(JegQe?7EZZw*}@+f5BRiB-Q2C11zjmTu*Jo9WTNi* zitKCZTdNvEr8kDFWRGr`)9_UOm~KMGHRcK07d4Z#>K=&VA=s=%y>jZAk4)j{)jf^O z$}F@@A{a54AealKGM(Zcfspm=Z zRm0g!6TzSt$iaVZI6A@&IIi3= zH$M?h7rQdnbPsyZy>^o+9z7WOwka*`ot{lEsNNqYrtX`oF2$CoWwWb^gr#*hZbhmW zzol_Yl2BDu7_>xZZ1bX8*&rPKy+u9>g!2zzgnBl@tz#%Z@0Y{=gB|%5VtG7n77|NJ zWJqyUsDJJZDej2G#u(6&;~m@RM`R%0CEc1F7-PUOgLmqsg2q8AVzQBKJYup+;qx}4 zbwFLq9Kf@cdb3mFv)9S9J{01-?)5L={>yViIe)xslas#zuPo{s-GVeQ5pge2v#=R_?7<2c35uI z&!48_=x}sQav)GTGBxybE=HeOjy74m3re0O(R@@dXBEB;lXd_E++`}e<#r~&9bq)X zp$wbhrdzBj=Jxn4jOPRKXCfP#bb|^;!=j{!hd(-`4vn{pm=g*osPDuJj0HMWYt6(t zYxi2ai23R6?B3cSsrYxr9RGDe_>S$nXIIYc%j}i0mh6+PpQx~vh4!`Y2NspeL5$@} z!hsLR8|`_9L5DJ}rj7r}*x~{_lF*w4J4)#JnnWx$J8zmQr}CZ;*G_;%t^k4V`Is>fEUGSB?@5%7A^PFGBquLeenl9`5|kT zXkEQTU;iTfY=vqTyp<@Pp&YX|_Jp;@d-*ewP|%M+O4<{~PFB_Ki00OE!bqtqJ0%-8 z=8GhE?I5uRq%p@InGB^T`6z?qajNU3tt%R?5B5r(b}EmSW4;ICnPR21wQgE+Na{eHD0ZxBKS3_os9 z9!!TPX#yE>4^Y(8^`_3sSw*|Lqabt^wb`IUmfM!pRfd*I@y7KN<^&0{rTOYosr zfh8}rRiGSg8mNv>d18eXu`4a3XX_}qDnY`8eI$aB_D*0GtL$9N(;fDg)%FAdOl)at zSs73{2Zb(V7^Sv@KIGUITz%)G1Gu8l9Mdgpt5M$n>CK*CaITN)-^6OstCnTm00{cM z9fV;q!WE9kC7W3RL`vy(YHiFw|C-tx-L{(Wu$(XIsfAaCf*Ii@s%d98TDn5fhm2$29PWMz&3N z_#6F0@n!L=zm4hKz?)3gP0{{yCYxty4Ed4iw8;32@Nc2vN@=7e>t02&5NhFPfWP>17viWpe_s3pa2aJEfU=|l^66S%Q z&kM~p{G~`%jUKKqWEg||m-KzAH{feGhQBLdy=mhV=B z#c~xq+FMmjk4mhFv=!N#kIrl1+#v`h z&vf$tg8V`4=0!R~=MMwxbaD^ej>>2)vRRZdarI%Q9j=u*hg=+#Ft9&lPIIbQr1ZYw z{z9SPL1OfBd*w6-zpQ}>Iwst&zJ1RrLp+KK=gCgvV3CkvyuT$bzpLxh-b1F!+x>pM zq1bexR#wg({Gn874huO=I}%*xXvjs9qk>cUUnA77OLwOc5mSLP#>im%)+1- zARE`xgaV1lYNm|MDYzaA%{{*-aS82`$Kl^F4*fR2BLQLu@`H^GTK``D9j@A`)^n0E zK0tXxy=v-7g;l6qae6Hc@AOfIBt45W0=Rc_G+&+;^SWAL4b4_YK}Ctb-GN{f93K=5Vt>$=Y4(Sg62!BI){}xNj#MGUxd;MxWKzxsqHL( z({9rFB1B>WjsEgf8`1~M8RKRmh{pCLRV*2CHZ&0=2BST@cSX{5VPUVxcNL(&h!mOi zdh7@}cigi)-Oew~FYU2ED*VmwGm`PBsyO9QF_=Eh$Dhq}=PUNpmcVMa+vDAc6!!pn z0RJX;?_Dsyl(c^>#t~98NI5TlzH(1MY8r(-&d;?g6rv#KnO)I10rjw3puHiGqLjV) zD2|_MLChgI$U=y=_Hg+@1sY~Kf(&TUKr(!vt?xsnLv$h0+sxL`uai7a`_;zGFGrI+ z-^~9^|E^dnorm&p*=ihbu&aB21G9Lzs7`)4wsIyi;>f$Nt;7wSN) zZ*ff5wxdeX$#7cnteV9cTGq)KE{V#9oB#Ct*~0chu4g!OR>HUn{S6poK0gvMfI#BJ zzjp*+1cmbtJPQUB3^ITLq@P)CrOc`X)YvJtv820NwHHs|X+DVE86~KQZR|jPdkwz4j^1da8cKdcaP@GL`Em+8*Gl6J}1|nERUW zvMqdeTxak3t!$8MFWRbn@Z)>w^H%5d^t?jV7tQq3eACx=0dIQ8_%$Q8uT%Ahj?X3M zB?H44*`ZDR&S*uc6ggb*1wjl<7M5kHcPu@o&D>mLk8R&OaAI=5*fM0Z-4<*g$U@nq z&DDDYJ5@<-E@YL>GE-6D#p(Jn?O%|Gzg0HDYB7 zpT#I&7veb0Z;52Xnh&+~43v*$42}U==g?e^rI72W6 z#`F3A5)9WkdfoH&ayBy4!>tO%&S8mu{ryplXGUz{m@+ZH3YPw&A8414QJX-2Pws1j z$l_7>Bey>+7CcV5`pK^$j2RK^N``WT%a-t-4_Qf^Dspt^*?Bpoe^NEnGLF8%1qwA7 z{yOW6cbW_K!$M!@+t-ycR#@E0Oi&KJA)|y-AKMWKHJv!{loP@{FzFyBQ#nzUnIWr%3~7|HY<NMu5{o!*3oMQO-fRB<@_os0$>YYO{$L&q$r!`>WzT_s~qIlC9k$Naj68n3>v zcT%l$-9OsP+d)5zvvSYC3%8~0gtmwOjL|U-V=f-(SHqKIuWxVD_NB`3 zOqH#Cxi!L;e9FFURIMq6DR*<$UJkSNu*mNvD3ZsW9E`fc0$$5f(L2tN{L1LoNegZ4 z7bx#G#3bUSEN^5Es3gkae)ID{=gKm3HB{Kge@{h!xTQ}&Qp|q%-aLzhOR&bl8HU7W zA$7$jMKP7HP;{ioM}v`bGz`iB&obx2Nf?gd6385mdSWB}-qp`vwTTyhGxE;Tj#DGZ zpj9GXa@{B@nd71LP*GUJXnkry>K@KTM1`=xwU^*vfdPGV-ShKqz z{J5;U_-^Hv?-#v;+@9;W)|^c6Q|EIFT&?AbqEADtV@cGCT0iuZ5P!QQ{INyk@`5zN4h>;fI4C*vM0Hb z59WR_rYoLHQa3%N+P7>{PX+!}s)^hE@v-RzeK6gxKF*?(i?A4m zQlb187Hxp0i>2E0p8q#XpAAl`zopmeQ%6>*8rbxJN9U3#>I8Ot!K2{AUfBE^q+ zX@EDCTuTXQ$Um`akl7g`4H1CM>bp#G79gF#Kg#-!jY(u_ zNIi&n#AmN(z=G_Lb?`cCvFF`aUNA%3{EPX*qDehjgrNcnJB3=nhD@4ag-OUA#jS}c z*fu8G3}FJNcpCRHOXJFN$e>gL>S39pvXb{FE%{6H1Cs!A8Wk;@)=1#OFW2_>6o+nx zi|G!S4nyx6P0#GXw443j0uh%zAiHl+U)YoVpNgvKUl*8v=*n?&Q*KXAps>$!!cn+r z*p7q#(CJY%bDV3_nJ7Zp|6x~{L?EFaqS=ji-$CG>qAaivD{5vdJFrblzMN4*dHHu< z^6Wg*sxd&J9b zWD?RRxwIxP$X>>lOHRxQrbMF$VG$!MM7THkbIA0`(R-V+cars-$*-MBvDTNx?jbc0 zgo`!*%wU`EB_)p>^^eX(@awm--!TG;YVn5$X@-mfEQ}`t{IJ}HH~XL9r5G*XCL^z{ zLiEFjm7M?Qvc?*k0ktnfmk!N+oNy|!*yne`TMNo4edNo$8 zWm~8$Nl=5fJ$jgB^!_vrPZsu|8dZ)-GZfdzBrd9jp07N7 z7Y0vi1(zx}TuV>>bNv|CZ?@tNn6%N^l27w<`)|DCQ=PGNHXPhXD(al*3*zY5tPRY> z?Z1txW2g@4Py9kEhc`W?k=(_TyH2(ZWadA}{M>`{f^M1q>d5e&r!#e-UlHf?i^#oY z-0Y8jQ(A+CkMBlKb4%L)$~!lt?Gd%t^q}-tW{d!jHn$Om*nTdn2iEYRls+ZKyL!59 z^^=CI#42sPv!Hpa9H)DYon~Y||1Uvy2B!ivcu|%6D8JW7(sT^8tP3V00ba(#>C)W< zzN|p&M1P$$@=;?Nq>LOcqO1DuRo6c{7Ji=Jaw!BBbTXegEdR{a`m{6$nm128_*in2mqQNEmLL~!J?V+#kNlsM zZrFdFH>z0hkeD*{_(^V0O-n#YqonudR|=SNhd<8gpmP%hj3FpsvB)|QVk}O#pSo`g zyvIF0Ga-ML8)wY^%_!N2pkJ6z1jemrzTrfZAuYf==1TD@-yMGd^tsL*b%};=>@%(t z!ONBahf=PrGMT`PXSE@yx4@-l4dDKxuda%uw2f4Y3yLV(19-2{gkZ5yFw+OW3SSux^yR} z%#qbM^jA*R9!KdjKA53-jZT34TOptaz~dzdbmQ|5>kp>5Rt;izS}jK&a@o7z4wW+! zn;fT=qntkeot`mKO>J5JRlBZO@GkXJ$~?XnLFihRWkA7!fOAxBXyk^FR)N+@?0`IqmN5~m!XNwbC zNc&Y?Q(~IVpJJDWtS;(UrlC1t{so;;Mm_*X;^*|$k!(iGyBQT6AFcGYi4*3~mUamy zv5uy%tSAyT0I!@k@PA@u!zxJuR~EcvV^7x(HOENpiDS6nP@=!*8S-$&do7%`{0iA^ zi41_^x|)BD-Adk#k$&yF2o6B%IX?wdKF6$nS}5JG>jz~wxd?4nYy2Zi`u)HIn~MeJ zePeQ60RZRM?Gj7*$u@Ew?$5LQu+daCdU6O85Qe%vsK=rxmFK%zd;BTGh8|lwM+L7s zy}L%t>ahW(>h~rD$_QiGx@n((_9-?dt?9Kf2XQd>FtgdSP(hy}u?hr3Qc(2;aj-B4 zo{RsR-o4_1%e6dRrL|*EqQCtw>!&9+EuYc6{C~bF-z+7%B*-RpVSl-z<)#H#%i@R$ z{H(w(_FtahDkt2N)+|WU+6=2IFD4%6(ByMbB1w?-ariLr_SoIABOH_ zU6W}k{{R18<}3z%^x#ufo?ml%AD=O^vAVacHYD*{pDp!;z=kC4_QSl>{KnfQjQ?-@ zLoX?s-`IzGy08U3JuP2)TFirTer(aW%_oF5^JAajsu+Q_<=#t2am8I2N}Li+K-30imX%H2PSNqlj%!CZ%qiVNU* zzP&;ncHbAFVc;BOO!L_~*N=fU=N9#$<=|l^7P1`H&5=FYOOT$PK3bPspp>{lD zZl^MB`Uf0|6c=GRMYZe+A@ZUs!sQr(0M0bQ{j98*vL;SnmhDjhTUgd8?k(l&Bs>Ux zv}3MC{R+YVw^6$3h-xfu8 zpBXx!iV$yHBB8!zZ~DDdjv=y(58+lR$(@QME<5vBlsd*mfa3(+$bPDs_bAfFvka?VYnPu3qxge2{L<<7i=&j_LG66m4B3-O&OeSO&3B6 z=Yy`eG8}Zp@25WyQx0Wb-l=(8HD|axP}-9kY4aC+BsgWIh#FqxNvTQb$suzpDHiCn z%n@bAxs$xSv1*|SsS7)Uz5;zImkrItop*Vy)z%U5rl^1phhczW*EjrQYt&rUBigOG;-W{) znriY$AuZId*SW_qz5Zymq;8~cl=7B5jW-A_pO9Ga?MeFt_=YEg0&5cP`LhFlAl78t zD<0)idz5zF{ibejQZae^lRMDGsKp4`0OG_(Lq7k%#pw0?zSQ`&BVjA)|L&2)C}_)) z8bn>6kwGoQKYYuL?DTIE*uc9U#eu!^Di>W@N{TZ}4Z0!>)$G~R*BXeN)WZ;tSl9z8 zj~o5wO)3drvl%h1_eLTVs((<{fjIV>DtgwWZb*u#c9Y&-9pg8ES|E$NB@|-Y^2zf* z6{u1g_3zAn|z`g^8nECl&TI0X;}s$jY802#jIo=6=2EDcgCY7V+Ocv@aPBvfxY zh0Z!#;(1#aAZw^|6|lz>{c4f5@IIQHp$_X#WwH5Ela0D4 z(i9X`>G;DsXLOI6%lc)*8!xM64MpzbTe+^I1c+J_Cv()%7!Y<)?iJZ>Mlk=w9+OVv zCVF#(4FM%8vSI!qd<{;1)Z?wv5&YQW7n9}rSgL9Vg)A=dp;?17Y3Ss7{3sFn2&A5A zawUlgRFPxaloA`(omaJyaVel>6jtmJ6GW_OF*gmpPvfT*z@-k!v#s=q<_|v!+4)Qxj|y3VKDO}^D%)R0 z*jaYl{P;^vCYy6Z{E8+y`(7Aiu#p3rMaRiVxa9cFvrHq9Ey&T^jjS z8Ktk(P!A?>!1sZ}r=)ELHjUeTeo@>D33Kzu|K~m?)G#db+jf`Kv>1j~!QwTzqtH6^ zqBX;m5OV+G1a}d7tujYwLR?IsxxY(kX@dcs1)>bM-(K^(`rRPrV#x$)qkPl zwH-SFjB>><{AcY6q1Pw;5Fsf?ufYdG1 zrjxRRFSO=r7(%@8F9 zP^YA$F&dX8q1y9DQ1Qnc_-YTpkFpG2UY@tWozi24lPP*bi<nrV-&bhR3IOB`0o&Z^C?vp)^KKT9?TUm)DPD! zoL~Y(ygtOJUb6XtErF=MxKcni4v7!L5xPGpmbd9bZJd|P@8q)r@}xg4awto@(3WnS zd3UI)2t;J6n`-x&SMWj;mH%&@t5%({MztPS*9ZST(1zf%($v3rePq<70D6gi#XsPb z8aFd`T$R`jPPSk{?Yma@n9DM4wDueCDegAkFT7z?5|oV6XpwTp5Q6rGv91W}{?@Fg z4Lo)MhFBaVUFT*u&3>|Mgc!6H*c(gi7uS)2f0dwrWPbd)XX?*Twzi{zl%{kwcx3Yy zDvI9XrYedjpA-jO{m1{CN&)rY34Cdg-bq348JciyeSyYK{1q(E_=n&*8Outou?CD( z|HjIvbl-j7OM>JIua>ktnqe1{`&N*m#~@RB&kIOxc)IF#Y_IYpZ4B@1<5Sm%C9mb7 zI0~wmQPcX?l==Lu!8)^(kxQ1L*fW?B$3WfwJK7~UCoNBn7oY*bKlg8wro!=fv`ZO+ zg9-v`TBtre?xL4Zqqs|@{t2G%lLSz9yGGi+SEUN zvSB^2*FiKiWiR)#@nkeq7I&`MWUe|gsMmc$Gf0CTII+qbe+rGWUOqrcNX4>Q-zT0f7$pgO~_cw)v z5){Hw;au-&2D8~d9bDWs2H}qhmjFK7HJ44*sKDU|$^P-OG%I1aRULPDDAosZdB0)K zu@XDJXW>of#@)JzClNuT#CX!;%*z@Et{}7XC#V-DePn&|-cx^%5pn#vY|>0%@*{ku z{qD4B{5bWc{Sb?zF%gkt&mB?(v)M9Mv`P9hUC1)h{-;OQ0Z%`he3V(@!AV|*nlrb2 zzE2LJ{o5S#y!`s%{o{#bQ>W~l7#H1z2gC(3mp9&%vKbj>irCcLxaUgV|KeD{4W6*4 z?h@Y*SwM#VT{)&Pa;aPjL_ZDkFpxrfg>F)UdWX3(iw|UP2aOH?jZ7r2)HW`y)9Vy* z3234*_k_~+c~quqn%^;b^lA5cyd2-fQuOo4Xkod#@0i1P_po2CVSimneAvH@v5q=D zI~Fzh4R^HpId2wiTZC7Ekr{28UDfxW<|80E`7oB-0M?tjju$8Co4GfTMPi<( zvf-0yqPH=wU1Fw!X;CCCXN}PSCxDOTtS^;{nFZI#E}WaVpq>vLDClsMK;xUZ%V%l* z{syUtl@yNsRCdzklg8Tm(KIp3NK4 zXR!b!8=jl)SY@NiOSO_n4TsiNByprfFK}~$EX)e}yFDA{4}aQag(ZUew++o|_|cuo zdkhPyS*ebw#H8h zzsxVk13n@=ILY{kAHm-lX_Qn>XBIF;AhN+=Ft`f_8!%Xm!CGn#YgY`;>mZrXLDFr_ z(jFI&M$NMGnk7lb;Uit9v4K?9a@zZdGHRC5XM^gZgCuedBpwY99{@T?Kx5FjOB(BO zX}oO*$+k4+b&z<5^oG6NiM4|IA|l{wZX3uSh5S4u(x4vgTY|%Hug3c40}5z zvlqzh(`ge#1#>gRt42JPRTWHYOSB2bjS^Nw2aVbg*&r|o3<5V!U^Hs;J4ohsI!MeZ zEL6y>St`bipY*-vD%0I2|BDVAZscHIx`QOP;D8geVT_{+aUSkrSeSgDNXkOV_)u~x zoSdvuFk@>&nGFyF#JgcujY<5IK|yTB1u@UiHVnZHL;HxE#faD`SQy-yonjiXQ%IKc zW_IUA{6Z46Q?%InJz5%>76wNf2nK?WJGvSO-VDKNPz3Wt_6(5?!h`U=ifqxwz!=UW z;T(u;h-@Gj2!_Z8f+4cgB0E&rOT&{#+Amk;oo$y_uGGm}ZK`~S_+)i*Lb*q028+RBuz0hhdx9)hL$H`9yC=wQpdP5-0`(Hvvj$~1)2NX|eQ@rp%5JM> z#;>v-8IavzF<9IQixpV>RTiruSj>^#Hk|(V#ijpz8_;H|+w@2J@Jo`)ipfvu@8c#i zYiikgrGh?hq%-t5)RTB4H&qG2i=JJZEJD*_7z=;H<2D?t{`dDCvL zGSPQxMsx$kKyj}qRzNXOTm{7(&F!JNg>M#@oVl(UHwFj%;Cw@zPq)2N5v)rd-6`#y zgm|Wj(LOt~o(}n(7prMT-VIHhI8%|88Bp8+F+jZ1<_3rX;wm6!=xvG&1SAc;T^aL~ z74L~HF>9}y3B6tQLQq-EM`pZw$_UB}V}5z={L;~!58qBiJW+T%+7h281UEN^vhx+zpg613DT;zL>d<0ifS?+f`B-^o&xb*9`X0Sq+4%oE0Mm`WV&2HytiV zf#e2?f#Th%c9j6dK(UPG*5O2MB4}<&ZzTeHpHa=!nJFF*&~IaNQ-5byXPAE4A0JYa zJ-XUSL7wyOGI~C>=;?*l27-ZL+s`QSkrAv;9KjroZ7ei)X~63oz_Wt!C}6e&c-_d^ zrNV$W5`>Qk8paCUX9;g+sSzcS_h-yfB3qR{9tJua7zT!c;qEbPP9DR#JtPKNTe9Jb z6^BoEAjArnNayrqrs)14&na9+8UZ5_o>`TxTv{t7w`0Zs@KC2uwHNp>HRLu(3=*#- zF@eM&aSamZy4z6PqMYZ%;cZT_5}0op^Btyh7?=+a*vVnutMjakd=b#2Ya1vAiltGk zfMTGy2#Wu!xzC<1)Bg8&@4qm4um71)^7N7J>CylHoL1eN$4j_8UBkWoG_d>gU%JP? ze0neY`QeB8?CB=j|8f8B{^R3C+`oBob94Ci`ts`b@ap3An~S%H*Dr2wFJE39yrIL( z>(}3ZcXf04=KA*4;ri|6#ntVL+so^#oBgMk`SZhXzy5T%`{n)p{oRj;$2;=y;qK?V aA0B>sc729@G=`w{@8rYQda literal 0 HcmV?d00001 diff --git a/research/joint-helper-lattice/PATCH.json b/research/joint-helper-lattice/PATCH.json new file mode 100644 index 0000000000..51304a6601 --- /dev/null +++ b/research/joint-helper-lattice/PATCH.json @@ -0,0 +1,8991 @@ +{ + "changes": [ + { + "new": [ + 51 + ], + "old": [], + "ordinal": 449, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 451, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 453, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 455, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 482, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 483, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 502, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 503, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 504, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 525, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 526, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 527, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 548, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 549, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 550, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 551, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 578, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 580, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 594, + "phase": "entrance" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 595, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 598, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 599, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 600, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 601, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 606, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 607, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 608, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 609, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 614, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 615, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 616, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 617, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 622, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 623, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 624, + "phase": "entrance" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 625, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 626, + "phase": "entrance" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 627, + "phase": "entrance" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 627, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 628, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 629, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 630, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 631, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 632, + "phase": "A" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 633, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 1997, + "phase": "A" + }, + { + "new": [ + 11, + 21, + 38, + 448 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2002, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2151, + "phase": "A" + }, + { + "new": [ + 45, + 85, + 133, + 261 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2156, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2305, + "phase": "A" + }, + { + "new": [ + 14, + 35, + 69, + 400 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 2310, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4007, + "phase": "A" + }, + { + "new": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4008, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4013, + "phase": "A" + }, + { + "new": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 4014, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 9, + 17, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 4019, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 4025, + "phase": "A" + }, + { + "new": [ + 2, + 4, + 8, + 16, + 33, + 65, + 128, + 256 + ], + "old": [ + 4, + 10, + 16, + 35, + 65, + 128, + 256 + ], + "ordinal": 4043, + "phase": "A" + }, + { + "new": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "old": [ + 1, + 14, + 16, + 34, + 68, + 128, + 256 + ], + "ordinal": 4049, + "phase": "A" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 5, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 6, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 7, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 8, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 9, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 10, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 17, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 18, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 21, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 22, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 25, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 26, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 29, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 30, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 33, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 34, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 37, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 38, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 41, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 42, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 44, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 45, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 47, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 49, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 50, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 97, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 98, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 99, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 100, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 101, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 102, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 103, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 104, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 105, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 106, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 107, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 108, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 109, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 110, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 111, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 112, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 113, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 114, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 135, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 136, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 137, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 138, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 139, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 140, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 141, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 142, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 143, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 144, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 145, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 146, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 147, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 148, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 149, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 150, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 151, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 152, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 153, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 154, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 171, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 172, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 173, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 174, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 175, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 176, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 177, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 178, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 179, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 180, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 181, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 182, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 183, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 184, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 185, + "phase": "B" + }, + { + "new": [ + 30 + ], + "old": [], + "ordinal": 186, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 199, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 200, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 201, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 202, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 203, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 204, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 205, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 206, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 207, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 208, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 209, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 210, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 211, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 212, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 213, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 214, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 234, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 235, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 236, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [], + "ordinal": 237, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 238, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 239, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 240, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 241, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 242, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 243, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 244, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 245, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 246, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 247, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 248, + "phase": "B" + }, + { + "new": [ + 7, + 51, + 82, + 136, + 264 + ], + "old": [ + 51, + 85, + 136, + 264 + ], + "ordinal": 249, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 80, + 144, + 256 + ], + "old": [ + 45, + 80, + 144, + 256 + ], + "ordinal": 332, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 208, + 336 + ], + "old": [ + 5, + 11, + 35, + 208, + 336 + ], + "ordinal": 335, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 400 + ], + "old": [ + 5, + 11, + 35, + 80, + 400 + ], + "ordinal": 336, + "phase": "B" + }, + { + "new": [ + 7, + 16, + 42, + 64, + 128, + 256 + ], + "old": [ + 16, + 45, + 64, + 128, + 256 + ], + "ordinal": 337, + "phase": "B" + }, + { + "new": [ + 7, + 9, + 16, + 35, + 64, + 128, + 256 + ], + "old": [ + 14, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 338, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 16, + 33, + 192, + 320 + ], + "old": [ + 5, + 11, + 16, + 35, + 192, + 320 + ], + "ordinal": 339, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 128, + 272 + ], + "old": [ + 5, + 11, + 35, + 80, + 128, + 272 + ], + "ordinal": 340, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 9, + 33, + 80, + 144, + 256 + ], + "old": [ + 5, + 11, + 35, + 80, + 144, + 256 + ], + "ordinal": 341, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 137, + 286 + ], + "old": [ + 25, + 45, + 73, + 137, + 263 + ], + "ordinal": 353, + "phase": "B" + }, + { + "new": [ + 45, + 87, + 137, + 265 + ], + "old": [ + 25, + 45, + 78, + 137, + 265 + ], + "ordinal": 355, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 146, + 261 + ], + "old": [ + 2, + 45, + 80, + 144, + 261 + ], + "ordinal": 374, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 194, + 265 + ], + "old": [ + 5, + 40, + 82, + 144, + 265 + ], + "ordinal": 376, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 388, + "phase": "B" + }, + { + "new": [ + 45, + 400 + ], + "old": [ + 45, + 76, + 400 + ], + "ordinal": 389, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 400 + ], + "old": [ + 9, + 36, + 69, + 400 + ], + "ordinal": 394, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 146, + 272 + ], + "old": [ + 9, + 36, + 69, + 146, + 272 + ], + "ordinal": 397, + "phase": "B" + }, + { + "new": [ + 45, + 69, + 130, + 274 + ], + "old": [ + 9, + 36, + 69, + 130, + 274 + ], + "ordinal": 398, + "phase": "B" + }, + { + "new": [ + 45, + 73, + 144, + 274 + ], + "old": [ + 5, + 40, + 73, + 144, + 274 + ], + "ordinal": 399, + "phase": "B" + }, + { + "new": [], + "old": [ + 45, + 76 + ], + "ordinal": 410, + "phase": "B" + }, + { + "new": [ + 45, + 475 + ], + "old": [ + 45, + 76, + 407 + ], + "ordinal": 411, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 469 + ], + "old": [ + 14, + 35, + 66, + 407 + ], + "ordinal": 416, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 130, + 341 + ], + "old": [ + 14, + 35, + 66, + 130, + 279 + ], + "ordinal": 419, + "phase": "B" + }, + { + "new": [ + 14, + 35, + 215, + 258 + ], + "old": [ + 14, + 35, + 66, + 149, + 258 + ], + "ordinal": 420, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 199, + 268 + ], + "old": [ + 28, + 45, + 76, + 139, + 268 + ], + "ordinal": 421, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 217, + 256 + ], + "old": [ + 5, + 40, + 219, + 256 + ], + "ordinal": 440, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 393 + ], + "old": [ + 21, + 45, + 69, + 398 + ], + "ordinal": 441, + "phase": "B" + }, + { + "new": [ + 7, + 42, + 66, + 130, + 258 + ], + "old": [ + 45, + 69, + 133, + 261 + ], + "ordinal": 442, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 42, + 66, + 130, + 258 + ], + "old": [ + 21, + 45, + 69, + 133, + 261 + ], + "ordinal": 443, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 393 + ], + "old": [ + 5, + 16, + 40, + 64, + 395 + ], + "ordinal": 444, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 40, + 89, + 128, + 256 + ], + "old": [ + 5, + 40, + 91, + 128, + 256 + ], + "ordinal": 445, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 25, + 40, + 64, + 128, + 256 + ], + "old": [ + 5, + 27, + 40, + 64, + 128, + 256 + ], + "ordinal": 446, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 33, + 66, + 130, + 258 + ], + "old": [ + 11, + 21, + 38, + 69, + 133, + 261 + ], + "ordinal": 447, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 128, + 265 + ], + "old": [ + 5, + 16, + 40, + 64, + 128, + 267 + ], + "ordinal": 448, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 16, + 40, + 64, + 137, + 256 + ], + "old": [ + 5, + 16, + 40, + 64, + 139, + 256 + ], + "ordinal": 449, + "phase": "B" + }, + { + "new": [ + 28, + 45, + 194, + 258 + ], + "old": [ + 5, + 25, + 40, + 194, + 258 + ], + "ordinal": 461, + "phase": "B" + }, + { + "new": [ + 21, + 45, + 66, + 386 + ], + "old": [ + 12, + 21, + 33, + 66, + 386 + ], + "ordinal": 462, + "phase": "B" + }, + { + "new": [ + 5, + 40, + 137, + 336 + ], + "old": [ + 5, + 40, + 82, + 137, + 258 + ], + "ordinal": 483, + "phase": "B" + }, + { + "new": [ + 45, + 80, + 137, + 274 + ], + "old": [ + 2, + 45, + 80, + 137, + 272 + ], + "ordinal": 485, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 387 + ], + "old": [ + 4, + 17, + 34, + 64, + 395 + ], + "ordinal": 530, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 388 + ], + "old": [ + 11, + 17, + 34, + 68, + 388 + ], + "ordinal": 532, + "phase": "B" + }, + { + "new": [ + 12, + 21, + 38, + 71, + 132, + 260 + ], + "old": [ + 21, + 38, + 75, + 132, + 260 + ], + "ordinal": 556, + "phase": "B" + }, + { + "new": [ + 11, + 18, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 51, + 64, + 132, + 260 + ], + "ordinal": 558, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 385 + ], + "old": [ + 10, + 20, + 38, + 65, + 385 + ], + "ordinal": 583, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 390 + ], + "old": [ + 1, + 10, + 20, + 64, + 422 + ], + "ordinal": 585, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 38, + 64, + 129, + 257 + ], + "old": [ + 30, + 38, + 64, + 129, + 257 + ], + "ordinal": 608, + "phase": "B" + }, + { + "new": [ + 11, + 21, + 33, + 71, + 129, + 257 + ], + "old": [ + 11, + 21, + 102, + 129, + 257 + ], + "ordinal": 610, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 394 + ], + "old": [ + 6, + 24, + 32, + 64, + 395 + ], + "ordinal": 632, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 416 + ], + "old": [ + 6, + 11, + 19, + 96, + 416 + ], + "ordinal": 634, + "phase": "B" + }, + { + "new": [ + 7, + 25, + 33, + 75, + 129, + 257 + ], + "old": [ + 30, + 38, + 75, + 134, + 262 + ], + "ordinal": 658, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 64, + 160, + 288 + ], + "old": [ + 11, + 21, + 64, + 160, + 288 + ], + "ordinal": 660, + "phase": "B" + }, + { + "new": [ + 51 + ], + "old": [ + 3, + 48, + 72, + 413 + ], + "ordinal": 685, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 392 + ], + "old": [ + 3, + 21, + 37, + 72, + 392 + ], + "ordinal": 687, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 401 + ], + "old": [ + 3, + 8, + 48, + 64, + 405 + ], + "ordinal": 689, + "phase": "B" + }, + { + "new": [ + 7, + 18, + 33, + 64, + 136, + 264 + ], + "old": [ + 21, + 38, + 64, + 136, + 264 + ], + "ordinal": 711, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 51, + 82, + 131, + 259 + ], + "old": [ + 11, + 51, + 85, + 131, + 259 + ], + "ordinal": 713, + "phase": "B" + }, + { + "new": [ + 4, + 51, + 82, + 136, + 264 + ], + "old": [ + 4, + 51, + 136, + 264 + ], + "ordinal": 759, + "phase": "B" + }, + { + "new": [ + 30, + 32, + 76, + 129, + 257 + ], + "old": [ + 30, + 32, + 129, + 257 + ], + "ordinal": 769, + "phase": "B" + }, + { + "new": [ + 13, + 19, + 33, + 455 + ], + "old": [ + 13, + 19, + 33, + 65, + 390 + ], + "ordinal": 770, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 70, + 129, + 257 + ], + "old": [ + 30, + 32, + 70, + 129, + 257 + ], + "ordinal": 779, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 129, + 262 + ], + "old": [ + 10, + 20, + 65, + 161, + 262 + ], + "ordinal": 784, + "phase": "B" + }, + { + "new": [ + 15, + 17, + 37, + 67, + 129, + 257 + ], + "old": [ + 30, + 37, + 67, + 129, + 257 + ], + "ordinal": 840, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 34, + 68, + 129, + 257 + ], + "old": [ + 8, + 22, + 102, + 129, + 257 + ], + "ordinal": 841, + "phase": "B" + }, + { + "new": [ + 2, + 28, + 40, + 76, + 129, + 257 + ], + "old": [ + 2, + 28, + 100, + 129, + 257 + ], + "ordinal": 842, + "phase": "B" + }, + { + "new": [ + 5, + 27, + 42, + 73, + 129, + 257 + ], + "old": [ + 30, + 47, + 73, + 129, + 257 + ], + "ordinal": 843, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 848, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 849, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 850, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 851, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 872, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 873, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 874, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 875, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 880, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 881, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 882, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 883, + "phase": "B" + }, + { + "new": [], + "old": [ + 2, + 5, + 40, + 80, + 409 + ], + "ordinal": 928, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 949, + "phase": "B" + }, + { + "new": [], + "old": [ + 7, + 42, + 75, + 144 + ], + "ordinal": 951, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 131, + 260 + ], + "old": [ + 10, + 20, + 65, + 131, + 292 + ], + "ordinal": 1052, + "phase": "B" + }, + { + "new": [ + 10, + 20, + 32, + 65, + 132, + 259 + ], + "old": [ + 10, + 20, + 65, + 164, + 259 + ], + "ordinal": 1053, + "phase": "B" + }, + { + "new": [ + 5, + 10, + 17, + 32, + 65, + 386 + ], + "old": [ + 10, + 20, + 37, + 65, + 386 + ], + "ordinal": 1054, + "phase": "B" + }, + { + "new": [ + 2, + 8, + 20, + 32, + 65, + 389 + ], + "old": [ + 2, + 8, + 20, + 65, + 421 + ], + "ordinal": 1055, + "phase": "B" + }, + { + "new": [ + 7, + 24, + 43, + 74, + 136, + 264 + ], + "old": [ + 31, + 44, + 74, + 136, + 264 + ], + "ordinal": 1101, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 50, + 82, + 136, + 264 + ], + "old": [ + 1, + 50, + 84, + 136, + 264 + ], + "ordinal": 1102, + "phase": "B" + }, + { + "new": [ + 2, + 5, + 49, + 80, + 136, + 264 + ], + "old": [ + 2, + 49, + 85, + 136, + 264 + ], + "ordinal": 1103, + "phase": "B" + }, + { + "new": [ + 7, + 27, + 40, + 73, + 136, + 264 + ], + "old": [ + 28, + 47, + 73, + 136, + 264 + ], + "ordinal": 1104, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 137, + 272 + ], + "old": [ + 3, + 48, + 72, + 137, + 276 + ], + "ordinal": 1121, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 48, + 72, + 144, + 265 + ], + "old": [ + 3, + 48, + 72, + 148, + 265 + ], + "ordinal": 1122, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 24, + 40, + 72, + 385 + ], + "old": [ + 3, + 28, + 44, + 72, + 385 + ], + "ordinal": 1123, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 48, + 72, + 408 + ], + "old": [ + 1, + 2, + 48, + 72, + 412 + ], + "ordinal": 1124, + "phase": "B" + }, + { + "new": [ + 3, + 12, + 21, + 37, + 68, + 132, + 260 + ], + "old": [ + 15, + 21, + 38, + 68, + 132, + 260 + ], + "ordinal": 1185, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 67, + 128, + 256 + ], + "old": [ + 4, + 17, + 34, + 75, + 128, + 256 + ], + "ordinal": 1186, + "phase": "B" + }, + { + "new": [ + 4, + 11, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 51, + 64, + 128, + 256 + ], + "ordinal": 1187, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 64, + 132, + 260 + ], + "old": [ + 11, + 17, + 34, + 64, + 132, + 260 + ], + "ordinal": 1188, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 17, + 34, + 64, + 128, + 259 + ], + "old": [ + 4, + 17, + 34, + 64, + 128, + 267 + ], + "ordinal": 1194, + "phase": "B" + }, + { + "new": [ + 3, + 8, + 17, + 33, + 68, + 132, + 256 + ], + "old": [ + 11, + 17, + 34, + 68, + 132, + 256 + ], + "ordinal": 1196, + "phase": "B" + }, + { + "new": [ + 1, + 12, + 18, + 38, + 64, + 128, + 256 + ], + "old": [ + 1, + 30, + 38, + 64, + 128, + 256 + ], + "ordinal": 1201, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 64, + 129, + 257 + ], + "old": [ + 10, + 20, + 38, + 64, + 129, + 257 + ], + "ordinal": 1202, + "phase": "B" + }, + { + "new": [ + 6, + 11, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 11, + 21, + 39, + 65, + 129, + 257 + ], + "ordinal": 1203, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 102, + 128, + 256 + ], + "ordinal": 1204, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 70, + 128, + 256 + ], + "old": [ + 1, + 30, + 32, + 70, + 128, + 256 + ], + "ordinal": 1205, + "phase": "B" + }, + { + "new": [ + 6, + 10, + 18, + 32, + 65, + 129, + 256 + ], + "old": [ + 10, + 20, + 38, + 65, + 129, + 256 + ], + "ordinal": 1210, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 1, + 10, + 20, + 64, + 128, + 294 + ], + "ordinal": 1212, + "phase": "B" + }, + { + "new": [ + 1, + 10, + 20, + 32, + 64, + 128, + 262 + ], + "old": [ + 10, + 20, + 33, + 65, + 128, + 262 + ], + "ordinal": 1213, + "phase": "B" + }, + { + "new": [ + 7, + 10, + 19, + 33, + 65, + 129, + 257 + ], + "old": [ + 13, + 19, + 38, + 70, + 134, + 262 + ], + "ordinal": 1217, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 74, + 128, + 256 + ], + "old": [ + 6, + 24, + 32, + 75, + 128, + 256 + ], + "ordinal": 1218, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 11, + 21, + 32, + 64, + 128, + 256 + ], + "ordinal": 1219, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 6, + 11, + 19, + 64, + 160, + 288 + ], + "ordinal": 1220, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 64, + 160, + 288 + ], + "old": [ + 1, + 12, + 18, + 70, + 160, + 288 + ], + "ordinal": 1221, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 24, + 32, + 64, + 128, + 266 + ], + "old": [ + 6, + 24, + 32, + 64, + 128, + 267 + ], + "ordinal": 1226, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 11, + 19, + 96, + 160, + 256 + ], + "ordinal": 1228, + "phase": "B" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 96, + 160, + 256 + ], + "old": [ + 6, + 10, + 18, + 96, + 161, + 256 + ], + "ordinal": 1229, + "phase": "B" + }, + { + "new": [ + 7, + 8, + 18, + 33, + 64, + 128, + 256 + ], + "old": [ + 8, + 21, + 38, + 64, + 128, + 256 + ], + "ordinal": 1233, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 64, + 136, + 264 + ], + "old": [ + 3, + 21, + 37, + 64, + 136, + 264 + ], + "ordinal": 1234, + "phase": "B" + }, + { + "new": [ + 7, + 11, + 17, + 34, + 67, + 131, + 259 + ], + "old": [ + 11, + 22, + 37, + 67, + 131, + 259 + ], + "ordinal": 1235, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 81, + 128, + 256 + ], + "old": [ + 3, + 8, + 48, + 85, + 128, + 256 + ], + "ordinal": 1236, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 17, + 33, + 72, + 136, + 256 + ], + "old": [ + 3, + 21, + 37, + 72, + 136, + 256 + ], + "ordinal": 1242, + "phase": "B" + }, + { + "new": [ + 3, + 4, + 8, + 48, + 64, + 128, + 273 + ], + "old": [ + 3, + 8, + 48, + 64, + 128, + 277 + ], + "ordinal": 1244, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1417, + "phase": "B" + }, + { + "new": [ + 8, + 22, + 37, + 71, + 135, + 263 + ], + "old": [ + 7, + 8, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 1418, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1433, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 67, + 131, + 259 + ], + "old": [ + 7, + 11, + 18, + 33, + 67, + 131, + 259 + ], + "ordinal": 1434, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1437, + "phase": "B" + }, + { + "new": [ + 4, + 8, + 18, + 33, + 192, + 320 + ], + "old": [ + 3, + 4, + 8, + 17, + 33, + 192, + 320 + ], + "ordinal": 1438, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1445, + "phase": "B" + }, + { + "new": [ + 12, + 18, + 33, + 70, + 134, + 262 + ], + "old": [ + 7, + 11, + 18, + 33, + 65, + 129, + 257 + ], + "ordinal": 1446, + "phase": "B" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 0, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 1, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 2, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 3, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 4, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 5, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 6, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 7, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 8, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 9, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 10, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 11, + "phase": "cleanup_tail" + }, + { + "new": [ + 2, + 5, + 24, + 40, + 72, + 385 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 12, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 20, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 21, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 22, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 23, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 24, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 25, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 26, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 27, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 28, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 29, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 30, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 31, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 32, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 33, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 34, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 35, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 36, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 37, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 38, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 39, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 47, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 48, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 49, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 50, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 51, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 52, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 55, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 56, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 60, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 61, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 62, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 63, + "phase": "cleanup_tail" + }, + { + "new": [ + 3, + 12, + 17, + 33, + 64, + 388 + ], + "old": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 67, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 73, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 74, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 75, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 76, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 85, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 88, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 94, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 95, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 96, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 97, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 98, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 99, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 100, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 101, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 102, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 103, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 104, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 105, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 106, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 107, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 108, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 109, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 110, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 111, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 116, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 117, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 121, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 122, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 123, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 124, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 125, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 126, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 127, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 128, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 129, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 130, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 131, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 132, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 133, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 134, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 135, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 136, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 137, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 138, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 139, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 140, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 141, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 142, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 143, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 144, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 145, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 146, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 147, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 148, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 149, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 150, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 151, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 152, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 153, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 154, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 155, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 156, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 157, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 158, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 159, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 160, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 161, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 162, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 163, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 164, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 165, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 166, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 167, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 168, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 169, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 170, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 171, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 172, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 173, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 174, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 175, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 176, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 177, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 178, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 179, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 180, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 181, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 182, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 183, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 188, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 189, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 191, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 192, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 193, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 194, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 195, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 196, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 197, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 198, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 199, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 200, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 201, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 202, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 204, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 205, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 206, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 207, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 208, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 209, + "phase": "cleanup_tail" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 226, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 228, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 4, + 10, + 16, + 34, + 64, + 128, + 256 + ], + "ordinal": 230, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 249, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 251, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 265, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 5, + 11, + 16, + 35, + 64, + 128, + 256 + ], + "ordinal": 267, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 299, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 304, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 320, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 331, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 363, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "ordinal": 395, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 408, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 412, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 424, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 428, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 448, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 449, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 450, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 451, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 452, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 453, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 454, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 455, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 482, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 4, + 11, + 17, + 34, + 64, + 128, + 256 + ], + "ordinal": 483, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 496, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 6, + 8, + 16, + 34, + 66, + 128, + 256 + ], + "ordinal": 497, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 503, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 10, + 20, + 38, + 64, + 128, + 256 + ], + "ordinal": 504, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 507, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 4, + 9, + 16, + 32, + 65, + 128, + 256 + ], + "ordinal": 508, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 526, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 11, + 19, + 32, + 64, + 128, + 256 + ], + "ordinal": 527, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 550, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 8, + 21, + 37, + 64, + 128, + 256 + ], + "ordinal": 551, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 566, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 567, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 568, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 3, + 5, + 9, + 17, + 33, + 65, + 128, + 256 + ], + "ordinal": 569, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 574, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 8, + 20, + 36, + 64, + 128, + 256 + ], + "ordinal": 575, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 576, + "phase": "exit" + }, + { + "new": [ + 1, + 2, + 4, + 8, + 16, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 2, + 12, + 16, + 32, + 68, + 128, + 256 + ], + "ordinal": 577, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 1, + 12, + 18, + 32, + 70, + 128, + 256 + ], + "ordinal": 580, + "phase": "exit" + }, + { + "new": [ + 1, + 6, + 10, + 18, + 32, + 64, + 128, + 256 + ], + "old": [ + 6, + 10, + 18, + 33, + 65, + 128, + 256 + ], + "ordinal": 582, + "phase": "exit" + } + ], + "source_head": "322e0ec764aa7ef7801383feb1f656e460dd8bed" +} diff --git a/research/joint-helper-lattice/PROOF.md b/research/joint-helper-lattice/PROOF.md new file mode 100644 index 0000000000..e41106031d --- /dev/null +++ b/research/joint-helper-lattice/PROOF.md @@ -0,0 +1,102 @@ +# Construction and proof obligations + +## 1. Exact predecessor and changed object + +The input is PR4447 at commit `322e0ec764aa7ef7801383feb1f656e460dd8bed`, with its credited THREE-base native word, PR4441 helper-boundary retiming, and the added three-dimensional frame at B/480. `SOURCES.json` binds all external proof inputs by Git blob and SHA-256. + +There are 632 persistent local fields: 224 main fields and 408 helpers. Each helper is an arbitrary independent input, not initialized scratch. The separate owned center is initialized and erased under the inherited native contract. None of its eight uses receives productive-input credit. + +The patch retains the scalar order and coefficients in each orientation. It retains all native warp events and every main-field boundary. It changes 38 helper entrance frames, 47 helper terminal frames, and 414 scalar contact frames. A source pin accompanies every changed boundary or contact. The two orientations retain their exact inverse-transpose scalar correspondence. + +The optional search jointly optimized both helper boundaries and every mutable scalar contact over the finite intervals of subspaces of F2^9. Fixed main and warp events bound those intervals. The largest quotient dimension was five, so its interval has 374 subspaces. The discovery model used one-hot frame choices and edge marginals, with negative whole-helper credit. Its floating-point solution is a proposal, not a certificate. The following construction and exact tests do not use its claimed optimum. + +## 2. Frame-coordinate invariant + +Let C_F be the source's exact canonical frame operator for subspace F. Interpret a field at frame F as C_F applied to its logical arbitrary value. For nested frames E contained in F, the paid transport is C_F C_E^{-1}. Its Fourier rank is dim(F)-dim(E). The implementation follows the source's `adjoint().then(...)` composition convention and lowers the operator itself, not only that rank formula. + +At each scalar operation, all participating persistent fields are first moved into its declared common frame. A scalar linear combination commutes with the common frame operator. Therefore the operation implements the unchanged logical scalar step. A native warp is run only at its original pinned input frame, and leaves the original pinned output frame. This proves the invariant by induction through the complete chronological word. + +At the end of the word, main fields have their unchanged original endpoints. Helper r has the whole residual C_{T_r} C_{S_r}^{-1}, where S_r and T_r are its new entrance and exit. Every checked S_r is a proper subspace of T_r. Its positive productive rank is dim(T_r)-dim(S_r). There is no duplicate field, discarded helper, clean-input assumption, or free temporary productive input. + +The helper normalizers are recomputed on these whole-job boundaries. Every new transport and each distinct helper boundary is lowered in both orientations with exact Clifford tableaux and absolute phases. The receipt contains 423 distinct transport/boundary pairs, including 406 newly occurring transport pairs relative to PR4447. Two retained literal interpreters check the complete 632-column endpoint. The argument is the frame-coordinate invariant; the finite replay independently checks its application to the submitted circuit. + +## 3. Complete local bill and uniform moment gain + +Write H_r for productive helpers of rank r and P_r for paid jobs of rank r. The predecessor has + + H_old = {4:26, 5:2, 7:29, 8:42, 9:309} + P_old = {1:2254, 2:514, 3:444, 4:103, 5:40, 8:8}. + +The new word has + + H_new = {4:28, 7:7, 8:47, 9:326} + P_new = {1:2237, 2:388, 3:494, 4:147, 5:36, 8:8}. + +There are 408 helpers in both words. The new paid list has 3,310 entries, 53 fewer than the predecessor. Helper rank mass increases from 3,434 to 3,471, and paid rank mass from 5,290 to 5,327. Their difference remains 1,856. In particular, the improvement is not obtained by keeping old productive credit after removing paid work. + +For 0D(1)=0 for every 0 theta^1000, + 145^(1024*TESTED) < 2^1000. + +Set kappa=0.00302015 and d=(TESTED-kappa)/7=1/1,400,000,000. The integer test + + (1,400,000,000*j + 1)^1000 < 2^j + +passes at j=45,868 and fails at j-1. Thus the retained theorem supplies the sufficient uniform rank N=2^64,215,200,000,000. This is an existence construction with explicit finite constants. The resulting word is not materialized and no practical implementation claim follows. + +The new local scalar and fixed-route bound remains below 10^7 per full call. Eighteen such calls, all 15 thin-query charges, every scalar controller and boundary operation fit the complete raw bound 10^9. The number of roles, private storage, coefficient matrices and tapes is finite for the compiled template. Their sizes affect the eventual threshold and are not claimed uniform while changing that template. + +Retain the source BIT ordinary saving 0.0034, with atom exponent 0.004. Its delayed-cover, weighted-child, row-stock and conversion conditions are rechecked through the source package. Use complex uniform saving kappa+6d, followed by b=kappa+5d, a=kappa+4d, q=kappa+3d, epsilon=1-d, beta=1-3d, r0=d/10, stop=d and layout=d. All nine outer cost rows, 54 strict predicates and four functional guards pass exactly. The old BIT cap and closed exponent gaps are explicit rejected controls. + +## 7. Status of the conclusion + +Subject to the retained all-column/native and physical-operation contracts, owned erasure, whole-job matching, finite-template compiler closure, precision and fixed-tape bounds, analytic decomposition, prime avoidance and exact recovery, this construction gives the source framework's conditional multiplication saving kappa=0.00302015. + +The submitted change establishes an exact finite native word and a fully charged conditional parameter transfer. It does not remove the inherited analytic or physical premises. It does not promote the selected frontier, certify global optimality, claim a runtime speedup, or claim independent human or proof-assistant acceptance. + +Credits: zxv's native and higher-moment/logarithmic work; Jacob Alan Sussman's finite mixed-flow theorem; Cinna Davis's prior p7 padding, query-thinned and retimed constructions; and the unchanged credited scalar, Clifford, geometry and outer-ledger sources. New material was prepared for Cinna Davis with substantial OpenAI assistance, Apache-2.0. diff --git a/research/joint-helper-lattice/README.md b/research/joint-helper-lattice/README.md new file mode 100644 index 0000000000..8c9bd69cd4 --- /dev/null +++ b/research/joint-helper-lattice/README.md @@ -0,0 +1,46 @@ +# Joint helper boundaries: conditional kappa = 0.00302015 + +This is an author-checked conditional construction, not an unconditional integer-multiplication theorem or a selected-frontier update. + +The new contribution is a joint finite optimization of helper entrances, exits and scalar contact frames. It builds on the exact native supplier of zxv, the retiming in PR4441, the missing span in PR4447, and the query-thinned controller in PR4440. The arithmetic scaffolding and logarithmic compiler test are adapted from PR4447 and the credited PR4433 lineage. + +The proposed saving is `0.00302015`, compared with `0.00300123` in PR4447: an absolute increase of `0.00001892`, or approximately **0.630408%**. This is a moderate incremental improvement. It is not a claim of a large asymptotic breakthrough. + +## What changed + +Relative to PR4447, `PATCH.json` changes 38 helper entrances, 47 helper exits and 414 scalar contact frames. Both scalar orders, every scalar coefficient, main endpoints, native warps, and the owned-center operations remain unchanged. All 408 helpers remain independent, strictly productive arbitrary inputs. + +The local helper profile becomes `{4:28, 7:7, 8:47, 9:326}`. The complete paid profile becomes `{1:2237, 2:388, 3:494, 4:147, 5:36, 8:8}`. This reduces local paid calls from 3,363 to 3,310. Both rank masses increase by 37, leaving the local rank-mass deficit unchanged. The eight whole rank-eight center jobs are included. + +The nonlinear helper credit couples the two boundaries. Separate entrance-only and exit-only updates do not represent that joint objective. The optional finite-lattice mixed-integer search found the patch; the proof does not trust that solver, its objective value, or its optimality status. + +The changed supplier is installed in an explicitly replayed 16-pair controller with 18 full native calls and 15 copied-query shears. Its complete invoice has 10,928 productive fields and 64,620 paid jobs. Target and paid rank masses are 239,886 and 239,134, respectively. The rank-one surplus is 752. The predecessor p17 invoice has a different number of inputs, so total call counts are not a like-for-like runtime comparison. + +`RESULT.json` encloses the new raw moment root in `(0.0030201659770, 0.0030201659771)`. It certifies paid tensor completion, splitting, a finite uniform compiler and every outer inequality at the smaller stated kappa. The unchanged source BIT supplier supports ordinary saving 0.0034. + +## Verification + +Run from the repository root: + +```sh +python3.12 -B scripts/research_package.py --package research/joint-helper-lattice --check-only +python3.12 -B scripts/research_package.py --package research/joint-helper-lattice +``` + +The registered replay has three required gates (dependencies, native, arithmetic) and uses only the Python standard library. It authenticates the declared sources, reconstructs the changed native word, replays all 632 arbitrary-input columns in both orientations using two retained interpreters, and lowers the new transports and helper boundaries including absolute phase. It regenerates the p16 Laurent and literal controller, checks its boundary factorization, cross-checks the moments with a second rational engine, and verifies the full compiler and outer ledger. Mutation controls reject false ranks, unsupported query orientation, unpaid full stages, the old invoice at the new saving, and invalid outer parameters. + +`--write` is an authoring path using saved native and predecessor receipts. It is not the registered full replay. `VALIDATION.md` records the commands actually completed. + +`PROOF.md` states the construction, complete cost argument and inherited assumptions. `DISCOVERY.json` contains floating-point search evidence only; no solver optimality claim is part of the theorem. `PATCH.json`, `NATIVE.json.gz`, `CONTROLLER.json` and `RESULT.json` are the mathematical replay artifacts. + +## Scope and credit + +The source all-column native contract, allowed erasure of owned storage, whole-job normalizers, finite-template closure, precision and monomial tape bounds, analytic decomposition, prime avoidance, and exact recovery remain explicit premises. The enormous uniform word is algorithmically specified, not materialized. No practical speedup, global optimum, formal-kernel acceptance, or independent human review is claimed. + +The branch is stacked on exact PR4447 head `322e0ec764aa7ef7801383feb1f656e460dd8bed`. Its ancestors retain PR4440/PR4441 and the pending PR4447 contribution. Those inherited changes are not new work in this package. Canonical main at the final research checkpoint was `2a13eb1827784206202db90e5dc8327cf8a250db`. + +Credit zxv's native and compiler work, Jacob Alan Sussman's mixed-target integer flow, Cinna Davis's PR4416 padding and PR4440/PR4441/PR4447 contributions, and the retained scalar, Clifford, geometry, precision and outer-ledger authors. Source notices remain unchanged. New work prepared for Cinna Davis with substantial OpenAI assistance. Apache-2.0. + +## Open next questions + +Can a costed scalar reordering or changed warp word beat this fixed chronological graph? Start with a small commuting contact block, derive its dependency graph, then reconstruct every physical endpoint before repricing it. The finite solver's optimum report is not an exact general barrier and does not cover changed scalar orders or warps. The structured question and blocker are in `TASK.json`. diff --git a/research/joint-helper-lattice/REPLAY-LOGS.json b/research/joint-helper-lattice/REPLAY-LOGS.json new file mode 100644 index 0000000000..38a7d9500e --- /dev/null +++ b/research/joint-helper-lattice/REPLAY-LOGS.json @@ -0,0 +1,21 @@ +{ + "environment": "Pyroam isolated Linux runner", + "gates": [ + { + "log": "2026-10-21T23:16:06Z\nPython 3.12.13\n{\"native\": {\"binary_charts\": 111, \"complex_contacts_and_inverses\": 896, \"owned_stream_restored_zero\": true, \"thin_paid_rank_per_port\": 1, \"thin_productive_credit\": 0}, \"ordinary_BIT\": {\"admitted\": \"17/5000\", \"after_cover\": \"69/20000\", \"atom\": \"1/250\", \"before_cover\": \"3459/1000000\", \"ordinary_saving\": \"8590884599/2500000000000\", \"prime_rule\": \"odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses\"}, \"status\": \"PASS_RETAINED_NATIVE_AND_BIT_DEPENDENCIES\"}\n2026-10-21T23:16:40Z\nDEPENDENCY_REPLAY_COMPLETE\n", + "part": "dependencies", + "sha256": "18a2445959efd5dbfa8dce0933f86074261149cccda2dc081c7edccb96e5403e" + }, + { + "log": "2026-10-21T23:16:56Z\n{\"helpers\": {\"4\": 28, \"7\": 7, \"8\": 47, \"9\": 326}, \"paid\": {\"1\": 2237, \"2\": 388, \"3\": 494, \"4\": 147, \"5\": 36, \"8\": 8}, \"physical_pairs\": 423, \"status\": \"PASS_JOINT_NATIVE_632_COLUMNS_BOTH_ORIENTATIONS\"}\n2026-10-21T23:21:26Z\nNATIVE_REPLAY_COMPLETE\n", + "part": "native", + "sha256": "3826b2360fff5f73485a7df1a23db81789f09fdcf49d1d26e31ae0728222741b" + }, + { + "log": "2026-10-21T23:27:41Z\nCHECK_JOINT_CONTROLLER\nPASS_JOINT_CONTROLLER\nCHECK_EXACT_CEILING\nPASS_EXACT_CEILING\nPASS_UNIFORM_LOCAL_GAIN\nPASS_COMPLETION_AND_COMPILER\n{\"compiler\": {\"H\": 64215200000000, \"N\": \"2^64215200000000\", \"eta\": {\"lower\": \"0.000000206231977820868640096499\", \"upper\": \"0.000000206231977820868640096500\"}, \"gap\": \"1/1400000000\", \"integer_test_exponent\": 45868, \"logarithm_power\": 1000, \"theta\": \"63/64\", \"uniform_saving\": \"528527/175000000\", \"word_materialized\": false}, \"gain_over_PR4447\": \"473/25000000\", \"kappa_decimal\": \"0.00302015\", \"replay_scope\": \"Arithmetic and p16 controller only; the registered native and dependency gates are separate required commands.\", \"status\": \"PASS_CONDITIONAL_JOINT_HELPER_KAPPA_00302015\"}\n2026-10-21T23:29:08Z\nARITHMETIC_REPLAY_COMPLETE\n", + "part": "arithmetic", + "sha256": "7d73c93e443a0f1fd95c2cd1cda64323fb6c7694df0ab85c43c19f29e2af4718" + } + ], + "python": "3.12.13" +} diff --git a/research/joint-helper-lattice/RESULT.json b/research/joint-helper-lattice/RESULT.json new file mode 100644 index 0000000000..edf41a49a0 --- /dev/null +++ b/research/joint-helper-lattice/RESULT.json @@ -0,0 +1,274 @@ +{ + "compiler": { + "H": 64215200000000, + "N": "2^64215200000000", + "eta": { + "lower": "0.000000206231977820868640096499", + "upper": "0.000000206231977820868640096500" + }, + "gap": "1/1400000000", + "integer_test_exponent": 45868, + "logarithm_power": 1000, + "theta": "63/64", + "uniform_saving": "528527/175000000", + "word_materialized": false + }, + "fixed_profile_ceiling": { + "decreasing_through_C": "1/20", + "headroom": [ + "15977/1000000000000", + "159771/10000000000000" + ], + "negative_derivative_upper": { + "lower": "-195970.145588045890401261885812812963", + "upper": "-195970.145588045890401261885812812962" + }, + "remaining_interval_moment_upper": { + "lower": "-6847.019825166589746262304732988153", + "upper": "-6847.019825166589746262304732988152" + }, + "root": [ + "3020165977/1000000000000", + "30201659771/10000000000000" + ] + }, + "full_calls": 18, + "gain_over_PR4416": "4171/12500000", + "gain_over_PR4440": "1203/20000000", + "gain_over_PR4441": "191/10000000", + "gain_over_PR4447": "473/25000000", + "kappa": "60403/20000000", + "kappa_decimal": "0.00302015", + "local_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 326 + }, + "local_paid": { + "1": 2237, + "2": 388, + "3": 494, + "4": 147, + "5": 36, + "8": 8 + }, + "negative_controls": { + "closed_epsilon": [ + "epsilon_below_one", + "global_gamma_power_slack", + "actual_logarithmic_gamma_guard", + "source_axis_superpolynomial", + "gaussian_above_main", + "new_semantic_guard_with_C1_one" + ], + "closed_uniform": [ + "new_complex_uniform_saving_above_b" + ], + "old_BIT": [ + "actual_bit_above_effective" + ], + "unfunded_endpoint": [ + "main_transform_above_kappa", + "global_coordinate_router_above_kappa", + "fused_gaussian_above_kappa", + "group_bit_router_above_kappa", + "boundary_algebraic_matrix_above_kappa" + ] + }, + "nonrecursive": { + "local_route_bound": 4814000, + "local_scalar_allowance": 158168, + "raw_budget": 1000000000, + "raw_upper": 181098496 + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "348599999253/350000000000", + "fixed_halo_explicit_metadata_branch": "26950000001/350000000", + "new_BIT_row_stock_sublinear_in_active_group": "1395799997009/1400000000000", + "new_semantic_group_guard": "3/1400000000" + }, + "margins": { + "boundary_algebraic_matrix": "5919499595771787/1960000000000000000", + "fused_gaussian": "5919499587315361/1960000000000000000", + "global_coordinate_router": "2114107/700000000", + "group_bit_router": "2959750493657679/980000000000000000", + "group_scans": "699999999/700000000", + "main_transform": "5919498195771787/1960000000000000000", + "microbox_face_corrections": "26950000001/350000000", + "polynomial_products": "1399999999/1400000000", + "sparse_union_movement": "802169499595771787/1960000000000000000" + }, + "parameters": { + "a": "2114107/700000000", + "b": "845643/280000000", + "beta": "1399999997/1400000000", + "bit_saving": "17/5000", + "cap_xi": "1782169498195771787/1960000000000000000", + "complex_uniform_saving": "528527/175000000", + "d": "1/1400000000", + "epsilon": "1399999999/1400000000", + "kappa": "60403/20000000", + "lambda_": "398791939/400000000", + "lambda_prime": "1395771787/1400000000", + "layout": "1/1400000000", + "q": "4228213/1400000000", + "r0": "1/14000000000", + "stop": "1/1400000000", + "tested_saving": "604031/200000000" + }, + "strict_checks": { + "actual_bit_above_effective": "265893/700000000", + "actual_logarithmic_gamma_guard": "1/1400000000", + "actual_logarithmic_group_guard": "177830503904228213/980000000000000000", + "alpha_logarithm_absorption": "1/14000000000", + "boundary_algebraic_matrix_above_kappa": "5595771787/1960000000000000000", + "cap_above_band": "802169498195771787/1960000000000000000", + "cap_below_cell": "177830500404228213/1960000000000000000", + "cap_below_phase_cell_power": "2137830501804228213/1960000000000000000", + "complex_above_effective": "1/1400000000", + "complex_below_one_over_32": "7904357/280000000", + "complex_endpoint": "1/700000000", + "epsilon_below_one": "1/1400000000", + "epsilon_positive": "1399999999/1400000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "5587315361/1960000000000000000", + "gaussian_above_main": "695771787/980000000000000000", + "global_coordinate_router_above_kappa": "1/350000000", + "global_gamma_power_slack": "9/14000000000", + "group_below_dimension": "1/700000000", + "group_bit_router_above_kappa": "3493657679/980000000000000000", + "group_gauge_power_slack": "177830503834228213/980000000000000000", + "group_key_fits_record": "1/700000000", + "group_positive": "1399999997/1400000000", + "group_scans_above_kappa": "348942947/350000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "644589790400418148631/500000000000000000000000", + "lambda_above_internal": "1/2800000000", + "lambda_above_sigma": "3/2800000000", + "lambda_above_tau": "1/2800000000", + "lambda_prime_above_lambda": "1/2800000000", + "lambda_prime_above_leaf": "559154357/392000000000000000", + "leaf_saving_above_effective": "279154357/392000000000000000", + "main_transform_above_kappa": "4195771787/1960000000000000000", + "membership_arithmetic_fits_record": "1/1400000000", + "microbox_face_corrections_above_kappa": "53897885897/700000000", + "microbox_halo_volume": "110600000003/1400000000", + "new_complex_uniform_saving_above_b": "1/1400000000", + "new_semantic_guard_with_C1_one": "1/1400000000", + "polynomial_products_above_kappa": "1395771789/1400000000", + "positive_layout_slack": "1/1400000000", + "q_below_effective": "1/1400000000", + "q_below_internal": "1/1400000000", + "q_below_leaf": "559154357/392000000000000000", + "q_positive": "4228213/1400000000", + "short_record_fallback": "279154357/280000000", + "source_axis_superpolynomial": "1/1400000000", + "sparse_union_movement_above_kappa": "796250005595771787/1960000000000000000", + "stop_below_one": "1399999999/1400000000", + "stop_positive": "1/1400000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/1400000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/1400000000", + "union_tag_work_per_visit_fits_record": "3/1400000000" + } + }, + "paid": { + "1": 41946, + "16": 448, + "2": 6984, + "24": 448, + "3": 8892, + "32": 448, + "4": 2646, + "40": 448, + "48": 448, + "5": 648, + "56": 448, + "64": 448, + "72": 224, + "8": 144 + }, + "paid_calls": 64620, + "pairs": 16, + "prefix_pairs": 7, + "productive_fields": 10928, + "query_shears": 15, + "scope": "Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.", + "source_heads": { + "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", + "PR4441_combination": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", + "PR4447": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "helper_retiming": "ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9" + }, + "source_inputs": 51, + "status": "PASS_CONDITIONAL_JOINT_HELPER_KAPPA_00302015", + "strictification": { + "alpha": { + "lower": "0.999999988558808354139963023136", + "upper": "0.999999988558808354139963023137" + }, + "cutoff": 20, + "delta": { + "lower": "0.958284435309221389866479909583", + "upper": "0.958284435309221389866479909584" + }, + "floor": 21, + "gamma": { + "lower": "0.956176646497545264598139374323", + "upper": "0.956176646497545264598139374324" + }, + "limits": [ + "999999999/1000000000", + "97/100", + "97/100" + ], + "normalized_paid_upper": "2097152001953127/2097154147483648", + "power": 1024, + "tail_offset": "1/5", + "tested": "604031/200000000" + }, + "targets": { + "145": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 504, + "41": 448, + "49": 448, + "57": 448, + "65": 448, + "7": 126, + "73": 224, + "8": 846, + "9": 5868 + }, + "uniform_local_gain": { + "coefficients": { + "1": 17, + "2": 126, + "3": -50, + "4": -42, + "5": 2, + "7": -22, + "8": 5, + "9": 17 + }, + "derivative_upper": { + "lower": "-16.327581880492435373215953558618", + "upper": "-16.327581880492435373215953558617" + }, + "intervals": 128, + "vanishes_at_one": true + } +} diff --git a/research/joint-helper-lattice/SOURCES.json b/research/joint-helper-lattice/SOURCES.json new file mode 100644 index 0000000000..02e8f76eab --- /dev/null +++ b/research/joint-helper-lattice/SOURCES.json @@ -0,0 +1,330 @@ +{ + "base_commit": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "files": [ + { + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "path": "certificates/selected-result.json", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9", + "usage": "provenance" + }, + { + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "path": "docs/research/agent-task-catalog.json", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96", + "usage": "provenance" + }, + { + "git_blob": "70373e1f92829cf16ea1836ae0cced06ed937a5e", + "path": "docs/research/current-priorities.md", + "sha256": "2df24baf0d8a5a714fdf36120e4075078c5455904e359ac6c0f9f7e39418fba1", + "usage": "provenance" + }, + { + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7", + "usage": "input" + }, + { + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "path": "research/fresh-helper-boundary/CHANGES.json", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624", + "usage": "input" + }, + { + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839", + "usage": "input" + }, + { + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "path": "research/fresh-helper-boundary/RESULT.json", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd", + "usage": "input" + }, + { + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "path": "research/fresh-helper-boundary/SOURCES.json", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0", + "usage": "input" + }, + { + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "path": "research/fresh-helper-boundary/arithmetic.py", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07", + "usage": "input" + }, + { + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "path": "research/fresh-helper-boundary/native.py", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29", + "usage": "input" + }, + { + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "path": "research/fresh-helper-boundary/verify.py", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf", + "usage": "input" + }, + { + "git_blob": "bf68dc2b987cb7de6431ff5e3514b60af48720a5", + "path": "research/fresh-helper-thinned/PROOF.md", + "sha256": "9883b3329fef7624d3471e27bb55258cd9dc18bb6d37779a3939de99add87347", + "usage": "input" + }, + { + "git_blob": "344616d6654a96085dd45cf2c3189ef283deeac1", + "path": "research/fresh-helper-thinned/README.md", + "sha256": "70c1c872c2327c3f71918e218d5f1ecb7a00037771a5dd1b8ae415b84cc90dc2", + "usage": "input" + }, + { + "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55", + "path": "research/fresh-helper-thinned/RESULT.json", + "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21", + "usage": "input" + }, + { + "git_blob": "4089ad37114540b23846596e2a641c4a4bd608e2", + "path": "research/fresh-helper-thinned/SOURCES.json", + "sha256": "5aec5df5096ee8a3e90618d311640b4bdfba42be5bc4bc5fab55e8be858ab2cb", + "usage": "input" + }, + { + "git_blob": "9ba85a59aa5dcc5cdaec85ee18607cb050530c55", + "path": "research/fresh-helper-thinned/verify.py", + "sha256": "c841265ccee9b6f79045ad818ce9d27cfd7ee1f60047525a75d491f0dd8b997a", + "usage": "input" + }, + { + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "path": "research/higher-moment-strictification/README.md", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d", + "usage": "input" + }, + { + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "path": "research/higher-moment-strictification/verify.py", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326", + "usage": "input" + }, + { + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85", + "usage": "input" + }, + { + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "usage": "input" + }, + { + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7", + "usage": "input" + }, + { + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "path": "research/kappa-function-composition/complex/prune_native.py", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257", + "usage": "input" + }, + { + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a", + "usage": "input" + }, + { + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef", + "usage": "input" + }, + { + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0", + "usage": "input" + }, + { + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443", + "usage": "input" + }, + { + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf", + "usage": "input" + }, + { + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7", + "usage": "input" + }, + { + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497", + "usage": "input" + }, + { + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e", + "usage": "input" + }, + { + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17", + "usage": "input" + }, + { + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6", + "usage": "input" + }, + { + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61", + "usage": "input" + }, + { + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39", + "usage": "input" + }, + { + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "path": "research/kappa-rebuild/complex/native_extensions.py", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3", + "usage": "input" + }, + { + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424", + "usage": "input" + }, + { + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5", + "usage": "input" + }, + { + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902", + "usage": "input" + }, + { + "git_blob": "2f41b11d02726a60da449aaa6c603716c0310ead", + "path": "research/missing-join-frame/NATIVE.json.gz", + "sha256": "96718b257db24f4f62d3b86b36cdd514e67d2cb99947ddd7bdcb9b55a2c17841", + "usage": "input" + }, + { + "git_blob": "f96d295d40014d4dd503f58eb3cdabcbb4b8e101", + "path": "research/missing-join-frame/PATCH.json", + "sha256": "9ab5328245ff02c9d0be21d39bcc375f50bc5d7909e9f7b9a3a9a6f812f5bd6e", + "usage": "input" + }, + { + "git_blob": "d240cd8e14e6d30e0e2c3d0ddcc7efa68349e24e", + "path": "research/missing-join-frame/PROOF.md", + "sha256": "50061c25d379ff5733135dbed53e8721bbd4dbee6766d1609d8a2ecdebb7dc06", + "usage": "input" + }, + { + "git_blob": "e653fb4358ded67ff1539151f4b670ad9a242fb1", + "path": "research/missing-join-frame/RESULT.json", + "sha256": "25f2cbcde988847ff86f44e804982069863ec99ff68097f16e9bb7a1a17c4cd0", + "usage": "input" + }, + { + "git_blob": "188135f81c9937af8232a06dc1e7b8b28260e6a8", + "path": "research/missing-join-frame/verify.py", + "sha256": "21429dd9c1b9c93ebb57e5fbb8ef674d0e4146ac8c25cc7c097c3352c02366a4", + "usage": "input" + }, + { + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598", + "usage": "input" + }, + { + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "path": "research/pr4359-p7-padding/TENSOR.md", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3", + "usage": "input" + }, + { + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15", + "usage": "input" + }, + { + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "path": "research/pr4359-p7-padding/native_inventory.py", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32", + "usage": "input" + }, + { + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "usage": "input" + }, + { + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088", + "usage": "input" + }, + { + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "path": "research/query-thinned-controllers/RESULT.json", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f", + "usage": "input" + }, + { + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "path": "research/query-thinned-controllers/SOURCES.json", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29", + "usage": "input" + }, + { + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "path": "research/query-thinned-controllers/controller.py", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2", + "usage": "input" + }, + { + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "path": "research/query-thinned-controllers/verify.py", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950", + "usage": "input" + }, + { + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "usage": "input" + } + ], + "schema_version": 1 +} diff --git a/research/joint-helper-lattice/TASK.json b/research/joint-helper-lattice/TASK.json new file mode 100644 index 0000000000..aa0123ac3e --- /dev/null +++ b/research/joint-helper-lattice/TASK.json @@ -0,0 +1,73 @@ +{ + "actual_scope": "Jointly change helper entrances, exits and scalar contact subspaces; carry the exact new supplier through a p16 query-thinned controller to conditional kappa 0.00302015.", + "ai_assistance": "Substantial OpenAI assistance in discovery, proof, implementation and verification; no independent human or proof-assistant review.", + "author": "Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance", + "base_commit": "322e0ec764aa7ef7801383feb1f656e460dd8bed", + "bottleneck_link": "Separate entrance/exit updates miss the coupled productive rank reward. The joint patch lowers the complete moment despite increasing both rank masses equally.", + "budget_minutes": 180, + "evidence": "PATCH.json, NATIVE.json.gz, CONTROLLER.json, RESULT.json, PROOF.md and VALIDATION.md", + "open_questions": [ + { + "blocked_by": "No verified changed-order candidate is included.", + "first_step": "Preserve exact scalar dependencies but alter a small commuting contact block, reconstruct its new graph, and replay any candidate on every arbitrary-input column.", + "question": "Can scalar reordering or a changed warp word improve beyond joint monotone retiming?", + "why_it_matters": "The finite all-subspace search reports no remaining improvement for the fixed word at the tested objective; this numerical solver status is not a universal barrier." + } + ], + "original_card": { + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "complex-new-helper-inventory", + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ], + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ] + }, + "outcome": "completed", + "priority_revision": 7, + "schema_version": 1, + "scope_change_reason": "Explicit kappa improvement assignment. Unlike separate one-label endpoint sweeps, optimize both helper boundaries and all intermediate contacts in one finite lattice model.", + "scope_status": "changed", + "stop_rule": "Publish only after both arbitrary-input native replays, all new absolute phases, the full paid tails and all outer inequalities pass.", + "task_id": "complex-new-helper-inventory", + "upstream_checkpoint": { + "checked_at_utc": "2026-10-21T21:14:00Z", + "coverage": "Latest open and merged PRs through #4446; no stronger declared kappa found.", + "frontier": "PR4446 kappa 0.003001053 uses the same prior invoice; new certificate here is stronger. PR4441 updated head 5f9d871c independently replayed before extending.", + "main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "priority_revision": 7 + } +} diff --git a/research/joint-helper-lattice/VALIDATION.md b/research/joint-helper-lattice/VALIDATION.md new file mode 100644 index 0000000000..dea1fb1479 --- /dev/null +++ b/research/joint-helper-lattice/VALIDATION.md @@ -0,0 +1,21 @@ +# Completed validation + +All three required proof gates passed on CPython 3.12.13 in the isolated Pyroam Linux runner, using the same public source closure. The complete outputs and SHA-256 values of the process logs are retained in REPLAY-LOGS.json. + +- Dependencies: 2026-10-21 23:16:06--23:16:40 UTC. Fresh native contact/phase checks, all 111 binary charts, owned-query clear/erase controls, binary controller and literal replay, both BIT tails, finite compiler and ordinary conversion passed. +- Native: 23:16:56--23:21:26 UTC. Both 632-column arbitrary-input orientations passed two retained interpreters; 423 distinct transport/helper pairs passed exact rank, Clifford and absolute-phase lowering. Changed-rank control rejected. +- Arithmetic: 23:27:41--23:29:08 UTC. Fresh p16 source word and its supplied factorization, independent literal replay, query mutants, exact root bracket, uniform local gain, both rational moment engines, complete paid tails, finite compiler and all outer inequalities passed. The exact RESULT.json matched. + +Reproduce the gates separately: + +```sh +python3.12 -B research/joint-helper-lattice/verify.py --part dependencies +python3.12 -B research/joint-helper-lattice/verify.py --part native +python3.12 -B research/joint-helper-lattice/verify.py --part arithmetic +``` + +VERIFY.json registers all three as required commands; none is an optional substitute for another. The package metadata and source-pin check passed before publication. The native gate is given a 600-second CI allowance; the package total remains within the 1,200-second limit. + +Earlier attempts exposed an initialization-order error in a redundant source replay and exceeded the 300-second execution-call limit. The final dependency gate initializes the retained engines and checks the actual unchanged BIT/native premises, while the new complex controller is checked in the arithmetic gate. The arithmetic verifier checks the supplied exact factorization instead of rerunning factorization discovery; it still reconstructs every source coefficient, emitted event, boundary program and invoice. No proof predicate was relaxed to obtain a pass. + +The single aggregate launcher was not completed locally because its three gates together exceed one execution-call limit. The three registered commands were each completed separately. Hosted CI, independent human review, formal-kernel verification and a full historical selected-frontier replay are not claimed. diff --git a/research/joint-helper-lattice/VERIFY.json b/research/joint-helper-lattice/VERIFY.json new file mode 100644 index 0000000000..7258f5000c --- /dev/null +++ b/research/joint-helper-lattice/VERIFY.json @@ -0,0 +1,94 @@ +{ + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "dependencies" + ], + "checks": "Fresh retained physical phases, owned-query primitives, complete binary controller, both BIT tails, compiler and ordinary conversion.", + "timeout_seconds": 300 + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "native" + ], + "checks": "Fresh exact 632-column replay in both orientations with two interpreters and 423 phase-bearing transport/helper pairs.", + "timeout_seconds": 600 + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "arithmetic" + ], + "checks": "Fresh p16 rational/Laurent word and literal boundaries; both rational interval engines; uniform local gain; paid tails; compiler and all outer predicates.", + "timeout_seconds": 300 + } + ], + "inputs": [ + "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "research/fresh-helper-boundary/CHANGES.json", + "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "research/fresh-helper-boundary/RESULT.json", + "research/fresh-helper-boundary/SOURCES.json", + "research/fresh-helper-boundary/arithmetic.py", + "research/fresh-helper-boundary/native.py", + "research/fresh-helper-boundary/verify.py", + "research/fresh-helper-thinned/PROOF.md", + "research/fresh-helper-thinned/README.md", + "research/fresh-helper-thinned/RESULT.json", + "research/fresh-helper-thinned/SOURCES.json", + "research/fresh-helper-thinned/verify.py", + "research/higher-moment-strictification/README.md", + "research/higher-moment-strictification/verify.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "research/kappa-function-composition/complex/prune_native.py", + "research/kappa-rebuild/architecture/mixed_target_probe.py", + "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "research/kappa-rebuild/bit/bit_native_binding.py", + "research/kappa-rebuild/bit/complex_controller_factor.py", + "research/kappa-rebuild/bit/mixed_productive_bit.py", + "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "research/kappa-rebuild/complex/native_extensions.py", + "research/kappa-rebuild/complex/power_two_balance.py", + "research/kappa-rebuild/complex/rebuild_native.py", + "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "research/missing-join-frame/NATIVE.json.gz", + "research/missing-join-frame/PATCH.json", + "research/missing-join-frame/PROOF.md", + "research/missing-join-frame/RESULT.json", + "research/missing-join-frame/verify.py", + "research/pr4359-p7-padding/P7-FACTOR.json", + "research/pr4359-p7-padding/TENSOR.md", + "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "research/pr4359-p7-padding/native_inventory.py", + "research/query-thinned-controllers/BIT-CONTROLLER.json", + "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "research/query-thinned-controllers/RESULT.json", + "research/query-thinned-controllers/SOURCES.json", + "research/query-thinned-controllers/controller.py", + "research/query-thinned-controllers/verify.py", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py" + ], + "python": "3.12", + "requirements": [], + "schema_version": 1, + "status": "ready" +} diff --git a/research/joint-helper-lattice/native_joint.py b/research/joint-helper-lattice/native_joint.py new file mode 100644 index 0000000000..0315f80e2f --- /dev/null +++ b/research/joint-helper-lattice/native_joint.py @@ -0,0 +1,118 @@ +"""Joint entrance/exit/contact retiming, with literal and phase replay. + +Apache-2.0. Substantial OpenAI assistance. Uses the credited native retiming +implementation of PR4441 and preserves PR4447's missing-span predecessor. +""" +from collections import Counter +from copy import deepcopy +from pathlib import Path +import json,gzip,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +sys.path.insert(0,str(ROOT/'research/fresh-helper-boundary')) +import native as F +need=F.need + +def construct(patch=None): + c=F.read(F.BASE/'THREE-base-FULL-IDENTITY-CANONICAL.json.gz') + original=F.read(F.BASE/'THREE-base-FULL-IDENTITY-NATIVE.json.gz') + parent=F.read(F.HERE/'CHANGES.json') + maps={d:F.gates(p) for d,p in original.items()} + need(set(maps['forward'])==set(maps['backward']),'Same scalar contact inventory') + for key in maps['forward']: + f=original['forward'][maps['forward'][key]];b=original['backward'][maps['backward'][key]] + need(b[1]==F.dual(f[1]) and b[2]==f[2],'Retained exact dual scalar words') + for key,field in [('entrances','start'),('exits','final')]: + for r,old,new in parent[key]: + need(c[field][r]==old,'Parent boundary pin');c[field][r]=new + for phase,ordinal,old,new in parent['gates']: + for d,p in original.items(): + i=maps[d][phase,ordinal];need(p[i][2]==old,'Parent scalar pin');p[i][2]=new + prior=F.read(ROOT/'research/missing-join-frame/PATCH.json') + need(prior['phase']=='B' and prior['ordinal']==480,'Exact prior contact') + prior_frame=len(c['frames']);c['frames'].append(prior['new_basis']) + for d,p in original.items(): + i=maps[d]['B',480];need(p[i][2]==prior['old_frame'],'Missing-span parent pin');p[i][2]=prior_frame + baseline=deepcopy(c) + before={d:F.synthesize(c,p) for d,p in original.items()} + patch=F.read(HERE/'PATCH.json') if patch is None else patch + need(patch['source_head']=='322e0ec764aa7ef7801383feb1f656e460dd8bed','Pinned candidate head') + labels={frozenset(F.span(b)):i for i,b in enumerate(c['frames'])} + def label(b): + s=frozenset(F.span(b));need(len(s)==2**len(b),'Independent binary basis') + if s not in labels:labels[s]=len(c['frames']);c['frames'].append(b) + return labels[s] + seen=set();counts=Counter() + for move in patch['changes']: + phase,r=move['phase'],move['ordinal'];key=(phase,r) + need(key not in seen,'No duplicate changed boundary/contact');seen.add(key) + a,b=F.span(move['old']),F.span(move['new']);need(a!=b,'No unchanged patch entry') + f=label(move['new']);counts[phase]+=1 + if phase in ('entrance','exit'): + need(224<=r<632,'Only independent helper boundaries may change') + field='start' if phase=='entrance' else 'final' + need(F.span(c['frames'][c[field][r]])==a,'Current helper source pin') + c[field][r]=f + else: + for d,p in original.items(): + i=maps[d][key];need(F.span(c['frames'][p[i][2]])==a,'Current scalar source pin');p[i][2]=f + programs={d:F.synthesize(c,p) for d,p in original.items()} + return c,programs,baseline,before,counts + +def run(phase_check=True): + c,programs,baseline,before,counts=construct() + V=F.load(ROOT/'research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py','joint_rows') + X=F.load(ROOT/'research/kappa-rebuild/complex/native_extensions.py','joint_literal') + checks={};profiles={} + for d,p in programs.items(): + rows,rec=X.literal_replay(V,c,p,d=='backward') + for r in range(632):need(rows['L',r]==V.expected(('L',r),[],d=='backward',False),'All 632 arbitrary-input endpoints') + profiles[d]=Counter({int(k):v for k,v in rec['paid_profile'].items()}) + rebound=deepcopy(c);rebound['local_profile']=dict(profiles[d]) + rec['second_literal']=V.replay(p,rebound,[],d=='backward',False);checks[d]=rec + need(profiles['forward']==profiles['backward'],'Both complete native rank tariffs') + H=Counter() + for r in range(224,632): + a,b=c['start'][r],c['final'][r] + need(F.span(c['frames'][a])0 and margin(ROOT_HIGH)[1]<0,'New complete profile root bracket') + derivative=None + for i in range(16): + l,r=Q(i,320),Q(i+1,320);low=Q(0) + for rank,n in signed.items(): + term=E.mul(E.power(rank,1-r if n>0 else 1-l),E.log_bounds(rank)) + low+=n*term[0 if n>0 else 1] + derivative=low if derivative is None else min(derivative,low) + upper=None + for i in range(128): + l,r=Q(1,20)+Q(19*i,2560),Q(1,20)+Q(19*(i+1),2560) + hi=sum(n*E.power(rank,1-l if n>0 else 1-r)[1 if n>0 else 0] for rank,n in signed.items()) + upper=hi if upper is None else max(hi,upper) + need(derivative>0 and upper<0,'Fixed-profile ceiling for every real 0after and 2**26>256/(before-after),'Explicit delayed-cover exponent gap and prime allowance') + need(atom>ordinary>Q(bit['admitted']) and atom<1-ordinary,'Complete ordinary BIT conversion and stock') + return {'status':'PASS_RETAINED_NATIVE_AND_BIT_DEPENDENCIES','native':source['native'],'ordinary_BIT':bit} + +def run(execute_sources=True): + count=authenticate() + fresh=ROOT/'research/fresh-helper-boundary' + query=ROOT/'research/query-thinned-controllers' + sys.path.insert(0,str(fresh));F=load(fresh/'verify.py','audited_fresh_boundary_package') + sys.path.insert(0,str(query));S=load(query/'verify.py','audited_query_thinning_package') + source_query=read(query/'RESULT.json') + if execute_sources: replay_dependencies() + local=J.run() if execute_sources else read(HERE/'NATIVE.json.gz') + need(json.loads(json.dumps(local))==read(HERE/'NATIVE.json.gz'),'Fresh exact missing-span native replay') + H={int(k):v for k,v in local['helpers'].items()};N={int(k):v for k,v in local['paid'].items()} + print('CHECK_JOINT_CONTROLLER',flush=True) + word=controller16(S.C) + print('PASS_JOINT_CONTROLLER',flush=True) + need(json.loads(json.dumps(word))==read(HERE/'CONTROLLER.json'),'Fresh p16 controller and literal boundary replay') + T,P=Counter(),Counter();full=thin=idle=0 + for event in word['physical_events']: + if event[0]=='LOCAL': + full+=1;T.update(H);P.update(N) + elif event[0]=='QUERY_SHEAR':thin+=1;P[1]+=112 + elif event[0]=='IDLE': + rank=8*len(event[2]);need(rank>0,'No nonzero charge for erased idle stage') + P[rank]+=224;idle+=224 + for term in word['diagonal']: + need(term[0] in (-1,1) and all(x in (0,1) for x in term[1:]),'Actual normalized main target') + T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(18,15,3360),'Every full, copied-query and whole-idle event') + need(sum(T.values())==10928 and sum(P.values())==64620,'Complete new productive/call counts') + need((sum(r*n for r,n in T.items()),sum(r*n for r,n in P.items()))==(239886,239134),'Preserve the exact surplus 752') + # Independent substitution into the source invoice must give the same ledger. + oldH={5:28,6:18,7:56,8:93,9:213};oldP={1:2487,2:713,3:224,4:102,5:20,8:8} + ref=word['invoice'] + for key,new,old_unit,new_unit in [('targets',T,oldH,H),('paid',P,oldP,N)]: + check=Counter({int(k):v for k,v in ref[key].items()}) + check.subtract({k:18*v for k,v in old_unit.items()});check.update({k:18*v for k,v in new_unit.items()}) + need(+check==new,'Literal event count equals whole-call substitution: '+key) + E=S.C.load(ROOT/'research/higher-moment-strictification/verify.py','combined_exact_intervals') + print('CHECK_EXACT_CEILING',flush=True) + root=ceiling(E,T,P) + print('PASS_EXACT_CEILING',flush=True) + # A finite interval proof of a uniform strict local moment improvement. + coefficients={1:17,2:126,3:-50,4:-42,5:2,7:-22,8:5,9:17} + prior_native=read(ROOT/'research/missing-join-frame/NATIVE.json.gz') + actual=Counter(H);actual.subtract(N) + actual.subtract({int(k):v for k,v in prior_native['helpers'].items()}) + actual.update({int(k):v for k,v in prior_native['paid'].items()}) + need({k:v for k,v in actual.items() if v}==coefficients,'Uniform gain is the actual source-bound profile difference') + need(sum(r*n for r,n in coefficients.items())==0,'Local gain vanishes at t=1') + derivative_upper=None + for i in range(128): + l,r=Q(i,128),Q(i+1,128) + bound=Q(0) + for rank,n in coefficients.items(): + product=E.mul(E.power(rank,r if n>0 else l),E.log_bounds(rank)) + bound+=n*product[1 if n>0 else 0] + derivative_upper=bound if derivative_upper is None else max(derivative_upper,bound) + need(derivative_upper<0,'Joint local moment gain for every 0ph and max(tl,target[0])<=min(th,target[1]),'Independent exact raw-moment engine') + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + alpha_gap=Q(1,1000000000);g,d=Q(97,100),Q(97,100) + need(alpha[1]<1-alpha_gap and gamma[1]theta**power,'Shifted exit and complement capacity') + need(E.power(145,v*TESTED)[1]<2**power,'Initial compiler range') + gap=(TESTED-KAPPA)/7;need(gap.numerator==1,'Integer compiler grid') + step=gap.denominator + def passes(j):return (step*j+1)**power<2**j + lo,hi=1,2 + while not passes(hi):lo,hi=hi,2*hi + while hi-lo>1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + height=step*hi + need(height>8*v and passes(hi) and not passes(hi-1),'Effective uniform rank integer inequality') + # The changed local list is charged under an explicit larger fixed bound. + local_scalar=max(x['real_scalar_allowance'] for x in local['native'].values()) + local_routes=(sum(N.values())+2*408+688)*1000 + need(local_scalar+local_routes<10**7,'Every new local scalar and monomial route fits') + scalar_upper=18*10**7+15*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program']) for k in ('left','right'))) + need(scalar_upper<10**9,'Retain the complete raw nonrecursive bound') + print('PASS_COMPLETION_AND_COMPILER',flush=True) + bit=source_query['ordinary_BIT'];atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']);need(atom==Q('.004') and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Complete stronger source BIT admission') + L=S.C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','combined_outer_ledger') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Complete outer predicate inventory') + need(all(x>0 for key in ('strict_checks','functional_checks') for x in outer[key].values()),'Every complete outer inequality') + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items() if x<=0] + need(failed,'Reject '+name);controls[name]=failed + return encode({'status':'PASS_CONDITIONAL_JOINT_HELPER_KAPPA_00302015', 'kappa':KAPPA,'kappa_decimal':'0.00302015', + 'source_inputs':count,'uniform_local_gain':local_gain,'source_heads':{'PR4447':'322e0ec764aa7ef7801383feb1f656e460dd8bed','PR4440':'40e22a83ed660d3d6074c4f2dbf14bfb621eee51','helper_retiming':'ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9','PR4441_combination':'5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39'}, + 'gain_over_PR4447':KAPPA-Q('.00300123'), 'gain_over_PR4441':KAPPA-Q('.00300105'), 'gain_over_PR4440':KAPPA-Q('.00296'),'gain_over_PR4416':KAPPA-Q('.00268647'), + 'targets':dict(sorted(T.items())),'paid':dict(sorted(P.items())),'full_calls':full,'query_shears':thin,'pairs':16,'prefix_pairs':7,'local_helpers':H,'local_paid':N, + 'paid_calls':sum(P.values()),'productive_fields':sum(T.values()),'fixed_profile_ceiling':root, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta), + 'limits':[1-alpha_gap,g,d],'normalized_paid_upper':bound}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'uniform_saving':params['complex_uniform_saving'], + 'gap':gap,'H':height,'N':'2^'+str(height),'integer_test_exponent':hi,'word_materialized':False}, + 'nonrecursive':{'local_scalar_allowance':local_scalar,'local_route_bound':local_routes,'raw_upper':scalar_upper,'raw_budget':10**9}, + 'ordinary_BIT':bit,'outer':outer,'negative_controls':controls, + 'scope':'Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.'}) + +if __name__=='__main__': + parser=argparse.ArgumentParser() + parser.add_argument('--write',action='store_true',help='Author arithmetic from pinned receipts; not a fresh native/dependency replay.') + parser.add_argument('--part',choices=('all','dependencies','native','arithmetic'),default='all') + args=parser.parse_args() + need(not args.write or args.part=='all','The authoring switch is separate from partial replay modes') + if args.part=='dependencies': + print(json.dumps(replay_dependencies(),sort_keys=True)) + elif args.part=='native': + authenticate();local=J.run() + need(json.loads(json.dumps(local))==read(HERE/'NATIVE.json.gz'),'Fresh complete native receipt') + print(json.dumps({'status':'PASS_JOINT_NATIVE_632_COLUMNS_BOTH_ORIENTATIONS','helpers':local['helpers'],'paid':local['paid'],'physical_pairs':len(local['new_physical_edges_and_boundaries'])},sort_keys=True)) + else: + result=run(execute_sources=args.part=='all' and not args.write) + if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:need(result==read(HERE/'RESULT.json'),'Exact combined arithmetic receipt') + keys=('status','kappa_decimal','gain_over_PR4447','compiler') + output={k:result[k] for k in keys} + if args.part=='arithmetic':output['replay_scope']='Arithmetic and p16 controller only; the registered native and dependency gates are separate required commands.' + print(json.dumps(output,sort_keys=True)) diff --git a/research/missing-join-frame/NATIVE.json.gz b/research/missing-join-frame/NATIVE.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..2f41b11d02726a60da449aaa6c603716c0310ead GIT binary patch literal 1462 zcmV;n1xflJiwFP!00002|LvR4bE7sC$M5+oGMs%t5@5Txbf?p1C!2KY?WH>zjSM1D zgMkVhC$p3Py-(P|faDk)XYFjbc+lfX=*L%|CkyfYRPvJZE25YlSBGsmEr3Gvk)}WHa*ez4ntE;E-aWnQnp<>BQK>s9CJ;15m z3==tH5ltlz#RH8Hcv#3AmyfVgCIYyfgd*bgDl1=jx>Knx29t}b7NW+?san)nBb!t# zYQP=4Vo(D;(%MqgM6&pf&REfXE*_V;EXko6na?67DT|_H!D3%k7`Y?ljY_wbM=05h zXVkyt{+&Mh8TXSoppnSAWKq4<$WPpTCI61#Y_~| z&251EfsowKMG~vwDwSS!cw~X_L4!ODg)cx`8D-F@*z`kqhXH3Y^vreaoyUD^p<5s|4?#H zRlR8f<*6wMAPLe$KnKrQ4nvUX{a*#jG?6k{z=K4b&hyp7>P%5HS!6|Nls~Xp8Wn|p zyRJCI{AMXOP+ksDp+JOOwK!r~UiMDe_f5SfQrrMRA{wxqtt)|Xbz*NMg^?8|T9|lY zB8Gt(4QkYtVI;>hUrs9C7U1w51`RZ}$K#Gs!|4pvfSL8lBLUQ)MQuMx6Z&pT?JeqFk!w~v{CuA@A-;p=>5*a08a z0_2upw~|OHg?JTwLG@~31tz#ic_U01{t7L_3J>#!O<6?@qNM*gjR;bNjX}d;AIMNk zU)OI#gvup^C71$Pn>IL2!>DOMUeiKI)8c8xAUtlGu&b4XUTjJdh8fT6ZvwCn-X6d#m#L;>F!WPO)03mK`-JH; zFKSxL7wt>FJEMMkHfOsc`o(vT;vU5ZKrz~bM~~wD%J*HOxW$^=8{@{3yS55n%>w6O zYi_btW%$@YuS;4VVQ<`O%Vg9&X6WI-J~Zjk4*LxUK)v%?)Z^|eX4HK%eES4IuMn@} zY$vpV>xAg&bM$Td(RSDyAljPtWVlJhs59^NIZN>N!O`2S2QR&3Jao2}3{O9r)prl& z9?I_)%IGb&Lbgu;@?oJoB70kezf&l;ScebS?>AmphvOf$4kv>n*@1b@tl5sdR{uV| z9XD9I5n%twC*8?+3_C9P?TL@yVtX9zllX>rjRul&?MzD2~lb{%`St#Ohmx Qlc$sa0fn9AIsH2T0P2?3WB>pF literal 0 HcmV?d00001 diff --git a/research/missing-join-frame/PATCH.json b/research/missing-join-frame/PATCH.json new file mode 100644 index 0000000000..f96d295d40 --- /dev/null +++ b/research/missing-join-frame/PATCH.json @@ -0,0 +1,24 @@ +{ + "phase": "B", + "ordinal": 480, + "old_frame": 732, + "new_basis": [ + 168, + 336, + 45 + ], + "old_basis": [ + 258, + 133, + 82, + 45 + ], + "incoming_frames": [ + 364, + 360 + ], + "outgoing_frames": [ + 736, + 692 + ] +} diff --git a/research/missing-join-frame/PROOF.md b/research/missing-join-frame/PROOF.md new file mode 100644 index 0000000000..d240cd8e14 --- /dev/null +++ b/research/missing-join-frame/PROOF.md @@ -0,0 +1,121 @@ +# One missing contact span and its conditional endpoint + +This is an author-checked conditional construction with declared saving +**kappa = 0.00300123**. It retains every native, arbitrary-column, owned-erasure, +whole-job matching, finite compiler, tape, precision, analytic, prime and recovery +premise of PR4440 and PR4441. It does not change the selected record or establish +an unconditional multiplication theorem. The increment is small; the concrete +new search lever is closure of the frame catalog under spans and intersections. + +## The actual changed contact + +Start at PR4441 head `5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39` and retain its +117 helper entrances, 42 exits and 395 scalar retimings. At persistent scalar +contact B/480, the forward gate is ADD(L90,L253,+1); the inverse-transpose gate +is the source's corresponding backward ADD. Both currently use frame 732, +with basis [258,133,82,45] of dimension four. + +The two incoming frames have bases [336,45] and [133,45], each of dimension +two. Their span has basis [168,336,45], dimension three. The equality +168 XOR 45 = 133 verifies the non-obvious inclusion. This three-space is absent +from the frozen 1,159-label catalog. It is contained in both outgoing spaces, +whose dimensions are five and seven. PATCH.json pins all four neighboring +labels, the old basis, and the exact phase/ordinal of the changed gate. + +Adjoin the three-space as frame 1159 and retime that single common-frame scalar +gate in both orientations. Use the source synthesizer to regenerate every +chronological climb. Every source nesting predicate remains in force. No scalar +coefficient/order, warp, center, main boundary or helper boundary changes. + +For frame operators C_a,C_b the physical transport is C_b C_a^-1. A common-frame +scalar gate preserves its logical row for arbitrary inputs, independently of +which common C is used. Thus the source retiming lemma applies. native_join.py +replays both words with two source interpreters and compares every one of the +632 independent arbitrary persistent input columns, retaining the independently +owned C0 input and its zero return. All four new transport operators are freshly +lowered and independently decoded in both orientations, checking their Pauli +tableaux and absolute phases. Their monomial factors are charged as fixed +routes; no assumption that the two factors are inverses is made. + +## A strict improvement for every exponent + +The four incident paid ranks change from [2,2,1,3] to [1,1,2,4]. Rank mass, +number of paid calls and all independent helper outputs remain unchanged. +For 0 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "348599999253/350000000000", + "fixed_halo_explicit_metadata_branch": "26950000001/350000000", + "new_BIT_row_stock_sublinear_in_active_group": "1395799997009/1400000000000", + "new_semantic_group_guard": "3/1400000000" + }, + "margins": { + "boundary_algebraic_matrix": "235296655831931/78400000000000000", + "fused_gaussian": "235296655495793/78400000000000000", + "global_coordinate_router": "2100863/700000000", + "group_bit_router": "2941208893697411/980000000000000000", + "group_scans": "699999999/700000000", + "main_transform": "235296599831931/78400000000000000", + "microbox_face_corrections": "26950000001/350000000", + "polynomial_products": "1399999999/1400000000", + "sparse_union_movement": "32085296655831931/78400000000000000" + }, + "parameters": { + "a": "2100863/700000000", + "b": "4201727/1400000000", + "beta": "1399999997/1400000000", + "bit_saving": "17/5000", + "cap_xi": "71285296599831931/78400000000000000", + "complex_uniform_saving": "16413/5468750", + "d": "1/1400000000", + "epsilon": "1399999999/1400000000", + "kappa": "300123/100000000", + "lambda_": "398799507/400000000", + "lambda_prime": "55831931/56000000", + "layout": "1/1400000000", + "q": "168069/56000000", + "r0": "1/14000000000", + "stop": "1/1400000000", + "tested_saving": "600247/200000000" + }, + "strict_checks": { + "actual_bit_above_effective": "279137/700000000", + "actual_logarithmic_gamma_guard": "1/1400000000", + "actual_logarithmic_group_guard": "7114703484168069/39200000000000000", + "alpha_logarithm_absorption": "1/14000000000", + "boundary_algebraic_matrix_above_kappa": "223831931/78400000000000000", + "cap_above_band": "32085296599831931/78400000000000000", + "cap_below_cell": "7114703344168069/78400000000000000", + "cap_below_phase_cell_power": "85514703400168069/78400000000000000", + "complex_above_effective": "1/1400000000", + "complex_below_one_over_32": "39548273/1400000000", + "complex_endpoint": "1/700000000", + "epsilon_below_one": "1/1400000000", + "epsilon_positive": "1399999999/1400000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "223495793/78400000000000000", + "gaussian_above_main": "27831931/39200000000000000", + "global_coordinate_router_above_kappa": "1/350000000", + "global_gamma_power_slack": "9/14000000000", + "group_below_dimension": "1/700000000", + "group_bit_router_above_kappa": "3493697411/980000000000000000", + "group_gauge_power_slack": "7114703481368069/39200000000000000", + "group_key_fits_record": "1/700000000", + "group_positive": "1399999997/1400000000", + "group_scans_above_kappa": "348949569/350000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "635129790400418148631/500000000000000000000000", + "lambda_above_internal": "1/2800000000", + "lambda_above_sigma": "3/2800000000", + "lambda_above_tau": "1/2800000000", + "lambda_prime_above_lambda": "1/2800000000", + "lambda_prime_above_leaf": "2795798273/1960000000000000000", + "leaf_saving_above_effective": "1395798273/1960000000000000000", + "main_transform_above_kappa": "167831931/78400000000000000", + "membership_arithmetic_fits_record": "1/1400000000", + "microbox_face_corrections_above_kappa": "53897899141/700000000", + "microbox_halo_volume": "110600000003/1400000000", + "new_complex_uniform_saving_above_b": "1/1400000000", + "new_semantic_guard_with_C1_one": "1/1400000000", + "polynomial_products_above_kappa": "1395798277/1400000000", + "positive_layout_slack": "1/1400000000", + "q_below_effective": "1/1400000000", + "q_below_internal": "1/1400000000", + "q_below_leaf": "2795798273/1960000000000000000", + "q_positive": "168069/56000000", + "short_record_fallback": "1395798273/1400000000", + "source_axis_superpolynomial": "1/1400000000", + "sparse_union_movement_above_kappa": "31850000223831931/78400000000000000", + "stop_below_one": "1399999999/1400000000", + "stop_positive": "1/1400000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/1400000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/1400000000", + "union_tag_work_per_visit_fits_record": "3/1400000000" + } + }, + "paid": { + "1": 44618, + "16": 448, + "2": 9766, + "24": 448, + "3": 8436, + "32": 448, + "4": 1957, + "40": 448, + "48": 448, + "5": 760, + "56": 448, + "64": 448, + "72": 448, + "8": 152 + }, + "paid_calls": 69273, + "productive_fields": 11560, + "query_shears": 16, + "scope": "Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.", + "source_heads": { + "PR4440": "40e22a83ed660d3d6074c4f2dbf14bfb621eee51", + "PR4441_combination": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39", + "helper_retiming": "ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9" + }, + "source_inputs": 46, + "status": "PASS_CONDITIONAL_MISSING_JOIN_KAPPA_00300123", + "strictification": { + "alpha": { + "lower": "0.999999995876754782344502280335", + "upper": "0.999999995876754782344502280336" + }, + "cutoff": 20, + "delta": { + "lower": "0.932537504513523310068879094384", + "upper": "0.932537504513523310068879094385" + }, + "floor": 21, + "gamma": { + "lower": "0.969136675521053502676120887993", + "upper": "0.969136675521053502676120887994" + }, + "limits": [ + "999999999/1000000000", + "97/100", + "19/20" + ], + "normalized_paid_upper": "2097152001953127/2097154147483648", + "power": 1024, + "tail_offset": "1/5", + "tested": "600247/200000000" + }, + "targets": { + "153": 224, + "17": 448, + "25": 448, + "33": 448, + "4": 494, + "41": 448, + "49": 448, + "5": 38, + "57": 448, + "65": 448, + "7": 551, + "73": 448, + "8": 798, + "9": 5871 + } +} diff --git a/research/missing-join-frame/SOURCES.json b/research/missing-join-frame/SOURCES.json new file mode 100644 index 0000000000..27681f1015 --- /dev/null +++ b/research/missing-join-frame/SOURCES.json @@ -0,0 +1,294 @@ +{ + "schema_version": 1, + "base_commit": "40f307e835b9a61e1b998bb17bd99d8c6b879a96", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "research/fresh-helper-boundary/ARITHMETIC-RESULT.json", + "usage": "input", + "git_blob": "686c36fb19680db327f797ebdfe612487d8c53f8", + "sha256": "5d25fec9ac4b036c93846a50dccfa4af030e2982f5cec02e28702193bf157cf7" + }, + { + "path": "research/fresh-helper-boundary/CHANGES.json", + "usage": "input", + "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9", + "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624" + }, + { + "path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz", + "usage": "input", + "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152", + "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839" + }, + { + "path": "research/fresh-helper-boundary/RESULT.json", + "usage": "input", + "git_blob": "e26608e20be115d28f8853a8c1a12bebfc8e8ec3", + "sha256": "34163eeeef1cd712de457d7fd3b0435f98a12ac456b82256b078f33225456fbd" + }, + { + "path": "research/fresh-helper-boundary/SOURCES.json", + "usage": "input", + "git_blob": "0b40275502f4263a19905f4fb50e346a3629c712", + "sha256": "01998e9b86222d10811fc0114dcd5c946ff9e95025a7cacd00e67a3eefe543d0" + }, + { + "path": "research/fresh-helper-boundary/arithmetic.py", + "usage": "input", + "git_blob": "4822f04ae09d84a16e8fa8656a533e23fd4068f0", + "sha256": "212bae96d0ddcbc25076afe2589a47736c66b77420057f28c44c937ad087fc07" + }, + { + "path": "research/fresh-helper-boundary/native.py", + "usage": "input", + "git_blob": "1b36f6cb5f205c33bf48811e0b1b3621c55e8154", + "sha256": "9b55a2d3c3972148fae9d112e745d9244968166bd89bd900c938f429fc76ab29" + }, + { + "path": "research/fresh-helper-boundary/verify.py", + "usage": "input", + "git_blob": "e434dbf7c68afa0390a307fd15f32348b0e87207", + "sha256": "4c18851214400cf955e10565d89357029d9e765140233831472ce23f0c3ee7bf" + }, + { + "path": "research/fresh-helper-thinned/PROOF.md", + "usage": "input", + "git_blob": "bf68dc2b987cb7de6431ff5e3514b60af48720a5", + "sha256": "9883b3329fef7624d3471e27bb55258cd9dc18bb6d37779a3939de99add87347" + }, + { + "path": "research/fresh-helper-thinned/README.md", + "usage": "input", + "git_blob": "344616d6654a96085dd45cf2c3189ef283deeac1", + "sha256": "70c1c872c2327c3f71918e218d5f1ecb7a00037771a5dd1b8ae415b84cc90dc2" + }, + { + "path": "research/fresh-helper-thinned/RESULT.json", + "usage": "input", + "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55", + "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21" + }, + { + "path": "research/fresh-helper-thinned/SOURCES.json", + "usage": "input", + "git_blob": "4089ad37114540b23846596e2a641c4a4bd608e2", + "sha256": "5aec5df5096ee8a3e90618d311640b4bdfba42be5bc4bc5fab55e8be858ab2cb" + }, + { + "path": "research/fresh-helper-thinned/verify.py", + "usage": "input", + "git_blob": "9ba85a59aa5dcc5cdaec85ee18607cb050530c55", + "sha256": "c841265ccee9b6f79045ad818ce9d27cfd7ee1f60047525a75d491f0dd8b997a" + }, + { + "path": "research/higher-moment-strictification/README.md", + "usage": "input", + "git_blob": "0a736ca89e1eafb73a30e1f2589cc45e6b5f76c3", + "sha256": "ebe80b68ff026ce90f71f274c31744f4c0b36132d15ebb7e39cf2d5df4df270d" + }, + { + "path": "research/higher-moment-strictification/verify.py", + "usage": "input", + "git_blob": "4b24a5096154736ce060474eb8c72dc64c303699", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py", + "usage": "input", + "git_blob": "8b40135a84e7f0f0cd44bed69655801310b916a7", + "sha256": "8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85" + }, + { + "path": "research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json", + "usage": "input", + "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + { + "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py", + "usage": "input", + "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb", + "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7" + }, + { + "path": "research/kappa-function-composition/complex/prune_native.py", + "usage": "input", + "git_blob": "8c3e11b2408fa96eefa3ebe7952d1b11b90b772b", + "sha256": "f2b37c183a10922eabc8e0436b426a08866430e96bd0adc7e178951c7fbb5257" + }, + { + "path": "research/kappa-rebuild/architecture/mixed_target_probe.py", + "usage": "input", + "git_blob": "4fc05ab08138218ba9f09e5c89b649afae7c914e", + "sha256": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a" + }, + { + "path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json", + "usage": "input", + "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a", + "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef" + }, + { + "path": "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json", + "usage": "input", + "git_blob": "e8c5e4f077fea0bef355e6c3013c7f252d3606cf", + "sha256": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0" + }, + { + "path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md", + "usage": "input", + "git_blob": "a58774e237c9362869a60a22bda35be09fb85872", + "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443" + }, + { + "path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json", + "usage": "input", + "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d", + "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf" + }, + { + "path": "research/kappa-rebuild/bit/bit_native_binding.py", + "usage": "input", + "git_blob": "f4c4082d89969ea311219d9af8013082d599f6f1", + "sha256": "bf6374225f388e7531fa6475cc255bd430100ff62c38d582c41601f0739de7b7" + }, + { + "path": "research/kappa-rebuild/bit/complex_controller_factor.py", + "usage": "input", + "git_blob": "cb0cff7c8be5f38f2ee52201d9d0907f9dfd7947", + "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497" + }, + { + "path": "research/kappa-rebuild/bit/mixed_productive_bit.py", + "usage": "input", + "git_blob": "9c7a8bd5d3ae4c19952648c815031858d6627b96", + "sha256": "b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e" + }, + { + "path": "research/kappa-rebuild/complex/FULL-IDENTITY.md", + "usage": "input", + "git_blob": "f97a23d7d21bd7f79c9d0cb14d8c6b44fddd3f23", + "sha256": "c4aa88c4943ef041e9542c519b7600ecf26ed6caff92558fdb07ac88ace64c17" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json", + "usage": "input", + "git_blob": "c6edcbdc43bf36bb11201235027d0ec170d07fc8", + "sha256": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz", + "usage": "input", + "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784", + "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61" + }, + { + "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz", + "usage": "input", + "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c", + "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39" + }, + { + "path": "research/kappa-rebuild/complex/native_extensions.py", + "usage": "input", + "git_blob": "7f84894efc309546a903d314c7ac1473e7f594a8", + "sha256": "50ad007d9c386393657e86c99a96ae0a63a8fbc52872579b185002cc626e88e3" + }, + { + "path": "research/kappa-rebuild/complex/power_two_balance.py", + "usage": "input", + "git_blob": "a55ae0ce78a1861965f899a82604b276260f636c", + "sha256": "76929bb3887911ccf100c4593574b8a1c82ee64e96f939a8aca196869438b424" + }, + { + "path": "research/kappa-rebuild/complex/rebuild_native.py", + "usage": "input", + "git_blob": "78a7b1b0e6e43a1347fb361f45c6e0eaff8dd27b", + "sha256": "f94c527cc02215de49350d477618188c4c0da48bc8fb05b4e37b24c482cad7d5" + }, + { + "path": "research/kappa-rebuild/transfer-audit/p3_native_audit.py", + "usage": "input", + "git_blob": "0f3a4067a4b4e20d0e6ca0f84f41851c5168f76d", + "sha256": "5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902" + }, + { + "path": "research/pr4359-p7-padding/P7-FACTOR.json", + "usage": "input", + "git_blob": "04c7ef620e760cc8f1764bbf0ccd7f32c6a5bd86", + "sha256": "6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598" + }, + { + "path": "research/pr4359-p7-padding/TENSOR.md", + "usage": "input", + "git_blob": "8ecfd3e4d0bcb449ecb1e150c4f1f4fbb39ca656", + "sha256": "b2eba86cb979b4dc2a045f2e74bbd29e4d9e5ec87d6a2bc23ba7b54f1f58e3e3" + }, + { + "path": "research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py", + "usage": "input", + "git_blob": "340e1f0ffb8a1a9c38fbbd9119580b6d23e01b59", + "sha256": "d097e55f06c3f244f2074ffd7c1a0a5f3c4b4b6a6accf9619d1dde5c0ae85e15" + }, + { + "path": "research/pr4359-p7-padding/native_inventory.py", + "usage": "input", + "git_blob": "8d2d96e3998254c2333c43fe47cdfd074cbd811e", + "sha256": "65539acaf45bdfe8c5aee6830f9c9b3d1107c442a60842ef803fdd7688de8f32" + }, + { + "path": "research/query-thinned-controllers/BIT-CONTROLLER.json", + "usage": "input", + "git_blob": "89c400d5970024b3debe870c36ce43889beed001", + "sha256": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d" + }, + { + "path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json", + "usage": "input", + "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9", + "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088" + }, + { + "path": "research/query-thinned-controllers/RESULT.json", + "usage": "input", + "git_blob": "e0695152c98d727edfd0d2034b58a1c7e8682c0c", + "sha256": "6ebfc8c0f09166f4834e9d7427410cb31aefff2cd4d4ce588c8e52c9c70e9a0f" + }, + { + "path": "research/query-thinned-controllers/SOURCES.json", + "usage": "input", + "git_blob": "0f061c87ff87c43ff1ea0fc418582e9ccea3bc1d", + "sha256": "74b73563d9f78a4562d376b6f33528d652e41097f65747667f112a3e1fa81d29" + }, + { + "path": "research/query-thinned-controllers/controller.py", + "usage": "input", + "git_blob": "d4557e08cfb9fe57cc1ae4024705a72dc95f3583", + "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2" + }, + { + "path": "research/query-thinned-controllers/verify.py", + "usage": "input", + "git_blob": "f1114036fff66f57014e5c1256141fb78ff4c4a9", + "sha256": "07dea601d6bbaa4d90e576f20c8607c37fb01e8778c798d919fa9df435049950" + }, + { + "path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + ] +} diff --git a/research/missing-join-frame/TASK.json b/research/missing-join-frame/TASK.json new file mode 100644 index 0000000000..014ccd44af --- /dev/null +++ b/research/missing-join-frame/TASK.json @@ -0,0 +1,73 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "priority_revision": 7, + "base_commit": "40f307e835b9a61e1b998bb17bd99d8c6b879a96", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json", + "research/selected-k8-unrestricted-ends/README.md" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.", + "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "scope_status": "changed", + "actual_scope": "Adjoin the missing incoming span at scalar B/480, replay both exact native words and carry the complete p17 invoice to conditional kappa 0.00300123.", + "scope_change_reason": "Explicit user assignment to push kappa. A new catalog label improves the audited #4441 supplier; no universal escape from older frame models is claimed.", + "bottleneck_link": "The finite catalog omits the three-dimensional span of two actual incoming frames, leaving a four-dimensional contact whose rank moment is strictly worse for every 00 and margin(ROOT_HIGH)[1]<0,'New complete profile root bracket') + derivative=None + for i in range(16): + l,r=Q(i,320),Q(i+1,320);low=Q(0) + for rank,n in signed.items(): + term=E.mul(E.power(rank,1-r if n>0 else 1-l),E.log_bounds(rank)) + low+=n*term[0 if n>0 else 1] + derivative=low if derivative is None else min(derivative,low) + upper=None + for i in range(128): + l,r=Q(1,20)+Q(19*i,2560),Q(1,20)+Q(19*(i+1),2560) + hi=sum(n*E.power(rank,1-l if n>0 else 1-r)[1 if n>0 else 0] for rank,n in signed.items()) + upper=hi if upper is None else max(hi,upper) + need(derivative>0 and upper<0,'Fixed-profile ceiling for every real 00,'No nonzero charge for erased idle stage') + P[rank]+=224;idle+=224 + for term in word['diagonal']: + need(term[0] in (-1,1) and all(x in (0,1) for x in term[1:]),'Actual normalized main target') + T[1+8*sum(term[1:])]+=112 + need((full,thin,idle)==(19,16,3584),'Every full, copied-query and whole-idle event') + need(sum(T.values())==11560 and sum(P.values())==69273,'Complete new productive/call counts') + need((sum(r*n for r,n in T.items()),sum(r*n for r,n in P.items()))==(260798,259998),'Preserve the exact surplus 800') + # Independent substitution into the source invoice must give the same ledger. + oldH={5:28,6:18,7:56,8:93,9:213};oldP={1:2487,2:713,3:224,4:102,5:20,8:8} + ref=source_query['complex_invoice'] + for key,new,old_unit,new_unit in [('targets',T,oldH,H),('paid',P,oldP,N)]: + check=Counter({int(k):v for k,v in ref[key].items()}) + check.subtract({k:19*v for k,v in old_unit.items()});check.update({k:19*v for k,v in new_unit.items()}) + need(+check==new,'Literal event count equals whole-call substitution: '+key) + E=S.C.load(ROOT/'research/higher-moment-strictification/verify.py','combined_exact_intervals') + root=ceiling(E,T,P) + t,u,v,c,b=1-TESTED,Q(1,5),1024,20,21 + target=E.moment(T,t);alpha=E.divide(E.moment(P,t),target) + other=S.C.load(ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','combined_separate_intervals') + tl,th=other.moment(T,TESTED);pl,ph=other.moment(P,TESTED) + need(tl>ph and max(tl,target[0])<=min(th,target[1]),'Independent exact raw-moment engine') + gamma=E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta=E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + alpha_gap=Q(1,1000000000);g,d=Q(97,100),Q(19,20) + need(alpha[1]<1-alpha_gap and gamma[1]Q(31,32),'The previous gamma limit fails and is explicitly replaced') + # Apply PR4433's general logarithmic majorant at the actual new ambient rank. + theta,power=Q(63,64),1000 + eta=E.scale(E.power(153,-v*TESTED),t) + need(2*(20**v)**64<=(153**v)**63 and eta[0]>theta**power,'Shifted exit and complement capacity') + need(E.power(153,v*TESTED)[1]<2**power,'Initial compiler range') + gap=(TESTED-KAPPA)/7;need(gap.numerator==1,'Integer compiler grid') + step=gap.denominator + def passes(j):return (step*j+1)**power<2**j + lo,hi=1,2 + while not passes(hi):lo,hi=hi,2*hi + while hi-lo>1: + mid=(lo+hi)//2 + if passes(mid):hi=mid + else:lo=mid + height=step*hi + need(height>8*v and passes(hi) and not passes(hi-1),'Effective uniform rank integer inequality') + # The changed local list is charged under an explicit larger fixed bound. + local_scalar=max(x['real_scalar_allowance'] for x in local['native'].values()) + local_routes=(sum(N.values())+2*408+688)*1000 + need(local_scalar+local_routes<10**7,'Every new local scalar and monomial route fits') + scalar_upper=19*10**7+16*1792+32*112*(len(word['physical_events'])+sum(len(word['boundaries'][k+'_program']) for k in ('left','right'))) + need(scalar_upper<10**9,'Retain the complete raw nonrecursive bound') + bit=source_query['ordinary_BIT'];atom=Q(bit['atom']);ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']);need(atom==Q('.004') and atom>ordinary>admitted>TESTED and atom<1-ordinary,'Complete stronger source BIT admission') + L=S.C.load(ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','combined_outer_ledger') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=L.ledger(params);outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + need(len(outer['strict_checks'])==54 and len(outer['functional_checks'])==4,'Complete outer predicate inventory') + need(all(x>0 for key in ('strict_checks','functional_checks') for x in outer[key].values()),'Every complete outer inequality') + controls={} + for name,patch in [('old_BIT',{'bit_saving':Q('.0027')}),('closed_uniform',{'complex_uniform_saving':params['b']}),('unfunded_endpoint',{'kappa':TESTED}),('closed_epsilon',{'epsilon':Q(1)})]: + bad=L.ledger(dict(params,**patch));failed=[k for k,x in bad['strict_checks'].items() if x<=0] + need(failed,'Reject '+name);controls[name]=failed + return encode({'status':'PASS_CONDITIONAL_MISSING_JOIN_KAPPA_00300123', 'kappa':KAPPA,'kappa_decimal':'0.00300123', + 'source_inputs':count,'source_heads':{'PR4440':'40e22a83ed660d3d6074c4f2dbf14bfb621eee51','helper_retiming':'ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9','PR4441_combination':'5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39'}, + 'gain_over_PR4441':KAPPA-Q('.00300105'), 'gain_over_PR4440':KAPPA-Q('.00296'),'gain_over_PR4416':KAPPA-Q('.00268647'), + 'targets':dict(sorted(T.items())),'paid':dict(sorted(P.items())),'full_calls':full,'query_shears':thin, + 'paid_calls':sum(P.values()),'productive_fields':sum(T.values()),'fixed_profile_ceiling':root, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta), + 'limits':[1-alpha_gap,g,d],'normalized_paid_upper':bound}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'uniform_saving':params['complex_uniform_saving'], + 'gap':gap,'H':height,'N':'2^'+str(height),'integer_test_exponent':hi,'word_materialized':False}, + 'nonrecursive':{'local_scalar_allowance':local_scalar,'local_route_bound':local_routes,'raw_upper':scalar_upper,'raw_budget':10**9}, + 'ordinary_BIT':bit,'outer':outer,'negative_controls':controls, + 'scope':'Author-checked conditional construction; retained native/all-column, owned-erasure, whole-job, analytic, precision, tape, prime and recovery contracts. No selected promotion or formal/human acceptance.'}) + +if __name__=='__main__': + parser=argparse.ArgumentParser() + parser.add_argument('--write',action='store_true',help='Author the new arithmetic receipt from already-audited dependency receipts; normal replay freshly reruns both dependencies.') + args=parser.parse_args();result=run(execute_sources=not args.write) + if args.write:(HERE/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else:need(result==read(HERE/'RESULT.json'),'Exact combined receipt replay') + print(json.dumps({k:result[k] for k in ('status','kappa_decimal','gain_over_PR4441','compiler')},sort_keys=True)) From 4cf054a50c5718616594ec4ca2c9114278120a8b Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 20:44:07 -0400 Subject: [PATCH 23/26] Exclude inherited shared-doc edits from the rank compiler PR --- docs/ci-verification.md | 12 ------------ docs/research/current-status.md | 6 ++---- 2 files changed, 2 insertions(+), 16 deletions(-) diff --git a/docs/ci-verification.md b/docs/ci-verification.md index 50e8120dc0..582e416aaf 100644 --- a/docs/ci-verification.md +++ b/docs/ci-verification.md @@ -2,18 +2,6 @@ ## Current selected-family replay -Resolve the [selected record](../certificates/selected-result.json) before -running a historical checkpoint. The current cold replay is -`make frontier4359-verify`, using the -[proof review](research/pr-intake-evidence/pr4359/PROOF-REVIEW.md), -[validation](research/pr-intake-evidence/pr4359/VALIDATION.json) and -[source manifest](../certificates/frontier4359-source.json). -The [frontier4359 workflow](../.github/workflows/frontier4359.yml) provides -hosted replay evidence. Metadata and source-pin checks are separate from -operator replay and do not discharge the inherited theorem assumptions. - -## Historical frontier1094 replay - Start with the [selected record](../certificates/selected-result.json). Its `reproduce`, `review`, `source_manifest` and `validation` fields identify the replay command, scoped assessment, source bindings and integration evidence. diff --git a/docs/research/current-status.md b/docs/research/current-status.md index 532af84312..62a8cbb097 100644 --- a/docs/research/current-status.md +++ b/docs/research/current-status.md @@ -1,14 +1,12 @@ # Current reviewed status -Selected conditional κ: **0.0023** (= 23/10000), zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. +Selected conditional κ: **0.0023 = 23/10000**, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage. [Selected record](../../certificates/selected-result.json) · [Proof review](pr-intake-evidence/pr4359/PROOF-REVIEW.md) · [Integration receipt](pr-intake-evidence/pr4359/INTEGRATION.json) · [Contributors](community-productive4359-contributors.md). Cold replay: `make frontier4359-verify`. The fresh 23-stage replay and 59 normalized artifacts pass; the changed interfaces have an AI-assisted proof review under retained analytic/native/fixed-tape hypotheses. Winning uniform templates are not materialized. This is not a complete formal or independent human verification. #4404 independently checks a narrower arithmetic/flow scope. -All sections below are a historical snapshot; the selected-result.json record above is authoritative. - -## Historical checkpoint through #1094 +## Historical selected status through #1094 Historical selected conditional κ: **0.001672660197076918**, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555. From 527dc558072f0336b3b0b8023fd972f0af398d15 Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 20:52:46 -0400 Subject: [PATCH 24/26] Prove padding-free adaptive rank compiler (199x smaller exponent) --- research/rank-convergence/BENCHMARKS.json | 164 ++++++ research/rank-convergence/PROOF.md | 430 ++++++++++++++++ research/rank-convergence/README.md | 177 +++++++ research/rank-convergence/RESULT.json | 467 ++++++++++++++++++ research/rank-convergence/SOURCES.json | 109 ++++ research/rank-convergence/TASK.json | 137 +++++ research/rank-convergence/VALIDATION.md | 41 ++ research/rank-convergence/VERIFY.json | 31 ++ research/rank-convergence/compiler.py | 174 +++++++ research/rank-convergence/flow.py | 141 ++++++ research/rank-convergence/intervals.py | 150 ++++++ research/rank-convergence/test_flow.py | 95 ++++ research/rank-convergence/test_independent.py | 140 ++++++ research/rank-convergence/verify.py | 175 +++++++ 14 files changed, 2431 insertions(+) create mode 100644 research/rank-convergence/BENCHMARKS.json create mode 100644 research/rank-convergence/PROOF.md create mode 100644 research/rank-convergence/README.md create mode 100644 research/rank-convergence/RESULT.json create mode 100644 research/rank-convergence/SOURCES.json create mode 100644 research/rank-convergence/TASK.json create mode 100644 research/rank-convergence/VALIDATION.md create mode 100644 research/rank-convergence/VERIFY.json create mode 100644 research/rank-convergence/compiler.py create mode 100644 research/rank-convergence/flow.py create mode 100644 research/rank-convergence/intervals.py create mode 100644 research/rank-convergence/test_flow.py create mode 100644 research/rank-convergence/test_independent.py create mode 100644 research/rank-convergence/verify.py diff --git a/research/rank-convergence/BENCHMARKS.json b/research/rank-convergence/BENCHMARKS.json new file mode 100644 index 0000000000..bc58c96abd --- /dev/null +++ b/research/rank-convergence/BENCHMARKS.json @@ -0,0 +1,164 @@ +{ + "schema_version": 1, + "cases": [ + { + "name": "p7", + "source": "research/higher-moment-strictification/RESULT.json", + "profile_key": "invoice_oracle", + "consumer_key": [ + "outer", + "ledger" + ], + "witness": { + "a": 1, + "b": 1, + "lambda": "1/10", + "mirror_slices": 20, + "t0": ".99731352", + "t_upper": ".997481", + "p": "1/10", + "c": "38", + "s": "1/10", + "height_base": 256, + "ell0": 100, + "guards": { + "U": ".961", + "V": ".903", + "Q": "1.001", + "d": "1.72", + "beta": ".321", + "eta": ".9845" + }, + "uniform_saving": "376107/140000000", + "kappa": ".00268647", + "H": 3040000000 + }, + "baseline": { + "source": "research/net-tax-rank-compiler/RESULT.json", + "path": [ + "examples", + "p7-net-shift-same-C", + "uniform" + ] + } + }, + { + "name": "native4453", + "source": "research/native-lattice-retiming/RESULT.json", + "profile_key": null, + "consumer_key": [ + "outer" + ], + "witness": { + "a": 1, + "b": 1, + "lambda": "1/10", + "mirror_slices": 20, + "t0": "29909963/30000000", + "t_upper": ".9971362", + "p": "2/5", + "c": "134", + "s": "1/20", + "height_base": 1024, + "ell0": 400, + "guards": { + "U": ".968", + "V": ".984", + "Q": "1.001", + "d": "1.02", + "beta": ".575", + "eta": ".982" + }, + "uniform_saving": "525213/175000000", + "kappa": ".00300120", + "H": 1300000000 + }, + "baseline": { + "source": "research/net-tax-rank-compiler/RESULT.json", + "path": [ + "examples", + "native-concentrated-balanced", + "uniform" + ] + } + }, + { + "name": "native4453-matched-uniform", + "source": "research/native-lattice-retiming/RESULT.json", + "profile_key": null, + "consumer_key": [ + "outer" + ], + "witness": { + "a": 1, + "b": 1, + "lambda": "1/10", + "mirror_slices": 20, + "t0": "29909963/30000000", + "t_upper": ".9971362", + "p": "2/5", + "c": "134", + "s": "1/20", + "height_base": 1024, + "ell0": 400, + "guards": { + "U": ".968", + "V": ".984", + "Q": "1.001", + "d": "1.02", + "beta": ".575", + "eta": ".982" + }, + "uniform_saving": "105043/35000000", + "kappa": ".00300120", + "H": 4300000000 + }, + "baseline": { + "source": "research/net-tax-rank-compiler/RESULT.json", + "path": [ + "examples", + "native-concentrated-balanced", + "uniform" + ] + } + }, + { + "name": "p16", + "source": "research/compact-joint-compiler/arithmetic/RESULT.json", + "profile_key": null, + "consumer_key": [ + "outer" + ], + "witness": { + "a": 1, + "b": 1, + "lambda": "1/10", + "mirror_slices": 20, + "t0": ".99697984", + "t_upper": ".997066", + "p": "2/5", + "c": "133", + "s": "1/20", + "height_base": 1024, + "ell0": 650, + "guards": { + "U": ".963", + "V": ".992", + "Q": "1.001", + "d": "1.03", + "beta": ".564", + "eta": ".982" + }, + "uniform_saving": "471898442219/156250001562500", + "kappa": ".00302015", + "H": 2800000000 + }, + "baseline": { + "source": "research/compact-joint-compiler/arithmetic/RESULT.json", + "path": [ + "compiler" + ] + } + } + ] +} diff --git a/research/rank-convergence/PROOF.md b/research/rank-convergence/PROOF.md new file mode 100644 index 0000000000..a3ece409d9 --- /dev/null +++ b/research/rank-convergence/PROOF.md @@ -0,0 +1,430 @@ +# Adaptive lockstep height and a shifted-logarithmic majorant + +This is a conditional finite compiler theorem. It changes the height of the +integer flow; it does not change the native productive/paid word, award new +productive credit, or assert its physical or analytic premises. A final +numerical witness must satisfy the directed inequalities below; exploratory +decimals alone are not a certificate. + +The finite integer/Pascal compiler is Jacob Alan Sussman's construction. +The capped overlapping-rank flow and its chronological interpretation are +zxv's PR4436. Ryanson Jonathan's corrected PR4459 supplies the mirror-window +identity and boundary-share method. PR4456, PR4465, PR4467 and PR4476 provide +independent finite checks and important warnings about the original height: +leaf exits need not be sublinear and their potential cannot be discarded. +The present argument changes that height, bounds root and leaf contributions, +and supplies the complete recurrence majorant. It does not repeat the +invalid assumption that the original flow's leaf ranks are uniformly o(n). +Substantial OpenAI Codex assistance, including separate mathematical agents; +new material is Apache-2.0. Source manifests retain predecessor authorship. + +## 1. Arbitrary-height finite flow + +Let W_k and P_r be positive integer target and chronological paid-rank +multiplicities of a fixed native unit. Assume + +``` +2 <= k_min <= k <= m=max(k), 1 <= r <= r_max < m. +``` + +The native contract, including the order of individual paid positions, is a +premise; two paid positions cannot be combined merely because ranks agree. +Fix an integer ambient rank n>=m and put C_n=floor(n/m). Choose any integer +G>=0. For a target multiindex alpha define + +``` +c(alpha)=product_k k^alpha_k, +u(alpha)=multinomial(|alpha|;alpha) product_k W_k^alpha_k. +``` + +For every paid-round path of length d<=G and multiplier rho, instantiate +u(alpha) units for every multiindex of degree G-d with + +``` +rho*c(alpha) <= C_n. +``` + +Each such unit has column multiplicity rho*c(alpha). At a paid position of +rank r, child demand at point gamma is the sum of W_k*u(gamma-e_k) over +eligible child units. The complete Pascal sum is u(gamma). Consequently +present parent supply dominates child demand. Match whole integer jobs; +retain excess parent supply as boundary exits, and supply demands with +absent parent points by distinct top input arrays. At depth G all paid +jobs are leaf exits. At the root all target demands are top sources. + +This is the same finite Pascal routing argument as PR4436. It does not +require G=floor(log_(k_min) C_n). In particular a root class may be empty +while later classes receive new top sources. These are finitely many +chronological classes with explicit fresh source endpoints. They do not +copy productive input data or obtain credit from a discarded request. +One may include empty classes in the finite schedule; a class and all its +exits return before the next suspended paid position resumes. + +Every source fits n: it is a target of an actual child or root unit of +column z<=n/m, hence has rank kz<=n. Every exit is an actual paid job of +rank rz<=r_max*n/mC_n, so its integer column is greater than n/m and +its source rank r*rho_parent*c(gamma)>n/m. **Only root sources lose this +lower bound when the height changes.** Root sources remain positive and +at most n; their complement jobs therefore have nonnegative rank below n. + +All recursive complement and exit ranks descend strictly. The original +integer batch-clearing construction, for example nested widths divisible +by all earlier widths, produces a finite uniform program. If S_s and E_e +are its source and exit inventories and its source count is positive, the +normalized paid-leaf recurrence is + +``` +L(n)=[sum_s S_s L(n-s)+sum_e E_e L(e)]/sum_s S_s. (1) +``` + +Below a chosen cutoff we may use the elementary L(n)=n construction. No +claims about small ranks need to be supplied by an empty adaptive flow. +The concrete profiles here have paid rank-one calls, which guarantee a +nonempty degree-zero leaf class at every height. More generally, the later +positive occupation bound guarantees nonempty flows in its certified range. + +## 2. Exact potentials and the height-independent mirror bound + +At a real exponent t in (0,1), put + +``` +T_t=sum_k W_k*k^t, P_t=sum_r P_r*r^t. +``` + +For one finite flow let H_t be the sum of column^t over all unit instances. +Let R_t and I_t be respectively root and nonroot source t-potentials; B_t +and F_t respectively boundary and leaf exit t-potentials. Matched jobs +cancel at their actual ranks, giving the exact identity + +``` +I_t+R_t = B_t+F_t+(T_t-P_t)H_t. (2) +``` + +Always + +``` +F_t <= P_t^(G+1). (3) +``` + +Indeed a capped leaf path is a subset of all paid paths of length G, +followed by one paid letter. Formula (3) is an upper bound; an exact +untruncated leaf law is not assumed. + +The mirror identity from corrected PR4459 remains valid at arbitrary G. +For a paid-prefix path rho of length dk, +``` + +and inner sources occur when + +``` +C_n/k < z <= C_n/r, k>r. +``` + +Both have rank rkz and coefficient P_r W_k. The complete Pascal expansion +accounts for multiplicities, including points with several eligible target +predecessors. These statements use the integer cutoff C_n, not an +inconsistent replacement of floor(n/m) by n/m at a boundary. + +Partition the positive z/C_n axis into intervals with endpoints 1/r and +1/k. On each interval J, let E_J(t) and S_J(t) be the sums of +P_r W_k(rk)^t whose respective windows contain J. If + +``` +E_J(t) <= beta S_J(t) for every elementary interval J, (4) +``` + +then B_t<=beta I_t for every n and every G. Intervals with S_J=0 must +also have E_J=0. This is a pointwise coefficient inequality against a +nonnegative base measure; no asymptotic distributional assumption enters. +A uniform interval certificate for (4) over all exponents used below is +required. A finite observed boundary share is insufficient. + +## 3. Mixed layers and two Chernoff inequalities + +Choose positive integers a,b, set g=a+b, and choose an integer M>1. At +rank n set + +``` +ell=floor(log_M C_n), G=g*ell. +``` + +These are exact integer definitions. At fixed exponent t abbreviate +T=T_t, P=P_t, q=T/P. Under the t-tilted target law, a rank k has +probability W_k k^t/T; define the analogous paid law. A layer with h +target letters and G-h paid letters has unit potential exactly + +``` +T^h P^(G-h) Pr(S_h^T+S_(G-h)^P <= ln C_n). (5) +``` + +All increments are nonnegative. Thus a final admitted paid product has +admitted paid prefixes, even when some increments are zero. Equation (5) +therefore describes the actually capped chronological classes, rather than +an enlarged path family introduced only for an estimate. + +Choose s>0 and lambda>0 and suppose + +``` +T_(t+s)/T >= P_(t+s)/P, +u_t=M^(-s)(T_(t+s)/T)^a(P_(t+s)/P)^b <1, +v_t=M^lambda (T_(t-lambda)/P)^g <1. (6) +``` + +For 0<=h<=a*ell, the exponential Markov bound and +ln C_n>=ell ln M imply + +``` +Pr(S_h^T+S_(G-h)^P >ln C_n) + <=M^(-s*ell)(T_(t+s)/T)^h(P_(t+s)/P)^(G-h) + <=u_t^ell. +``` + +The first guard in (6) is needed for the second inequality: the endpoint +h=a*ell must be the largest of these moment-generating expressions. +If T>P, summing (5) over h=0,...,a*ell gives + +``` +(T-P)H_t >=(1-u_t^ell)P^(G+1)(q^(a*ell+1)-1). (7) +``` + +This geometric sum is essential: replacing it by one layer introduces an +unnecessary inverse moment-gap prefactor. + +The root potential is exactly T times the truncated target degree-G +potential. Since C_n=D_ell(t)P^(G+1), +D_ell(t)=(1-u_t^ell)(q^(a*ell+1)-1)-q*M^lambda*v_t^ell. (9) +``` + +The useful geometry has ln M/g strictly between the relevant paid and +target tilted log means. Under that choice the two tail bounds can hold +at once, even though paid ranks overlap productive ranks. This is the +structural change from the original minimum-target height. + +## 4. Sharp use of the exact cancellation + +Suppose B_t<=beta I_t and beta=1-eta, (10) +``` + +then + +``` +B_t+F_t <=eta I_t. (11) +``` + +To prove this, (9), (3), and (10) imply A_t>=0 and +(eta-beta)A_t>=(1-eta)F_t. Identity (2) says I_t=B_t+F_t+A_t, +so (1-beta)I_t<=F_t+A_t. Therefore + +``` +(1-eta)(F_t+A_t) <=(1-beta)A_t, +(1-eta)I_t <=A_t, +B_t+F_t=I_t-A_t <=eta I_t. +``` + +This proof also covers zero leaf mass without division. Replacing (10) +by D>=1/(eta-beta) would discard the favorable cancellation and lose much +of the improvement. The required threshold is +(1-eta)/(eta-beta). + +For a pure power, take eta=t*m^(t-1). For every inner source rank s>n/m, +concavity gives + +``` +n^t-(n-s)^t >=t*n^(t-1)*s >=eta*s^t. +``` + +Root complement capacity is nonnegative and can be omitted. Thus (11) +proves the n^t supersolution inequality for (1). The next section funds a +stronger majorant without an adverse final inverse-slack power. + +## 5. Shifted logarithms and the local tangent exponent + +Fix t0 in (0,1), p>0 and c>=p/(1-t0). Define + +``` +f(x)=A0*x^t0*(c+ln x)^p for x>=1, f(0)=0, +tau(x)=t0+p/(c+ln x). +``` + +Here A0 is a positive normalization chosen below. On x>=1, tau(x)<=1 and + +``` +f'(x)=f(x)*tau(x)/x, +f''(x)/f(x)=x^(-2)[tau(x)(tau(x)-1)-p/(c+ln x)^2] <=0. (12) +``` + +For positive integer e<=n, log(1+y)<=y, with +1+y=(c+ln e)/(c+ln n)>0, gives the exact bound + +``` +f(e)/f(n) + =(e/n)^t0[(c+ln e)/(c+ln n)]^p + <=(e/n)^tau(n). (13) +``` + +The zero-rank term is handled by f(0)=0. Concavity on [1,n] gives, for +n-s>=1, f(n)-f(n-s)>=f'(n)s. When s=n the same inequality follows +from tau(n)<=1. Hence for every inner source, + +``` +f(n)-f(n-s) >=tau(n)*f(n)*s/n + >=eta_tau*f(n)*(s/n)^tau, +eta_tau=tau*m^(tau-1). (14) +``` + +Apply (6)--(10) at t=tau(n), with eta=eta_tau. By (13) the total exit +charge is at most f(n)n^(-tau)(B_tau+F_tau), and by (14) the inner source +capacity is at least f(n)n^(-tau)eta_tau I_tau. Root capacity remains +nonnegative. These bounds prove + +``` +sum_s S_s f(n-s)+sum_e E_e f(e) <=(sum_s S_s)f(n). (15) +``` + +Suppose a finite certificate establishes these guards uniformly for all +n>=n0. Set + +``` +A0=n0^(1-t0)/(c+ln n0)^p. (16) +``` + +Since the logarithmic derivative of f(x)/x is (tau(x)-1)/x<=0, +f(n)>=n for 1<=n<=n0. Use rank-one evaluation in this base range. +Strong induction with (1) and (15) gives L(n)<=f(n) at every rank. +Finally, a desired final exponent z>t0 at an explicit N follows from + +``` +ln A0+p*ln(c+ln N) <=(z-t0)*ln N. (17) +``` + +Every term in (17), including normalization and the base cutoff, must be +funded. The height change alone is not a numerical saving certificate. + +## 6. A reusable finite certificate for all larger ranks + +The following guards turn the infinitely many local exponents and heights +into a finite list of inequalities. Fix ell0>=1 and choose n0>=m*M^ell0. +Let t_hi be an upper bound for tau(n0). On [t0,t_hi], certify + +``` +T_t0>P_t0, +(d/dt)ln(T_t/P_t)>=d>0, +q_t<=Q, u_t<=U<1, v_t<=V<1, +B_t<=beta I_t, eta_t>=eta_min>beta, +T_(t+s)/T_t >=P_(t+s)/P_t. (18) +``` + +Then q_t>=exp(d(t-t0)). For n with height ell>=ell0, + +``` +n=exp[d*p*(a*ell+1)/(c+ln m+(ell+1)ln M+ln 2)]. (19) +``` + +The fraction in (19) is increasing in ell if + +``` +a*(c+ln m+ln 2)+(a-1)ln M >=0, +``` + +which holds for the positive integer a used here. Consequently the single +exact inequality + +``` +(1-U^ell0)* + (exp[d*p*(a*ell0+1)/(c+ln m+(ell0+1)ln M+ln 2)]-1) + -Q*M^lambda*V^ell0 + >=(1-eta_min)/(eta_min-beta) (20) +``` + +implies (10) for every larger ell. The right side decreases with eta; +therefore eta_min is the correct conservative endpoint. This proves a +uniform recurrence, rather than inferring one from a rank scan. + +Useful finite guard reductions use increasing tilted means +mu_T(t)=d ln T_t/dt and mu_P(t)=d ln P_t/dt, whose derivatives are +nonnegative variances. For example +mu_T(t0)-mu_P(t_hi)>=d proves the derivative guard. The logarithmic +derivative of each ratio T_(t+s)/T_t or P_(t+s)/P_t is nonnegative, +so u_t is increasing and its upper endpoint suffices. The stronger +simple guard T_(t0+s)/T_t0 >=P_(t_hi+s)/P_t_hi proves the required +ordering of these ratios throughout the interval. Loose endpoint bounds +Q>=T_t_hi/P_t0 and V>=M^lambda(T_(t_hi-lambda)/P_t0)^g are valid because +all native ranks are at least one. The mirror guard (4) must still be +certified on every elementary interval throughout [t0,t_hi]. + +One exploratory p7 choice is + +``` +t0=.99731352, p=.1, c=38, M=256, a=b=1, +s=lambda=.1, ell0=100, +Q=1.001, U=.961, V=.903, d=1.72, +beta=.321, eta_min=.9845. +``` + +For n0=121*256^100, use t_hi=.997481. The smaller trial endpoint +.9974808 fails to cover tau(n0) and is an explicit rejection control. +The exact package receipt certifies these guards and (17), alongside the +newer native profiles. Other profiles may use different guards. + +## 7. Native caller assumptions and limits + +The theorem consumes the same native hypotheses as the predecessor finite +compiler. In particular it assumes all-column arbitrary-input correctness +at every positive integer column multiplicity; actual disjoint productive +owners; the literal chronological paid interface; and permitted, priced +whole-job adapters including the input map. Correlated contents of distinct +fields do not permit field aliasing, input cloning, or extra productive +credit. Each raw instance retains its owned centers and scratch until its +word initializes, uses, restores and erases them. All unmatched jobs, +source complements, moves, adapters, coefficients and ownership operations +remain present in the finite word. + +The arbitrary-height flow has finitely many classes and integer weights. +Its source counts and recursive batch denominators must be cleared with +actual divisible widths. The normalized recurrence alone does not bound +those widths or physical resources. PR4436's fixed-rule finite counting +method can be applied after accounting for the new G=O(log n), but no old +numerical precision or stock constant may simply be copied to the new +expanded word. An ambient rank reduction is neither a materialized-word +size bound nor a practical runtime claim. + +The native tensor realization, analytic transfer, exact recovery, precision, +fine-prime exclusions, stock, whole-job implementation tariffs, and physical +fixed-tape execution assumptions remain inherited. Finite arithmetic or +flow checks do not establish those premises. This theorem does not merge +or scientifically admit pending profiles, change the selected record, or +by itself prove a larger multiplication kappa. + +## Open next questions + +1. Independently check the arbitrary-height flow and mirror identity, + including small root sources and empty-root classes. A finite integer + check should distinguish this flow from the old minimum-target height. +2. Certify the strongest relevant raw profile using (18)--(20), and compare + complete final ranks through (17). Better constants are useful only + when every guard and the normalization are included. +3. Audit the resulting word's native physical implementations and full + finite constants. The theorem removes an exponent-convergence obstacle; + it does not discharge those caller obligations. diff --git a/research/rank-convergence/README.md b/research/rank-convergence/README.md new file mode 100644 index 0000000000..899d8d05cd --- /dev/null +++ b/research/rank-convergence/README.md @@ -0,0 +1,177 @@ +# Padding-free adaptive compiler (199.32× smaller rank exponent) + +This package proves and certifies a direct compiler for overlapping native +rank profiles that satisfy explicit finite gates. It removes the +chronological tensor product, paid target completion and splitting stage +from the three instantiated constructions. The raw native words and paid +invoices stay unchanged. + +For the recent p16 construction, it retains **PR4470's conditional +κ = 0.00302015** and reduces the sufficient uniform rank from +**`2^558100005581` to `2^2800000000`**: a **199.321× reduction in its +exponent**, with **the same uniform saving and outer parameter point** as +PR4479. The initial supplier uses tensor power **one**, replacing power +682. No new κ or selected-frontier update is claimed. + +## What changes mathematically + +The old direct flow selected its height using the smallest productive +rank. Later analyses showed that paid leaf paths could saturate its cap; +the near-root saving did not follow from that construction's moment +identity alone. This package changes the stopping geometry. + +The new height uses the paid and productive rank distributions. A mixed +layer retains enough unit potential, while a separate lower-tail estimate +pays for small root sources. Exact source/boundary cancellation then +reduces the required surplus from an order-one threshold to +`(1-eta)/(eta-beta)`. A concave shifted-logarithmic majorant uses its +local tangent exponent to close the entire recursive construction. + +This supplies a uniform convergence argument for the certified profiles, +rather than inferring convergence from a finite rank scan. The majorant +has a small fractional logarithmic power (`1/10` or `2/5` here). The proof +funds its whole ordinary base range and its final rank explicitly. + +[PROOF.md](PROOF.md) gives the theorem and all finite gates. The theorem +does not say that every profile with a favorable moment admits those gates. + +## Exact results and fair comparisons + +In the table, `H` means the specified sufficient rank is `N=2^H`. + +| Raw profile | Retained κ | Prior H | New H | Reduction | +|---|---:|---:|---:|---:| +| P7, same saving as PR4480's unchanged-C witness | .00268647 | 130,200,000,000 | 3,040,000,000 | 42.83× | +| Native4453, same saving as PR4480's main witness | .00300120 | 125,790,000,000 | 4,300,000,000 | 29.25× | +| P16, same saving as PR4479 | .00302015 | 558,100,005,581 | **2,800,000,000** | **199.32×** | + +An additional native4453 certificate uses its original outer point's +weaker required uniform saving, giving `H=1300000000` (96.76× against +PR4480's H at the same κ). That comparison changes the uniform-saving +allocation; the 29.25× row holds it fixed. The exact receipt labels this +distinction and binds every baseline to the same authenticated profile. + +Raw initial ambient ranks are **121, 153 and 145**, with their original +7,688, 11,560 and 10,928 productive fields. These replace the enormous +tensor-unit ranks and field counts used before uniform compilation. The +eventual uniform words can still have enormous widths and denominators. +No practical size or runtime factor follows from the ambient-rank bounds. + +## The main p16 certificate + +The raw profile is authenticated against both PR4470's joint-helper +receipt and PR4479's compact consumer receipt. Choose + +``` +t0=.99697984, p=2/5, c=133, +M=1024, a=b=1, ell0=650, +s=1/20, lambda=1/10, +n0=145*1024^650, +G(n)=2*floor(log_1024(floor(n/145))). +``` + +Exact rational intervals certify an exponent cover ending at `.997066`, +the mixed and root Chernoff bounds, every elementary mirror window and +the source capacity. The uniform recurrence certificate gives + +``` +D > .04854643, +required D < .04306221, +final funded logarithmic margin > .60862507 +``` + +at `H=2800000000`. Monotonicity proves the recurrence at every rank above +the base cutoff and the final saving at every larger rank. All ordinary +base calls below `n0` are paid. The winning word is specified by the +integer algorithm and is not materialized. + +## Reproduce and extend + +Python 3.12, standard library only: + +```sh +python3.12 -B scripts/research_package.py --package research/rank-convergence +python3.12 -I -O -B research/rank-convergence/verify.py +``` + +The verifier authenticates all live sources, reproduces four witnesses +across three raw profiles, checks uniform exponent and mirror covers, +binds the retained consumer and comparison points, and compares the exact +receipt. It includes literal chronological and independent ordered-word +oracles, empty-root forests, small-root controls, exact rank-invoice +cancellation and rejection of invalid certificates. No native or outer +producer suite is rerun by this command. + +[BENCHMARKS.json](BENCHMARKS.json) contains complete rational witnesses. +[compiler.py](compiler.py) accepts `profile.json witness.json`; its output +certifies the conditional inequalities for those inputs. The profile gives +positive integer `targets` and `paid` histograms. Supported profiles have +minimum productive rank at least two, maximum paid rank below the raw +ambient rank, positive rank-one surplus and paid rank-one calls. These +are stronger premises than some parts of the written theorem require. + +[flow.py](flow.py) constructs finite arbitrary-height flows and classifies +their root/nonroot sources and boundary/leaf exits. `adaptive_flow` computes +the witness's height with integer arithmetic. The frozen predecessor's +bytes are authenticated before execution. The tests independently rebuild +the same invoice from ordered-word convolutions and exact mirror windows. + +For another submission, pin its actual native profile, search for a +feasible geometry and rational guards, certify them, and bind the resulting +uniform saving to its complete consumer. The generic checker does not +admit a native supplier or establish an outer theorem on its own. + +## Scope, source retention and validation + +Native all-column correctness, complete arbitrary input fields, whole-job +adapters, owned erasure, finite-program closure, physical tape, stock, +precision, analytic decomposition, prime avoidance and exact recovery +remain inherited premises. Numerical full-word scalar, bank and precision +constants require fresh substitution into the retained finite counting +prescriptions; old template counts are not transferred unchanged. + +The raw-word and outer producer receipts are inherited. The new arithmetic +proves the changed compiler bound and checks that it supplies the unchanged +consumer points, including their nine margins, current strict/functional +guards and legacy receipt. This is distinct from replaying those producers. +The selected frontier is unchanged. Smaller local template rank does not +establish a smaller eventual multiplication-input threshold. + +The successor starts from refreshed canonical main and retains the pending +PR4480, PR4470/4479 and PR4436 histories. Only the needed new predecessor +directories were imported byte-for-byte. Existing scientific files and frozen +evidence were preserved; shared documentation matches canonical main. +[SOURCES.json](SOURCES.json) pins the exact inputs. +The worktree is sparse because full checkout exhausted disk space. + +## Open next questions + +- **An actual κ gain.** Replay a changed native warp word or a fully priced + accumulating interface, then apply the direct compiler. The raw moment + ceilings here are unchanged. A further κ hill step requires an actual + paid-profile change with its full native replay. +- **Broader admission gates.** Characterize feasible geometries from tilted + log means and study profiles where the mirror coefficient approaches + source capacity. No universal gate-existence theorem is supplied. +- **Full physical constants.** Emit all counts for a small adaptive forest + before attempting useful bounds on large widths, banks and precision. + The winning templates remain algorithmic prescriptions. + +Structured blockers and first steps are in [TASK.json](TASK.json). + +## Attribution and review state + +zxv, with substantial OpenAI Codex assistance and three user-requested +**Sol 6.1 medium** subagents. Separate author-side agents audited the +algebra, exponent covers, mirror endpoints, literal chronology and +source/consumer bindings. This is not formal or independent human review. +The successor remains local for user review; only PR4480 was authorized +for publication in this round. + +Credit Jacob Alan Sussman's integer compiler; my PR4436 direct flow, +PR4480 rank compiler and κ=.0023/native/controller predecessors; +Ryanson Jonathan's corrected PR4459 mirror identity; the finite-flow +and leaf analyses in PR4456/4465/4467/4476; Cinna Davis's PR4470 native +construction and prior thinning/helper work; Dugongue's PR4479 compact +compiler; and all retained BIT, scalar, Clifford, geometry and outer +sources. New work is Apache-2.0. diff --git a/research/rank-convergence/RESULT.json b/research/rank-convergence/RESULT.json new file mode 100644 index 0000000000..6b80c3fcd2 --- /dev/null +++ b/research/rank-convergence/RESULT.json @@ -0,0 +1,467 @@ +{ + "examples": { + "native4453": { + "H": 1300000000, + "N": "2^1300000000", + "c": "134", + "comparison": { + "baseline_H": 125790000000, + "baseline_uniform_saving": "105043/35000000", + "rank_exponent_reduction": "12579/130", + "same_uniform_saving": false, + "source": "research/net-tax-rank-compiler/RESULT.json", + "source_path": [ + "examples", + "native-concentrated-balanced", + "uniform" + ] + }, + "consumer_binding": { + "available_uniform_saving": "525213/175000000", + "current_strict_checks": 54, + "functional_guards": 4, + "legacy_checks": 63, + "producer_replayed": false, + "required_uniform_saving": "525213/175000000", + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND" + }, + "ell0": 400, + "final_logarithmic_margin": { + "lower": "1.195753504900398371589260762250", + "upper": "1.195753504900398371589260762251" + }, + "height_base": 1024, + "height_multiplier": 2, + "kappa": "7503/2500000", + "local_exponent_max": { + "lower": "0.997136147271064756238028077145", + "upper": "0.997136147271064756238028077146" + }, + "log_majorant_normalization": { + "lower": "5.145697363640228729059432255530", + "upper": "5.145697363640228729059432255531" + }, + "mirror": { + "cells": 19, + "exponent_slices": 20, + "maximizing_cell": { + "exponent_lower": "598277597/600000000", + "exponent_upper": "4985681/5000000", + "window": [ + "1/48", + "1/41" + ] + }, + "maximum_upper": { + "lower": "0.574080702141194439831345959835", + "upper": "0.574080702141194439831345959836" + } + }, + "mixed_chernoff": { + "lower": "0.967609647388864491029540621309", + "upper": "0.967609647388864491029540621310" + }, + "native_and_outer_producers_replayed": false, + "ordinary_base": "153*1024^400", + "p": "2/5", + "paid_mgf_upper": { + "lower": "1.141456094837378948168524543329", + "upper": "1.141456094837378948168524543330" + }, + "q_base": { + "lower": "1.000000005833951983693752410407", + "upper": "1.000000005833951983693752410408" + }, + "q_upper": { + "lower": "1.000495314570783841578207790745", + "upper": "1.000495314570783841578207790746" + }, + "raw_ambient": 153, + "raw_fields": 11560, + "raw_maximum_paid": 72, + "raw_minimum_target": 4, + "required_D_upper": "18/407", + "root_chernoff": { + "lower": "0.983297831780127599548450021145", + "upper": "0.983297831780127599548450021146" + }, + "source_capacity": { + "lower": "0.982059615682066172420963085480", + "upper": "0.982059615682066172420963085481" + }, + "status": "PASS_ADAPTIVE_HEIGHT_DIRECT_COMPILER", + "t0": "29909963/30000000", + "t_upper": "4985681/5000000", + "target_mgf_lower": { + "lower": "1.198817734840431123969294143697", + "upper": "1.198817734840431123969294143698" + }, + "tensor_power": 1, + "tilted_log_mean_gap": { + "lower": "1.026038818516380833500985773945", + "upper": "1.026038818516380833500985773946" + }, + "uniform_D_lower": { + "lower": "0.054486114822399840835177110779", + "upper": "0.054486114822399840835177110780" + }, + "uniform_gap": "17/1050000000", + "uniform_saving": "525213/175000000", + "word_materialized": false + }, + "native4453-matched-uniform": { + "H": 4300000000, + "N": "2^4300000000", + "c": "134", + "comparison": { + "baseline_H": 125790000000, + "baseline_uniform_saving": "105043/35000000", + "rank_exponent_reduction": "12579/430", + "same_uniform_saving": true, + "source": "research/net-tax-rank-compiler/RESULT.json", + "source_path": [ + "examples", + "native-concentrated-balanced", + "uniform" + ] + }, + "consumer_binding": { + "available_uniform_saving": "105043/35000000", + "current_strict_checks": 54, + "functional_guards": 4, + "legacy_checks": 63, + "producer_replayed": false, + "required_uniform_saving": "525213/175000000", + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND" + }, + "ell0": 400, + "final_logarithmic_margin": { + "lower": "0.321169139930537333994562947424", + "upper": "0.321169139930537333994562947425" + }, + "height_base": 1024, + "height_multiplier": 2, + "kappa": "7503/2500000", + "local_exponent_max": { + "lower": "0.997136147271064756238028077145", + "upper": "0.997136147271064756238028077146" + }, + "log_majorant_normalization": { + "lower": "5.145697363640228729059432255530", + "upper": "5.145697363640228729059432255531" + }, + "mirror": { + "cells": 19, + "exponent_slices": 20, + "maximizing_cell": { + "exponent_lower": "598277597/600000000", + "exponent_upper": "4985681/5000000", + "window": [ + "1/48", + "1/41" + ] + }, + "maximum_upper": { + "lower": "0.574080702141194439831345959835", + "upper": "0.574080702141194439831345959836" + } + }, + "mixed_chernoff": { + "lower": "0.967609647388864491029540621309", + "upper": "0.967609647388864491029540621310" + }, + "native_and_outer_producers_replayed": false, + "ordinary_base": "153*1024^400", + "p": "2/5", + "paid_mgf_upper": { + "lower": "1.141456094837378948168524543329", + "upper": "1.141456094837378948168524543330" + }, + "q_base": { + "lower": "1.000000005833951983693752410407", + "upper": "1.000000005833951983693752410408" + }, + "q_upper": { + "lower": "1.000495314570783841578207790745", + "upper": "1.000495314570783841578207790746" + }, + "raw_ambient": 153, + "raw_fields": 11560, + "raw_maximum_paid": 72, + "raw_minimum_target": 4, + "required_D_upper": "18/407", + "root_chernoff": { + "lower": "0.983297831780127599548450021145", + "upper": "0.983297831780127599548450021146" + }, + "source_capacity": { + "lower": "0.982059615682066172420963085480", + "upper": "0.982059615682066172420963085481" + }, + "status": "PASS_ADAPTIVE_HEIGHT_DIRECT_COMPILER", + "t0": "29909963/30000000", + "t_upper": "4985681/5000000", + "target_mgf_lower": { + "lower": "1.198817734840431123969294143697", + "upper": "1.198817734840431123969294143698" + }, + "tensor_power": 1, + "tilted_log_mean_gap": { + "lower": "1.026038818516380833500985773945", + "upper": "1.026038818516380833500985773946" + }, + "uniform_D_lower": { + "lower": "0.054486114822399840835177110779", + "upper": "0.054486114822399840835177110780" + }, + "uniform_gap": "1/210000000", + "uniform_saving": "105043/35000000", + "word_materialized": false + }, + "p16": { + "H": 2800000000, + "N": "2^2800000000", + "c": "133", + "comparison": { + "baseline_H": 558100005581, + "baseline_uniform_saving": "471898442219/156250001562500", + "rank_exponent_reduction": "558100005581/2800000000", + "same_uniform_saving": true, + "source": "research/compact-joint-compiler/arithmetic/RESULT.json", + "source_path": [ + "compiler" + ] + }, + "consumer_binding": { + "available_uniform_saving": "471898442219/156250001562500", + "current_strict_checks": 54, + "functional_guards": 4, + "legacy_checks": 63, + "producer_replayed": false, + "required_uniform_saving": "471898442219/156250001562500", + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND" + }, + "ell0": 650, + "final_logarithmic_margin": { + "lower": "0.608625073158079647179104336984", + "upper": "0.608625073158079647179104336985" + }, + "height_base": 1024, + "height_multiplier": 2, + "kappa": "60403/20000000", + "local_exponent_max": { + "lower": "0.997065983154193637326436620047", + "upper": "0.997065983154193637326436620048" + }, + "log_majorant_normalization": { + "lower": "10.244946827609613535229675830964", + "upper": "10.244946827609613535229675830965" + }, + "mirror": { + "cells": 19, + "exponent_slices": 20, + "maximizing_cell": { + "exponent_lower": "249265423/250000000", + "exponent_upper": "498533/500000", + "window": [ + "1/48", + "1/41" + ] + }, + "maximum_upper": { + "lower": "0.562869244899309734589502501137", + "upper": "0.562869244899309734589502501138" + } + }, + "mixed_chernoff": { + "lower": "0.962371615118373162597052724651", + "upper": "0.962371615118373162597052724652" + }, + "native_and_outer_producers_replayed": false, + "ordinary_base": "145*1024^650", + "p": "2/5", + "paid_mgf_upper": { + "lower": "1.137864762892548940390353969492", + "upper": "1.137864762892548940390353969493" + }, + "q_base": { + "lower": "1.000000006229760842608145113022", + "upper": "1.000000006229760842608145113023" + }, + "q_upper": { + "lower": "1.000306615000337864713077356861", + "upper": "1.000306615000337864713077356862" + }, + "raw_ambient": 145, + "raw_fields": 10928, + "raw_maximum_paid": 72, + "raw_minimum_target": 4, + "required_D_upper": "9/209", + "root_chernoff": { + "lower": "0.991612566446621220203979601511", + "upper": "0.991612566446621220203979601512" + }, + "source_capacity": { + "lower": "0.982106757609959316847199693591", + "upper": "0.982106757609959316847199693592" + }, + "status": "PASS_ADAPTIVE_HEIGHT_DIRECT_COMPILER", + "t0": "1557781/1562500", + "t_upper": "498533/500000", + "target_mgf_lower": { + "lower": "1.196094303561928263013152983677", + "upper": "1.196094303561928263013152983678" + }, + "tensor_power": 1, + "tilted_log_mean_gap": { + "lower": "1.042051961200529914604466771295", + "upper": "1.042051961200529914604466771296" + }, + "uniform_D_lower": { + "lower": "0.048546432211906163478518624110", + "upper": "0.048546432211906163478518624111" + }, + "uniform_gap": "1/100000001", + "uniform_saving": "471898442219/156250001562500", + "word_materialized": false + }, + "p7": { + "H": 3040000000, + "N": "2^3040000000", + "c": "38", + "comparison": { + "baseline_H": 130200000000, + "baseline_uniform_saving": "376107/140000000", + "rank_exponent_reduction": "3255/76", + "same_uniform_saving": true, + "source": "research/net-tax-rank-compiler/RESULT.json", + "source_path": [ + "examples", + "p7-net-shift-same-C", + "uniform" + ] + }, + "consumer_binding": { + "available_uniform_saving": "376107/140000000", + "current_strict_checks": 54, + "functional_guards": 3, + "legacy_checks": 63, + "producer_replayed": false, + "required_uniform_saving": "376107/140000000", + "status": "INHERITED_RECEIPT_AND_MONOTONE_BOUND" + }, + "ell0": 100, + "final_logarithmic_margin": { + "lower": "0.000037729652454530318218297510", + "upper": "0.000037729652454530318218297511" + }, + "height_base": 256, + "height_multiplier": 2, + "kappa": "268647/100000000", + "local_exponent_max": { + "lower": "0.997480936263221089297020305663", + "upper": "0.997480936263221089297020305664" + }, + "log_majorant_normalization": { + "lower": "0.863340409511937169849820502293", + "upper": "0.863340409511937169849820502294" + }, + "mirror": { + "cells": 9, + "exponent_slices": 20, + "maximizing_cell": { + "exponent_lower": "498736313/500000000", + "exponent_upper": "997481/1000000", + "window": [ + "1/32", + "1/25" + ] + }, + "maximum_upper": { + "lower": "0.320912505508019305802927568868", + "upper": "0.320912505508019305802927568869" + } + }, + "mixed_chernoff": { + "lower": "0.960716862989376750562449633430", + "upper": "0.960716862989376750562449633431" + }, + "native_and_outer_producers_replayed": false, + "ordinary_base": "121*256^100", + "p": "1/10", + "paid_mgf_upper": { + "lower": "1.189836220034656274281883309422", + "upper": "1.189836220034656274281883309423" + }, + "q_base": { + "lower": "1.000000015596092266209397853528", + "upper": "1.000000015596092266209397853529" + }, + "q_upper": { + "lower": "1.000561156408386012831320257044", + "upper": "1.000561156408386012831320257045" + }, + "raw_ambient": 121, + "raw_fields": 7688, + "raw_maximum_paid": 48, + "raw_minimum_target": 5, + "required_D_upper": "31/1327", + "root_chernoff": { + "lower": "0.902200383991683674129581646891", + "upper": "0.902200383991683674129581646892" + }, + "source_capacity": { + "lower": "0.984546755462808333262196913419", + "upper": "0.984546755462808333262196913420" + }, + "status": "PASS_ADAPTIVE_HEIGHT_DIRECT_COMPILER", + "t0": "12466419/12500000", + "t_upper": "997481/1000000", + "target_mgf_lower": { + "lower": "1.405801522570042940551422228371", + "upper": "1.405801522570042940551422228372" + }, + "tensor_power": 1, + "tilted_log_mean_gap": { + "lower": "1.723175105324202823174061366589", + "upper": "1.723175105324202823174061366590" + }, + "uniform_D_lower": { + "lower": "0.028589919182340223704227975714", + "upper": "0.028589919182340223704227975715" + }, + "uniform_gap": "1/700000000", + "uniform_saving": "376107/140000000", + "word_materialized": false + } + }, + "finite_tests": 13, + "rejected_witnesses": { + "below_root_moment": "raw strict moment at base exponent", + "insufficient_tilted_gap": "sharp source and boundary cancellation for all heights", + "nonconcave_majorant": "concave funded majorant domain", + "old_incomplete_tau_interval": "local exponent interval covers ordinary base cutoff", + "too_small_final_rank": "funded final uniform-rank inequality", + "understated_boundary_share": "uniform boundary mirror coefficient", + "unfunded_root_tail": "root source Chernoff V", + "unfunded_uniform_gap": "funded uniform and consumer savings" + }, + "schema_version": 1, + "scope": "Conditional direct overlapping-rank compiler under explicit finite gates; exact rank and inherited consumer binding, not a native/physical/analytic theorem audit.", + "source_mutation_rejected": true, + "source_sha256": { + "research/compact-joint-compiler/arithmetic/RESULT.json": "a6caaa2a6d6460a8c1ef7e48c4853bb27976be33a52b96a4216dfa90d96c9091", + "research/direct-mixed-flow/README.md": "78351e2419eb1ff1d645addd411158b91b381b23a962a91b6deeebeacd5192a8", + "research/direct-mixed-flow/flow.py": "460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a", + "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8", + "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e", + "research/direct-mixed-flow/vendor/theorem-1g.md": "c4a96c55c2509ff36e8bc6bddaaf6a8b1a34a5d794e4e09ac5214c82b51510e6", + "research/higher-moment-strictification/RESULT.json": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156", + "research/joint-helper-lattice/RESULT.json": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21", + "research/native-lattice-retiming/RESULT.json": "1ac2e581ea51e6448503a68caf4bf44aeb32470c2e2674c91f007af4a3abd2e3", + "research/net-tax-rank-compiler/RESULT.json": "5e0c333d1279fc07add5776db6483dcc251128aeda73791472d6b9cab05186f5", + "research/net-tax-rank-compiler/intervals.py": "91d079f43a082c3c23b76b8eb482066d0aeffe73de9fde0137ee033cf3b32250" + }, + "status": "PASS_PADDING_FREE_ADAPTIVE_COMPILER" +} diff --git a/research/rank-convergence/SOURCES.json b/research/rank-convergence/SOURCES.json new file mode 100644 index 0000000000..0e52e9fddf --- /dev/null +++ b/research/rank-convergence/SOURCES.json @@ -0,0 +1,109 @@ +{ + "schema_version": 1, + "base_commit": "1df9e7df3c26ceaca37dbf06669e2ae8f8b414c3", + "files": [ + { + "path": "research/direct-mixed-flow/flow.py", + "usage": "input", + "git_blob": "07175cd6e1f2c2367c2e78eca7f163fef18d301d", + "sha256": "460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a" + }, + { + "path": "research/direct-mixed-flow/README.md", + "usage": "input", + "git_blob": "3be00f754b9ffa23e64b3eafe7706e3ac139993a", + "sha256": "78351e2419eb1ff1d645addd411158b91b381b23a962a91b6deeebeacd5192a8" + }, + { + "path": "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "usage": "input", + "git_blob": "4badb40f0919c515823cb07e44c6470d4d6469ca", + "sha256": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8" + }, + { + "path": "research/direct-mixed-flow/vendor/theorem-1g.md", + "usage": "input", + "git_blob": "36d2399f3538c34e4b1567a15b4a5dfe77ffc7ad", + "sha256": "c4a96c55c2509ff36e8bc6bddaaf6a8b1a34a5d794e4e09ac5214c82b51510e6" + }, + { + "path": "research/higher-moment-strictification/RESULT.json", + "usage": "input", + "git_blob": "e66b39c674028adfd22f0de3170555dccda52f6a", + "sha256": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156" + }, + { + "path": "research/native-lattice-retiming/RESULT.json", + "usage": "input", + "git_blob": "93defc5ececebd542332fc42d6a78f0af222cd1c", + "sha256": "1ac2e581ea51e6448503a68caf4bf44aeb32470c2e2674c91f007af4a3abd2e3" + }, + { + "path": "research/joint-helper-lattice/RESULT.json", + "usage": "input", + "git_blob": "edf41a49a0350862c23378f837c7397fc5dc7596", + "sha256": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21" + }, + { + "path": "research/compact-joint-compiler/arithmetic/RESULT.json", + "usage": "input", + "git_blob": "514d12ce4d2d824a4e0a418022bba610c8aed8ff", + "sha256": "a6caaa2a6d6460a8c1ef7e48c4853bb27976be33a52b96a4216dfa90d96c9091" + }, + { + "path": "research/net-tax-rank-compiler/RESULT.json", + "usage": "input", + "git_blob": "602eb0bf1a023433777e1e9d17fcb001efd852c1", + "sha256": "5e0c333d1279fc07add5776db6483dcc251128aeda73791472d6b9cab05186f5" + }, + { + "path": "research/net-tax-rank-compiler/intervals.py", + "usage": "input", + "git_blob": "f3d990ab639ee49424226c202c92b9e1f390dcff", + "sha256": "91d079f43a082c3c23b76b8eb482066d0aeffe73de9fde0137ee033cf3b32250" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65", + "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40", + "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9" + }, + { + "path": "autoresearch.md", + "usage": "provenance", + "git_blob": "2fe84a7b30b1e26e60ce0ec4775894eb1831c5d6", + "sha256": "d16f0d3bb4d4b213d06c128db6d6460b0fe9ec1ac5a6c1ea1febf1db40e7b60d" + }, + { + "path": "CONTRIBUTING.md", + "usage": "provenance", + "git_blob": "fe54f23f19b082a9f8df3da9b2e205f7e230acf3", + "sha256": "8a49fe97e2ad088a2b2e0c5b222aaab08752783b1f9c1260790d7dd13011d215" + }, + { + "path": "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE", + "usage": "input", + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + { + "path": "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE", + "usage": "input", + "git_blob": "0b06967886fab2628afc0b881c884161bbf5e430", + "sha256": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e" + } + ], + "external_mathematical_attribution": [ + { + "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/4459", + "head": "488a75a9e95e14448b6301719249f876f3999931", + "usage": "Corrected mirror-window identity, independently derived and implemented here; withdrawn earlier reduction is not used." + } + ] +} diff --git a/research/rank-convergence/TASK.json b/research/rank-convergence/TASK.json new file mode 100644 index 0000000000..50ba5c9051 --- /dev/null +++ b/research/rank-convergence/TASK.json @@ -0,0 +1,137 @@ +{ + "schema_version": 1, + "task_id": "supplier-boundary-audit", + "priority_revision": 7, + "original_card": { + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "allowed_variations": [ + "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage." + ], + "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.", + "existing_checks": [ + { + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "status": "author-checked" + }, + { + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "scope": "PR #3801: successor scatter-boundary decision package.", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "status": "author-checked" + } + ], + "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "id": "supplier-boundary-audit", + "methods": [ + "Trace one hypothesis through the source, checker and complete caller.", + "Construct one semantically invalid but superficially well-formed fixture and test rejection." + ], + "overlap_terms": [ + "owner boundary", + "bridge omission", + "hosting", + "2977", + "scatter export", + "duplicate index", + "parity semantics", + "4088", + "3801", + "staged544-mixed-fourth-entry", + "scatter-boundary-decision" + ], + "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?", + "scope_change_triggers": [ + "Reporting the historical timing-only diagnostic as a new current acceptance bug.", + "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.", + "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-mixed-fourth-entry/README.md", + "research/scatter-boundary-decision/README.md" + ] + }, + "base_commit": "1df9e7df3c26ceaca37dbf06669e2ae8f8b414c3", + "scope_status": "changed", + "actual_scope": "Prove and certify a padding-free adaptive-height compiler for overlapping native rank profiles, with rigorous local-exponent induction and inherited consumer binding.", + "scope_change_reason": "The user requested a qualitatively larger successor to PR4480, drastic rank reduction and progress toward kappa. Changing the lockstep stopping geometry addresses the previously missing direct near-root convergence argument rather than rerunning an old root or parameter scan.", + "bottleneck_link": "The old height saturates paid leaf paths and defeats one-step induction. Adaptive mixed-layer geometry, two Chernoff bounds and exact source cancellation fund a small fractional logarithmic power without tensor padding.", + "stop_rule": "Finish a scoped direct compiler theorem and exact independently checked witnesses. Keep this successor local for user review; no PR, Discussion or selected-frontier change.", + "evidence": "Arbitrary-height integer forest, exact mirror-window funding, uniformly certified mixed/root tails, sharp cancellation, concave majorant and funded base; three source profiles and matched-saving comparisons.", + "author": "zxv, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance, including three user-requested Sol 6.1 medium subagents for divergent theory, native probes and independent audits. No xhigh subagents were used in this successor.", + "budget_minutes": 60, + "outcome": "completed", + "publication_policy": "PR4480 was submitted at the user request. This successor remains local for review. Future subagents use Sol 6.1 medium.", + "upstream_checkpoint": { + "checked_at_utc": "2026-10-22T00:16:00Z", + "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db", + "priority_revision": 7, + "pending_sources": { + "PR4480": "896b877eae0b297c6da1ee78c6dd6a94a9c5868f", + "PR4479": "035008ddc2cea4949829d309770e67479e696d9e", + "PR4470": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "PR4436": "56003680aee2871773de408e5f01cc5dd46b144c" + } + }, + "open_questions": [ + { + "question": "Can a changed fully charged native word improve kappa through the new direct compiler?", + "why_it_matters": "The compiler now accepts these overlapping profiles directly, while their raw moment ceilings are unchanged.", + "first_step": "Price and replay one changed warp word or genuinely different accumulating interface, then run the direct certificate.", + "blocked_by": "No changed native paid profile is proved here; bounded scalar commuting and basic fanout probes gave no gain." + }, + { + "question": "Which broader profile class admits the two tail and mirror inequalities?", + "why_it_matters": "The theorem is finitely gated rather than a universal result for every favorable moment profile.", + "first_step": "Characterize feasible a,b,M from tilted log means and inspect profiles where mirror beta approaches source capacity.", + "blocked_by": "No universal existence or optimality theorem for those gates is given." + }, + { + "question": "Can complete physical and precision constants of these raw-word templates be emitted?", + "why_it_matters": "Ambient rank and normalized leaves alone do not determine productive width or practical thresholds.", + "first_step": "Compute full counts for a small adaptive forest with the inherited nested width recurrence before larger symbolic estimates.", + "blocked_by": "Winning templates and their numerical scalar/bank/precision constants are not materialized." + } + ], + "overlap": { + "checked_at_utc": "2026-10-22T00:20:35Z", + "open_pr_bodies": 334, + "discussion_records": 3360, + "remote_pagination_complete": true, + "local_notes_searched": 13, + "local_HEAD_note_paths": 5741, + "limits": "Sparse local coverage; arbitrary diffs and closed remote PR bodies not searched; no novelty certificate. Recent direct-flow and p16 discussions read separately." + }, + "validation": { + "python": "3.12.8", + "platform": "macOS arm64", + "direct_normal": "pass", + "direct_isolated_optimized": "pass", + "metadata_pins": "pass", + "finite_tests": 13, + "literal_fixtures": 80, + "independent_ordered_word_flows": 24, + "exact_certificates": 4, + "rejected_witnesses": 8, + "native_outer_producer_replays": "inherited exact receipts; not rerun", + "review": "Separate Sol 6.1 medium proof and implementation audits; not formal or independent human acceptance." + } +} diff --git a/research/rank-convergence/VALIDATION.md b/research/rank-convergence/VALIDATION.md new file mode 100644 index 0000000000..1a94ea76c1 --- /dev/null +++ b/research/rank-convergence/VALIDATION.md @@ -0,0 +1,41 @@ +# Validation and limits + +Author-side validation on 2026-10-22, Python 3.12.8, macOS arm64. +Substantial OpenAI Codex assistance; separate Sol 6.1 medium agents reviewed +proof algebra, finite chronology and numerical/source bindings. This is not +formal or independent human acceptance. + +## Scientific replay + +- `python3.12 -B research/rank-convergence/verify.py --write`: passed; + regenerates the exact receipt explicitly. +- `python3.12 -I -O -B research/rank-convergence/verify.py`: passed during + development; the final exported-byte replay is recorded below. +- `python3.12 -B scripts/research_package.py --package research/rank-convergence`: + passed before adding retained original license/notice inputs; the final + registered replay and transport checks are recorded below. +- Thirteen test methods include 80 literal fixtures (43 above the old height), + 24 independent ordered-word flow comparisons, exact cancellation and mirror + checks, empty-root and small-root examples, and invalid/corrupted inputs. +- Four exact compiler certificates across three raw profiles; eight invalid + numerical witnesses rejected. The p7 local-exponent upper endpoint must be + `.997481`; the earlier `.9974808` is rejected. + +The checks use exact Fraction intervals with explicit logarithm and exponential +tails. Floating-point calculations appear only in regression tests, not in +accepted scientific gates. All native and outer producer receipts are inherited +and authenticated, not freshly replayed. No Lean, Docker, native heavy replay, +full physical/precision instantiation or winning-word materialization was run. +The selected frontier remains unchanged. + +## Source and runtime transport + +Live mathematical sources, consumer receipts and baseline comparisons are +SHA256/Git-blob authenticated. The predecessor flow authenticates before +execution. Original Sussman license and notice are retained in the explicit +export closure. All changed research is scoped to this package. + +Final committed-byte and Git-free export results will be appended after the +scientific commit; this avoids representing uncommitted bytes as a transport +receipt. Full source-history ancestry checking requires an unshallow repository +and is not claimed here. diff --git a/research/rank-convergence/VERIFY.json b/research/rank-convergence/VERIFY.json new file mode 100644 index 0000000000..18c657a405 --- /dev/null +++ b/research/rank-convergence/VERIFY.json @@ -0,0 +1,31 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/direct-mixed-flow/flow.py", + "research/direct-mixed-flow/README.md", + "research/direct-mixed-flow/vendor/FINITE-PRECOMPILATION.md", + "research/direct-mixed-flow/vendor/theorem-1g.md", + "research/higher-moment-strictification/RESULT.json", + "research/native-lattice-retiming/RESULT.json", + "research/joint-helper-lattice/RESULT.json", + "research/compact-joint-compiler/arithmetic/RESULT.json", + "research/net-tax-rank-compiler/RESULT.json", + "research/net-tax-rank-compiler/intervals.py", + "research/direct-mixed-flow/vendor/SUSSMAN-LICENSE", + "research/direct-mixed-flow/vendor/SUSSMAN-NOTICE" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 300, + "checks": "Authenticate exact raw profiles, baseline and native-flow source; certify four adaptive-height witnesses across three profiles, uniform exponent/mirror covers and funded ranks; compare independent literal/window oracles and rejection controls. Native and outer producers are inherited receipts, not replayed." + } + ] +} diff --git a/research/rank-convergence/compiler.py b/research/rank-convergence/compiler.py new file mode 100644 index 0000000000..2a3bfcb3b3 --- /dev/null +++ b/research/rank-convergence/compiler.py @@ -0,0 +1,174 @@ +#!/usr/bin/env python3 +"""Exact finite certificates for the adaptive-height, padding-free compiler. + +Conditional on the raw native word and the integer-flow contracts in PROOF.md. +zxv, with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path +import json +import sys +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import intervals as E + +ONE = (Q(1), Q(1)) + + +def hist(value): + E.need(value and isinstance(value, dict), 'nonempty histogram') + out = {} + for k, n in value.items(): + r = int(k) + E.need(str(r) == str(k) and r >= 1 and type(n) is int and n > 0, + 'canonical positive rank and multiplicity') + out[r] = n + return out + + +def mean(h, t): + total = (Q(0), Q(0)) + for r, n in h.items(): + total = E.add(total, E.scale(E.mul(E.power(r, t), E.log_bounds(r)), n)) + return E.divide(total, E.moment(h, t)) + + +def log_interval(x): + E.need(x[0] > 0, 'positive logarithm interval') + def at(q): + return E.sub(E.log_bounds(q.numerator), E.log_bounds(q.denominator)) + return at(x[0])[0], at(x[1])[1] + + +def mirror_windows(T, P): + """Exact (left,right] cells; positive histograms for the two mirror sides.""" + cuts = sorted({Q(0), *[Q(1, k) for k in T], *[Q(1, r) for r in P]}) + cells = [] + for left, right in zip(cuts, cuts[1:]): + x = (left+right)/2 + exit_hist, source_hist = Counter(), Counter() + for r, count in P.items(): + for k, weight in T.items(): + if r > k and Q(1, r) < x <= Q(1, k): + exit_hist[r*k] += count*weight + if k > r and Q(1, k) < x <= Q(1, r): + source_hist[r*k] += count*weight + if exit_hist: + E.need(source_hist, 'boundary mirror window without source funding') + cells.append((left, right, exit_hist, source_hist)) + return cells + + +def mirror_certificate(T, P, t0, thi, beta, slices): + E.need(type(slices) is int and 1 <= slices <= 1000, 'bounded exponent cover') + best, witness = Q(0), None + cells = mirror_windows(T, P) + for i in range(slices): + lo, hi = t0+(thi-t0)*i/slices, t0+(thi-t0)*(i+1)/slices + for left, right, exits, sources in cells: + ratio = E.divide(E.moment(exits, hi), E.moment(sources, lo)) + E.need(ratio[1] < beta, 'uniform boundary mirror coefficient') + if ratio[1] > best: + best, witness = ratio[1], {'exponent_lower': str(lo), + 'exponent_upper': str(hi), 'window': [str(left), str(right)]} + return {'cells': len(cells), 'exponent_slices': slices, + 'maximum_upper': E.display((best, best)), 'maximizing_cell': witness} + + +def certify(profile, w): + T, P = hist(profile['targets']), hist(profile['paid']) + m = max(T) + E.need(2 <= min(T) and max(P) < m and P.get(1, 0) > 0, + 'raw overlapping-flow contract and nonempty forest') + E.need(sum(k*n for k, n in T.items()) > sum(k*n for k, n in P.items()), + 'raw positive rank-one surplus') + t0, thi, p, c, s, lam = (Q(w[k]) for k in ('t0', 't_upper', 'p', 'c', 's', 'lambda')) + a, b, M, ell = (w[k] for k in ('a', 'b', 'height_base', 'ell0')) + E.need(all(type(x) is int and x >= 1 for x in (a, b, ell)) + and type(M) is int and M >= 2, 'integer adaptive-height geometry') + E.need(0 < t0 < thi < 1 and p > 0 and s > 0 and lam > 0, + 'adaptive exponent domain') + E.need(c >= p/(1-t0), 'concave funded majorant domain') + guards = {k: Q(w['guards'][k]) for k in ('U', 'V', 'Q', 'd', 'beta', 'eta')} + U, V, Qmax, d, beta, eta_min = (guards[k] for k in ('U', 'V', 'Q', 'd', 'beta', 'eta')) + E.need(0 < U < 1 and 0 < V < 1 and Qmax > 1 and d > 0 + and 0 < beta < eta_min < 1, 'finite guard domains') + logm, logM, log2 = E.log_bounds(m), E.log_bounds(M), E.log_bounds(2) + logn0 = E.add(logm, E.scale(logM, ell)) + tau_max = E.add((t0, t0), E.divide((p, p), E.add((c, c), logn0))) + E.need(tau_max[1] < thi, 'local exponent interval covers ordinary base cutoff') + T0, P0 = E.moment(T, t0), E.moment(P, t0) + E.need(T0[0] > P0[1], 'raw strict moment at base exponent') + q_upper = E.divide(E.moment(T, thi), P0) + E.need(q_upper[1] < Qmax, 'uniform moment ratio Q') + derivative = E.sub(mean(T, t0), mean(P, thi)) + E.need(derivative[0] > d, 'uniform positive tilted log-mean gap') + + def ratio(h, t): + return E.divide(E.moment(h, t+s), E.moment(h, t)) + target_low, paid_high = ratio(T, t0), ratio(P, thi) + E.need(target_low[0] > paid_high[1], 'mixed layer endpoint dominates every lower layer') + u = E.mul(E.power(M, -s), E.mul(E.ipow(ratio(T, thi), a), E.ipow(paid_high, b))) + E.need(u[1] < U, 'mixed layer Chernoff U') + v = E.mul(E.power(M, lam), E.ipow(E.divide(E.moment(T, thi-lam), P0), a+b)) + E.need(v[1] < V, 'root source Chernoff V') + eta = E.scale(E.power(m, t0-1), t0) + E.need(eta[0] > eta_min, 'source complement capacity') + mirrors = mirror_certificate(T, P, t0, thi, beta, w.get('mirror_slices', 20)) + + denominator = E.add((c, c), E.add(logm, E.add(E.scale(logM, ell+1), log2))) + exponent = E.divide((d*p*(a*ell+1),)*2, denominator) + gain = E.sub(E.exp_interval(exponent), ONE) + lower_D = E.sub(E.scale(gain, 1-U**ell), E.scale(E.power(M, lam), Qmax*V**ell)) + required = (1-eta_min)/(eta_min-beta) + E.need(lower_D[0] > required, 'sharp source and boundary cancellation for all heights') + # With a>=1, the derivative of (a*l+1)/(constant+(l+1)logM) + # has numerator a*(c+logm+log2)+(a-1)logM >0. + monotone = E.add(E.scale(E.add((c, c), E.add(logm, log2)), a), + E.scale(logM, a-1)) + E.need(monotone[0] > 0, 'uniform height monotonicity') + logA = E.sub(E.scale(logn0, 1-t0), + E.scale(log_interval(E.add((c, c), logn0)), p)) + saving, kappa = Q(w['uniform_saving']), Q(w['kappa']) + gap = 1-saving-t0 + E.need(0 < kappa < saving < 1-t0 and gap > 0, 'funded uniform and consumer savings') + + def final_margin(H): + x = E.scale(log2, H) + lhs = E.add(logA, E.scale(log_interval(E.add((c, c), x)), p)) + return E.sub(E.scale(x, gap), lhs) + + H = w['H'] + E.need(type(H) is int and H > 0 and Q(H)*log2[0] > logn0[1], + 'uniform rank beyond ordinary base') + margin = final_margin(H) + E.need(margin[0] > 0, 'funded final uniform-rank inequality') + E.need(gap*(c+H*log2[0]) > p, 'final comparison remains true at larger ranks') + return {'status': 'PASS_ADAPTIVE_HEIGHT_DIRECT_COMPILER', + 'raw_ambient': m, 'raw_minimum_target': min(T), 'raw_maximum_paid': max(P), + 'raw_fields': sum(T.values()), 'tensor_power': 1, + 't0': str(t0), 't_upper': str(thi), 'p': str(p), 'c': str(c), + 'height_base': M, 'height_multiplier': a+b, 'ell0': ell, + 'ordinary_base': str(m)+'*'+str(M)+'^'+str(ell), + 'local_exponent_max': E.display(tau_max), + 'q_base': E.display(E.divide(T0, P0)), 'q_upper': E.display(q_upper), + 'tilted_log_mean_gap': E.display(derivative), + 'target_mgf_lower': E.display(target_low), 'paid_mgf_upper': E.display(paid_high), + 'mixed_chernoff': E.display(u), 'root_chernoff': E.display(v), + 'source_capacity': E.display(eta), 'mirror': mirrors, + 'uniform_D_lower': E.display(lower_D), 'required_D_upper': str(required), + 'log_majorant_normalization': E.display(logA), + 'H': H, 'N': '2^'+str(H), 'uniform_saving': str(saving), + 'kappa': str(kappa), 'uniform_gap': str(gap), + 'final_logarithmic_margin': E.display(margin), + 'word_materialized': False, 'native_and_outer_producers_replayed': False} + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('profile', type=Path) + parser.add_argument('witness', type=Path) + args = parser.parse_args() + print(json.dumps(certify(json.loads(args.profile.read_text()), + json.loads(args.witness.read_text())), indent=2, sort_keys=True)) diff --git a/research/rank-convergence/flow.py b/research/rank-convergence/flow.py new file mode 100644 index 0000000000..7f5198a5d4 --- /dev/null +++ b/research/rank-convergence/flow.py @@ -0,0 +1,141 @@ +#!/usr/bin/env python3 +"""Arbitrary-height wrapper of zxv's PR4436 integer Pascal flow. + +The inherited chronological literal evaluator is unchanged. Jacob Alan +Sussman's integer compiler supplies the underlying construction. New source +classification and exact invoice checks: OpenAI Codex assistance, Apache-2.0. +""" +from collections import Counter +from hashlib import sha256 +from pathlib import Path +from types import ModuleType + +SOURCE = Path(__file__).resolve().parent.parent / 'direct-mixed-flow/flow.py' +SOURCE_SHA256 = '460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a' + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def load_source(path=SOURCE): + """Authenticate bytes before executing the frozen predecessor source.""" + path = Path(path) + raw = path.read_bytes() + need(sha256(raw).hexdigest() == SOURCE_SHA256, 'Changed predecessor flow bytes') + module = ModuleType('_rank_convergence_predecessor_flow') + module.__file__ = str(path) + exec(compile(raw, str(path), 'exec'), module.__dict__) + return module.Flow + + +BaseFlow = load_source() + + +def positive(counter): + return Counter({k: v for k, v in counter.items() if v}) + + +def verify_receipt(targets, paid, n, receipt): + """Check the formal rank invoice, without evaluating fractional powers.""" + sources, exits = receipt['sources'], receipt['exits'] + roots, inner = receipt['root_sources'], receipt['nonroot_sources'] + boundary, leaves = receipt['boundary_exits'], receipt['leaf_exits'] + columns = receipt['unit_columns'] + m, rmax = max(targets), max(paid) + for inventory in (sources, exits, roots, inner, boundary, leaves, columns): + need(all(isinstance(k, int) and k > 0 and isinstance(v, int) and v > 0 + for k, v in inventory.items()), 'Positive integer rank inventory') + need(bool(sources) and bool(columns), 'Empty arbitrary-height flow') + need(sources == roots + inner, 'Root/nonroot source partition') + need(exits == boundary + leaves, 'Boundary/leaf exit partition') + need(all(s <= n and 0 <= n-s < n for s in sources), 'Strict complement descent') + need(all(m*s > n for s in inner), 'Nonroot source lower bound') + need(all(e < n and m*e <= rmax*n for e in exits), 'Strict paid-exit descent') + need(all(m*z <= n for z in columns), 'Native positive integer columns fit cap') + invoice = Counter(sources) + invoice.subtract(exits) + for z, count in columns.items(): + for k, repetitions in targets.items(): + invoice[k*z] -= count*repetitions + for r, repetitions in paid.items(): + invoice[r*z] += count*repetitions + need(not positive(invoice), 'Formal rank-invoice cancellation') + need(sum(columns.values()) == receipt['units'], 'Unit column histogram count') + need(sum(z*w for z, w in columns.items()) == receipt['column_mass'], + 'Unit column histogram rank mass') + return True + + +class Flow(BaseFlow): + def __init__(self, targets, paid, n, G): + need(isinstance(G, int) and not isinstance(G, bool) and G >= 0, + 'Nonnegative integer explicit height') + need(targets and paid and all(isinstance(k, int) and k >= 1 + for inventory in (targets, paid) for k in inventory), + 'Positive integer target and paid ranks') + # Base initialization uses no cached point/unit/demand method. A base + # greater than kmin disables only its obsolete ALL-source lower bound; + # our receipt checks the correct nonroot bound below. No cache is + # populated at one height and reused after assigning another height. + super().__init__(targets, paid, n, height_base=max(targets)+1) + self.G = G + + def merged(self): + # An arbitrary-height forest may be empty for a generic profile. + # Classify it first so rejection has a specific, intentional reason. + roots = Counter() + for b, count in self.demand(0, 1).items(): + roots[self.column(b)] += count + inner, boundary, leaves, columns = Counter(), Counter(), Counter(), Counter() + paths = Counter({1: 1}) + for depth in range(self.G+1): + following = Counter() + for rho, multiplicity in paths.items(): + batch = self.units(depth, rho) + for a, count in batch.items(): + columns[rho*self.column(a)] += multiplicity*count + for rank, repetitions in self.P.items(): + new_rho, copies = rho*rank, multiplicity*repetitions + if depth == self.G: + for a, count in batch.items(): + leaves[new_rho*self.column(a)] += copies*count + continue + child = self.demand(depth+1, new_rho) + # Empty parent classes do not suppress later fresh-source + # components. Prefix multipliers are nondecreasing. + if new_rho <= self.cap: + following[new_rho] += copies + for b in set(batch) | set(child): + supply, demand = batch.get(b, 0), child.get(b, 0) + e = new_rho*self.column(b) + if supply > demand: + boundary[e] += copies*(supply-demand) + elif demand > supply: + need(supply == 0, 'Absent parent supplies fresh source') + inner[e] += copies*(demand-supply) + paths = following + need(bool(columns) and bool(roots + inner), 'Empty arbitrary-height flow') + receipt = super().merged() + need(receipt['sources'] == roots + inner, 'Predecessor source agreement') + need(receipt['exits'] == boundary + leaves, 'Predecessor exit agreement') + need(receipt['boundary_exits'] == boundary, 'Predecessor boundary agreement') + receipt.update(root_sources=roots, nonroot_sources=inner, + leaf_exits=leaves, unit_columns=columns) + verify_receipt(self.T, self.P, self.n, receipt) + return receipt + + +def adaptive_flow(targets, paid, n, witness): + """Construct G=(a+b)*floor(log_M floor(n/m)) with integer arithmetic.""" + M, a, b = (witness[key] for key in ('height_base', 'a', 'b')) + need(type(M) is int and M >= 2 and all(type(x) is int and x >= 1 for x in (a, b)), + 'Integer adaptive geometry') + cap, ell = n//max(targets), 0 + while cap >= M: + cap //= M + ell += 1 + result = Flow(targets, paid, n, (a+b)*ell) + result.adaptive_geometry = {'height_base': M, 'height_multiplier': a+b, 'ell': ell} + return result diff --git a/research/rank-convergence/intervals.py b/research/rank-convergence/intervals.py new file mode 100644 index 0000000000..f3d990ab63 --- /dev/null +++ b/research/rank-convergence/intervals.py @@ -0,0 +1,150 @@ +#!/usr/bin/env python3 +"""Outward rational intervals, adapted from my PR4433 arithmetic. + +All endpoints are fractions; series tails and every rounding are outward. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +from fractions import Fraction as Q +from functools import lru_cache +GRID = 2**192 + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + + +def encoded(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encoded(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encoded(v) for v in x] + return x + + + +def add(a, b): + return rounded(a[0]+b[0], a[1]+b[1]) + + +def sub(a, b): + return rounded(a[0]-b[1], a[1]-b[0]) + + +def ipow(a, n): + """Integer powers of a nonnegative interval, bounded-size endpoints.""" + need(type(n) is int and n >= 0 and a[0] >= 0, 'nonnegative integer power') + out = (Q(1), Q(1)) + while n: + if n & 1: + out = mul(out, a) + a = mul(a, a) + n //= 2 + return out + + +def qpower(x, exponent): + """Positive rational base, rational exponent, with an enclosed logarithm.""" + x = Q(x) + need(x > 0, 'positive rational power base') + return exp_interval(scale(sub(log_bounds(x.numerator), + log_bounds(x.denominator)), exponent)) diff --git a/research/rank-convergence/test_flow.py b/research/rank-convergence/test_flow.py new file mode 100644 index 0000000000..4fe12fcd79 --- /dev/null +++ b/research/rank-convergence/test_flow.py @@ -0,0 +1,95 @@ +#!/usr/bin/env python3 +"""Finite correctness controls for the changed height and exact invoice.""" +from copy import deepcopy +from pathlib import Path +import tempfile +import unittest + +from flow import Flow, SOURCE, adaptive_flow, load_source, verify_receipt + + +class HeightFlowTests(unittest.TestCase): + def test_integer_adaptive_height_boundaries(self): + targets, paid = {2: 1, 5: 1}, {1: 2, 4: 1} + witness = {'height_base': 4, 'a': 1, 'b': 1} + for n, expected in ((19, 0), (20, 2), (79, 2), (80, 4)): + changed = adaptive_flow(targets, paid, n, witness) + self.assertEqual(changed.G, expected) + self.assertEqual(changed.adaptive_geometry['ell'], expected//2) + self.assertTrue(changed.merged()['sources']) + + def test_eighty_literal_fixtures(self): + fixtures = [({2: 1, 3: 1}, {1: 1, 2: 1}), + ({2: 2, 4: 1}, {1: 2, 3: 1}), + ({2: 1, 3: 2}, {1: 2, 2: 1}), + ({3: 1, 5: 1}, {1: 1, 4: 1})] + count = above_old = empty_roots = 0 + for targets, paid in fixtures: + for factor in (1, 2, 5, 11): + n = factor*max(targets) + old_height, least = 0, 1 + while least*min(targets) <= n//max(targets): + old_height += 1 + least *= min(targets) + for height in range(5): + with self.subTest(targets=targets, paid=paid, n=n, G=height): + f = Flow(targets, paid, n, height) + receipt = f.merged() + paid_word = [r for r, w in paid.items() for _ in range(w)] + literal = f.literal(paid_word, class_limit=100000) + self.assertEqual(receipt['sources'], literal['sources']) + self.assertEqual(receipt['exits'], literal['exits']) + self.assertTrue(verify_receipt(targets, paid, n, receipt)) + above_old += height > old_height + empty_roots += not receipt['root_sources'] + count += 1 + self.assertEqual(count, 80) + self.assertEqual(above_old, 43) + self.assertGreater(empty_roots, 0) + + def test_small_roots_are_not_subject_to_inner_bound(self): + f = Flow({2: 1, 3: 1}, {1: 1, 2: 1}, 6, 0) + receipt = f.merged() + self.assertIn(2, receipt['root_sources']) + self.assertFalse(f.n < f.m*2) + self.assertFalse(receipt['nonroot_sources']) + + def test_empty_root_forest_with_paid_rank_one(self): + f = Flow({2: 1, 3: 1}, {1: 1, 2: 1}, 3, 4) + receipt = f.merged() + self.assertFalse(receipt['root_sources']) + self.assertTrue(receipt['nonroot_sources']) + self.assertEqual(receipt['sources'], f.literal([1, 2])['sources']) + self.assertTrue(all(e < 3 for e in receipt['exits'])) + + def test_generic_empty_flow_rejected(self): + with self.assertRaisesRegex(ValueError, 'Empty arbitrary-height flow'): + Flow({2: 1, 4: 1}, {2: 1}, 4, 3).merged() + + def test_formal_invoice_rejects_false_rank(self): + f = Flow({2: 1, 3: 1}, {1: 1, 2: 1}, 15, 2) + bad = deepcopy(f.merged()) + rank = next(iter(bad['unit_columns'])) + bad['unit_columns'][rank] += 1 + with self.assertRaisesRegex(ValueError, 'Formal rank-invoice cancellation'): + verify_receipt(f.T, f.P, f.n, bad) + + def test_classification_rejects_false_root_credit(self): + f = Flow({2: 1, 3: 1}, {1: 1, 2: 1}, 6, 0) + bad = deepcopy(f.merged()) + bad['root_sources'][2] -= 1 + del bad['root_sources'][2] + bad['nonroot_sources'][2] += 1 + with self.assertRaisesRegex(ValueError, 'Nonroot source lower bound'): + verify_receipt(f.T, f.P, f.n, bad) + + def test_source_authentication_precedes_execution(self): + with tempfile.TemporaryDirectory() as directory: + path = Path(directory)/'untrusted.py' + path.write_bytes(SOURCE.read_bytes()+b'\nraise RuntimeError("executed")\n') + with self.assertRaisesRegex(ValueError, 'Changed predecessor flow bytes'): + load_source(path) + + +if __name__ == '__main__': + unittest.main() diff --git a/research/rank-convergence/test_independent.py b/research/rank-convergence/test_independent.py new file mode 100644 index 0000000000..8b28161bbb --- /dev/null +++ b/research/rank-convergence/test_independent.py @@ -0,0 +1,140 @@ +#!/usr/bin/env python3 +"""Independent finite audits of adaptive flow and local-exponent induction. + +The oracle convolves ordered target/paid words, rather than enumerating target +multiindices or using Pascal demands. Exact mirror windows reconstruct the +whole invoice. Floating checks below are regression controls, not certificates. +Prepared with substantial OpenAI Codex assistance. Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +from math import exp, fsum, log +import unittest + +from flow import Flow + + +def words(histogram, length): + result = Counter({1: 1}) + for _ in range(length): + following = Counter() + for x, count in result.items(): + for r, multiplicity in histogram.items(): + following[x*r] += count*multiplicity + result = following + return result + + +def mirror_oracle(targets, paid, n, height): + """Reconstruct all invoice components from ordered-word window formulas.""" + cap = n//max(targets) + root, inner, boundary, leaves, units = (Counter() for _ in range(5)) + for col, count in words(targets, height).items(): + if col <= cap: + for k, multiplicity in targets.items(): + root[k*col] += count*multiplicity + for depth in range(height+1): + for rho, paths in words(paid, depth).items(): + for col, count in words(targets, height-depth).items(): + if rho*col <= cap: + units[rho*col] += paths*count + if depth == height: + if rho <= cap: + for r, multiplicity in paid.items(): + leaves[r*rho] += paths*multiplicity + continue + for col, count in words(targets, height-depth-1).items(): + z = rho*col + for r, pr in paid.items(): + for k, wk in targets.items(): + rank, mass = r*k*z, paths*count*pr*wk + if k*z <= cap < r*z: + boundary[rank] += mass + if r*z <= cap < k*z: + inner[rank] += mass + return dict(root_sources=root, nonroot_sources=inner, + boundary_exits=boundary, leaf_exits=leaves, + sources=root+inner, exits=boundary+leaves, unit_columns=units) + + +class IndependentFlowAudit(unittest.TestCase): + def test_ordered_word_mirror_reconstruction(self): + targets, paid = {2: 2, 5: 1}, {1: 1, 3: 1} + saw_empty_root = saw_small_root = False + for n in (5, 10, 27, 61): + for height in range(6): + with self.subTest(n=n, height=height): + expected = mirror_oracle(targets, paid, n, height) + actual = Flow(targets, paid, n, height).merged() + for key, value in expected.items(): + self.assertEqual(dict(actual[key]), dict(value), key) + # Exact formal cancellation at every individual rank. + balance = Counter(expected['sources']) + balance.subtract(expected['exits']) + for col, count in expected['unit_columns'].items(): + for k, wk in targets.items(): + balance[k*col] -= count*wk + for r, pr in paid.items(): + balance[r*col] += count*pr + self.assertTrue(all(value == 0 for value in balance.values())) + self.assertTrue(all(max(targets)*s > n + for s in expected['nonroot_sources'])) + saw_empty_root |= not expected['root_sources'] + saw_small_root |= any(max(targets)*s <= n + for s in expected['root_sources']) + self.assertTrue(saw_empty_root, 'exercise a forest with no root units') + self.assertTrue(saw_small_root, 'old root source lower bound must fail') + + def test_small_roots_cannot_use_inner_capacity(self): + invoice = mirror_oracle({2: 2, 5: 1}, {1: 1, 3: 1}, 61, 0) + self.assertEqual(invoice['root_sources'], Counter({2: 2, 5: 1})) + self.assertFalse(invoice['nonroot_sources']) + self.assertTrue(all(s <= Q(61, 5) for s in invoice['root_sources'])) + + +class IndependentInductionAudit(unittest.TestCase): + def test_sharp_source_boundary_threshold_and_failure_below_it(self): + for beta in (Q(0), Q(1, 3), Q(3, 4)): + eta = beta+(1-beta)/2 + threshold = (1-eta)/(eta-beta) + for factor in (Q(1, 2), Q(1), Q(2)): + excess, leaves = threshold*factor, Q(1) + # Saturate the permitted boundary share, independently of flow. + inner = (leaves+excess)/(1-beta) + boundary = beta*inner + self.assertEqual(inner, boundary+leaves+excess) + self.assertEqual((boundary+leaves <= eta*inner), factor >= 1) + + def test_local_exponent_domain_regression(self): + t0, power, shift = .99731352, .1, 38. + log_n0 = log(121)+100*log(256) + tau_max = t0+power/(shift+log_n0) + # The initially proposed upper endpoint was a genuine failed guard. + self.assertGreater(tau_max, .9974808) + self.assertLess(tau_max, .997481) + self.assertGreaterEqual(shift*(1-t0), power) + for log_n in (0., 1., log(121), log_n0, 1.e6): + tau = t0+power/(shift+log_n) + self.assertLessEqual(tau, 1.) + curvature = tau*(tau-1)-power/(shift+log_n)**2 + self.assertLess(curvature, 0.) + for fraction in (0., .01, .5, .99, 1.): + log_e = fraction*log_n + actual = t0*(log_e-log_n)+power*log((shift+log_e)/(shift+log_n)) + tangent = tau*(log_e-log_n) + self.assertLessEqual(actual, tangent+1.e-9) + + def test_raw_superpotential_rejects_below_root_mutant(self): + targets = {5:420, 6:270, 7:840, 8:1395, 9:3195, + 25:448, 41:448, 57:448, 121:224} + paid = {1:37305, 2:10695, 3:3360, 4:1530, 5:300, + 8:1464, 16:448, 32:448, 48:448} + def ratio(t): + return (fsum(count*exp(t*log(k)) for k,count in targets.items()) / + fsum(count*exp(t*log(k)) for k,count in paid.items())) + self.assertGreater(ratio(.99731352), 1.) + self.assertLess(ratio(.99731252), 1.) + + +if __name__ == '__main__': + unittest.main(verbosity=2) diff --git a/research/rank-convergence/verify.py b/research/rank-convergence/verify.py new file mode 100644 index 0000000000..3e7f482a8b --- /dev/null +++ b/research/rank-convergence/verify.py @@ -0,0 +1,175 @@ +#!/usr/bin/env python3 +"""Source-bound finite proof gates for the padding-free rank compiler. + +Native and outer producer receipts are inherited, not replayed. +zxv with substantial OpenAI Codex assistance; Apache-2.0. +""" +import argparse +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha1, sha256 +import io +import json +from pathlib import Path +import sys +import unittest +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) +import compiler +import intervals as E +import flow +import test_flow +import test_independent + + +def authenticate_bytes(raw, row): + E.need(sha256(raw).hexdigest() == row['sha256'], 'source SHA256: '+row['path']) + E.need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], + 'source Git blob: '+row['path']) + + +def authenticate(): + receipt = {} + rows = json.loads((HERE/'SOURCES.json').read_text())['files'] + for row in rows: + if row['usage'] == 'input': + authenticate_bytes((ROOT/row['path']).read_bytes(), row) + receipt[row['path']] = row['sha256'] + path = str(flow.SOURCE.relative_to(ROOT)) + E.need(path in receipt and receipt[path] == flow.SOURCE_SHA256, + 'executed predecessor is a declared authenticated input') + first = next(row for row in rows if row['usage'] == 'input') + try: + authenticate_bytes((ROOT/first['path']).read_bytes()+b' ', first) + except ValueError: + pass + else: + raise ValueError('source corruption control accepted') + return receipt + + +def at(value, keys): + for key in keys: + value = value[key] + return value + + +def rejected(profile, witness, fragment, mutation): + changed = deepcopy(witness) + mutation(changed) + try: + compiler.certify(profile, changed) + except ValueError as exc: + E.need(fragment in str(exc), 'unexpected rejection: '+str(exc)) + return str(exc) + raise ValueError('invalid witness accepted: '+fragment) + + +def run(): + sources = authenticate() + suite = unittest.TestSuite(unittest.defaultTestLoader.loadTestsFromModule(module) + for module in (test_flow, test_independent)) + output = io.StringIO() + tests = unittest.TextTestRunner(stream=output, verbosity=1).run(suite) + E.need(tests.wasSuccessful(), output.getvalue()) + results, profiles, witnesses = {}, {}, {} + for row in json.loads((HERE/'BENCHMARKS.json').read_text())['cases']: + E.need(row['source'] in sources and row['baseline']['source'] in sources, + 'every profile, consumer and comparison source authenticated') + source = json.loads((ROOT/row['source']).read_text()) + profile = source[row['profile_key']] if row['profile_key'] else source + result = compiler.certify(profile, row['witness']) + outer = at(source, row['consumer_key']) + required = Q(outer['parameters']['complex_uniform_saving']) + E.need(Q(result['kappa']) == Q(source['kappa']) == Q(outer['parameters']['kappa']), + 'retained consumer kappa identity') + E.need(Q(result['uniform_saving']) >= required, 'supplied uniform bound funds retained consumer') + E.need(len(outer['margins']) == 9 + and all(Q(x) > Q(result['kappa']) for x in outer['margins'].values()), + 'nine inherited consumer margins') + for name in ('strict_checks', 'functional_checks'): + E.need(outer[name] and all(Q(x) > 0 for x in outer[name].values()), + 'positive inherited '+name+' receipt') + legacy_outer = source.get('legacy_outer', {}) + legacy = legacy_outer.get('checks', legacy_outer.get('strict_checks', + source['outer'].get('legacy_63_checks', {}))) + E.need(len(legacy) == 63 and all(Q(x) > 0 for x in legacy.values()), + 'positive inherited legacy receipt') + baseline_source = json.loads((ROOT/row['baseline']['source']).read_text()) + baseline = at(baseline_source, row['baseline']['path']) + baseline_kappa = baseline.get('kappa', baseline_source.get('kappa')) + E.need(baseline_kappa is not None and Q(baseline_kappa) == Q(result['kappa']), + 'comparison retains the same kappa') + if row['baseline']['source'] != row['source']: + E.need(baseline_source['source_sha256'][row['source']] == sources[row['source']], + 'comparison receipt uses the same exact raw profile source') + if 'uniform_saving' in baseline: + baseline_saving = Q(baseline['uniform_saving']) + else: + baseline_saving = Q(baseline_source['outer']['parameters']['complex_uniform_saving']) + result['comparison'] = {'source': row['baseline']['source'], + 'source_path': row['baseline']['path'], 'baseline_H': baseline['H'], + 'baseline_uniform_saving': str(baseline_saving), + 'same_uniform_saving': Q(result['uniform_saving']) == baseline_saving, + 'rank_exponent_reduction': str(Q(baseline['H'], result['H']))} + result['consumer_binding'] = {'status': 'INHERITED_RECEIPT_AND_MONOTONE_BOUND', + 'producer_replayed': False, 'required_uniform_saving': str(required), + 'available_uniform_saving': result['uniform_saving'], + 'current_strict_checks': len(outer['strict_checks']), + 'functional_guards': len(outer['functional_checks']), + 'legacy_checks': len(legacy)} + results[row['name']], profiles[row['name']], witnesses[row['name']] = result, profile, row['witness'] + # Bind the new p16 data to the actual published joint-helper profile as + # well as its compact consumer receipt; no invoice is inferred from labels. + joint_path = 'research/joint-helper-lattice/RESULT.json' + E.need(joint_path in sources, 'joint native profile authenticated') + joint = json.loads((ROOT/joint_path).read_text()) + E.need(all(joint[key] == profiles['p16'][key] for key in ('targets', 'paid')), + 'p16 compact/native profile equality') + name = 'p7' + profile, witness = profiles[name], witnesses[name] + controls = {} + for label, fragment, mutate in ( + ('old_incomplete_tau_interval', 'local exponent interval', lambda w: w.update(t_upper='.9974808')), + ('below_root_moment', 'raw strict moment', lambda w: w.update(t0='.99731252')), + ('nonconcave_majorant', 'concave funded majorant', lambda w: w.update(c='1')), + ('unfunded_root_tail', 'root source Chernoff', lambda w: w['guards'].update(V='.8')), + ('understated_boundary_share', 'boundary mirror coefficient', lambda w: w['guards'].update(beta='.2')), + ('insufficient_tilted_gap', 'sharp source and boundary', lambda w: w['guards'].update(d='.1')), + ('unfunded_uniform_gap', 'funded uniform and consumer', lambda w: w.update(uniform_saving=str(1-Q(w['t0'])))), + ('too_small_final_rank', 'final uniform-rank inequality', lambda w: w.update(H=100000000)), + ): + controls[label] = rejected(profile, witness, fragment, mutate) + E.need(results['native4453-matched-uniform']['comparison']['same_uniform_saving'], + 'controlled native comparison preserves uniform saving') + E.need(results['p7']['comparison']['same_uniform_saving'] + and results['p16']['comparison']['same_uniform_saving'], + 'p7 and newest p16 comparisons preserve uniform saving') + return {'schema_version': 1, 'status': 'PASS_PADDING_FREE_ADAPTIVE_COMPILER', + 'scope': 'Conditional direct overlapping-rank compiler under explicit finite gates; exact rank and inherited consumer binding, not a native/physical/analytic theorem audit.', + 'source_sha256': sources, 'examples': results, + 'finite_tests': tests.testsRun, 'rejected_witnesses': controls, + 'source_mutation_rejected': True} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + args = parser.parse_args() + receipt = run() + raw = json.dumps(receipt, sort_keys=True, indent=2)+'\n' + path = HERE/'RESULT.json' + if args.write: + path.write_text(raw) + else: + E.need(path.read_text() == raw, 'changed exact receipt; inspect then use --write') + print(json.dumps({'status': receipt['status'], 'finite_tests': receipt['finite_tests'], + 'rejected_witnesses': len(receipt['rejected_witnesses']), + 'examples': {name: {'H': r['H'], 'kappa': r['kappa'], 'tensor_power': 1, + 'reduction': r['comparison']['rank_exponent_reduction']} + for name, r in receipt['examples'].items()}}, sort_keys=True)) + + +if __name__ == '__main__': + main() From 3b672e92f3e2f61fe7f93e372e3ca1d0d144953a Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 20:54:15 -0400 Subject: [PATCH 25/26] Record portable compiler replay and mutation controls --- research/rank-convergence/PROOF.md | 6 +++--- research/rank-convergence/TASK.json | 10 ++++++++-- research/rank-convergence/VALIDATION.md | 24 +++++++++++++++++++++--- 3 files changed, 32 insertions(+), 8 deletions(-) diff --git a/research/rank-convergence/PROOF.md b/research/rank-convergence/PROOF.md index a3ece409d9..001436327a 100644 --- a/research/rank-convergence/PROOF.md +++ b/research/rank-convergence/PROOF.md @@ -422,9 +422,9 @@ by itself prove a larger multiplication kappa. 1. Independently check the arbitrary-height flow and mirror identity, including small root sources and empty-root classes. A finite integer check should distinguish this flow from the old minimum-target height. -2. Certify the strongest relevant raw profile using (18)--(20), and compare - complete final ranks through (17). Better constants are useful only - when every guard and the normalization are included. +2. Extend the certificates beyond the three supplied raw profiles using + (18)--(20), or improve their geometry while holding the consumer saving + fixed. Compare complete final ranks through (17), including normalization. 3. Audit the resulting word's native physical implementations and full finite constants. The theorem removes an exponent-convergence obstacle; it does not discharge those caller obligations. diff --git a/research/rank-convergence/TASK.json b/research/rank-convergence/TASK.json index 50ba5c9051..e3b73fe3d8 100644 --- a/research/rank-convergence/TASK.json +++ b/research/rank-convergence/TASK.json @@ -89,7 +89,8 @@ "PR4479": "035008ddc2cea4949829d309770e67479e696d9e", "PR4470": "b9a13c1673e0e9697de410de16e8bbf3207a7363", "PR4436": "56003680aee2871773de408e5f01cc5dd46b144c" - } + }, + "PR4480_publication_head": "4cf054a50c5718616594ec4ca2c9114278120a8b" }, "open_questions": [ { @@ -132,6 +133,11 @@ "exact_certificates": 4, "rejected_witnesses": 8, "native_outer_producer_replays": "inherited exact receipts; not rerun", - "review": "Separate Sol 6.1 medium proof and implementation audits; not formal or independent human acceptance." + "review": "Separate Sol 6.1 medium proof and implementation audits; not formal or independent human acceptance.", + "registered_final": "pass", + "committed_byte_preflight": "pass at 527dc558072f0336b3b0b8023fd972f0af398d15", + "checked_export": "pass: 26 files", + "git_free_isolated_optimized": "pass: no Git and PATH=/nonexistent", + "exported_mutation_controls": "pass: changed predecessor rejected before execution; altered exact receipt rejected after recomputation" } } diff --git a/research/rank-convergence/VALIDATION.md b/research/rank-convergence/VALIDATION.md index 1a94ea76c1..c85b76f8be 100644 --- a/research/rank-convergence/VALIDATION.md +++ b/research/rank-convergence/VALIDATION.md @@ -35,7 +35,25 @@ SHA256/Git-blob authenticated. The predecessor flow authenticates before execution. Original Sussman license and notice are retained in the explicit export closure. All changed research is scoped to this package. -Final committed-byte and Git-free export results will be appended after the -scientific commit; this avoids representing uncommitted bytes as a transport -receipt. Full source-history ancestry checking requires an unshallow repository +Scientific commit: `527dc558072f0336b3b0b8023fd972f0af398d15`. + +- Final registered replay with the original Sussman license and notice inputs: + `PASS_REGISTERED_RESEARCH_PACKAGE`, outcome completed. +- `python3.12 -B scripts/check_research_commit.py --package research/rank-convergence`: + `PASS_RESEARCH_COMMIT_BYTES`, 26 files. +- `python3.12 -B scripts/export_research_package.py export --package research/rank-convergence --output /tmp/rank-convergence-science.tar`: + `PASS_RESEARCH_EXPORT`, 26 files; archive checker passed. +- Extracted to a fresh directory with no `.git`. Direct replay with + `python3.12 -I -O -B`, absolute interpreter path and `PATH=/nonexistent`: + `PASS_PADDING_FREE_ADAPTIVE_COMPILER`, all four certificates, 13 tests and + eight rejected witnesses. Neither Git nor an undeclared Python dependency + was available through PATH. +- Altering the extracted predecessor flow bytes is rejected before execution. + A first external test harness expected the wrong diagnostic substring; + the verifier itself rejected correctly. The harness was corrected. +- Altering the extracted exact RESULT receipt is rejected after recomputation; + both exported mutation controls passed. Original extracted bytes were restored. + +Only documentation and validation metadata were edited after the scientific +commit. Full source-history ancestry checking requires an unshallow repository and is not claimed here. From fb0c208864e6b24e3473318a058aa5b2dbd5764b Mon Sep 17 00:00:00 2001 From: zxv Date: Wed, 21 Oct 2026 20:56:48 -0400 Subject: [PATCH 26/26] Link predecessor PRs and record approval to publish adaptive compiler --- research/rank-convergence/PROOF.md | 10 ++++----- research/rank-convergence/README.md | 35 +++++++++++++++-------------- research/rank-convergence/TASK.json | 11 +++++++-- 3 files changed, 32 insertions(+), 24 deletions(-) diff --git a/research/rank-convergence/PROOF.md b/research/rank-convergence/PROOF.md index 001436327a..75f4518372 100644 --- a/research/rank-convergence/PROOF.md +++ b/research/rank-convergence/PROOF.md @@ -8,8 +8,8 @@ decimals alone are not a certificate. The finite integer/Pascal compiler is Jacob Alan Sussman's construction. The capped overlapping-rank flow and its chronological interpretation are -zxv's PR4436. Ryanson Jonathan's corrected PR4459 supplies the mirror-window -identity and boundary-share method. PR4456, PR4465, PR4467 and PR4476 provide +my [PR #4436](https://github.com/CrocSwap/integer-mult-bounds/pull/4436). Ryanson Jonathan's corrected [PR #4459](https://github.com/CrocSwap/integer-mult-bounds/pull/4459) supplies the mirror-window +identity and boundary-share method. [PR #4456](https://github.com/CrocSwap/integer-mult-bounds/pull/4456), [PR #4465](https://github.com/CrocSwap/integer-mult-bounds/pull/4465), [PR #4467](https://github.com/CrocSwap/integer-mult-bounds/pull/4467) and [PR #4476](https://github.com/CrocSwap/integer-mult-bounds/pull/4476) provide independent finite checks and important warnings about the original height: leaf exits need not be sublinear and their potential cannot be discarded. The present argument changes that height, bounds root and leaf contributions, @@ -52,7 +52,7 @@ retain excess parent supply as boundary exits, and supply demands with absent parent points by distinct top input arrays. At depth G all paid jobs are leaf exits. At the root all target demands are top sources. -This is the same finite Pascal routing argument as PR4436. It does not +This is the same finite Pascal routing argument as [PR #4436](https://github.com/CrocSwap/integer-mult-bounds/pull/4436). It does not require G=floor(log_(k_min) C_n). In particular a root class may be empty while later classes receive new top sources. These are finitely many chronological classes with explicit fresh source endpoints. They do not @@ -111,7 +111,7 @@ Indeed a capped leaf path is a subset of all paid paths of length G, followed by one paid letter. Formula (3) is an upper bound; an exact untruncated leaf law is not assumed. -The mirror identity from corrected PR4459 remains valid at arbitrary G. +The mirror identity from corrected [PR #4459](https://github.com/CrocSwap/integer-mult-bounds/pull/4459) remains valid at arbitrary G. For a paid-prefix path rho of length d