From 09d9dd91525be8758dbe228d5076b8e13b3ddade Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 12:18:45 -0500 Subject: [PATCH 1/2] Construct conditional kappa 0.00268647 with paid target padding --- research/pr4359-p7-padding/ENDPOINT.md | 194 + .../pr4359-p7-padding/EXPORTED-SOURCES.json | 215 + research/pr4359-p7-padding/NATIVE.md | 180 + research/pr4359-p7-padding/P7-FACTOR.json | 5114 +++++++++++++++++ research/pr4359-p7-padding/README.md | 94 + research/pr4359-p7-padding/RESULT.json | 295 + research/pr4359-p7-padding/SOURCES.json | 18 + research/pr4359-p7-padding/TASK.json | 96 + research/pr4359-p7-padding/TENSOR.md | 223 + research/pr4359-p7-padding/VERIFY.json | 18 + .../dependencies/compiler-refill/endpoint.py | 240 + .../compiler-refill/template_bound.py | 152 + .../native_inventory.py | 214 + research/pr4359-p7-padding/endpoint.py | 133 + research/pr4359-p7-padding/factor_receipt.py | 60 + .../pr4359-p7-padding/native_inventory.py | 270 + .../carrier-reuse/reference/joint_pair_dag.py | 731 +++ .../direct-decoder/sources/DATA-PHASES.json | 1 + .../architecture/FINITE-PRECOMPILATION.md | 313 + .../identity_mixed_certificate.py | 135 + .../architecture/mixed_forest_search.py | 311 + .../architecture/mixed_target_probe.py | 291 + .../bit/BIT-ALLSIZE-PARAMETERS.json | 69 + .../bit/complex_controller_factor.py | 270 + .../kappa-rebuild/bit/mixed_productive_bit.py | 617 ++ .../THREE-base-HELPER-BOUNDARIES.json.gz | Bin 0 -> 25720 bytes .../full-identity-certificates/RESULT.json | 1 + ...THREE-base-FULL-IDENTITY-CANONICAL.json.gz | Bin 0 -> 82793 bytes .../THREE-base-FULL-IDENTITY-NATIVE.json.gz | Bin 0 -> 198063 bytes .../complex/full_identity_rebuild.py | 173 + .../controller/P3-NATIVE-COVER.json.gz | Bin 0 -> 176694 bytes .../controller/p3_native_cover.py | 274 + .../transfer-audit/FINITE-TEMPLATE-CLOSURE.md | 339 ++ .../transfer-audit/OUTER-TRANSFER-AUDIT.md | 426 ++ .../transfer-audit/p3_cover_audit.py | 163 + .../transfer-audit/p3_native_audit.py | 283 + research/pr4359-p7-padding/strictification.py | 133 + research/pr4359-p7-padding/verify.py | 101 + 38 files changed, 12147 insertions(+) create mode 100644 research/pr4359-p7-padding/ENDPOINT.md create mode 100644 research/pr4359-p7-padding/EXPORTED-SOURCES.json create mode 100644 research/pr4359-p7-padding/NATIVE.md create mode 100644 research/pr4359-p7-padding/P7-FACTOR.json create mode 100644 research/pr4359-p7-padding/README.md create mode 100644 research/pr4359-p7-padding/RESULT.json create mode 100644 research/pr4359-p7-padding/SOURCES.json create mode 100644 research/pr4359-p7-padding/TASK.json create mode 100644 research/pr4359-p7-padding/TENSOR.md create mode 100644 research/pr4359-p7-padding/VERIFY.json create mode 100644 research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py create mode 100644 research/pr4359-p7-padding/dependencies/compiler-refill/template_bound.py create mode 100644 research/pr4359-p7-padding/dependencies/tensor-strictification/native_inventory.py create mode 100644 research/pr4359-p7-padding/endpoint.py create mode 100644 research/pr4359-p7-padding/factor_receipt.py create mode 100644 research/pr4359-p7-padding/native_inventory.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/identity_mixed_certificate.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/mixed_forest_search.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/mixed_target_probe.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/bit/complex_controller_factor.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/bit/mixed_productive_bit.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/complex/fresh-certificates/THREE-base-HELPER-BOUNDARIES.json.gz create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/complex/full-identity-certificates/RESULT.json create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/complex/full_identity_rebuild.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/controller/P3-NATIVE-COVER.json.gz create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/controller/p3_native_cover.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/FINITE-TEMPLATE-CLOSURE.md create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/OUTER-TRANSFER-AUDIT.md create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_cover_audit.py create mode 100644 research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_native_audit.py create mode 100644 research/pr4359-p7-padding/strictification.py create mode 100644 research/pr4359-p7-padding/verify.py diff --git a/research/pr4359-p7-padding/ENDPOINT.md b/research/pr4359-p7-padding/ENDPOINT.md new file mode 100644 index 0000000000..47008a4b90 --- /dev/null +++ b/research/pr4359-p7-padding/ENDPOINT.md @@ -0,0 +1,194 @@ +# Conditional p7 outer saving 0.00268647 + +The native p7 construction in `NATIVE.md`, together with the tensor and +target-padding construction in `TENSOR.md`, supports the proposed conditional +bound + +``` +T(n) = O(n (log n)^(1-kappa)), kappa = 0.00268647. +``` + +This raises the exponent saving by `0.00038647` over PR4359's `0.0023`, and +by `0.00000660` over PR4414's p6 point `0.00267987`. These compare exponent +savings, not measured running times. The selected frontier is unchanged. + +The result remains conditional on the documented all-column native, +whole-job adapter, spectator, finite compiler, storage, precision, analytic, +fixed-tape, and recovery hypotheses inherited from zxv's PR4359 at +`da637c87c89482bc4c86be36bd0071b3d400dbed`. The p7 Laurent factorization, +geometry and native ownership are checked in this package. Finite checks do +not constitute a formal proof of the full multiplication theorem. + +The native source is credited to zxv's PR4359 and integer mixed flow to +Jacob Alan Sussman's Theorem 1G. The outer slack family and executable +ledger are retained from PR4405 at +`873d1b3c96a83b701a5c0bba8e37a861e6672fef`, with its attribution to +@Vlado-V's PR1673, @jeremykothe2's PR1758, @chafreaky's PR1786, and their +cited predecessors. Apache-2.0; substantial OpenAI assistance. + +## Native invoice and why target padding is needed + +The exact all-fresh p7 invoice is + +``` +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}. +``` + +It has 7,688 productive fields, target rank-one moment 131723, and paid +rank-one moment 131115, leaving surplus 608. Its raw paid ranks exceed its +smallest target ranks. Moreover, a rank-one tail bound with cutoff below +the raw minimum target rank does not suffice near this proposed saving. + +The new construction tensors the native word `v=30000` times, completes +every productive endpoint of rank smaller than `8^v` to rank `8^v` on +unused disjoint axes, and splits every paid call, including those endpoint +completions, into consecutive pieces of size at most `7^v`. Endpoint +completion occurs only after the whole native tensor word has finished. +It uses the same arbitrary productive array, without new productive credit +for copied inputs or work storage. The ambient rank `121^v` has room for +each completion. + +At `C_test=0.00268648`, write `tau=1-C_test` and let `P_tau,T_tau` denote +the raw moments. The certificate proves + +``` +P_tau/T_tau < 1 - 1/10^8, +131115/(7^C_test*T_tau) < 9995/10000, +7688*8/(7^C_test*T_tau) < 1/2. +``` + +The first bound controls the original tensor word. The second pays for +splitting its large calls. The third pays for completing small productive +endpoints and splitting those completion calls. For a completion of rank +`D<8^v`, writing `D=q*J+r` with `J=7^v` gives, including `q=0`, + +``` +q*J^tau+r^tau <= D*J^(-C_test)+J^tau + < 2*8^v/J^C_test. +``` + +Thus the complete normalized paid moment is bounded by +`alpha^v+2*gamma^v+2*padding^v`, while the target moment only increases. +The exact block bound `(9995/10000)^2000<1/2`, with 15 blocks and +`padding<1/2`, gives the simpler sufficient inequality + +``` +1/(1+30000/10^8) + 4/2^15 < 1. +``` + +Every paid rank is now at most `7^v`, and target ranks lie between `8^v` +and `121^v`. Rank-one surplus is unchanged: each endpoint completion adds +the same rank to the paid and target totals, and paid splitting preserves +rank. Hence it remains `131723^v-131115^v>0`. + +## An explicit uniform rank + +Choose + +``` +kappa = 0.00268647, +d = (C_test-kappa)/7 = 1/700000000, +uniform = kappa+6*d = 376107/140000000, +t = 1-C_test, +z = 1-uniform, +z0 = (t+z)/2, +delta = z0-t = 1/1400000000. +``` + +The source compiler now has `m=121^v`, `k_min=8^v`, and `r_max<=7^v`. +The exact integer inequality `7^16<8^15` gives exit exponent below +`15/16`, so use `h=1/16`. For ambient rank `x>=m`, + +``` +m E(x)/x < m^h*r_max*x^(-h) + < 2^B*x^(-h), B=(55/16)*v=103125. +``` + +This follows from `7<2^3` and `121<2^7`. The exact complement coefficient +is `eta=z0*m^(z0-1)`. Since `z0>1/2`, + +``` +-log2(eta) < 1+7*v*(1-z0) = 11303213/20000. +``` + +The entirely rational sufficient formulas + +``` +H0 = ceil((B*delta+1+7*v*(1-z0))/(h*delta)), +H1 = floor(H0*(1-z0)/(z-z0))+1 +``` + +therefore give + +``` +H0 = 12659600210000, +H1 = 47613655221424910001, +N = 2^47613655221424910001. +``` + +The verifier checks `H0>=7*v`, covering the entire finite base range. +Below `2^H0`, the rank-one surplus gives `L(x)<=x`; above it the exit +coefficient is below the complement coefficient. Strong induction yields +`L(x)<=A*x^z0`, with `A=(2^H0)^(1-z0)`, for every positive integer rank. +The strict final power gap is `1/1400000000`, proving +`P_N/B_N 0`. + +The inherited 63-row ledger was compared with this current predicate set +in PR4405: all 50 common predicates and all nine costs agreed, and the +13 omitted rows were historical endpoint comparisons. The larger kappa +preserves those comparisons; this package reruns the current 54 plus three +functional predicates. + +Apply the source precision and stock theorem using the new p7 word, +tensor/padding recipe, compiler counts, scalar word, and owned storage. +No p3 or p6 raw scalar constant is substituted for the new word. Its new +fixed constants and denominators are absorbed after an effective threshold +by the positive semantic, support, stopping, and fine-prime spare powers. +The unchanged BIT template retains its separately compiled and covered +construction. + +## Replay and remaining work + +``` +python3 -I -O -B research/pr4359-p7-padding/endpoint.py +``` + +The integrated command checks the native p7 invoice and geometry, the +tensor/cutoff/padding moment, the specified uniform rank, and every outer +predicate. Mutation controls reject closing the precision or uniform gap, +requesting the unfunded tested endpoint as kappa, and reducing BIT below +the required effective saving. Complete source authentication is a separate +package-verifier stage. + +Next questions include independently formalizing the native tensor and +endpoint-completion construction, improving the controller family, and +reducing the tensor power and sufficient rank. The bounded controller +search does not establish global optimality. 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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. 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+ 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/pr4359-p7-padding/README.md b/research/pr4359-p7-padding/README.md new file mode 100644 index 0000000000..ff595b2899 --- /dev/null +++ b/research/pr4359-p7-padding/README.md @@ -0,0 +1,94 @@ +# Conditional κ = 0.00268647 with paid productive-rank padding + +This contribution improves the conditional construction of +[PR #4359](https://github.com/CrocSwap/integer-mult-bounds/pull/4359) from +κ = 0.0023 to **κ = 0.00268647**, continuing the native tensor and p6 results +in [PR #4412](https://github.com/CrocSwap/integer-mult-bounds/pull/4412) and +[PR #4414](https://github.com/CrocSwap/integer-mult-bounds/pull/4414). +The proposed conditional multiplication bound is + +``` +T(n) = O(n (log n)^(1 - 0.00268647)). +``` + +The new mechanism pays to enlarge small productive transforms **after** +tensor composition. Its cost decays relative to the total productive moment, +allowing a strict paid-rank cutoff above the raw supplier's minimum rank. +This resolves the tail obstruction that prevented direct admission of the +stronger p7 controller. + +## Native construction and charged padding + +The exact fixed controller is `pairs=7, keep_idle_mask=232127`. The source +Laurent factorization code regenerates this one case. The complete native +audit then binds its actual program on 121 axes, with 15 local calls, all +independent main and fresh helper inputs, original rank-eight centers, and +every full idle window. Coordinate maps, inverses and Z4 phase polynomials +check all main contacts and endpoints. [NATIVE.md](NATIVE.md) gives the +construction and source bindings; a tariff alone is insufficient evidence. + +[TENSOR.md](TENSOR.md) first forms a chronological native tensor power. +For each completed productive rank K below `8^30000`, it pays for the +transform on the missing disjoint axes of that same arbitrary input field. +The resulting target has rank `8^30000`. No new input or productive field +is credited. All original and added paid jobs are split at cutoff `7^30000`. +The new minimum target strictly exceeds the maximum paid rank, while the +rank-one surplus is unchanged. + +At tested saving **0.00268648**, exact bounds certify the original mixed +moment, the entire original paid rank-one tail, and the entire added padding +bill. These are three separate terms; the padding is never treated as free. +The resulting tensor power is 30,000. [ENDPOINT.md](ENDPOINT.md) specifies +the sufficient uniform ambient rank `N = 2^47613655221424910001` and +verifies every inherited outer cost +using the unchanged ordinary BIT admission of 0.0027. + +[RESULT.json](RESULT.json) records exact source authentication, the native +replay, complete padding/cutoff arithmetic, outer checks and rejection +controls. An independent rational interval engine cross-checks the critical +moment and both tails. The enormous tensor and uniform words are defined +by finite algorithms; their instruction lists have not been emitted. + +## Reproduction and provenance + +Python standard library only. Normal replay reads source exports, regenerates +the fixed native controller and arithmetic, and compares the saved receipt. + +```sh +python3 -I -O -B research/pr4359-p7-padding/verify.py +python3.12 -B scripts/research_package.py --package research/pr4359-p7-padding +``` + +`EXPORTED-SOURCES.json` pins focused unchanged files from PR4359 at +`da637c87c89482bc4c86be36bd0071b3d400dbed`, interval/outer-ledger dependencies +from PR4405 at `873d1b3c96a83b701a5c0bba8e37a861e6672fef`, and the all-fresh +native source gate from PR4412 at `9f0df9bf6f49942faf5f31389e7e387fdfe511b3`. +Each export is compared with the original Git blob and SHA256. Unmerged +source heads are not represented as publication ancestry. The standard +`SOURCES.json` records task and selected-result provenance from canonical +main `12fa8c5`. The new p7 controller receipt is generated from the pinned +factorization code; it is not presented as an old published source artifact. + +## Scope and credit + +This is a conditional research result awaiting review. It retains the source +all-column arbitrary-input native words, permitted physical operations, +analytic decomposition, fixed-tape model and outer transfer assumptions. +Finite replay does not formally verify the complete multiplication theorem. +No selected-frontier update, practical implementation or global optimum is +claimed. + +Controller and native source: @zxv, PR4359. Underlying mixed flow: Jacob Alan +Sussman, Theorem 1G. Earlier attribution and notices remain in copied sources. +New native audit, paid-padding proof, exact arithmetic and integration were +prepared for @1337isnot1337 with substantial OpenAI Codex assistance. +Apache-2.0. + +## Open next questions + +[TASK.json](TASK.json) records first steps and blockers. Larger or different +controllers require a new complete native audit before their moments support +an exponent claim. Higher-moment tails or tighter padding thresholds could +reduce the sufficient ranks; the current values are not asserted minimal. +The inherited BIT interface must also be revisited if a future complex saving +crosses its admitted value. diff --git a/research/pr4359-p7-padding/RESULT.json b/research/pr4359-p7-padding/RESULT.json new file mode 100644 index 0000000000..961537d658 --- /dev/null +++ b/research/pr4359-p7-padding/RESULT.json @@ -0,0 +1,295 @@ +{ + "endpoint": { + "compiler": { + "H0": 12659600210000, + "H1": 47613655221424910001, + "N_encoding": "2^47613655221424910001", + "delta": "1/1400000000", + "exit_coefficient_log2_upper": "103125", + "final_strict_power_gap": "1/1400000000", + "h": "1/16", + "materialized_tensor_rule_or_uniform_word": false, + "negative_log2_eta_upper": "11303213/20000", + "paid_max_bound_encoding": "7^30000", + "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": "121^30000", + "target_min_encoding": "8^30000", + "tensor_power": 30000, + "theta_upper": "15/16", + "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": 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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", + "controls": { + "one_decay_block_rejected": true, + "undamped_completion_rejected": true, + "unpadded_rank_one_tail_rejected": true + }, + "cutoff_base": 7, + "cutoff_encoding": "7^30000", + "decay_block_count": 15, + "decay_block_length": 2000, + "delta_interval": { + "lower": "0.46868503106323215655720547807230369", + "upper": "0.46868503106323215655720547807230370" + }, + "delta_upper": "1/2", + "exponent": 30000, + "gamma_interval": { + "lower": "0.99914863826508331502012871126187076", + "upper": "0.99914863826508331502012871126187077" + }, + "gamma_upper": "1999/2000", + "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; 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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": "0.00017783971449190242927121863440967", + "upper": "0.00017783971449190242927121863440968" + }, + "strictification_gap_rational": "14573/81944576", + "target_floor_base": 8, + "target_floor_encoding": "8^30000", + "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": "15/16" + } +} diff --git a/research/pr4359-p7-padding/SOURCES.json b/research/pr4359-p7-padding/SOURCES.json new file mode 100644 index 0000000000..fcfba8aa31 --- /dev/null +++ b/research/pr4359-p7-padding/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/pr4359-p7-padding/TASK.json b/research/pr4359-p7-padding/TASK.json new file mode 100644 index 0000000000..b02a5ae81b --- /dev/null +++ b/research/pr4359-p7-padding/TASK.json @@ -0,0 +1,96 @@ +{ + "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": "Construct and audit the balanced p7/keep232127 native controller, then pad low productive ranks after tensor composition to certify conditional kappa0.00268647.", + "scope_change_reason": "The user assigned PR4359 review and continued improvement. After the p6 result, its tail method rejects the p7 raw minimum-rank constraint; post-composition productive padding is a distinct complete compiler-admission mechanism.", + "bottleneck_link": "Productive padding raises the minimum target after composition while charging every added transform. It permits a paid cutoff whose full rank-one tail is contractive, recovering a stronger native raw moment.", + "budget_minutes": 120, + "stop_rule": "Reject an unbound Laurent factor, missing physical phase or endpoint, unpaid target padding, noncontractive complete tail, or failed outer predicate. Keep all negative claims finite and do not change the selected frontier.", + "outcome": "completed", + "evidence": "NATIVE.md/native_inventory.py for full p7 realization; TENSOR.md/strictification.py for paid productive padding; ENDPOINT.md/endpoint.py and independent verify.py for complete admission.", + "author": "1337isnot1337 with OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance; four agents divide native controller generation, composition/padding proof, exact outer arithmetic, and independent integration/replay.", + "open_questions": [ + { + "question": "Can another fully audited controller improve the p7 endpoint?", + "why_it_matters": "The current construction approaches the inherited BIT admission, while finite menu screens give no global optimum.", + "first_step": "Search a declared bounded controller family, then reconstruct every phase, owner and whole-job tariff for a positive candidate.", + "blocked_by": "A numerical tariff or relaxed search alone is not a native supplier." + }, + { + "question": "Can a higher-moment tail or tighter padding threshold reduce the sufficient finite ranks?", + "why_it_matters": "The current word is effective but astronomical.", + "first_step": "Derive the complete cutoff and padding bound before optimizing rational constants.", + "blocked_by": "No minimal power or practical implementation is claimed." + } + ] +} diff --git a/research/pr4359-p7-padding/TENSOR.md b/research/pr4359-p7-padding/TENSOR.md new file mode 100644 index 0000000000..30cfe796c8 --- /dev/null +++ b/research/pr4359-p7-padding/TENSOR.md @@ -0,0 +1,223 @@ +# Native tensor products with paid completion of small targets + +This construction applies to the all-fresh p7/keep232127 native word in +`NATIVE.md`. It retains the source all-column arbitrary-input semantics, +complete spectators, whole-job matchers, finite-program closure and integer +uniform compiler. The local word and controller come from zxv's PR4359; +the integer compiler is Jacob Alan Sussman's Theorem 1G. The tensor product +construction follows PR4414. Apache-2.0; substantial OpenAI/Codex assistance. + +The new step is to complete small productive endpoints before choosing the +paid-rank cutoff. The enormous finite program is specified algorithmically; +it has not been materialized. Finite moment checks do not prove the inherited +analytic, precision, storage, fixed-tape or recovery premises. The selected +frontier is unchanged. + +## 1. Chronological native product + +Let U have productive ranks k_i and chronological paid ranks r_l, and V +have productive ranks h_j and paid ranks s_a. Their ambient ranks equal +their maximum productive ranks and contain every paid job. Work in the +product ambient space, retaining every unused coordinate as an arbitrary +spectator. + +For each role j of V, instantiate a separate U copy at column count h_j. +Its independent arbitrary productive fields have labels (i,j). Give each +copy its own initialized, erased and uncredited center banks. Run these +copies in lockstep through their common scalar and paid-call list. + +At paid position l, pause all copies. Copy j requests a rank r_l*h_j job +on its current physical owner. The owners are distinct across the copies; +they may include centers and may contain correlated values. Invoke V at +column count r_l on these j-indexed fields, using permitted role-specific +whole-job matchers. Its endpoints provide the requested ranks h_j*r_l. +Its owned centers have separate identities. Complete V and restore every +matcher before resuming the suspended U copies. Never combine different +paid positions of the same U copy. + +This is a finite acyclic chronological substitution. Arbitrary-input +correctness allows correlated data in distinct slots; no input is copied +to create productive credit. Its final targets have ranks k_i*h_j and its +remaining paid jobs have ranks r_l*s_a. Thus both moments multiply. +The same argument lifts at every further positive column multiplicity by +substitution of the fixed coordinate, phase and scalar generators. It does +not tensor a sum of matrix operators. + +For v copies of the p7 unit, write T_tau and P_tau for the raw target and +paid moments and B for the number of raw productive fields. The product +has B^v distinct productive fields, target moment T_tau^v, paid moment +P_tau^v, and ambient m^v where m=121. + +## 2. Paid completion on the actual productive owners + +Choose integers 1=L receive no completion. + +For precision about coordinates, conjugate the complete existing product +word by its permitted per-role whole-job normalizers: the inverse map is +applied to each input and the corresponding map to its final output. This +gives the canonical rank-K endpoint on that field. After the whole product +has finished, apply the positive transform on axes K,...,L-1. The disjoint +factors commute and give exactly the canonical rank-L endpoint. Restore +the external matchers where the surrounding interface requires them. +A map only on the output would not be a whole-job conjugation. + +Every field remains an arbitrary original productive input. There is no +new productive credit and no new owned bank. Since LJ by consecutive +jobs on disjoint axes of ranks J,...,J,r where R=qJ+r and 0<=rJ, its new charge satisfies + +``` +q*J^tau+r^tau <= R*J^(-C)+J^tau <= 2*R*J^(-C). +``` + +Retaining the original moment as an overcount for the lower paid jobs +therefore bounds the original paid part by + +``` +P_tau^v + 2*P_1^v/J^C. +``` + +For each added completion D=m_new the inherited exit estimate gives + +``` +m_new*E(x)/x <= r_max*m_new^h*x^(-h) + < 2^((55/16)*v)*x^(-h), +``` + +using 7<8=2^3 and 121<128=2^7. For a desired uniform exponent +z>t=1-C, put z0=(t+z)/2 and d=z0-t. The exact complement coefficient +eta=z0*m_new^(z0-1), with z0>1/2, satisfies + +``` +-log2(eta) < 1+7*v*(1-z0). +``` + +Thus rational sufficient choices are + +``` +H0 = ceil((((55/16)*v)*d+1+7*v*(1-z0))/(h*d)), +H1 = floor(H0*(1-z0)/(z-z0))+1, +N = 2^H1. +``` + +Check H0>=7v to cover all base ranks. Below the threshold, positive +rank-one surplus gives L(x)<=x. Above it, the source strong induction gives +L(x)<=A*x^z0 with A=(2^H0)^(1-z0). The strict H1 inequality then gives +L(N) Q(1, 2) and (1-z0)*E.log_interval(m)[1] < E.log_interval(2)[0], + 'Original eta strictly exceeds 1/4') + H0 = ceil((3+4*delta)/(h*delta)) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= m.bit_length() and H0*h*delta >= 3+4*delta, 'Induction starts') + need(H1*(z-z0) > H0*(1-z0), 'Strict winning uniform rank') + need((H0-1)*h*delta < 3+4*delta, 'Reject one lower threshold exponent') + need((H1-1)*(z-z0) <= H0*(1-z0), 'Reject one lower final exponent') + return {'t': t, 'z0': z0, 'z': z, 'theta_upper': Q(9, 10), + 'H0': H0, 'H1': H1, 'N_encoding': '2^H1', + 'strict_final_gap': H1*(z-z0)-H0*(1-z0), + 'winning_word_materialized': False, + 'bound': 'Original sufficient inequality; a sharper bound is separate.'} + + +def run(source_root): + base = source_root/PREFIX + interval_path = base/'architecture/mixed_target_probe.py' + spec = importlib.util.spec_from_file_location('pr4359_moment', interval_path) + E = importlib.util.module_from_spec(spec) + spec.loader.exec_module(E) + cover = read(base/'controller/P3-NATIVE-COVER.json.gz')['cover'] + targets = {int(k): int(v) for k, v in cover['targets'].items()} + paid = {int(k): int(v) for k, v in cover['paid'].items()} + need(targets == {6: 192, 7: 56, 8: 93, 9: 1229, 25: 448, 57: 224}, + 'Exact source productive inventory') + need(paid == {1: 17623, 2: 5065, 3: 1738, 4: 714, 5: 254}, + 'Exact source paid inventory') + signed = Counter(targets) + signed.subtract(paid) + need(sum(k*v for k, v in signed.items()) == 224, 'Rank-one surplus') + bracket = {'lower': E.moment(signed, TESTED), 'upper': E.moment(signed, ROOT_UPPER)} + need(bracket['lower'][0] > 0 and bracket['upper'][1] < 0, + 'Strict mixed test and upper root bound') + + original = read(base/'controller/OUTER-PARAMETERS.json')['outer'] + old = ledger({'kappa': Q('0.0023'), 'complex_uniform_saving': Q('0.002304'), + 'b': Q('0.002303'), 'a': Q('0.0023025'), 'q': Q('0.002302'), + 'bit_saving': Q('0.0027'), 'epsilon': Q('0.99999'), + 'beta': Q('0.99997'), 'r0': Q(1, 10**6), + 'stop': Q(1, 10**8), 'layout': Q(1, 10**6)}) + for group in ('margins', 'strict_checks'): + frozen = {key: Q(value['rational']) for key, value in original[group].items()} + need(old[group] == frozen, 'Exact reproduction of every old '+group) + p = family(KAPPA, TESTED) + result = ledger(p) + need(all(v > 0 for v in result['strict_checks'].values()), 'All 54 new outer predicates') + need(all(v > 0 for v in result['functional_checks'].values()), 'Additional functional predicates') + need(min(result['margins'].values()) == result['margins']['main_transform'], + 'Main transform remains limiting') + need(result['parameters']['cap_xi'] == Q(29, 32)+(1-p['d'])*p['q'], + 'Cofinal cap simplification') + controls = {} + for label, updates in [('closed_epsilon_gap', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': Q('0.002306')}), + ('BIT_below_effective', {'bit_saving': OLD_BASELINE}), + ('no_complex_slack', {'complex_uniform_saving': p['b']})]: + tested = ledger(dict(p, **updates)) + failures = {k: v for k, v in tested['strict_checks'].items() if v <= 0} + need(failures, 'Mutation rejected: '+label) + controls[label] = failures + need(E.moment(signed, Q('0.004'))[1] < 0, 'Unsupported mixed target is rejected') + inputs = [interval_path, base/'controller/P3-NATIVE-COVER.json.gz', + base/'controller/OUTER-PARAMETERS.json'] + return encode({'schema': 'pr4359-cofinal-outer-refill/1', + 'status': 'PASS_EXACT_CONDITIONAL_ENDPOINT_REFILL', + 'kappa': KAPPA, 'gain_over_PR4359': KAPPA-Q('0.0023'), + 'unchanged_paid': paid, 'unchanged_targets': targets, + 'mixed_test_saving': TESTED, 'mixed_test_margin': E.show(bracket['lower']), + 'root_upper_test': ROOT_UPPER, 'root_upper_margin': E.show(bracket['upper']), + 'old_ledger_crosscheck': {'matched_savings': len(old['margins']), + 'matched_checks': len(old['strict_checks'])}, + 'outer': result, 'limiting_margin': min(result['margins'].values())-KAPPA, + 'compiler': compiler_rank(E, targets, paid, TESTED, p['complex_uniform_saving']), + 'negative_controls': controls, + 'source_sha256': {str(p.relative_to(source_root)): sha256(p.read_bytes()).hexdigest() + for p in inputs}, + 'scope': 'Conditional arithmetic and specified finite rank. The PR4359 native, compiler, cover, precision, fixed-tape and outer hypotheses remain premises; no full theorem or practical word is certified.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root', type=Path, default=HERE/'source') + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = run(args.source_root) + if args.out: + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({key: result[key] for key in + ('status', 'kappa', 'gain_over_PR4359', 'limiting_margin', 'compiler')}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/pr4359-p7-padding/dependencies/compiler-refill/template_bound.py b/research/pr4359-p7-padding/dependencies/compiler-refill/template_bound.py new file mode 100644 index 0000000000..ddc852c4fa --- /dev/null +++ b/research/pr4359-p7-padding/dependencies/compiler-refill/template_bound.py @@ -0,0 +1,152 @@ +#!/usr/bin/env python3 +"""Exact tighter sufficient ranks for PR4359's conditional finite compiler. + +Standard library only; no generated file is modified unless --out is given. +Apache-2.0. Substantial OpenAI/Codex assistance. The compiler and its inherited +native premises are those of PR4359, based on Jacob Alan Sussman's Theorem 1G. +""" +import argparse +from functools import lru_cache +from fractions import Fraction as Q +import json +from math import factorial +from pathlib import Path + + +CASES = ( + {"family": "complex", "targets": {6:192, 7:56, 8:93, 9:1229, 25:448, 57:224}, + "paid": {1:17623, 2:5065, 3:1738, 4:714, 5:254}, + "tested_saving": "0.002305", "uniform_saving": "0.002304", + "theta_upper": "9/10", "old_H0": 60000040, "old_H1": 276540184361}, + {"family": "BIT", "targets": {8:3073, 22:444, 50:222}, + "paid": {1:9261, 2:9394, 3:553, 4:308, 5:714, 6:77, 7:1465}, + "tested_saving": "0.002769", "uniform_saving": "0.002760", + "theta_upper": "15/16", "old_H0": 10666731, "old_H1": 6552928412}, +) + + +def need(ok, message): + if not ok: + raise AssertionError(message) + + +@lru_cache(maxsize=None) +def log_interval(value): + """Rational lower/upper bounds from the positive atanh series.""" + value = Q(value) + need(value > 0, "logarithm needs positive argument") + if value < 1: + lo, hi = log_interval(1/value) + return -hi, -lo + power = 0 + while value > 2: + value /= 2 + power += 1 + u = (value-1)/(value+1) + count = 96 + lo = 2*sum((u**(2*j+1)/(2*j+1) for j in range(count)), Q(0)) + tail = 2*u**(2*count+1)/((2*count+1)*(1-u*u)) + hi = lo+tail + if power: + a, b = log_interval(Q(2)) + lo, hi = lo+power*a, hi+power*b + return lo, hi + + +def exp_interval(value): + need(0 <= value < Q(1,10), "small positive exponential argument") + count = 32 + lo = sum((value**j/factorial(j) for j in range(count+1)), Q(0)) + tail = value**(count+1)/factorial(count+1)/(1-value/(count+2)) + return lo, lo+tail + + +def moment_margin(targets, paid, saving): + """Enclose sum targets*k^(1-saving) - sum paid*r^(1-saving).""" + lo = hi = Q(0) + for rank in sorted(set(targets) | set(paid)): + count = targets.get(rank, 0)-paid.get(rank, 0) + a, b = log_interval(Q(rank)) + lower = Q(rank)/exp_interval(saving*b)[1] + upper = Q(rank)/exp_interval(saving*a)[0] + lo += count*(lower if count >= 0 else upper) + hi += count*(upper if count >= 0 else lower) + return lo, hi + + +def rank_bound(test_saving, uniform_saving, m, theta_bar): + """Conditional bound: caller supplies the source/exit recurrence hypotheses. + + In particular m*E(n)/n < 16*n^(-(1-theta_bar)) and the strict tested + superpotential must hold. This function does not assert either premise. + """ + test_saving, uniform_saving, theta_bar = map(Q, (test_saving, uniform_saving, theta_bar)) + t, z = 1-test_saving, 1-uniform_saving + z0, h = (t+z)/2, 1-theta_bar + delta = z0-t + need(0 < t < z0 < z < 1 and 0 < h < 1 and m >= 2, + "strict rational savings and exit contraction") + log2_lo, log2_hi = log_interval(Q(2)) + logm_lo, logm_hi = log_interval(Q(m)) + invz_lo, invz_hi = log_interval(1/z0) + # eta=z0*m^(z0-1); these enclose -log(eta). + debt_lo = invz_lo+(1-z0)*logm_lo + debt_hi = invz_hi+(1-z0)*logm_hi + H0 = ((4+debt_hi/(delta*log2_lo))/h).__ceil__() + need(H0 >= m.bit_length(), "threshold covers the finite base range") + exit_gap = delta*(h*H0-4)*log2_lo-debt_hi + need(exit_gap >= 0, "exit coefficient is at most eta") + final_ratio = H0*(1-z0)/(z-z0) + H1 = final_ratio.__floor__()+1 + final_gap = H1*(z-z0)-H0*(1-z0) + need(H1 > H0 and final_gap > 0, "strict winning-rank inequality") + # The interval width is small enough to determine these two integers. + need(debt_lo > delta*(h*(H0-1)-4)*log2_hi, + "one smaller H0 violates the same sufficient exit inequality") + need((H1-1)*(z-z0) <= H0*(1-z0), + "one smaller H1 fails the strict final inequality") + return {"H0": H0, "H1": H1, "t": str(t), "z0": str(z0), "z": str(z), + "delta": str(delta), "h": str(h), "m": m, + "eta_definition": "z0*m^(z0-1)", + "exit_condition": "delta*(h*H0-4)*log(2) >= -log(eta)", + "certified_exit_gap_positive": exit_gap > 0, + "strict_final_power_gap": str(final_gap), + "controls": {"H0_minus_one_rejected": True, "H1_minus_one_rejected": True}} + + +def verify(): + rows = [] + for case in CASES: + m, kmin, rmax = max(case["targets"]), min(case["targets"]), max(case["paid"]) + theta = Q(case["theta_upper"]) + h = 1-theta + need(1 <= rmax < kmin <= m, "native mixed rank separation") + need(rmax**theta.denominator < kmin**theta.numerator, "exit exponent bound") + need(m**h.numerator < 2**h.denominator and 2*rmax <= 16, + "inherited exit coefficient constant 16") + surplus = sum(k*v for k,v in case["targets"].items())-sum(k*v for k,v in case["paid"].items()) + need(surplus > 0, "rank-one potential proves L(n)<=n") + margin = moment_margin(case["targets"], case["paid"], Q(case["tested_saving"])) + need(margin[0] > 0, "strict source profile superpotential") + need(moment_margin(case["targets"], case["paid"], Q("0.004"))[1] < 0, + "unsupported .004 superpotential is rejected") + result = rank_bound(case["tested_saving"], case["uniform_saving"], m, theta) + need(result["H1"] < case["old_H1"], "strictly smaller sufficient fixed rank") + rows.append({**case, **result, "rank_one_surplus": surplus, + "strict_superpotential_verified": True, + "old_to_new_log_rank_ratio": str(Q(case["old_H1"], result["H1"])), + "materialized_winning_word": False}) + return {"status": "PASS_EXACT_TIGHTER_TEMPLATE_RANKS", "cases": rows, + "scope": "Conditional quantitative refinement of PR4359's finite compiler; unchanged uniform savings and inherited native, precision, and outer premises.", + "new_kappa_from_template_refinement": False} + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path) + args = parser.parse_args() + result = verify() + serialized = json.dumps(result, indent=2, sort_keys=True)+"\n" + if args.out: + args.out.write_text(serialized) + print(serialized, end="") diff --git a/research/pr4359-p7-padding/dependencies/tensor-strictification/native_inventory.py b/research/pr4359-p7-padding/dependencies/tensor-strictification/native_inventory.py new file mode 100644 index 0000000000..417fefe5fb --- /dev/null +++ b/research/pr4359-p7-padding/dependencies/tensor-strictification/native_inventory.py @@ -0,0 +1,214 @@ +#!/usr/bin/env python3 +"""Bind an all-fresh p3 native unit and its exact full idle operators. + +Finite source, ownership, contraction and exact-moment checks. The written +all-column tensor construction and inherited transfer remain proof premises. +Apache-2.0; substantial OpenAI/Codex assistance. +""" +from collections import Counter, defaultdict +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +import sys + +sys.dont_write_bytecode = True +PINS = { + 'controller/P3-NATIVE-COVER.json.gz': 'facfc6d6ecde151afb7e6a167776f3fdaac1c816e785a21a39f7f0bfd9140f3f', + 'controller/p3_native_cover.py': 'fae71fcbbd20b9ee73b049cf6f43ea1d048217fb15feb6055a007e47da3363fe', + 'complex/full-identity-certificates/RESULT.json': '943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6', + 'complex/full_identity_rebuild.py': '9af2ffbb0038c92e2a7d281081b0daaeadce75b11b566e5427845dc1af91e33d', + 'transfer-audit/p3_cover_audit.py': 'a0fe9a26f77556e83b31b0c91fea909d6f3d8209d0f9f7ad4e5bc1375d33615e', +} + + +def need(condition, message): + if not condition: + raise AssertionError(message) + + +def read(path): + raw = path.read_bytes() + return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw) + + +def counter(row): + return Counter({int(k): int(v) for k, v in row.items()}) + + +def paid_histogram(program): + return Counter(event[-1] for event in program if event[0] in ('climb', 'center')) + + +def independent_axes(axes): + basis = {} + for axis in axes: + value = axis + while value: + pivot = value.bit_length()-1 + if pivot in basis: + value ^= basis[pivot] + else: + basis[pivot] = value + break + if not value: + return False + return True + + +def polynomial(terms, dimension): + linear = [0]*dimension + quadratic = [0]*dimension + for axis, coefficient in terms: + support = [i for i in range(dimension) if axis >> i & 1] + for i in support: + linear[i] = (linear[i]+coefficient) % 4 + if coefficient % 2: + for j in support: + if j > i: + quadratic[i] ^= 1 << j + return tuple(linear), tuple(quadratic) + + +def fuse_centers(program): + out, count, index = [], 0, 0 + while index < len(program): + event = program[index] + if event[0] != 'center': + out.append(event) + index += 1 + continue + following = program[index+1] + need(following[0] == 'center' and event[1] == following[1] == 0, + 'Both adjacent children use the same owned center') + need(event[3] == following[2] and sorted((event[4], following[4])) == [3, 5], + 'The exact intermediate frame cancels in the 3+5 center path') + out.append(['center', 0, event[2], following[3], 8]) + index += 2 + count += 1 + need(count == 8, 'Exactly eight center paths in each native invocation') + return out + + +def run(root): + base = root/'research/kappa-rebuild' + sources = {} + for name, wanted in PINS.items(): + path = base/name + actual = sha256(path.read_bytes()).hexdigest() + need(actual == wanted, 'Exact original source pin: '+name) + sources[str(path.relative_to(root))] = actual + receipt = read(base/'controller/P3-NATIVE-COVER.json.gz') + cover = receipt['cover'] + native_base = base/'complex/full-identity-certificates' + provider = read(native_base/'RESULT.json')['providers']['THREE-base'] + for name, wanted in provider['artifacts'].items(): + path = native_base/name + need(sha256(path.read_bytes()).hexdigest() == wanted, 'Exact native artifact '+name) + sources[str(path.relative_to(root))] = wanted + native = read(native_base/'THREE-base-FULL-IDENTITY-NATIVE.json.gz') + collapsed = {} + for direction, program in native.items(): + collapsed[direction] = fuse_centers(program) + need(paid_histogram(collapsed[direction]) == counter(provider['unsplit_replays'][direction]['paid_profile']), + 'Restored program has the pinned unsplit native paid profile') + need(all(row['product_exact_including_phase'] for row in provider['split_center_phase_recipes'][direction]), + 'The original split replay checked absolute phase of every center path') + + # Every helper now has its own independent physical input. The native + # all-column autonomous contract supplies the same main operator. + helper_path = root/provider['helper_boundary']['certificate'] + helper_hash = provider['helper_boundary']['certificate_sha256'] + need(sha256(helper_path.read_bytes()).hexdigest() == helper_hash, 'Actual complete helper boundaries') + sources[str(helper_path.relative_to(root))] = helper_hash + helper = read(helper_path) + widths = {row['role']: row['width'] for row in helper['recipes']} + need(set(widths) == set(range(224, 632)), 'All408 actual arbitrary-input helper roles') + need(provider['all_408_helpers_autonomous'] and provider['all_632_persistent_inputs_arbitrary'], + 'Fresh helper inputs are independent arbitrary fields') + targets = Counter(row['target_rank'] for row in receipt['main_endpoint_normalizers']) + need(targets == Counter({25:448, 57:224}), 'Exact unchanged main endpoint census') + by_stage = defaultdict(list) + for row in cover['helper_bindings']: + by_stage[row['stage']].append(row) + for stage in range(7): + need(len(by_stage[stage]) == 408 and {row['role'] for row in by_stage[stage]} == set(widths), + 'Every actual helper receives its own new productive owner') + for row in by_stage[stage]: + need(row['width'] == widths[row['role']], 'Native boundary backs the helper target width') + targets[row['width']] += 1 + # Check the full idle operator, including its affine phase, directly. + phase_path = root/'research/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json' + if not phase_path.exists(): + phase_path = root/'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json' + phase_hash = 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa' + need(sha256(phase_path.read_bytes()).hexdigest() == phase_hash, 'Exact native port phase source') + sources[str(phase_path.relative_to(root))] = phase_hash + phases = read(phase_path) + need(len(phases['recipes']) == 112, 'All actual port recipes') + axes = [1 << i for i in range(57)] + idle = Counter() + missing_phase_rejected = 0 + window_keys = set() + for window in cover['windows']: + key = window['index'], window['owner'] + need(key not in window_keys, 'One whole idle job per actual window/owner') + window_keys.add(key) + q = phases['recipes'][window['port']]['q'] + desired = [] + for stage in window['stages']: + desired += ([(a,1) for a in axes[:9]]+[(q,-1)] if stage == 0 + else [(a,1) for a in axes[9+8*(stage-1):9+8*stage]]) + actual = [(a,1) for a in window['axes']]+[(window['translation_after'],2)] + need(independent_axes(window['axes']), 'Whole idle axis list is independent') + need(polynomial(actual,57) == polynomial(desired,57), 'Exact whole idle operator including translation') + if window['translation_after']: + need(polynomial([(a,1) for a in window['axes']],57) != polynomial(desired,57), + 'Dropping the nonzero whole-idle phase correction fails') + missing_phase_rejected += 1 + idle[len(window['axes'])] += 1 + need(idle == Counter({8:448,16:448}), 'Allfour retained windows paid on all224 owners') + paid = idle.copy() + for direction in ('forward', 'backward', 'forward', 'backward', 'forward', 'backward', 'forward'): + paid.update(paid_histogram(collapsed[direction])) + need(targets == Counter({5:196,6:126,7:392,8:651,9:1491,25:448,57:224}), 'All-fresh native target census') + need(paid == Counter({1:17409,2:4991,3:1568,4:714,5:140,8:504,16:448}), 'Complete paid native and whole-idle tariff') + need(sum(k*v for k,v in targets.items())-sum(k*v for k,v in paid.items()) == 224, + 'Rank surplus of the complete actual all-fresh word') + bad = [list(row) for row in native['forward']] + index = next(i for i, row in enumerate(bad) if row[0] == 'center') + bad[index+1][2] = -1 + rejected = False + try: + fuse_centers(bad) + except AssertionError: + rejected = True + need(rejected, 'Wrong intermediate center frame is rejected') + return { + 'schema': 'native-all-fresh-full-idle-inventory/1', + 'source_head': 'da637c87c89482bc4c86be36bd0071b3d400dbed', + 'status': 'PASS_ACTUAL_ARBITRARY_HELPERS_AND_COMPLETE_PHASE_CORRECT_IDLE_JOBS', + 'source_sha256': sources, + 'targets': dict(sorted(targets.items())), 'paid': dict(sorted(paid.items())), + 'fresh_helper_fields': 2856, 'main_fields': 672, + 'restored_native_centers': 56, 'whole_idle_profile': dict(sorted(idle.items())), + 'ambient_rank': 57, 'productive_fields': 3528, + 'paid_calls': sum(paid.values()), 'rank_surplus': 224, + 'native_scalar_allowance': 1147304, + 'controls': {'wrong_intermediate_center_rejected': rejected, + 'whole_idle_missing_phase_rejected_count': missing_phase_rejected, + 'raw_rule_not_strictly_separated': max(paid) >= min(targets)}, + 'scope': 'Exact finite all-fresh controller inventory. Native all-column closure is inherited; the raw rule requires the separate tensor strictification before the old strict compiler applies.', + } + + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--root', type=Path, required=True) + parser.add_argument('--output', type=Path, required=True) + args = parser.parse_args() + result = run(args.root.resolve()) + args.output.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({key: result[key] for key in ('status', 'targets', 'paid', 'productive_fields', 'paid_calls')})) diff --git a/research/pr4359-p7-padding/endpoint.py b/research/pr4359-p7-padding/endpoint.py new file mode 100644 index 0000000000..06444a96fb --- /dev/null +++ b/research/pr4359-p7-padding/endpoint.py @@ -0,0 +1,133 @@ +#!/usr/bin/env python3 +"""Conditional outer endpoint from the source-bound tensor strictification. + +Apache-2.0. Substantial OpenAI assistance. The native productive rule is zxv's +PR4359. Integer mixed flow is Jacob Alan Sussman's Theorem 1G. The outer ledger +is frozen from PR4405 and retains the predecessor attribution stated there. +""" +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import importlib.util +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +KAPPA = Q('0.00268647') +TESTED = Q('0.00268648') + + +def need(value, message): + if not value: + raise AssertionError(message) + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + result = importlib.util.module_from_spec(spec) + spec.loader.exec_module(result) + return result + + +def encode(value): + if isinstance(value, Q): + return str(value) + if isinstance(value, dict): + return {str(k): encode(v) for k, v in value.items()} + if isinstance(value, (tuple, list)): + return [encode(v) for v in value] + return value + + +def compiler_rank(exponent, tested, uniform): + """Explicit sufficient ambient rank after target padding to 8^exponent and paid cutoff 7^exponent.""" + n = exponent + t, z = 1-tested, 1-uniform + z0, h = (t+z)/2, Q(1, 16) + delta = z0-t + need(n >= 1 and Q(1, 2) < t < z0 < z < 1, 'Strict compiler exponents') + need(7**16 < 8**15, 'log(7)/log(8) < 15/16') + need(7 < 2**3 and 121 < 2**7, 'Exact power bounds for exit and complement') + # r_max=7^n, k_min=8^n, m=121^n. Thus m*E(x)/x is + # below 2^B*x^-h, with B=(3+7h)n. Also -log2(eta)<1+7n(1-z0). + B = (3+7*h)*n + debt = 1+7*n*(1-z0) + ratio = (delta*B+debt)/(h*delta) + H0 = -((-ratio.numerator)//ratio.denominator) + need(H0 >= 7*n, 'Initial threshold covers every base rank below m') + need(H0*h*delta >= delta*B+debt, 'Exact sufficient exit/complement inequality') + final_ratio = H0*(1-z0)/(z-z0) + H1 = final_ratio.numerator//final_ratio.denominator+1 + need(H1 > H0 and H1*(z-z0) > H0*(1-z0), 'Strict final uniform moment') + need((H0-1)*h*delta < delta*B+debt, 'One lower H0 fails the stated sufficient bound') + need((H1-1)*(z-z0) <= H0*(1-z0), 'One lower H1 fails the final strict bound') + return {'tensor_power': n, 'target_min_encoding': '8^'+str(n), + 'target_max_encoding': '121^'+str(n), + 'paid_max_bound_encoding': '7^'+str(n), + 'theta_upper': Q(15, 16), 'h': h, 't': t, 'z0': z0, 'z': z, + 'delta': delta, 'exit_coefficient_log2_upper': B, + 'negative_log2_eta_upper': debt, 'H0': H0, 'H1': H1, + 'N_encoding': '2^'+str(H1), + 'final_strict_power_gap': H1*(z-z0)-H0*(1-z0), + 'rank_one_induction': '131723^n > 131115^n; target padding adds equal paid and target rank, and splitting preserves rank', + 'materialized_tensor_rule_or_uniform_word': False} + + +def run(source_root, strict_result=None): + if strict_result is None: + strict_result = module('tensor_strictification', HERE/'strictification.py').run(source_root) + need(strict_result['strict_moment_verified'], 'Strict mixed moment was certified') + need(strict_result['cutoff_base'] == 7 and strict_result['target_floor_base'] == 8 + and Q(strict_result['tested_saving']) == TESTED, + 'Compiler inputs bind to the certified cutoff and saving') + ledger_path = HERE/'dependencies/compiler-refill/endpoint.py' + previous = module('pr4405_outer_ledger', ledger_path) + d = (TESTED-KAPPA)/7 + p = {'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': Q('0.0027'), + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, + 'stop': d, 'layout': d, 'd': d} + outer = previous.ledger(p) + need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 3, + 'Complete preserved outer predicate set') + need(all(v > 0 for v in outer['strict_checks'].values()), 'All 54 strict outer predicates') + need(all(v > 0 for v in outer['functional_checks'].values()), 'All three functional predicates') + need(min(outer['margins'].values()) == outer['margins']['main_transform'], + 'Main transform remains limiting') + controls = {} + for label, updates in [('closed_epsilon', {'epsilon': Q(1)}), + ('closed_uniform_gap', {'complex_uniform_saving': p['b']}), + ('unfunded_outer_point', {'kappa': TESTED}), + ('insufficient_BIT', {'bit_saving': Q('0.0023')})]: + tested = previous.ledger(dict(p, **updates)) + failed = {k: v for k, v in tested['strict_checks'].items() if v <= 0} + need(failed, 'Reject '+label) + controls[label] = failed + rank = compiler_rank(strict_result['exponent'], TESTED, p['complex_uniform_saving']) + return encode({'schema': 'native-p7-padding-strictification-outer-endpoint/1', + 'status': 'PASS_CONDITIONAL_P7_OUTER_POINT', 'kappa': KAPPA, + 'gain_over_PR4359': KAPPA-Q('0.0023'), + 'gain_over_PR4405': KAPPA-Q('0.00230509'), + 'gain_over_allfresh_p3': KAPPA-Q('0.00247755'), + 'gain_over_PR4414': KAPPA-Q('0.00267987'), + 'tested_saving': TESTED, 'outer': outer, 'compiler': rank, + 'minimum_outer_margin': min(outer['margins'].values())-KAPPA, + 'negative_controls': controls, + 'ledger_source_sha256': sha256(ledger_path.read_bytes()).hexdigest(), + 'strictification_source_sha256': sha256((HERE/'strictification.py').read_bytes()).hexdigest(), + '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.'}) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root', type=Path, default=HERE/'source') + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = run(args.source_root) + if args.out: + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({key: result[key] for key in + ('status', 'kappa', 'gain_over_PR4359', 'minimum_outer_margin', 'compiler')}, sort_keys=True)) diff --git a/research/pr4359-p7-padding/factor_receipt.py b/research/pr4359-p7-padding/factor_receipt.py new file mode 100644 index 0000000000..e17133b81e --- /dev/null +++ b/research/pr4359-p7-padding/factor_receipt.py @@ -0,0 +1,60 @@ +#!/usr/bin/env python3 +"""Regenerate one exact p7 mask with authenticated original factor code.""" +from hashlib import sha256 +from pathlib import Path +import importlib.util +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +PINS = { + 'research/kappa-rebuild/bit/complex_controller_factor.py': '1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497', + 'research/kappa-rebuild/bit/mixed_productive_bit.py': 'b32291b0db7fc0d332ec444c70746ab0fb03351d2e50546f8bcb64060e3ff95e', + 'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py': '8a0de761642d21919e969475c3f13e5d01a4bae7343c1e1f37c586d94b676a85', +} +RECEIPT_SHA256 = '6f96f6be5d8441f71cbe6ebb1657c69b543eb085b848b92b591b7ac01d6e6598' + + +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 run(source_root): + root = Path(source_root).resolve() + for relative, expected in PINS.items(): + if sha256((root/relative).read_bytes()).hexdigest() != expected: + raise AssertionError('Original factor source changed: '+relative) + paths = list(PINS) + # Explicit imports avoid the original generator's historical reference path. + load(root/paths[2], 'joint_pair_dag') + load(root/paths[1], 'mixed_productive_bit') + generator = load(root/paths[0], 'original_complex_controller_factor') + coefficients, events, idles = generator.controller(7, 232127) + factored = generator.factor(coefficients) + if factored is None: + raise AssertionError('The chosen p7 mask has no exact factorization') + case = generator.serialize_case(7, 232127, coefficients, events, idles, factored) + receipt = HERE/'P7-FACTOR.json' + if sha256(receipt.read_bytes()).hexdigest() != RECEIPT_SHA256: + raise AssertionError('Checked p7 factor receipt changed') + # JSON normalizes integer histogram keys in the freshly generated case. + if json.loads(json.dumps(case)) != json.loads(receipt.read_text()): + raise AssertionError('Fresh exact factorization differs from the receipt') + return json.loads(receipt.read_text()), dict(PINS) + + +if __name__ == '__main__': + import argparse + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root', type=Path, default=HERE/'source') + args = parser.parse_args() + case, pins = run(args.source_root) + print(json.dumps({'status': 'PASS_EXACT_FIXED_MASK_REGENERATION', + 'p': case['pairs'], 'keep': case['keep_idle_mask'], + 'coefficient_matrices': len(case['coefficient_matrices']), + 'receipt_sha256': RECEIPT_SHA256, 'source_sha256': pins}, sort_keys=True)) diff --git a/research/pr4359-p7-padding/native_inventory.py b/research/pr4359-p7-padding/native_inventory.py new file mode 100644 index 0000000000..8d2d96e399 --- /dev/null +++ b/research/pr4359-p7-padding/native_inventory.py @@ -0,0 +1,270 @@ +#!/usr/bin/env python3 +"""Dimension-independent exact native phase audit for an all-fresh controller. + +Uses the original nine-axis native supplier, with fresh eight-axis blocks. +No helper is hosted in a main idle field. Source all-column semantics remain +a written premise; this checks each finite raw contact and endpoint phase. +""" +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import gzip +import importlib.util +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +NATIVE = HERE/'dependencies/tensor-strictification/native_inventory.py' + + +def need(test, why): + if not test: + raise AssertionError(why) + + +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 read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def norm(terms): + out = Counter() + for axis, value in terms: + out[axis] += value + return tuple(sorted((axis, value % 4) for axis, value in out.items() if axis and value % 4)) + + +def act(columns, value): + result = 0 + while value: + low = value & -value + result ^= columns[low.bit_length()-1] + value ^= low + return result + + +@lru_cache(None) +def polynomial(terms, dimension): + linear = [0]*dimension + quadratic = [0]*dimension + for axis, value in terms: + support = [i for i in range(dimension) if axis >> i & 1] + for i in support: + linear[i] = (linear[i]+value) % 4 + if value % 2: + for j in support: + if i < j: + quadratic[i] ^= 1 << j + return tuple(linear), tuple(quadratic) + + +def contact(old, new, route, dimension): + moved = norm((act(route, axis), value) for axis, value in old) + left, right = polynomial(moved, dimension), polynomial(new, dimension) + need(left[1] == right[1], 'Actual native contact has identical quadratic part') + delta = tuple((a-b) % 4 for a, b in zip(right[0], left[0])) + need(all(value in (0, 2) for value in delta), 'Even linear phase is a physical translation') + shift = sum((value//2) << i for i, value in enumerate(delta)) + need(polynomial(norm(list(moved)+[(shift, 2)]), dimension) == right, 'Full native forward phase') + inverse_shift = act(route, shift) + inverse = norm([(act(route, axis), value) for axis, value in new]+[(inverse_shift, 2)]) + need(polynomial(inverse, dimension) == polynomial(old, dimension), 'Full inverse contact phase') + return {'translation': shift, 'inverse_translation': inverse_shift} + + +def scalar_invoice(case, native_scalar): + word = case['right_program']+case['left_program'] + counts = Counter(row[0] for row in word) + need(all(Q(row[-1]) in (1, -1) for row in word if row[0] in ('ADD', 'SCALE')), + 'Literal boundary word has only unit coefficients') + adds = counts['ADD']+3*counts['SWAP'] + negs = counts['SCALE']+counts['SWAP'] + bridges = sum(row[0] == 'ADD' for row in case['physical_events']) + swaps = sum(row[0] == 'SIGNED_SWAP' for row in case['physical_events']) + return native_scalar+112*(8*(adds+bridges+3*swaps)+2*negs) + + +def run(source_root, p=7, keep=232127, output_dir=None): + root = Path(source_root).resolve() + base = root/'research/kappa-rebuild' + need((p, keep) == (7, 232127), 'This source-bound native admission is p7 keep232127') + inventory = load(NATIVE, 'checked_native_inventory') + native_gate = inventory.run(root) + factor = load(HERE/'factor_receipt.py', 'fixed_p7_factor') + case, factor_pins = factor.run(root) + replay_path = base/'transfer-audit/p3_native_audit.py' + need(sha256(replay_path.read_bytes()).hexdigest() == '5504a55a50546418d10c522984438cdeedb44993f7c1dab7bd4aa1ae0515d902', + 'Exact independent Laurent replay source') + audit = load(replay_path, 'independent_laurent_replay') + audit.replay(case) + corrupted = json.loads(json.dumps(case)) + next(row for row in corrupted['physical_events'] if row[0] == 'LOCAL' and row[3])[3] = False + wrong_orientation_rejected = False + try: + audit.replay(corrupted) + except AssertionError: + wrong_orientation_rejected = True + need(wrong_orientation_rejected, 'A wrong native reverse orientation fails the exact whole Laurent word') + phase_path = root/'research/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json' + if not phase_path.exists(): + phase_path = root/'research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json' + need(sha256(phase_path.read_bytes()).hexdigest() == 'c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa', + 'Exact original native port phase source') + phases = read(phase_path) + dimension = 9+16*p + axes = tuple(1 << i for i in range(dimension)) + def completed(stage): + return norm((axis, 1) for axis in axes[:9+8*stage]) + def stage_frame(stage, q): + return norm([(axis, 1) for axis in axes[:9]]+[(q, -1)] if stage == 0 + else [(axis, 1) for axis in axes[9+8*(stage-1):9+8*stage]]) + contacts = [] + stages = [row for row in case['physical_events'] if row[0] == 'LOCAL'] + need([row[1] for row in stages] == list(range(2*p+1)), 'Exact chronological stage sequence') + for _, stage, pair, backward in stages: + sign = -1 if backward else 1 + spectator = norm((axis, 1) for axis in axes[9:9+8*stage]) + for port, recipe in enumerate(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), 'Actual owner basis is orthogonal to q') + need(all((a & b).bit_count() % 2 == int(i == j) for i, a in enumerate(basis) + for j, b in enumerate(basis)), 'Actual eight-vector basis is orthonormal') + swaps = [] if stage == 0 else [b ^ axes[9+8*(stage-1)+i] for i, b in enumerate(basis)] + route = tuple(e ^ act(swaps, sum(((e & v).bit_count() % 2) << i for i, v in enumerate(swaps))) + for e in axes) + need(all(act(route, route[i]) == axes[i] for i in range(dimension)), 'Full dimension route is an involution') + need(all((a & b).bit_count() % 2 == int(i == j) for i, a in enumerate(route) + for j, b in enumerate(route)), 'Full dimension route is orthogonal') + need(act(route, q) == q, 'Actual q is fixed') + raw_x = norm([(q, 1)]) if stage == 0 else completed(stage-1) + raw_y = () if stage == 0 else norm(list(raw_x)+[(q, -1)]) + local_x0 = norm(list(spectator)+[(q, sign)]) + local_y0 = spectator + local_x1 = norm(list(spectator)+[(axis, sign) for axis in axes[:9]]) + local_y1 = norm(list(local_x1)+[(q, -sign)]) + out_x = completed(stage) + out_y = norm(list(out_x)+[(q, -1)]) + maps = {name: contact(old, new, route, dimension) for name, old, new in ( + ('entry_X', raw_x, local_x0), ('entry_Y', raw_y, local_y0), + ('exit_X', local_x1, out_x), ('exit_Y', local_y1, out_y))} + delta = stage_frame(stage, q) + for incoming, outgoing in ((raw_x, out_x), (raw_y, out_y)): + need(polynomial(norm(list(outgoing)+[(a, -c) for a, c in incoming]), dimension) + == polynomial(delta, dimension), 'Raw diagonal operator is exactly D_s') + cross = norm(list(out_y if sign == 1 else out_x)+ + [(a, -c) for a, c in (raw_x if sign == 1 else raw_y)]) + need(polynomial(cross, dimension) == polynomial(norm(list(delta)+[(q, -sign)]), dimension), + 'Raw cross operator is exactly D_s Q^(-sign)') + contacts.append({'stage': stage, 'pair': pair, 'port': port, 'backward': backward, + 'route': route, 'maps': maps}) + endpoints = [] + target_main = Counter() + omitted_endpoint_phase_rejected = 0 + for role, term in enumerate(case['exact_diagonal_monomials']): + qp, selected = term[0], term[1:] + need(qp in (-1, 1) and set(selected) <= {0, 1}, 'Actual endpoint exponent alphabet') + for port, recipe in enumerate(phases['recipes']): + q = recipe['q'] + physical = norm([(q, qp)]+[entry for stage, yes in enumerate(selected) if yes for entry in stage_frame(stage, q)]) + positive = list(axes[:9]) if selected[0] else [q] + positive += [axis for stage in range(1, len(selected)) if selected[stage] + for axis in axes[9+8*(stage-1):9+8*stage]] + shift = q if qp == -1 else 0 + need(inventory.independent_axes(positive), 'Actual endpoint target axes independent') + need(len(positive) == 1+8*sum(selected), 'Exact productive endpoint rank') + need(polynomial(norm(list(physical)+[(shift, 2)]), dimension) + == polynomial(norm((axis, 1) for axis in positive), dimension), 'Complete endpoint phase normalization') + if shift: + need(polynomial(physical, dimension) != polynomial(norm((axis, 1) for axis in positive), dimension), + 'Omitting the endpoint translation fails') + omitted_endpoint_phase_rejected += 1 + endpoints.append({'role': role, 'port': port, 'rank': len(positive), 'axes': positive, 'translation': shift}) + target_main[len(positive)] += 1 + recorded = Counter((row['pair'], tuple(row['stages'])) for row in case['retained_idle_windows']) + literal = Counter((row[1], tuple(row[2])) for row in case['physical_events'] if row[0] == 'IDLE') + need(recorded == literal, 'Bijection of every paid whole idle and every literal controller IDLE') + need(all(row['rank'] == 8*len(row['stages']) for row in case['retained_idle_windows']), + 'Every paid window rank matches the literal stage count') + idle = Counter() + idle_records = [] + for window in case['retained_idle_windows']: + selected = window['stages'] + need(case['physical_events'].count(['IDLE', window['pair'], selected]) == 1, + 'Each full idle is attached to its original literal pair and event') + for port, recipe in enumerate(phases['recipes']): + q = recipe['q'] + if 0 in selected: + need(selected == list(range(len(selected))) and len(selected) >= 2, 'Initial window contiguous from stage0') + positive = recipe['idle_children'][0]['orthogonal_axes'][:] + positive += [axis for stage in selected[2:] for axis in axes[9+8*(stage-1):9+8*stage]] + shift = recipe['idle_children'][0]['translation_after'] + else: + positive = [axis for stage in selected for axis in axes[9+8*(stage-1):9+8*stage]] + shift = 0 + desired = norm(entry for stage in selected for entry in stage_frame(stage, q)) + actual = norm([(axis, 1) for axis in positive]+[(shift, 2)]) + need(inventory.independent_axes(positive) and len(positive) == window['rank'], 'Exact whole idle rank') + need(polynomial(actual, dimension) == polynomial(desired, dimension), 'Exact complete whole idle phase') + idle[len(positive)] += 2 + idle_records.append({'window': window['index'], 'pair': window['pair'], 'stages': selected, + 'port': port, 'owners': [f'X{window["pair"]}:{port}', f'Y{window["pair"]}:{port}'], + 'axes': positive, 'translation': shift}) + receipt = read(base/'complex/full-identity-certificates/RESULT.json')['providers']['THREE-base'] + target_helpers = Counter({int(k): v*(2*p+1) for k, v in receipt['helper_boundary']['widths'].items()}) + targets = target_main+target_helpers + paid = Counter({int(k): v*(2*p+1) for k, v in receipt['unsplit_replays']['forward']['paid_profile'].items()}) + paid.update(idle) + scalar = scalar_invoice(case, sum(receipt['split_replays']['backward' if row[3] else 'forward'] + ['independent_native_replay']['conservative_real_scalar_primitive_allowance'] for row in stages)) + artifact = {'contacts': contacts, 'endpoints': endpoints, 'whole_idles': idle_records, 'formal': case} + artifact_json = json.dumps(artifact, sort_keys=True, separators=(',', ':')).encode() + artifact_bytes = gzip.compress(artifact_json, compresslevel=9, mtime=0) + if output_dir is not None: + output = Path(output_dir) + output.mkdir(parents=True, exist_ok=True) + (output/'NATIVE-GEOMETRY.json.gz').write_bytes(artifact_bytes) + result = {'status': 'PASS_EXACT_LAURENT_ALL_MAIN_CONTACTS_ENDPOINTS_AND_FULL_IDLE_PHASES', + 'p': p, 'keep': keep, 'dimension': dimension, 'contacts': 4*len(contacts), + 'main_fields': 224*p, 'fresh_helper_fields': 408*(2*p+1), + 'targets': dict(sorted(targets.items())), 'paid': dict(sorted(paid.items())), + 'native_scalar_allowance': scalar, 'scalar_allowance': scalar, + 'productive_fields': sum(targets.values()), 'paid_calls': sum(paid.values()), 'whole_idle_profile': dict(sorted(idle.items())), + 'rank_margin': sum(k*v for k, v in targets.items())-sum(k*v for k, v in paid.items()), + 'artifact_sha256': sha256(artifact_json).hexdigest(), + 'artifact_hash_encoding': 'Uncompressed UTF-8 JSON, sort_keys=True, separators=(comma,colon)', + 'native_source_gate': native_gate['status'], + 'negative_controls': {'wrong_native_orientation_rejected': wrong_orientation_rejected, + 'omitted_endpoint_translation_rejected': omitted_endpoint_phase_rejected}, + 'source_sha256': {str(path.relative_to(root)): sha256(path.read_bytes()).hexdigest() + for path in (phase_path, base/'transfer-audit/p3_native_audit.py', + base/'complex/full-identity-certificates/RESULT.json')}, + '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.'} + result['source_sha256'].update(native_gate['source_sha256']) + result['source_sha256'].update(factor_pins) + result['factor_receipt_sha256'] = factor.RECEIPT_SHA256 + result['schema'] = 'source-bound-p7-all-fresh-complete-native-controller/1' + return result + + +if __name__ == '__main__': + import argparse + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root', type=Path, default=HERE/'source') + parser.add_argument('--output-dir', type=Path) + args = parser.parse_args() + result = run(args.source_root, output_dir=args.output_dir) + if args.output_dir: + (args.output_dir/'NATIVE.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({k:result[k] for k in ('status','contacts','dimension','productive_fields','paid_calls','targets','paid','native_scalar_allowance')}, sort_keys=True)) diff --git a/research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py b/research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py new file mode 100644 index 0000000000..8b40135a84 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/bit-compression/carrier-reuse/reference/joint_pair_dag.py @@ -0,0 +1,731 @@ +#!/usr/bin/env python3 +"""Joint side/pair-total monotone DAG with a fully paid copied output interface. + +The tensor recurrence and equal-support interning follow the pinned upstream +ternary_side.py / disjoint_tensor.py construction. The additional total query, +shared observation word, explicit enclosure frames and invoice are this probe. +No installed numerical packages and no external files are needed at replay. +""" +from array import array +from collections import Counter +from functools import cache +from fractions import Fraction as Q +from hashlib import sha256 +from itertools import combinations +from math import comb, exp, log +from pathlib import Path +import argparse +import json +import sys + + +def require(p, message): + if not p: + raise ValueError(message) + + +def mask(t): + return sum(1 << i for i in t) + + +@cache +def subsets(points, size): + return tuple(mask(t) for t in combinations(points, size)) + + +@cache +def tensor_plan(n, a, b): + require(0 <= a <= n and 0 <= b <= n, "Invalid tensor size") + if a+b > n: + return 0, "empty" + if not a: + return 0, "copy" + if not b: + return comb(n, a)-1, "sum" + best = comb(n, b)*(comb(n-b, a)-1), "rows" + for left in range(1, n//2+1): + right = n-left + cost = 0 + for j in range(max(0, b-right), min(left, b)+1): + parts = 0 + for i in range(max(0, a-right), min(left, a)+1): + if i+j > left or a-i+b-j > right: + continue + A = tensor_plan(left, i, j)[0] + B = tensor_plan(right, a-i, b-j)[0] + cost += min(comb(right, a-i)*A+comb(left, j)*B, + comb(left, i)*B+comb(right, b-j)*A) + parts += 1 + if parts: + cost += comb(left, j)*comb(right, b-j)*(parts-1) + if cost < best[0]: + best = cost, left + return best + + +class TripleTemplate: + """Cancellation-free triple queries, augmented by the complete total.""" + def __init__(self, h): + self.inputs = list(subsets(tuple(range(h)), 3)) + self.support = [0]+[1 << i for i in range(len(self.inputs))] + self.args = [None]*len(self.support) + self.lookup = {s: i for i, s in enumerate(self.support)} + values = {s: i+1 for i, s in enumerate(self.inputs)} + self.outputs = self.transform(tuple(range(h)), 3, 3, values) + self.total_root = self.total(list(values.values())) + self.active = set() + todo = [*self.outputs.values(), self.total_root] + while todo: + node = todo.pop() + if not node or node in self.active: + continue + self.active.add(node) + if self.args[node]: + todo.extend(self.args[node]) + for node in sorted(self.active): + if self.args[node]: + a, b = self.args[node] + require(a < node and b < node, "Noncausal template edge") + require(not self.support[a] & self.support[b], "Overlapping summands") + require(self.support[node] == self.support[a] | self.support[b], + "Wrong template support") + all_inputs = (1 << len(self.inputs))-1 + require(self.support[self.total_root] == all_inputs, "Wrong total query") + for t, node in self.outputs.items(): + expected = sum(1 << i for i, s in enumerate(self.inputs) if not s & t) + require(self.support[node] == expected, "Wrong disjoint-triple query") + + def add(self, a, b): + if not a or not b: + return a or b + require(not self.support[a] & self.support[b], "Addition is not cancellation-free") + s = self.support[a] | self.support[b] + node = self.lookup.get(s) + if node is None: + node = len(self.support) + self.lookup[s] = node + self.support.append(s) + self.args.append((a, b)) + return node + + def total(self, nodes): + if not nodes: + return 0 + if len(nodes) == 1: + return nodes[0] + m = len(nodes)//2 + return self.add(self.total(nodes[:m]), self.total(nodes[m:])) + + def transform(self, points, a, b, values): + n = len(points) + _, method = tensor_plan(n, a, b) + outputs = subsets(points, b) + if method == "empty": + return {t: 0 for t in outputs} + if method == "copy": + return {t: values[0] for t in outputs} + if method == "sum": + return {0: self.total(list(values.values()))} + if method == "rows": + return {t: self.total([values[s] for s in subsets(points, a) if not s & t]) + for t in outputs} + left, right = points[:method], points[method:] + l, r = len(left), len(right) + terms = {t: [] for t in outputs} + for j in range(max(0, b-r), min(l, b)+1): + for i in range(max(0, a-r), min(l, a)+1): + if i+j > l or a-i+b-j > r: + continue + A = tensor_plan(l, i, j)[0] + B = tensor_plan(r, a-i, b-j)[0] + if comb(r, a-i)*A+comb(l, j)*B <= comb(l, i)*B+comb(r, b-j)*A: + middle = {s: self.transform(left, i, j, + {u: values[u | s] for u in subsets(left, i)}) + for s in subsets(right, a-i)} + for t in subsets(left, j): + row = self.transform(right, a-i, b-j, + {s: v[t] for s, v in middle.items()}) + for u, node in row.items(): + terms[t | u].append(node) + else: + middle = {s: self.transform(right, a-i, b-j, + {u: values[u | s] for u in subsets(right, a-i)}) + for s in subsets(left, i)} + for t in subsets(right, b-j): + row = self.transform(left, i, j, + {s: v[t] for s, v in middle.items()}) + for u, node in row.items(): + terms[t | u].append(node) + return {t: self.total(nodes) for t, nodes in terms.items()} + + +def array_digest(*arrays): + out = sha256() + for a in arrays: + if a.itemsize > 1 and sys.byteorder != "little": + a = array(a.typecode, a) + a.byteswap() + out.update(a.tobytes()) + return out.hexdigest() + + +def build(h, exact_support=False): + require(type(h) is int and 8 <= h <= 24, "Probe budget is 8 <= h <= 24") + require(not exact_support or h <= 9, "Dense coefficient certificate budget exceeded") + template = TripleTemplate(h) + triples = template.inputs + pairs = list(subsets(tuple(range(h)), 2)) + labels = list(subsets(tuple(range(h)), 5)) + V, c = len(labels), len(pairs) + source_id = {t: i+1 for i, t in enumerate(labels)} + pair_id = {t: i for i, t in enumerate(pairs)} + left = array("I", [0])*(V+1) + right = array("I", [0])*(V+1) + common = array("I", [0]+labels) + union = array("I", [0]+labels) + roots, targets = array("I"), array("I") + centers = array("I") + exact = [0]+[1 << i for i in range(V)] if exact_support else None + table = {} + nodes = sorted(template.active) + + def allocate(a, b): + require(0 < a < len(left) and 0 < b < len(left) and a != b, "Invalid DAG input") + node = len(left) + require(node < 2**32, "DAG index overflow") + left.append(a) + right.append(b) + common.append(common[a] & common[b]) + union.append(union[a] | union[b]) + require(common[node].bit_count() >= 2, "Source enclosure lost the common pair") + if exact is not None: + require(not exact[a] & exact[b], "Overlapping exact source supports") + exact.append(exact[a] | exact[b]) + return node + + for pair in pairs: + good = sum(1 << i for i, t in enumerate(triples) if not t & pair) + image = array("I", [0])*len(template.args) + inter = array("I", [0])*len(template.args) + uni = array("I", [0])*len(template.args) + within = {} + for i, t in enumerate(triples): + if not t & pair: + image[i+1] = source_id[pair | t] + inter[i+1] = uni[i+1] = t + for x in nodes: + if not template.args[x]: + continue + u, v = template.args[x] + a, b = image[u], image[v] + if not a or not b: + image[x] = a or b + inter[x] = inter[u] if a else inter[v] + uni[x] = uni[u] if a else uni[v] + continue + I, U = inter[u] & inter[v], uni[u] | uni[v] + inter[x], uni[x] = I, U + support = template.support[x] & good + require(I.bit_count() <= 2, "Two distinct triples have three common points") + if not I: + y = within.get(support) + if y is None: + y = allocate(a, b) + within[support] = y + else: + if I.bit_count() == 1: + residual = 0 + bits = support + while bits: + bit = bits & -bits + bits ^= bit + residual |= 1 << pair_id[triples[bit.bit_length()-1] ^ I] + else: + residual = U ^ I + key = ((pair | I) << c) | residual + y = table.get(key) + if y is None: + y = allocate(a, b) + table[key] = y + require(common[y] == common[a] & common[b] and + union[y] == union[a] | union[b], "Interned enclosure mismatch") + if exact is not None: + require(exact[y] == exact[a] | exact[b] and not exact[a] & exact[b], + "Interned unequal formal source sums") + image[x] = y + for t, x in template.outputs.items(): + if t & pair: + continue + y = image[x] + target = t | pair + require(y != 0, "Empty side output") + roots.append(y) + targets.append(source_id[target]-1) + if exact is not None: + expected = sum(1 << i for i, s in enumerate(labels) if s & target == pair) + require(exact[y] == expected, "Wrong complete side coefficient row") + center = image[template.total_root] + centers.append(center) + require(common[center] == pair and union[center] == (1 << h)-1, + "Pair total is not at its h-2 enclosure") + if exact is not None: + expected = sum(1 << i for i, s in enumerate(labels) if s & pair == pair) + require(exact[center] == expected, "Wrong pair-total coefficient row") + require(len(roots) == 10*V and len(centers) == c, "Missing query outputs") + require(Counter(targets) == {i: 10 for i in range(V)}, "Wrong side target multiplicity") + active = bytearray(len(left)) + for root in [*roots, *centers]: + active[root] = 1 + additions = 0 + for node in range(len(left)-1, V, -1): + if active[node]: + additions += 1 + active[left[node]] = active[right[node]] = 1 + require(sum(active[1:V+1]) == V, "A source is missing") + return dict(h=h, V=V, c=c, labels=labels, pairs=pairs, left=left, right=right, + common=common, union=union, roots=roots, targets=targets, centers=centers, + active=active, additions=additions, exact=exact, + template_active_additions=sum(template.args[i] is not None for i in template.active), + template_total_augmented=True) + + +def frame_rank(I, U): + k = I.bit_count() + require(I & ~U == 0 and 2 <= k <= 5, "Invalid enclosure") + if k == 5: + require(I == U, "A common five-subset can only be a singleton") + return 1 + return U.bit_count()-k + + +def compile_native(g, retain=False): + h, V, c = g["h"], g["V"], g["c"] + L, R, active = g["left"], g["right"], g["active"] + size = len(L) + uses = array("I", [0])*size + lo = array("I", [0])*size + ro = array("I", [0])*size + for node in range(V+1, size): + if active[node]: + lo[node] = uses[L[node]] + uses[L[node]] += 1 + ro[node] = uses[R[node]] + uses[R[node]] += 1 + query_roots = [*g["roots"], *g["centers"]] + ordinals = array("I") + for node in query_roots: + ordinals.append(uses[node]) + uses[node] += 1 + pivot = array("I", [0])*size + first = array("I", [0])*size + frames = [] + hist = Counter() + moves = 0 + scalar_L = [] if retain else None + scalar_L_count = 0 + source_slots = [] + transition_hash = sha256() + unique_enclosures = set() + + def slot(node, ordinal): + return pivot[node] if ordinal == 0 else first[node]+ordinal-1 + + def move(s, node): + nonlocal moves + old = frames[s] + if old == node: + return + I, U = g["common"][node], g["union"][node] + new_rank = frame_rank(I, U) + if old: + old_I, old_U = g["common"][old], g["union"][old] + require(I & ~old_I == 0 and old_U & ~U == 0, + "Physical forward edge does not have nested enclosures") + old_rank = frame_rank(old_I, old_U) + else: + old_rank = 0 + d = new_rank-old_rank + require(d >= 0, "Negative monotone rank increment") + if d: + hist[d] += 1 + moves += 1 + frames[s] = node + if retain: + unique_enclosures.add((I, U)) + transition_hash.update(f"{s}:{old}>{node}:{d};".encode()) + + for node in range(1, size): + if not active[node]: + continue + require(uses[node] > 0, "Active node has no user") + if node <= V: + p = len(frames) + frames.append(0) + ins = [p] + source_slots.append((node-1, p)) + else: + ins = [slot(L[node], lo[node]), slot(R[node], ro[node])] + p = ins[0] + pivot[node] = p + first[node] = len(frames) + new_slots = range(len(frames), len(frames)+uses[node]-1) + frames.extend([0]*(uses[node]-1)) + outs = [p, *new_slots] + require(len(set(ins+outs)) == len(ins)+len(outs)-1, "Pivot aliasing error") + for s in [*ins, *outs[1:]]: + move(s, node) + for s in ins[1:]: + scalar_L_count += 1 + if retain: + scalar_L.append((p, s, 1)) + for s in outs[1:]: + scalar_L_count += 1 + if retain: + scalar_L.append((s, p, 1)) + A = len(frames) + require(A == g["additions"]+10*V+c, "Wrong reversible role count") + output_slots = [slot(node, ordinal) for node, ordinal in zip(query_roots, ordinals)] + require(len(set(output_slots)) == len(output_slots), "Query outputs share a physical slot") + center_slots = output_slots[10*V:] + side_slots = output_slots[:10*V] + # Query reads happen after the producer and before any inverse update. + # Center original streams stay put; each private copy is discarded after its read. + for s, center in zip(center_slots, g["centers"]): + require(frames[s] == center, "Center original was consumed before its read") + r = frame_rank(g["common"][center], g["union"][center]) + require(r == h-2, "Center rank is not h-2") + hist[r] += 1 + moves += 1 + # Side output uses meet the actual target at its fixed hyperplane. + side_checks = 0 + for s, target in zip(side_slots, g["targets"]): + node = frames[s] + I, U = g["common"][node], g["union"][node] + T = g["labels"][target] + if I.bit_count() == 5: + require((I & T).bit_count() == 2, "Singleton side is not orthogonal") + else: + # All coordinates on I equal a; total is 5a. Only a pair of I + # occurs in the target; its other coordinates are outside U. + require((I & T).bit_count() == 2 and (T & U) == (T & I), + "Output enclosure is not below the target hyperplane") + d = h-1-frame_rank(I, U) + require(d >= 0, "Side output rank exceeds its hyperplane") + if d: + hist[d] += 1 + moves += 1 + frames[s] = -1 # distinct actual target hyperplane, rank h-1 + side_checks += 1 + for node in frames: + r = h-1 if node == -1 else frame_rank(g["common"][node], g["union"][node]) + d = h-r + require(d >= 0, "Helper endpoint rank exceeds I") + if d: + hist[d] += 1 + moves += 1 + # Data source Pi -> I; data target 0 -> I-Pi. + hist[h-1] += 2*V + moves += 2*V + mass = sum(r*n for r, n in hist.items()) + minimum = (2*V+A)*h-2*V + require(mass == minimum+c*(h-2), "Joint native rank telescoping failed") + global_hist = Counter({r: 3*n for r, n in hist.items()}) + global_hist[2] += 2*V + W, m = 2*V+A, 3*h + global_mass = sum(r*n for r, n in global_hist.items()) + delta = W*m-global_mass + require(delta == 2*V-3*c*(h-2), "Padded cover saving failed") + out = dict(persistent_auxiliaries=A, data_roles=2*V, W=W, m=m, + local_profile=dict(sorted(hist.items())), local_rank_mass=mass, + monotone_endpoint_minimum=minimum, local_excess=c*(h-2), + physical_rank_moves=moves, forward_mixer_primitives=scalar_L_count, + complete_scalar_primitives=4*scalar_L_count+42*V, + side_output_inclusions_checked=side_checks, + central_private_copies=c, central_copy_rank=h-2, + global_profile=dict(sorted(global_hist.items())), + global_rank_mass=global_mass, global_output_mass=W*m, + global_rank_saving=delta, + physical_transition_sha256=transition_hash.hexdigest()) + if retain: + out["_program"] = dict(L=scalar_L, sources=source_slots, side=side_slots, + centers=center_slots, enclosures=sorted(unique_enclosures)) + return out + + +def f3add(a, b, coefficient=1): + u, v = a + x, y = b + coefficient %= 3 + if coefficient == 0: + return a + if coefficient == 2: + x, y = y, x + return ((u & ~(x | y)) | (x & ~(u | v)) | (v & y), + (v & ~(x | y)) | (y & ~(u | v)) | (u & x)) + + +def scalar_certificate(g, ledger, sign=1, omit=None): + p = ledger["_program"] + V, A, W = g["V"], ledger["persistent_auxiliaries"], ledger["W"] + values = [(1 << i, 0) for i in range(W)] + operations = 0 + + def add(dst, src, coefficient): + nonlocal operations + values[dst] = f3add(values[dst], values[src], coefficient) + operations += 1 + + def mixer(inverse=False): + ops = reversed(p["L"]) if inverse else p["L"] + for dst, src, coefficient in ops: + add(2*V+dst, 2*V+src, -coefficient if inverse else coefficient) + + def observation(k, which): + if omit != which+"_center": + for pair, slot in zip(g["pairs"], p["centers"]): + for i, label in enumerate(g["labels"]): + if label & pair == pair: + add(V+i, 2*V+slot, k) + if omit != which+"_side": + for i, slot in zip(g["targets"], p["side"]): + add(V+i, 2*V+slot, -k) + + mixer() + observation(-sign, "old") + mixer(True) + for i, s in p["sources"]: + add(2*V+s, i, 1) + mixer() + observation(sign, "new") + mixer(True) + for i, s in reversed(p["sources"]): + add(2*V+s, i, -1) + expected = [(1 << i, 0) for i in range(W)] + for i in range(V): + expected[V+i] = f3add(expected[V+i], expected[i], sign) + changed_rows = sum(a != b for a, b in zip(values, expected)) + changed_coefficients = 0 + for a, b in zip(values, expected): + d = f3add(a, b, -1) + changed_coefficients += (d[0] | d[1]).bit_count() + helper_rows = sum(values[i] != expected[i] for i in range(2*V, W)) + if omit is None: + require(changed_rows == 0, "Complete scalar operator failed") + require(operations == ledger["complete_scalar_primitives"], "Scalar count mismatch") + else: + require(changed_coefficients > 0, "Negative control was not detected") + return dict(sign=sign, independent_roles=W, all_operator_coefficients=W*W, + scalar_primitives=operations, changed_rows=changed_rows, + changed_coefficients=changed_coefficients, changed_helper_rows=helper_rows, + arbitrary_dirty_helper_columns=True, omitted_phase=omit) + + +def eye(n): + return [[Q(i == j) for j in range(n)] for i in range(n)] + + +def mm(A, B): + return [[sum(a*b for a, b in zip(row, col)) for col in zip(*B)] for row in A] + + +def transpose(A): + return [list(x) for x in zip(*A)] + + +def enclosure_projector(h, I, U): + H = [[Q(i == j)-Q(2, 25) for j in range(h)] for i in range(h)] + k = I.bit_count() + if k == 5: + basis = [[Q(bool(I >> i & 1))] for i in range(h)] + inverse_gram = [[Q(1, 3)]] + else: + outside = [i for i in range(h) if U >> i & 1 and not I >> i & 1] + basis = [[Q(i == j)+Q(bool(I >> i & 1), 5-k) for j in outside] + for i in range(h)] + alpha = Q(k-2, (5-k)**2) + n = len(outside) + inverse_gram = [[Q(i == j)-alpha/(1+n*alpha) for j in range(n)] for i in range(n)] + gram = mm(mm(transpose(basis), H), basis) + require(mm(gram, inverse_gram) == eye(len(gram)), "Closed-form Gram inverse failed") + E = mm(mm(mm(basis, inverse_gram), transpose(basis)), H) + require(mm(E, E) == E and mm(transpose(E), H) == mm(H, E), "Invalid rational projector") + require(sum(E[i][i] for i in range(h)) == frame_rank(I, U), "Projector rank mismatch") + return E + + +def exact_enclosure_certificate(g, ledger): + h = g["h"] + enclosures = ledger["_program"]["enclosures"] + digest = sha256() + for I, U in enclosures: + E = enclosure_projector(h, I, U) + digest.update(json.dumps([[str(x) for x in row] for row in E], + separators=(",", ":")).encode()) + return dict(h=h, distinct_enclosures=len(enclosures), + exact_rational_projector_entries=len(enclosures)*h*h, + idempotence_checked=True, H_self_adjointness_checked=True, + closed_form_Gram_inverse_checked=True, + projector_sha256=digest.hexdigest(), + all_large_frame_inclusions="Checked as exact mask constraints; proved by the enclosure equations") + + +@cache +def log_interval(n, d=1, terms=50): + """Rational bounds from atanh, reducing the argument to [1,2).""" + x = Q(n, d) + require(x >= 1, "Log interval currently expects x >= 1") + k = 0 + while x >= 2: + x /= 2 + k += 1 + + def unit(y): + z = (y-1)/(y+1) + z2 = z*z + term = z + lower = Q(0) + for j in range(terms): + lower += 2*term/(2*j+1) + term *= z2 + upper = lower+2*term/((2*terms+1)*(1-z2)) + return lower, upper + + a, b = unit(x) + c, d2 = unit(Q(2)) + return dyadic_enclose(a+k*c, b+k*d2) + + +def dyadic_enclose(lo, hi, bits=128): + scale = 1 << bits + lower = (lo.numerator*scale)//lo.denominator + upper = -((-hi.numerator*scale)//hi.denominator) + return Q(lower, scale), Q(upper, scale) + + +def exp_interval(lo, hi, terms=20): + require(0 <= lo <= hi < 1, "Exp argument outside the fixed probe interval") + def partial(t): + s = Q(1) + term = Q(1) + for k in range(1, terms+1): + term *= t/k + s += term + return s, term*t/(terms+1) + lower = partial(lo)[0] + s, next_term = partial(hi) + upper = s+next_term/(1-hi/(terms+2)) + return dyadic_enclose(lower, upper) + + +def moment_interval(ledger, a): + require(0 <= a <= Q(1, 100), "Only small primitive exponents are screened") + lo = hi = Q(0) + W, m = ledger["W"], ledger["m"] + for r, count in ledger["global_profile"].items(): + lower, upper = log_interval(m, r) + lower, upper = exp_interval(a*lower, a*upper) + weight = Q(count*r, W*m) + lo += weight*lower + hi += weight*upper + return lo, hi + + +def quotient(x): + return f"{x.numerator}/{x.denominator}" + + +def moment_gate(ledger): + # Floating arithmetic locates a candidate only. Every pass/fail below is + # proved independently by rational interval arithmetic. + W, m = ledger["W"], ledger["m"] + prof = ledger["global_profile"] + f = lambda a: sum(count*r*exp(a*log(m/r)) for r, count in prof.items())/(W*m) + if f(0) >= 1: + candidate = Q(0) + else: + lo, hi = 0.0, 0.01 + for _ in range(64): + mid = (lo+hi)/2 + if f(mid) < 1: + lo = mid + else: + hi = mid + candidate = Q(int(lo*10**9), 10**9) + targets = sorted({candidate, candidate+Q(1, 10**9), Q(1, 1000), Q(1, 250)}) + gates = [] + for a in targets: + lo, hi = moment_interval(ledger, a) + gates.append(dict(a=quotient(a), moment_lower=float(lo), moment_upper=float(hi), + lower_exact=quotient(lo), upper_exact=quotient(hi), + strict_pass=hi < 1, strict_fail=lo > 1, + enclosure_method="Exact rational atanh/log and Taylor/exp tails")) + if candidate > 0: + require(gates[targets.index(candidate)]["strict_pass"], "Rounded candidate not certified") + require(gates[targets.index(candidate+Q(1, 10**9))]["strict_fail"], "Endpoint bracket not certified") + return dict(certified_primitive_a=quotient(candidate) if candidate > 0 else None, + candidate_location_only="Float bisection; never used as certificate", + targets=gates, multiplication_kappa_claim=False) + + +def summarize(g, ledger): + return dict(h=g["h"], V=g["V"], c=g["c"], + active_additions=g["additions"], allocated_additions=len(g["left"])-g["V"]-1, + side_query_uses=len(g["roots"]), center_query_uses=len(g["centers"]), + tensor_total_augmented=g["template_total_augmented"], + template_active_additions=g["template_active_additions"], + DAG_sha256=array_digest(g["left"], g["right"], g["common"], g["union"]), + query_sha256=array_digest(g["roots"], g["targets"], g["centers"]), + active_sha256=sha256(g["active"]).hexdigest(), + exact_formal_supports_expanded=g["exact"] is not None, + native={k: v for k, v in ledger.items() if not k.startswith("_")}, + primitive_moment=moment_gate(ledger)) + + +def main(): + ap = argparse.ArgumentParser() + ap.add_argument("--h", type=int, nargs="+", default=[8, 14, 19]) + ap.add_argument("--receipt", type=Path, default=Path(__file__).with_name("JOINT-PAIR-DAG.json")) + ap.add_argument("--skip-projector-matrices", action="store_true") + args = ap.parse_args() + result = dict(schema="joint-pair-total-monotone-native-DAG/1", + status="PASS_PAID_NATIVE_REFERENCE", new_admitted_kappa=False, + scalar_field="F3; rational geometry is separate", + geometry="H=I-(2/25)J, five-subset lines of norm 3", + word=["L@0", "-J@0", "L^-1@0", "V@P_i", "L@nested E(I,U)", + "J_center via immutable copies E_pair->0", "J_side@(I-P_i)", + "L^-1@I", "-V@I"], + upstream_algorithm_pin="12fa8c5c844be21bfefb38a19503fbd867a11244", + scalar_count_scope=("Counts pointwise scalar ADDs in the algebraic word. Complete stream " + "copying, retirement, routing and tape work are additional linear work; " + "recursive copy transforms are included in the rank profile."), + runtime_scope=("Native local/cover phase construction and exact moment gate under the " + "retained complete-stream contract; no new outer arbitrary-precision " + "engine or multiplication-runtime certificate is supplied."), + cases=[], scalar_checks=[], negative_controls=[], rational_projectors=[]) + for h in args.h: + exact = h == 8 + g = build(h, exact_support=exact) + ledger = compile_native(g, retain=exact) + if exact: + for sign in (1, -1): + result["scalar_checks"].append(scalar_certificate(g, ledger, sign)) + for omit in ("old_center", "new_center", "old_side", "new_side"): + result["negative_controls"].append(scalar_certificate(g, ledger, omit=omit)) + if not args.skip_projector_matrices: + result["rational_projectors"].append(exact_enclosure_certificate(g, ledger)) + case = summarize(g, ledger) + result["cases"].append(case) + print(json.dumps({"h": h, "V": g["V"], "A": ledger["persistent_auxiliaries"], + "delta": ledger["global_rank_saving"], + "certified_a": case["primitive_moment"]["certified_primitive_a"]}), flush=True) + result["program_sha256"] = sha256(Path(__file__).read_bytes()).hexdigest() + result["scope"] = ("The paid local F3 word has standard data/helper endpoints. The global profile uses the " + "previously proved shared padded 3h cover. This is a large-state reference, not a new " + "selected primitive or multiplication record; no complex supplier claim is made.") + args.receipt.parent.mkdir(parents=True, exist_ok=True) + args.receipt.write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps({"receipt": str(args.receipt), "status": result["status"]})) + + +if __name__ == "__main__": + main() diff --git a/research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json b/research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json new file mode 100644 index 0000000000..d9a4f84211 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-0023-productive-jobs/dependencies/kappa-next-regime/direct-decoder/sources/DATA-PHASES.json @@ -0,0 +1 @@ +{"cover_correction":{"complete_small_cover_checks":[{"n":1,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":1},{"n":2,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":2},{"n":3,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":6},{"n":4,"nonzero_full_kernel_corrections":24,"orthogonal_matrices":48},{"n":5,"nonzero_full_kernel_corrections":600,"orthogonal_matrices":720}],"formula":"delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.","mandatory":true,"reason":"P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector."},"global_phase_argument":"Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as 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complete recipe is unchanged except its port index; the retained parent polynomial checks establish every selected equality.","scope":"All compressed data boundary operators, idle children, terminal X_q and all-live cover correction. Internal arbitrary-subspace canonical labels are checked separately.","source_parent_sha256":"f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a","status":"PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES","terminal_omission_controls_rejected":112} diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md b/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md new file mode 100644 index 0000000000..4badb40f09 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/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)0:lo=mid + else:hi=mid + scale=10**30 + integer=int((lo*scale).to_integral_value(rounding=ROUND_FLOOR)) + left,right=Q(integer,scale),Q(integer+1,scale) + low_bounds=E.moment(signed,left) + high_bounds=E.moment(signed,right) + E.need(low_bounds[0]>0 and high_bounds[1]<0,'Exact strict root bracket') + return {'lower':str(Decimal(integer)/scale), + 'upper':str(Decimal(integer+1)/scale), + 'margin_at_lower':E.show(low_bounds),'margin_at_upper':E.show(high_bounds), + 'uniqueness':'The paid/target ratio is strictly increasing in C because every paid rank is smaller than every target rank.'} + +def source_binding(): + data=json.loads(NATIVE.read_text()) + bound={str(NATIVE.relative_to(ROOT)):sha256(NATIVE.read_bytes()).hexdigest()} + for name in ('THREE-base','THREE-extra'): + row=data['providers'][name] + E.need(row['all_408_helpers_autonomous'] and row['all_632_persistent_inputs_arbitrary'], + 'Authenticated arbitrary helper/data input contract') + E.need(row['external_cleanup_fields']==0 and row['owned_C_fields']==1, + 'Zero external bank and one explicitly owned center') + for orientation in ('forward','backward'): + replay=row['split_replays'][orientation]['independent_native_replay'] + profile={int(r):int(n) for r,n in replay['paid_profile'].items()} + E.need(profile==dict(E.split_profile(F.IDENTITY,5)),'Actual native split profile') + helpers={int(r):int(n) for r,n in row['helper_boundary']['widths'].items()} + E.need(helpers==dict(E.HELPERS),'Actual THREE helper inventory') + for name2,wanted in row['artifacts'].items(): + path=NATIVE.parent/name2 + E.need(sha256(path.read_bytes()).hexdigest()==wanted,'Native bytes '+name2) + bound[str(path.relative_to(ROOT))]=wanted + boundary=ROOT/row['helper_boundary']['certificate'] + wanted=row['helper_boundary']['certificate_sha256'] + E.need(sha256(boundary.read_bytes()).hexdigest()==wanted,'Helper boundary bytes') + bound[str(boundary.relative_to(ROOT))]=wanted + return bound + +def run(prefix_cut=False): + sources=source_binding() + solution=[] + for f in ((1,) if prefix_cut else (0,2)): + solution.extend({'family':f,'pattern':[a,b],'count':str(n)} for n,a,b in PAIRS) + solution.extend({'family':0 if prefix_cut else 1,'pattern':[a],'count':str(n)} for n,a in MIDDLE) + case=F.verify(2,6,solution,'identity',prefix_cut=prefix_cut) + wanted_targets=({'6':'165','7':'112','8':'186','9':'934','25':'224','41':'224'} + if prefix_cut else {'6':'146','9':'803','41':'448'}) + wanted_paid=({'1':'12584','2':'3602','3':'1217','4':'510','5':'169'} + if prefix_cut else {'1':'12565','2':'3621','3':'1217','4':'510','5':'169'}) + E.need(case['targets']==wanted_targets,'Literal output census') + E.need(case['paid']==wanted_paid,'Literal paid census') + out=F.serialize(case,('0.001730970419199163702738','0.001745','0.00175','0.00177','0.002','0.004')) + out['root_bracket']=root_bracket(case['signed']) + bad=[dict(x) for x in solution] + bad[0]=dict(bad[0],count=str(int(bad[0]['count'])+1)) + rejected=False + try:F.verify(2,6,bad,'identity',prefix_cut=prefix_cut) + except AssertionError:rejected=True + E.need(rejected,'Duplicated owner is rejected') + illegal=Counter(case['signed']);illegal[1]+=1 + E.need(sum(r*n for r,n in illegal.items())!=128,'Unfunded output rejected by rank budget') + return {'schema':'source-bound-identity-mixed-tariff/1', + 'status':'PASS_EXACT_NATIVE_BOUND_PROFILE_AND_FINITE_RECURSIVE_INVOICE', + 'source_sha256':sha256(Path(__file__).read_bytes()).hexdigest(), + 'native_sources':sources, + 'enclosure_source_sha256':sha256((HERE/'mixed_target_probe.py').read_bytes()).hexdigest(), + 'invoice':out, + 'controls':{'duplicate_original_idle_owner_rejected':rejected, + 'unfunded_output_credit_rejected':True, + 'rank5_target_with_rank5_child_rejected':not(5<5)}, + 'explicitly_charged':['all five native full-identity calls', + 'all forty rank8 centers split into rank5 plus rank3', + 'each unused original idle portion', + ('rank1 completions for all ninety-three width5 fresh helpers' if prefix_cut else + 'rank1 completions for all seventy-four width5 fresh helpers'), + 'every productive output field at its actual target rank'], + 'prefix_cut':prefix_cut, + 'not_a_recursive_output':['one owned center field, erased after use'], + 'not_proved':['physical global helper placement and controller binding', + 'all-size mixed-target causal routing on fixed tapes', + 'rounded whole-caller precision and stock conversion', + 'outer integer-multiplication transfer'], + 'new_kappa':False} + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--output',type=Path) + parser.add_argument('--prefix-cut',action='store_true') + args=parser.parse_args() + result=run(args.prefix_cut) + output=args.output or HERE/('IDENTITY-PREFIX-CUT-CERTIFICATE.json' if args.prefix_cut else + 'IDENTITY-MIXED-CERTIFICATE.json') + output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({'status':result['status'],'root':result['invoice']['root_bracket'], + 'margin_001745':result['invoice']['invoices']['0.001745']},sort_keys=True)) + +if __name__=='__main__':main() diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/mixed_forest_search.py b/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/mixed_forest_search.py new file mode 100644 index 0000000000..9b5213bf3f --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/architecture/mixed_forest_search.py @@ -0,0 +1,311 @@ +#!/usr/bin/env python3 +"""Column generation plus exact reconstruction for mixed-target idle forests. + +This searches p-pair controllers with two wide idle windows and one short +window for each j=1,...,p-1. A fresh productive job completes every unhosted +helper. The receipt checks exact rational multiplicities and the full +displayed child profile; numerical optimality is not a proof of a global +optimum. Native frame/emission and outer supplier obligations remain open. +Apache-2.0; substantial OpenAI assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import lcm +from pathlib import Path +import argparse +import json +import sys + +import mixed_target_probe as E +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +IDENTITY=Counter({1:2487,2:713,3:224,4:102,5:20,8:8}) +WIDTHS=(0,5,6,7,8,9) + +def windows(p,prefix_cut=False): + """Literal pair-controller idle chronology, 224 fields per window.""" + out=[] + for j in range(1,p): + if not prefix_cut: + out.append({'name':f'early{j}','capacity':16*j,'stages':list(range(2*j))}) + out.append({'name':f'middle{j}','capacity':8,'stages':[2*j]}) + out.append({'name':f'late{j}','capacity':16*j,'stages':list(range(2*p+1-2*j,2*p+1))}) + expected=1792*(2*p+1)*(p-1)-(224*16*p*(p-1)//2 if prefix_cut else 0) + E.need(sum(224*w['capacity'] for w in out)==expected,'General idle rank identity') + return out + +def numerical_split(r,maximum,c): + return sum(n*k**(1-c) for k,n in E.split_rank(r,maximum).items()) + +def reconstruct_exact(numbers,columns,families,resource,inventory): + """Recover an exact feasible basic solution, not rounded inventories. + + Small denominators suffice for most screens. Degenerate larger masters + can have a denominator above that guess; recover their active integer + linear system and independently replay it instead of waiving an equality. + """ + support=[i for i,x in enumerate(numbers) if x>1e-7] + approximate=[Q(float(numbers[i])).limit_denominator(10**6) for i in support] + def equations(): + rows=[];rhs=[] + for f in range(len(families)): + if not families[f].get('unbounded'): + rows.append([int(columns[i][0]==f) for i in support]);rhs.append(families[f].get('field_count',224)) + for stage,r in resource: + row=[] + for i in support: + f,pattern=columns[i] + w=families[f] + row.append(sum(int(s==stage and v==r) for s,v in zip(w['stages'],pattern))) + usage=sum(x*float(numbers[i]) for x,i in zip(row,support)) + if abs(usage-inventory[r])<1e-7: + rows.append(row);rhs.append(inventory[r]) + return rows,rhs + rows,rhs=equations() + if any(sum(a*x for a,x in zip(row,approximate))!=b for row,b in zip(rows,rhs)): + n=len(support) + basis={} + for row,b in zip(rows,rhs): + vector=[Q(x) for x in row]+[Q(b)] + for pivot in sorted(basis): + factor=vector[pivot] + if factor: + old=basis[pivot] + for j in range(pivot,n+1):vector[j]-=factor*old[j] + pivot=next((j for j,x in enumerate(vector[:-1]) if x),None) + if pivot is None: + E.need(vector[-1]==0,'Active integer system consistent') + else: + factor=vector[pivot] + basis[pivot]=[x/factor for x in vector] + E.need(len(basis)==n,'Active support is uniquely reconstructed') + approximate=[Q(0)]*n + for pivot in sorted(basis,reverse=True): + row=basis[pivot] + approximate[pivot]=row[-1]-sum(row[j]*approximate[j] for j in range(pivot+1,n)) + E.need(all(abs(float(x)-numbers[i])<1e-4 for x,i in zip(approximate,support)), + 'Exact active solution agrees with numerical discovery') + E.need(all(x>=0 for x in approximate),'Reconstructed multiplicities nonnegative') + return [{'family':columns[i][0],'pattern':list(columns[i][1]),'count':str(x)} + for i,x in zip(support,approximate) if x] + +def discover(p,minimum,c,max_rounds=300,fresh_groups=False,prefix_cut=False, + custom_windows=None,custom_targets=None): + import numpy as np + from scipy.optimize import linprog + from scipy.sparse import coo_matrix + families=windows(p,prefix_cut) if custom_windows is None else [dict(w) for w in custom_windows] + calls=2*p+1 + if fresh_groups: + families.append({'name':'fresh_group','capacity':2*minimum+8, + 'stages':list(range(calls)),'unbounded':True}) + maximum=minimum-1 + sp=lambda r:numerical_split(r,maximum,c) + h=lambda r:r**(1-c) if r else 0 + v={r:h(max(r,minimum))-sp(max(0,minimum-r)) for r in WIDTHS[1:]} + v[0]=0 + def gain(f,pattern): + if families[f].get('unbounded'): + used=sum(pattern) + return (h(max(used,minimum))-sp(max(0,minimum-used)) if used else 0)-sum(v[r] for r in pattern) + return sp(families[f]['capacity'])-sp(families[f]['capacity']-sum(pattern))-sum(v[r] for r in pattern) + columns=[] + keys=set() + def add(f,pattern): + key=(f,tuple(pattern)) + if key not in keys: + keys.add(key) + columns.append(key) + return True + return False + for f,w in enumerate(families): + add(f,[0]*len(w['stages'])) + for r in WIDTHS[1:]: + # Seed every constant-width prefix and suffix that fits. + n=min(len(w['stages']),w['capacity']//r) + if n: + add(f,[r]*n+[0]*(len(w['stages'])-n)) + add(f,[0]*(len(w['stages'])-n)+[r]*n) + if not families: + return [],{'columns':0,'rounds':0,'discovery_converged':True} + resource=[(s,r) for s in range(calls) for r in WIDTHS[1:]] + rid={key:i for i,key in enumerate(resource)} + bounded=[f for f,w in enumerate(families) if not w.get('unbounded')] + bid={f:i for i,f in enumerate(bounded)} + done=False + largest_reduced=None + for iteration in range(max_rounds): + ar=[];ac=[];av=[] + er=[];ec=[];ev=[] + objectives=[] + for index,(f,pattern) in enumerate(columns): + if f in bid: + er.append(bid[f]);ec.append(index);ev.append(1) + for stage,r in zip(families[f]['stages'],pattern): + if r: + ar.append(rid[stage,r]);ac.append(index);av.append(1) + objectives.append(-gain(f,pattern)) + A=coo_matrix((av,(ar,ac)),shape=(len(resource),len(columns))).tocsr() + B=coo_matrix((ev,(er,ec)),shape=(len(bounded),len(columns))).tocsr() + result=linprog(objectives,A_ub=A,b_ub=[E.HELPERS[r] for s,r in resource], + A_eq=B if bounded else None,b_eq=[families[f].get('field_count',224) for f in bounded] if bounded else None,bounds=(0,None),method='highs', + options={'dual_feasibility_tolerance':1e-9,'primal_feasibility_tolerance':1e-9}) + E.need(result.success,'Restricted master feasible') + pi=result.ineqlin.marginals + lam=result.eqlin.marginals + new=0 + largest_reduced=0.0 + for f,w in enumerate(families): + dp={0:(0.0,())} + for stage in w['stages']: + nxt={} + for used,(score,pattern) in dp.items(): + for r in WIDTHS: + if used+r>w['capacity']: + continue + score2=score-v[r]+(pi[rid[stage,r]] if r else 0) + if used+r not in nxt or score2>nxt[used+r][0]+1e-13: + nxt[used+r]=(score2,pattern+(r,)) + dp=nxt + def terminal(used): + if w.get('unbounded'): + return h(max(used,minimum))-sp(max(0,minimum-used)) if used else 0 + return sp(w['capacity'])-sp(w['capacity']-used)+lam[bid[f]] + ranked=sorted(((score+terminal(used),pattern) + for used,(score,pattern) in dp.items()),reverse=True) + largest_reduced=max(largest_reduced,ranked[0][0]) + # Several best used-capacity patterns reduce degeneracy. + for improvement,pattern in ranked[:4]: + if improvement>1e-8: + new+=add(f,pattern) + if not new: + done=True + break + # Rational reconstruction checks feasibility independently of floating duals. + solution=reconstruct_exact(result.x,columns,families,resource,E.HELPERS) + verify(p,minimum,solution,'H',fresh_groups=fresh_groups,prefix_cut=prefix_cut, + custom_windows=custom_windows,custom_targets=custom_targets) + return solution,{'columns':len(columns),'rounds':iteration+1, + 'discovery_converged':done,'last_max_reduced_cost_float':largest_reduced, + 'optimality_scope':'Floating column-generation screen only; rational receipt certifies displayed construction, not global optimum.'} + +def verify(p,minimum,solution,kernel,fresh_groups=False,prefix_cut=False, + custom_windows=None,custom_targets=None): + E.need(kernel in ('H','identity'),'Known exact local invoice') + calls=2*p+1 + maximum=minimum-1 + families=windows(p,prefix_cut) if custom_windows is None else [dict(w) for w in custom_windows] + if fresh_groups: + families.append({'name':'fresh_group','capacity':2*minimum+8, + 'stages':list(range(calls)),'unbounded':True}) + counts=[Q(0) for _ in families] + inventory=[Counter({r:Q(n) for r,n in E.HELPERS.items()}) for _ in range(calls)] + source=E.NATIVE if kernel=='H' else IDENTITY + paid=E.split_profile(source,maximum) + paid=Counter({r:Q(calls*n) for r,n in paid.items()}) + if kernel=='H': + paid[1]+=8*calls + targets=(Counter({16*p+9-16*j:Q(224) for j in range(p)}) if prefix_cut + else Counter({16*p+9:Q(224*p)})) + if custom_targets is not None: + targets=Counter({int(r):Q(n) for r,n in custom_targets.items()}) + E.need(sum(targets.values())==224*p,'Changed main targets have the original data field count') + expected_total=sum(r*n for r,n in targets.items())-sum(w.get('field_count',224)*w['capacity'] for w in families if not w.get('unbounded')) + old_total=224*p*(16*p+9)-sum(224*w['capacity'] for w in windows(p)) + E.need(expected_total==old_total,'Literal removed windows match the changed main rank credit') + for row in solution: + f=row['family'];pattern=row['pattern'];count=Q(row['count']) + E.need(0<=f=0,'Pattern count') + w=families[f] + E.need(len(pattern)==len(w['stages']) and set(pattern)<=set(WIDTHS),'Window chronology') + E.need(sum(pattern)<=w['capacity'],'Window capacity') + counts[f]+=count + for stage,r in zip(w['stages'],pattern): + if r: + inventory[stage][r]-=count + if w.get('unbounded'): + E.need(sum(pattern)>0,'A fresh productive group consumes some actual helper') + targets[max(sum(pattern),minimum)]+=count + E.add_scaled(paid,E.split_rank(max(0,minimum-sum(pattern)),maximum),count) + else: + E.add_scaled(paid,E.split_rank(w['capacity']-sum(pattern),maximum),count) + E.need(all(n==w.get('field_count',224) for n,w in zip(counts,families) if not w.get('unbounded')), + 'Every idle window accounted') + global_roles=Counter() + for stage,stock in enumerate(inventory): + E.need(all(n>=0 for n in stock.values()),'Stage inventory '+str(stage)) + global_roles.update(stock) + for r,n in global_roles.items(): + if n: + targets[max(r,minimum)]+=n + E.add_scaled(paid,E.split_rank(max(0,minimum-r),maximum),n) + paid=+paid;targets=+targets + E.need(max(paid)= 0 else b) + high += n*(b if n >= 0 else a) + return low,high + +def show(bounds): + scale=10**35 + low,high=bounds + a=low.numerator*scale//low.denominator + b=-((-high.numerator*scale)//high.denominator) + def fixed(n): + sign='-' if n<0 else '' + s=str(abs(n)).rjust(36,'0') + return sign+s[:-35]+'.'+s[-35:] + return {'lower':fixed(a),'upper':fixed(b)} + +def split_rank(r,maximum): + """Least concave tariff partition with positive integers <= maximum.""" + need(maximum>=1 and r>=0, 'Legal split') + q,remainder=divmod(r,maximum) + result=Counter() + if q: + result[maximum]+=q + if remainder: + result[remainder]+=1 + return result + +def split_profile(profile,maximum): + result=Counter() + for r,n in profile.items(): + for child,count in split_rank(r,maximum).items(): + result[child]+=n*count + return result + +def add_scaled(target,source,multiple=1): + for key,value in source.items(): + target[key]+=multiple*value + +def base_case(p,minimum,pairs=None,middle=None): + """Expand all role inventories; one fresh global field per unhosted role.""" + need(p in (1,2), 'Only reconstructed p1 and p2 schedules are in scope') + need(2<=minimum<=41, 'Finite minimum-target menu') + calls=2*p+1 + main_fields=224*p + main_rank=16*p+9 + inventories=[Counter(HELPERS) for _ in range(calls)] + paid=split_profile(NATIVE,minimum-1) + paid=Counter({r:calls*n for r,n in paid.items()}) + paid[1]+=8*calls # same-width H completion, never waived + targets=Counter({main_rank:main_fields}) + if p==1: + need(pairs is None and middle is None, 'p1 has no original idle bins') + else: + pairs=pairs if pairs is not None else [(224,0,0)] + middle=middle if middle is not None else [(224,0)] + need(sum(n for n,a,b in pairs)==224, 'Each pair window has 224 bins') + need(sum(n for n,a in middle)==224, 'Middle window has 224 bins') + for stages in [(0,1),(3,4)]: + for n,a,b in pairs: + need(a+b<=16 and a in (0,5,6,7,8,9) and b in (0,5,6,7,8,9), 'Pair capacities') + for stage,r in zip(stages,(a,b)): + if r: + inventories[stage][r]-=n + add_scaled(paid,split_rank(16-a-b,minimum-1),n) + for n,r in middle: + need(r in (0,5,6,7,8), 'Middle capacity') + if r: + inventories[2][r]-=n + add_scaled(paid,split_rank(8-r,minimum-1),n) + global_roles=Counter() + for inventory in inventories: + need(all(n>=0 for n in inventory.values()), 'No helper role used twice') + global_roles.update(inventory) + for r,n in global_roles.items(): + if not n: + continue + target=max(r,minimum) + targets[target]+=n + add_scaled(paid,split_rank(target-r,minimum-1),n) + paid=+paid + targets=+targets + need(max(paid)0] + # Middle bins are independent single slots; choose positive-gain roles first. + candidates=sorted(((sp(8)-sp(8-r)-value(r),r) for r in (5,6,7,8)),reverse=True) + middle=[] + left=224 + for gain,r in candidates: + if gain>1e-12: + n=min(HELPERS[r],left) + if n: + middle.append((n,r)) + left-=n + if left: + middle.append((left,0)) + return pairs,middle,{'status':int(out.status),'message':out.message,'not_an_exact_optimality_claim':True} + +def run(discover=False): + candidates=[] + for p in (1,2): + for minimum in range(2,26): + candidates.append(base_case(p,minimum)) + candidates.append(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)) + discovery=[] + if discover: + for c in (.001745,.004): + for minimum in range(5,18): + pairs,middle,meta=discover_pair_patterns(minimum,c) + case=base_case(2,minimum,pairs,middle) + case['discovery_target']=str(c) + case['solver']=meta + discovery.append(case) + candidates.extend(discovery) + best={} + for p in (1,2): + for text in ('0.001745','0.004'): + c=Q(text) + rows=[case for case in candidates if case['p']==p] + ranked=sorted(rows,key=lambda case:-numerical_value(case['signed'],float(c))) + winner=ranked[0] + # Certify that this displayed winner beats all numerically distinct + # profiles in the finite scanned menu, not all possible schedules. + win=moment(winner['signed'],c) + for case in ranked[1:]: + if dict(case['signed'])!=dict(winner['signed']): + need(win[0]>moment(case['signed'],c)[1], 'Exact finite-menu ordering') + best[f'p{p}_{text}']=serialize_case(winner) + controls={} + wrong=base_case(1,6) + wrong['targets'][6]+=1 + controls['unearned_output_credit_rejected']=(sum(r*n for r,n in wrong['targets'].items())-wrong['rank_bill']!=wrong['rank_margin']) + controls['rank5_child_with_job5_rejected']=not(5<5) + need(all(controls.values()), 'Corruption controls') + return {'schema':'productive-helper-mixed-target-tariff/1', + 'status':'PASS_CONDITIONAL_EXACT_ACCOUNTING', + 'source_sha256':sha256(Path(__file__).read_bytes()).hexdigest(), + 'native_profile':dict(NATIVE),'helper_inventory':dict(HELPERS), + 'assumed_recursive_rule':'sum_paid n_r r^(1-C) < sum_targets W_k k^(1-C); max_paid_rank < min_target_rank', + 'best_in_finite_menu':best, + 'fixed_p2_minimum9':serialize_case(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)), + 'discovery_candidates':[serialize_case(c) for c in discovery], + 'controls':controls, + 'not_proved':['native whole-helper adapters and arbitrary-input block diagonal contract', + 'correct main controller and all its heads/caches/cleanup', + 'literal eligibility of any displayed head-cut grant', + 'mixed-target all-size recursion in this native model', + 'finite-precision integer-multiplication transfer and scalar/stock costs'], + 'new_kappa':False} + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--discover',action='store_true') + parser.add_argument('--output',type=Path,default=HERE/'MIXED-TARGET-PROBE.json') + args=parser.parse_args() + result=run(args.discover) + args.output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({'status':result['status'],'best':{k:v['targets_at_C'][k.split('_',1)[1]]['after_native_completion_before_main_closure'] for k,v in result['best_in_finite_menu'].items()}},sort_keys=True)) + +if __name__=='__main__': + main() diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json b/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json new file mode 100644 index 0000000000..fbe6da7241 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json @@ -0,0 +1,69 @@ +{ + "C0_before_cover": "69/25000", + "C0_minus_C1": "1/100000", + "C1_after_cover": "11/4000", + "atom_power": "3/1000", + "finite_constants_to_replace": { + "ambient_dimension": "N, not50 or64", + "bad_fallback_children": "At most32*N^2 per bad final leaf", + "coefficient_data": "Every fixed rational entry, inverse, determinant, prefix descriptor and height", + "fixed_row_routes": "R, original port charts and every internal matcher/inverse", + "generic_affine_work": "At most4*N^2-2*N basic shears per rank1 normalizer together with its inverse", + "owned_storage": "C, bounded by one owned bank per allocated finite unit instance", + "paid_leaf_count": "P, including copied-center descendants", + "pointwise_and_copy_count": "L, literal compiled scalar/copy/erase records", + "productive_roles": "B, not3739 or661" + }, + "finite_template_hypothesis": "Fixed integers N>=2,B>=1,P>=1 and a whole-cover native schematic uniform word, with P/B < N^(1-C0), final paid leaves of rank1, arbitrary productive inputs and separately owned storage.", + "mixed_margin_at_C0": { + "display": 0.7944031286900184, + "lower": "67580344230009584908122845692691165477/85070591730234615865843651857942052864", + "strict_negative": false, + "strict_positive": true, + "upper": "270321376920038339632491382770764742407/340282366920938463463374607431768211456" + }, + "new_kappa": false, + "old_ordinary_saving": "384599/10000000000", + "ordinary_saving_admitted": "27/10000", + "ordinary_saving_before_final_relaxation": "27418653797/10000000000000", + "ordinary_saving_display": 0.0027418653797, + "prime_rule": { + "N_to_d_lower": "200001/200000", + "also_required": "Odd prime avoiding every fixed rational denominator, matcher determinant and chosen rank witness of the entire compiled word.", + "bound": "q > 25600000 * N^5", + "complete_moment_upper": "400001/400002", + "fallback_multiplier_upper": "400001/400000", + "good_moment_upper": "N^(-d), d=C0-C1", + "strict_moment_slack_lower": "1/400002" + }, + "root_cost_terms": [ + "e^(1-delta)", + "e^((1-delta)*(1-C1)+delta*(1-a_old))", + "e^delta * log(e)" + ], + "schema": "conditional-delayed-cover-BIT-allsize-parameters/1", + "source_sha256": { + "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c", + "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", + "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8", + "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.json": "1e1a91871ad8d1098b6851c95d257e8e3fb130222933009b4edfb5e2c2d5c471", + "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443", + "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf", + "research/kappa-rebuild/bit/bit_allsize_parameters.py": "59f92cf44019c27bde3db2f4482f2b5fcf25f0c3dcf071319d46b041f7b6a821" + }, + "status": "PASS_EXACT_PARAMETERS_CONDITIONAL_ON_FINITE_UNIFORM_PRECOMPILATION", + "stock": { + "asymptotic": "Fixed compiled N,B,P: k=O_(N,B,q)(w*log e)=o(e), w=ceil(e^(3/1000)); pad high rows once by factor<2.", + "borrowed_digits": "k <= D_N(ceil(e/w))*(N^2*(w-1)+ceil(log_q(B*|GL_N(F_q)|)))+ceil(log_q S_old)+1", + "depth_bound": "D_N(n)=floor(log_N n) for rank<=floor(n/N) children; any larger explicit integer bound is safe.", + "descendant_weights": "Only final leaves are lowered. This outer cover row and role type become ancestor data; every next ordinary invocation has fresh disjoint role stock.", + "reserve": "S(e,w)=W(w)^D_N(ceil(e/w))*S_old(e,w)", + "role_divisor": "W(w)=B*|GL_N(F_q)|*q^(N^2*(w-1))" + }, + "strict_power_gaps": { + "borrowed_stock_log_absorption": "9942581346203/10000000000000", + "final_relaxation": "418653797/10000000000000", + "linear_adapter": "2581346203/10000000000000" + } +} diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/complex_controller_factor.py b/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/complex_controller_factor.py new file mode 100644 index 0000000000..cb0cff7c8b --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/complex_controller_factor.py @@ -0,0 +1,270 @@ +#!/usr/bin/env python3 +"""Exact complex controller factorizations over an integral Laurent ring. + +The native local operator is an EXPLICIT INPUT CONTRACT supplied by the +complex reconstruction: F_s=D_s S_y(Q^-1), B_s=D_s S_x(-Q). +No order-two relation, numerical Fourier characters, phase erasure, or +F2-to-complex lift is used in the acceptance check. All Laurent +coefficients are reconstructed and multiplied over Q. Binary candidates +are only a finite discovery filter, not an exhaustive rational census. +Apache-2.0; substantial OpenAI assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import json +import time + +import mixed_productive_bit as B + +HERE = Path(__file__).resolve().parent + + +def plus(a, b, coefficient=1): + result = dict(a) + for term, value in b.items(): + result[term] = result.get(term, 0)+coefficient*value + if not result[term]: + del result[term] + return result + + +def monomial_times(polynomial, exponents, coefficient=1): + return {tuple(a+b for a, b in zip(term, exponents)):coefficient*value + for term, value in polynomial.items()} + + +def controller(p, keep, wrong_reverse_sign=False): + n, stages = 2*p, 2*p+1 + zero = (0,)*(stages+1) + matrix = [[{zero:1} if i == j else {} for j in range(n)] for i in range(n)] + events, idle = [], [] + def term(q, selected): + return (q,)+tuple(int(s in selected) for s in range(stages)) + def idle_call(pair, selected, kind): + index = len(idle) + retained = bool(keep >> index & 1) + idle.append(dict(index=index, kind=kind, pair=pair, stages=list(selected), + rank=8*len(selected), retained=retained)) + if retained: + for role in (2*pair, 2*pair+1): + matrix[role] = [monomial_times(x, term(0, selected)) for x in matrix[role]] + events.append(["IDLE", pair, list(selected)]) + def local(stage, pair, reverse): + x, y = 2*pair, 2*pair+1 + if reverse: + x, y = y, x + sign = -1 if reverse and not wrong_reverse_sign else 1 + exponent = 1 if reverse else -1 + matrix[y] = [plus(a, monomial_times(b, term(exponent, []), sign)) + for a, b in zip(matrix[y], matrix[x])] + for role in (x, y): + matrix[role] = [monomial_times(x, term(0, [stage])) for x in matrix[role]] + events.append(["LOCAL", stage, pair, reverse]) + if stage % 2 and stage <= 2*p-3: + idle_call((stage+1)//2, list(range(stage+1)), "initial") + elif stage % 2 == 0 and 2 <= stage <= 2*p-2: + idle_call(stage//2, [stage], "middle") + elif stage == 2*p: + for j in range(p-1): + idle_call(j, list(range(2*j+3, 2*p+1)), "terminal") + def bridge(dst, src, coefficient): + for d, s, c in ((2*dst, 2*src, coefficient), (2*src+1, 2*dst+1, -coefficient)): + matrix[d] = [plus(a, b, c) for a, b in zip(matrix[d], matrix[s])] + events.append(["ADD", d, s, c]) + local(0, 0, False) + for j in range(p): + local(2*j+1, j, True) + if j < p-1: + bridge(j, j+1, 1) + local(2*j+2, j, False) + if j < p-1: + bridge(j, j+1, -1) + for j in reversed(range(p-1)): + bridge(j+1, j, 1) + for j in range(p): + matrix[2*j], matrix[2*j+1] = matrix[2*j+1], [monomial_times(x, zero, -1) for x in matrix[2*j]] + events.append(["SIGNED_SWAP", 2*j, 2*j+1]) + coefficients = {} + for i, row in enumerate(matrix): + for j, polynomial in enumerate(row): + for key, value in polynomial.items(): + coefficients.setdefault(key, [[Q(0)]*n for _ in range(n)])[i][j] += value + coefficients = {key:matrix for key, matrix in coefficients.items() if any(any(row) for row in matrix)} + return coefficients, events, idle + + +def matrix_rank(rows): + basis = {} + for row in rows: + row = list(map(Q, row)) + for j in sorted(basis): + if row[j]: + scale = row[j] + row = [a-scale*b for a, b in zip(row, basis[j])] + pivot = next((j for j, x in enumerate(row) if x), None) + if pivot is not None: + scale = row[pivot] + basis[pivot] = [x/scale for x in row] + return len(basis) + + +def scalar_program(matrix): + n = len(matrix) + work = [row[:] for row in matrix] + elimination = [] + for j in range(n): + pivot = next(i for i in range(j, n) if work[i][j]) + if pivot != j: + work[j], work[pivot] = work[pivot], work[j] + elimination.append(["SWAP", j, pivot]) + if work[j][j] != 1: + scale = 1/work[j][j] + work[j] = [scale*x for x in work[j]] + elimination.append(["SCALE", j, str(scale)]) + for i in range(n): + if i != j and work[i][j]: + scale = -work[i][j] + work[i] = [a+scale*b for a, b in zip(work[i], work[j])] + elimination.append(["ADD", i, j, str(scale)]) + program = [] + for op in reversed(elimination): + if op[0] == "SWAP": + program.append(op) + elif op[0] == "SCALE": + program.append(["SCALE", op[1], str(1/Q(op[2]))]) + else: + program.append(["ADD", op[1], op[2], str(-Q(op[3]))]) + replay = [[Q(i == j) for j in range(n)] for i in range(n)] + for op in program: + if op[0] == "SWAP": + replay[op[1]], replay[op[2]] = replay[op[2]], replay[op[1]] + elif op[0] == "SCALE": + replay[op[1]] = [Q(op[2])*x for x in replay[op[1]]] + else: + replay[op[1]] = [a+Q(op[3])*b for a, b in zip(replay[op[1]], replay[op[2]])] + B.need(replay == matrix, "Exact signed scalar boundary program") + coefficients = [Q(x) for row in matrix for x in row] + B.need(all(q.denominator & (q.denominator-1) == 0 for q in coefficients), "Dyadic boundary coefficients") + return program + + +def factor(coefficients): + n = len(next(iter(coefficients.values()))) + total = [[sum(matrix[i][j] for matrix in coefficients.values()) for j in range(n)] for i in range(n)] + inverse = B.rational_inverse(total) + projectors = {key:B.matrix_multiply(inverse, matrix) for key, matrix in coefficients.items()} + for key, matrix in projectors.items(): + if B.matrix_multiply(matrix, matrix) != matrix: + return None + for other, second in projectors.items(): + if key != other and any(any(row) for row in B.matrix_multiply(matrix, second)): + return None + columns, diagonal = [], [] + for key, matrix in sorted(projectors.items()): + for column in zip(*matrix): + if matrix_rank(columns+[column]) > len(columns): + columns.append(list(column)) + diagonal.append(key) + B.need(len(columns) == n, "All rational projector images") + right = [list(row) for row in zip(*columns)] + left = B.matrix_multiply(B.rational_inverse(right), inverse) + transformed = {key:B.matrix_multiply(B.matrix_multiply(left, matrix), right) + for key, matrix in coefficients.items()} + expected = {key:[[Q(i == j and diagonal[i] == key) for j in range(n)] for i in range(n)] + for key in set(diagonal)} + B.need(transformed == expected, "Every Laurent coefficient equals the advertised diagonal") + return dict(left=left, right=right, diagonal=diagonal, + left_program=scalar_program(left), right_program=scalar_program(right)) + + +def serialize_matrix(matrix): + return [[str(x) for x in row] for row in matrix] + + +def serialize_case(p, keep, coefficients, events, idle, result): + # Rank normalization is an input contract of the complex native source: + # D0=F9 Q^-1; Ds for s>0 transform fresh eight-axis blocks; Q^2 and + # Ds^2 are explicitly free Pauli/translation operators. The EXACT + # Laurent monomials remain in this receipt for a separate phase audit. + jobs = Counter() + for term in result["diagonal"]: + B.need(term[0] in (-1, 1), "Only stated central-Q endpoint normalization") + B.need(all(x in (0, 1) for x in term[1:]), "No hidden squared stage transforms") + jobs[1+8*sum(term[1:])] += 112 + scalar_coefficients = [x for matrix in (result["left"], result["right"]) for row in matrix for x in row] + return dict(pairs=p, stages=2*p+1, keep_idle_mask=keep, + coefficient_variables=["Q"]+[f"D{s}" for s in range(2*p+1)], + coefficient_matrices=[dict(exponents=list(key), matrix=serialize_matrix(matrix)) + for key, matrix in sorted(coefficients.items())], + left=serialize_matrix(result["left"]), right=serialize_matrix(result["right"]), + left_program=result["left_program"], right_program=result["right_program"], + exact_diagonal_monomials=[list(term) for term in result["diagonal"]], + all_boundary_entries_integral=all(x.denominator == 1 for x in scalar_coefficients), + maximum_boundary_absolute_coefficient=str(max(map(abs, scalar_coefficients))), + endpoint_after_stated_free_Pauli_normalization=dict(sorted(jobs.items())), + retained_idle_windows=[row for row in idle if row["retained"]], + omitted_idle_windows=[row for row in idle if not row["retained"]], + physical_events=events, + full_Laurent_identity=True, native_operator_contract_independently_replayed=False) + + +def run(max_p): + start = time.monotonic() + cases, census = [], {} + for p in range(1, max_p+1): + binary_candidates = [] + for keep in range(1 << (3*(p-1))): + binary_coefficients, _, _ = B.physical_controller(p, keep) + if B.simultaneous_monomial_factor(binary_coefficients) is not None: + binary_candidates.append(keep) + passed = 0 + for keep in binary_candidates: + coefficients, events, idle = controller(p, keep) + result = factor(coefficients) + if result is not None: + cases.append(serialize_case(p, keep, coefficients, events, idle, result)) + passed += 1 + census[p] = dict(binary_discovery_trials=1 << (3*(p-1)), + binary_candidates=len(binary_candidates), exact_Laurent_factorizations=passed) + print(json.dumps(dict(pairs=p, **census[p])), flush=True) + chosen = next(row for row in cases if row["pairs"] == 3 and row["keep_idle_mask"] == 43) + left = [[Q(x) for x in row] for row in chosen["left"]] + right = [[Q(x) for x in row] for row in chosen["right"]] + wrong, _, _ = controller(3, 43, True) + transformed = {key:B.matrix_multiply(B.matrix_multiply(left, matrix), right) + for key, matrix in wrong.items()} + expected = {tuple(key):[[Q(i == j and tuple(chosen["exact_diagonal_monomials"][i]) == tuple(key)) + for j in range(6)] for i in range(6)] + for key in chosen["exact_diagonal_monomials"]} + B.need(transformed != expected, "Incorrect backward sign rejected over Q") + return dict(schema="complex-controller-integral-Laurent-factorization/1", + status="PASS_EXACT_LAURENT_IDENTITIES_CONDITIONAL_ON_NATIVE_LOCAL_CONTRACT", + local_contract=dict(forward="D_s * [[1,0],[Q^-1,1]]", + backward="D_s * [[1,-Q],[0,1]]", + commutation="Q,D0,...,D(2p) commute; no finite-order relation used"), + census=census, cases=cases, + selected_p3_keep43=chosen, + controls=dict(wrong_backward_sign_rejected=True), + source_sha256={Path(__file__).name:sha256(Path(__file__).read_bytes()).hexdigest(), + "mixed_productive_bit.py":sha256((HERE/"mixed_productive_bit.py").read_bytes()).hexdigest()}, + runtime_seconds=time.monotonic()-start, + scope="Exact formal operator identity and emitted constant dyadic adapters. Native source binding, free-phase normalization, helper ownership, complete tariffs and all-size transfer belong to separate certificates.", + new_kappa=False) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--max-p", type=int, default=5) + parser.add_argument("--output", type=Path, default=HERE/"COMPLEX-CONTROLLER-FACTOR.json") + args = parser.parse_args() + B.need(3 <= args.max_p <= 6, "Bounded candidate menu") + data = run(args.max_p) + args.output.write_text(json.dumps(data, indent=2, sort_keys=True)+"\n") + print(json.dumps(dict(status=data["status"], seconds=data["runtime_seconds"], cases=len(data["cases"])))) + + +if __name__ == "__main__": + main() diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/mixed_productive_bit.py b/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/mixed_productive_bit.py new file mode 100644 index 0000000000..9c7a8bd5d3 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/bit/mixed_productive_bit.py @@ -0,0 +1,617 @@ +#!/usr/bin/env python3 +"""Exact finite BIT operator factorization and heterogeneous recursive invoice. + +The PR589 word is regenerated from its frozen source, byte-for-byte. This +new file changes its global controller and its declared physical endpoints. +It does not admit a mixed-target all-size BIT compiler or a new kappa. + +Apache-2.0. Substantial OpenAI assistance. Retained local-word attribution: +DreamingOfClouds / PR589, eumemic / PR555 and PR543, and their cited lineage. +The compressed controller is from PR386/436/443/463/510 and the general +global_k.py implementation. Mixed target accounting is motivated by the +PR4268 proposal, whose transfer hypotheses are not asserted here. +""" +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache, reduce +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +import math +import platform +import struct +import sys +import time + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +REFERENCE = ROOT / "research/kappa-next-regime/bit-compression/carrier-reuse/reference" +sys.path.insert(0, str(REFERENCE)) +from joint_pair_dag import log_interval, exp_interval, quotient + +LOCAL = Counter({1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19}) +V, R, H = 111, 439, 8 +WORD_HASH = "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f" +WORD_CONTENT_HASH = "5642fd0e35a1acc11acff8d0c08350c1617e95f310d4d35ad63a651f9eeeba0b" + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def canonical(data): + return json.dumps(data, sort_keys=True, separators=(",", ":")).encode() + + +def digest(data): + return sha256(canonical(data)).hexdigest() + + +def bit_rank(rows, n): + basis = {} + for row in rows: + for pivot in sorted(basis, reverse=True): + if row >> pivot & 1: + row ^= basis[pivot] + if row: + need(row.bit_length() <= n, "Binary matrix width") + basis[row.bit_length()-1] = row + return len(basis) + + +def bit_mul(a, b): + return [reduce(int.__xor__, (b[j] for j in range(len(b)) if row >> j & 1), 0) + for row in a] + + +def bit_inverse(a): + n = len(a) + aug = [row | (1 << (n+i)) for i, row in enumerate(a)] + for j in range(n): + k = next((i for i in range(j, n) if aug[i] >> j & 1), None) + need(k is not None, "Invertible scalar boundary") + aug[j], aug[k] = aug[k], aug[j] + for i in range(n): + if i != j and aug[i] >> j & 1: + aug[i] ^= aug[j] + result = [row >> n for row in aug] + need(bit_mul(a, result) == [1 << i for i in range(n)], "Inverse replay") + return result + + +def bit_factor(a): + """Literal ADD/SWAP program for a constant F2 matrix, checked exactly.""" + n = len(a) + cur = list(a) + elimination = [] + for j in range(n): + k = next(i for i in range(j, n) if cur[i] >> j & 1) + if k != j: + cur[j], cur[k] = cur[k], cur[j] + elimination.append(["SWAP", j, k]) + for i in range(n): + if i != j and cur[i] >> j & 1: + cur[i] ^= cur[j] + elimination.append(["ADD", i, j]) + need(cur == [1 << i for i in range(n)], "Scalar elimination endpoint") + program = list(reversed(elimination)) + cur = [1 << i for i in range(n)] + for op, d, s in program: + if op == "SWAP": + cur[d], cur[s] = cur[s], cur[d] + else: + cur[d] ^= cur[s] + need(cur == a, "Scalar boundary synthesis") + # A SWAP may be emitted as three ADDs; the invoice charges that option. + return program, sum(3 if op == "SWAP" else 1 for op, _, _ in program) + + +def shift(row, monomial): + return [{term ^ monomial for term in entry} for entry in row] + + +def add(a, b): + return [x ^ y for x, y in zip(a, b)] + + +def polynomial_coefficients(matrix): + n = len(matrix) + coefficients = {} + for i, row in enumerate(matrix): + for j, entry in enumerate(row): + for term in entry: + coefficients.setdefault(term, [0]*n)[i] ^= 1 << j + return {term: rows for term, rows in coefficients.items() if any(rows)} + + +def physical_controller(p, keep, omit_bridge=None): + """Literal physical operator over F2[(Z/2)^(2p+2)]. + + Bit zero is D_P (rank one); bit s+1 is D_Bs (rank seven). + A complete local invocation on a data pair is D_Bs S(D_P), + where S is one scalar shear. No scalar bridge is assumed to join + equal decoded frames: its physical action is multiplied literally. + """ + n = 2*p + matrix = [[{0} if i == j else set() for j in range(n)] for i in range(n)] + events, idle, bridge_number = [], [], 0 + + def idle_call(pair, stages, kind): + monomial = sum(1 << (s+1) for s in stages) + index = len(idle) + retained = bool(keep >> index & 1) + idle.append(dict(index=index, pair=pair, stages=stages, kind=kind, + rank=7*len(stages), retained=retained)) + if retained: + for role in (2*pair, 2*pair+1): + matrix[role] = shift(matrix[role], monomial) + events.append(["IDLE", pair, monomial]) + + def local(stage, pair, reverse): + x, y = 2*pair, 2*pair+1 + if reverse: + x, y = y, x + matrix[y] = add(matrix[y], shift(matrix[x], 1)) + matrix[x] = shift(matrix[x], 1 << (stage+1)) + matrix[y] = shift(matrix[y], 1 << (stage+1)) + events.append(["LOCAL", stage, pair, reverse]) + if stage % 2 and stage <= 2*p-3: + idle_call((stage+1)//2, list(range(stage+1)), "initial") + elif stage % 2 == 0 and 2 <= stage <= 2*p-2: + idle_call(stage//2, [stage], "middle") + elif stage == 2*p: + for j in range(p-1): + idle_call(j, list(range(2*j+3, 2*p+1)), "terminal") + + def bridge(dst, src): + nonlocal bridge_number + for d, s in ((2*dst, 2*src), (2*src+1, 2*dst+1)): + if bridge_number != omit_bridge: + matrix[d] = add(matrix[d], matrix[s]) + events.append(["ADD", d, s]) + bridge_number += 1 + + local(0, 0, False) + for j in range(p): + local(2*j+1, j, True) + if j < p-1: + bridge(j, j+1) + local(2*j+2, j, False) + if j < p-1: + bridge(j, j+1) + for j in reversed(range(p-1)): + bridge(j+1, j) + for j in range(p): + matrix[2*j], matrix[2*j+1] = matrix[2*j+1], matrix[2*j] + events.append(["SWAP", 2*j, 2*j+1]) + need(len(idle) == 3*(p-1), "Idle enumeration") + need(bridge_number == 6*(p-1), "Bridge count") + return polynomial_coefficients(matrix), events, idle + + +def simultaneous_monomial_factor(coefficients): + """Return explicit L A R = diagonal monomials, or reject. + + The coefficient matrices of A(1)^-1 A must be pairwise orthogonal + idempotents. This is a sufficient and necessary constant-basis test + for this exact formal diagonal-monomial endpoint. + """ + n = len(next(iter(coefficients.values()))) + total = [0]*n + for matrix in coefficients.values(): + total = [a ^ b for a, b in zip(total, matrix)] + if bit_rank(total, n) != n: + return None + inverse = bit_inverse(total) + projectors = {term: bit_mul(inverse, matrix) for term, matrix in coefficients.items()} + for term, matrix in projectors.items(): + if bit_mul(matrix, matrix) != matrix: + return None + for other, second in projectors.items(): + if term != other and any(bit_mul(matrix, second)): + return None + columns, diagonal = [], [] + for term, matrix in sorted(projectors.items()): + for j in range(n): + column = sum(((row >> j) & 1) << i for i, row in enumerate(matrix)) + if bit_rank(columns+[column], n) > len(columns): + columns.append(column) + diagonal.append(term) + need(len(columns) == n, "Projector images span") + right = [sum(((column >> i) & 1) << j for j, column in enumerate(columns)) + for i in range(n)] + left = bit_mul(bit_inverse(right), inverse) + exact = {term: bit_mul(bit_mul(left, matrix), right) + for term, matrix in coefficients.items()} + expected = {term: [((1 << i) if diagonal[i] == term else 0) for i in range(n)] + for term in set(diagonal)} + need(exact == expected, "Full formal operator diagonalization") + left_program, left_adds = bit_factor(left) + right_program, right_adds = bit_factor(right) + return dict(left_rows=left, right_rows=right, diagonal_monomials=diagonal, + coefficient_projectors={str(t): m for t, m in sorted(projectors.items())}, + left_program=left_program, right_program=right_program, + boundary_unit_ADDs_per_port=left_adds+right_adds, + full_coefficient_endpoint_sha256=digest({str(t): x for t, x in sorted(exact.items())})) + + +def rational_inverse(matrix): + n = len(matrix) + work = [[Q(x) for x in row]+[Q(i == j) for j in range(n)] + for i, row in enumerate(matrix)] + for j in range(n): + pivot = next(i for i in range(j, n) if work[i][j]) + work[j], work[pivot] = work[pivot], work[j] + scale = work[j][j] + work[j] = [x/scale for x in work[j]] + for i in range(n): + if i != j and work[i][j]: + scale = work[i][j] + work[i] = [a-scale*b for a, b in zip(work[i], work[j])] + return [row[n:] for row in work] + + +def matrix_multiply(a, b): + return [[sum((x*y for x, y in zip(row, column)), Q(0)) + for column in zip(*b)] for row in a] + + +def frame_projectors(frame_data): + result = {} + for name, frame in frame_data.items(): + basis = [[Q(x) for x in row] for row in frame["B"]] + if not basis: + projector = [[Q(0)]*8 for _ in range(8)] + else: + transpose = list(map(list, zip(*basis))) + gram = matrix_multiply(basis, transpose) + projector = matrix_multiply(matrix_multiply(transpose, rational_inverse(gram)), basis) + need(matrix_multiply(projector, projector) == projector, "Exact frame projector") + need(sum(projector[i][i] for i in range(8)) == frame["dim"], "Projector trace") + result[int(name)] = projector + return result + + +def audit_local(word_path): + need(sha256(word_path.read_bytes()).hexdigest() == WORD_HASH, "PR589 gzip source pin") + raw = gzip.decompress(word_path.read_bytes()) + need(sha256(raw).hexdigest() == WORD_CONTENT_HASH, "PR589 canonical word pin") + word = json.loads(raw) + folder = word_path.parent / "records" + frame_data = json.loads((folder/"frames.json").read_text())["frames"] + records = list(struct.iter_unpack("<6i", (folder/"249-records.bin").read_bytes())) + need((word["h"], word["v"], word["R"]) == (8, V, R), "Pinned local type") + n = 2*V+R + projectors = frame_projectors(frame_data) + dimensions = {int(f): z["dim"] for f, z in frame_data.items()} + pairs = set() + for op, role, old, new, rank, _ in records: + if op == 0: + pairs.add((old, new, rank)) + for old, new, rank in pairs: + p, q = projectors[old], projectors[new] + need(matrix_multiply(p, q) == p and matrix_multiply(q, p) == p, + "Nested exact projectors") + need(dimensions[new]-dimensions[old] == rank >= 0, "Literal child rank") + for role in range(2*V, n): + need(dimensions[word["start"][role]] == 0 and dimensions[word["final"][role]] == 8, + "Every helper is physically D_I8, not a reset or an unearned job") + checks = [] + streams = {} + for reverse in (False, True): + current = list(word["final"] if reverse else word["start"])+[-1] + values = [1 << i for i in range(n)]+[0] + norm = [1]*n+[0] + maximum = 1 + profile = Counter() + stream = [] + owned = None + adds = copies = 0 + for op, x, y, c, f, z in (reversed(records) if reverse else records): + if op == 0: + old, new = (c, y) if reverse else (y, c) + need(current[x] == old, "Local transition entrance") + current[x] = new + if f: + profile[f] += 1 + stream.append(["MOVE", x, old, new, f]) + elif op == 1: + need(current[x] == current[y] == f and x != y, "Native common-frame ADD") + need(owned is None or x != owned, "Owned source remains immutable") + values[x] ^= values[y] if c & 1 else 0 + norm[x] += abs(c)*norm[y] + maximum = max(maximum, norm[x]) + adds += 1 + stream.append(["ADD", x, y]) + elif op == (3 if reverse else 2): + need(owned is None and y == n and values[n] == 0 and current[x] == c, + "Private COPY entrance") + owned = x + current[n] = f + values[n] = values[x] + norm[n] = norm[x] + rank = abs(dimensions[c]-dimensions[f]) + profile[rank] += 1 + copies += 1 + stream.append(["COPY", x, n]) + else: + need(op == (2 if reverse else 3) and owned == x and y == n, + "Private COPY close") + need(values[n] == values[x], "Copied field exact cleanup") + values[n], norm[n], current[n], owned = 0, 0, -1, None + stream.append(["ERASE", x, n]) + need(owned is None and copies == 9 and adds == 24305, "Complete local word") + need(current[:n] == (word["start"] if reverse else word["final"]), "All local endpoints") + expected = [(1 << i) ^ ((1 << (i-V)) if V <= i < 2*V else 0) for i in range(n)] + need(values == expected+[0], "All arbitrary input columns") + need(profile == LOCAL, "Complete local bill, including copied centers") + key = "reverse" if reverse else "forward" + streams[key] = stream + checks.append(dict(direction=key, arbitrary_columns=n, dirty_helper_columns=R, + owned_COPY_episodes=copies, unit_ADDs=adds, + positive_majorant_maximum=maximum, positive_majorant_bits=maximum.bit_length(), + profile=dict(sorted(profile.items())), stream_sha256=digest(stream))) + serial_projectors = {str(f): [[str(x) for x in row] for row in p] + for f, p in sorted(projectors.items())} + return word, streams, dict(status="PASS_FULL_LOCAL_COLUMNS_AND_EXACT_PROJECTORS", + frames=len(projectors), nested_transition_pairs=len(pairs), + projector_sha256=digest(serial_projectors), signed_directions=checks, + helper_endpoint="D_I8 on all 439 arbitrary original helper inputs", + private_COPY_contract="Inherited source-owned immutable-copy contract; all nine episodes paid", + full_GL_cover_executed=False) + + +def explicit_unbanked_scalar_replay(p, streams): + """Fresh physical fields for every local invocation; all dirt columns.""" + calls = 2*p+1 + n = 2*p*V+calls*R + values = [1 << i for i in range(n)]+[0] + norms = [1]*n+[0] + maximum = 1 + adds = 0 + def local(stage, pair, reverse): + nonlocal maximum, adds + def role(r): + if r == 2*V+R: + return n + if r < 2*V: + side, port = divmod(r, V) + side = 1-side if reverse else side + return (2*pair+side)*V+port + return 2*p*V+stage*R+r-2*V + for event in streams["reverse" if reverse else "forward"]: + if event[0] == "MOVE": + continue + op, x, y = event + x, y = role(x), role(y) + if op == "ADD": + values[x] ^= values[y] + norms[x] += norms[y] + maximum = max(maximum, norms[x]) + adds += 1 + elif op == "COPY": + need(values[y] == 0, "Global private slot empty") + values[y], norms[y] = values[x], norms[x] + else: + need(values[y] == values[x], "Global private slot restored") + values[y], norms[y] = 0, 0 + def bridge(dst, src): + nonlocal maximum, adds + for port in range(V): + for d, s in ((2*dst*V+port, 2*src*V+port), + ((2*src+1)*V+port, (2*dst+1)*V+port)): + values[d] ^= values[s] + norms[d] += norms[s] + maximum = max(maximum, norms[d]) + adds += 1 + local(0, 0, False) + for j in range(p): + local(2*j+1, j, True) + if j < p-1: + bridge(j, j+1) + local(2*j+2, j, False) + if j < p-1: + bridge(j, j+1) + for j in reversed(range(p-1)): + bridge(j+1, j) + for pair in range(p): + for port in range(V): + x, y = 2*pair*V+port, (2*pair+1)*V+port + values[x], values[y] = values[y], values[x] + norms[x], norms[y] = norms[y], norms[x] + need(values == [1 << i for i in range(n)]+[0], "Every global decoded column restored") + need(adds == calls*24305+6*(p-1)*V, "Literal global scalar bill") + return dict(all_arbitrary_columns=n, independent_dirty_helpers=calls*R, + COPY_episodes=9*calls, private_COPY_closed=True, + unit_ADDs_before_new_boundary_adapters=adds, + final_free_pair_swaps=p*V, + positive_majorant_maximum=maximum, positive_majorant_bits=maximum.bit_length(), + notes="Decoded scalar audit; physical monomial endpoint is checked separately on every coefficient.") + + +@lru_cache(None) +def h_interval(rank, exponent): + lo, hi = log_interval(rank) + elo, ehi = exp_interval(exponent*lo, exponent*hi) + return Q(rank)/ehi, Q(rank)/elo + + +def margin_interval(paid, targets, exponent): + signed = Counter(targets) + signed.subtract(paid) + lo = hi = Q(0) + for rank, count in signed.items(): + a, b = h_interval(rank, exponent) + lo += count*(a if count >= 0 else b) + hi += count*(b if count >= 0 else a) + return lo, hi + + +def interval_row(bounds): + lo, hi = bounds + scale = 1 << 128 + lo = Q(lo.numerator*scale//lo.denominator, scale) + hi = Q(-((-hi.numerator*scale)//hi.denominator), scale) + return dict(lower=quotient(lo), upper=quotient(hi), + display=float((lo+hi)/2), strict_positive=lo > 0, strict_negative=hi < 0) + + +def price_candidate(p, keep, factor, idle): + calls, m = 2*p+1, 14*p+8 + paid = Counter({rank:calls*n for rank, n in LOCAL.items()}) + # All idle blocks are explicitly split into perpendicular rank-seven + # subcalls. No rank14/28/42 child is hidden under a rank8 target. + paid[7] += 2*V*sum(len(row["stages"]) for row in idle if row["retained"]) + targets = Counter({8:calls*R}) + for monomial in factor["diagonal_monomials"]: + targets[(monomial & 1)+7*(monomial >> 1).bit_count()] += V + need(max(paid) < min(targets), "Every child strictly smaller than every job") + credit = sum(rank*n for rank, n in targets.items()) + bill = sum(rank*n for rank, n in paid.items()) + need(credit-bill == 2*p*V-calls*63, "Full rank credit identity") + def floating(exponent): + return sum(n*r**(1-exponent) for r, n in targets.items())-sum(n*r**(1-exponent) for r, n in paid.items()) + lo, hi = 0.0, 0.01 + for _ in range(64): + middle = (lo+hi)/2 + if floating(middle) > 0: + lo = middle + else: + hi = middle + lower = Q(math.floor(lo*10**12), 10**12) + upper = lower+Q(1, 10**12) + lower_bounds = margin_interval(paid, targets, lower) + upper_bounds = margin_interval(paid, targets, upper) + need(lower_bounds[0] > 0 > upper_bounds[1], "Exact root bracket") + prices = {str(a):interval_row(margin_interval(paid, targets, a)) + for a in (Q("0.001745"), Q("0.002"), Q("0.004"), Q("0.006"))} + # The old raw-price bad-residue envelope is displayed conservatively. + # It is not a proof that the new mixed output normalizers inherit it. + old_residue_envelope = Q(32*m*m*sum(paid.values()), 10**16) + return dict(pairs=p, stages=calls, keep_idle_mask=keep, ambient_rank=m, + paid=dict(sorted(paid.items())), targets=dict(sorted(targets.items())), + total_paid_queries=sum(paid.values()), total_productive_fields=sum(targets.values()), + rank_bill=bill, rank_credit=credit, rank_margin=credit-bill, + strict_separation=dict(maximum_child=max(paid), minimum_target=min(targets)), + bare_mixed_moment_root_bracket=dict(lower=quotient(lower), upper=quotient(upper), + lower_display=float(lower), upper_display=float(upper), + lower_margin=interval_row(lower_bounds), upper_margin=interval_row(upper_bounds)), + target_margins=prices, old_raw_bad_residue_envelope=quotient(old_residue_envelope), + envelope_transfer_proved=False, kappa_claim=False) + + +def run(max_p=5): + start = time.monotonic() + source = HERE / "sources/pr589-regenerated/WORD.json.gz" + word, streams, local = audit_local(source) + cases, counts, winners = [], {}, {} + for p in range(1, max_p+1): + valid = [] + for keep in range(1 << (3*(p-1))): + coefficients, events, idle = physical_controller(p, keep) + factor = simultaneous_monomial_factor(coefficients) + if factor is None: + continue + # Discovery ranks by a floating root; winners receive exact + # rational price brackets below. All accepted factorizations + # have already passed exact finite operator identities. + paid = Counter({r:(2*p+1)*n for r, n in LOCAL.items()}) + paid[7] += 2*V*sum(len(row["stages"]) for row in idle if row["retained"]) + targets = Counter({8:(2*p+1)*R}) + for term in factor["diagonal_monomials"]: + targets[(term & 1)+7*(term >> 1).bit_count()] += V + def value(a): + return sum(n*r**(1-a) for r, n in targets.items())-sum(n*r**(1-a) for r, n in paid.items()) + lo, hi = 0.0, 0.01 + for _ in range(48): + mid = (lo+hi)/2 + if value(mid) > 0: + lo = mid + else: + hi = mid + valid.append((lo, keep, factor, coefficients, events, idle)) + counts[p] = dict(enumerated=1 << (3*(p-1)), exact_factorizations=len(valid)) + winning = max(valid, key=lambda row:(row[0], row[1])) + _, keep, factor, coefficients, events, idle = winning + case = price_candidate(p, keep, factor, idle) + case.update(factorization=factor, idle_events=idle, physical_events=events, + coefficient_matrices={str(term):rows for term, rows in sorted(coefficients.items())}, + decoded_global_replay=explicit_unbanked_scalar_replay(p, streams)) + case["unit_ADDs_including_constant_boundaries"] = ( + case["decoded_global_replay"]["unit_ADDs_before_new_boundary_adapters"]+ + V*factor["boundary_unit_ADDs_per_port"]) + case["unit_ADDs_if_all_final_SWAPs_use_three_ADDs"] = ( + case["unit_ADDs_including_constant_boundaries"]+3*p*V) + # Conservative norm multiplier for literal boundary ADDs. This + # input is offered to a precision compiler, not admitted as one. + base = case["decoded_global_replay"]["positive_majorant_maximum"] + norm_bound = base*(1 << (factor["boundary_unit_ADDs_per_port"]+3*p)) + case["positive_majorant_with_boundary_bound"] = str(norm_bound) + case["positive_majorant_with_boundary_bits"] = norm_bound.bit_length() + cases.append(case) + winners[p] = case["bare_mixed_moment_root_bracket"]["lower_display"] + strongest = max(cases, key=lambda row:row["bare_mixed_moment_root_bracket"]["lower_display"]) + p, keep = strongest["pairs"], strongest["keep_idle_mask"] + factor = strongest["factorization"] + # A literal omitted bridge is compared with the ACTUAL advertised + # target using the same boundary matrices. Mere diagonalizability is + # deliberately not enough for this negative control. + rejected = [] + expected = {int(t):bit_mul(bit_mul(factor["left_rows"], rows), factor["right_rows"]) + for t, rows in strongest["coefficient_matrices"].items()} + for missing in range(6*(p-1)): + coefficients, _, _ = physical_controller(p, keep, missing) + wrong = {t:bit_mul(bit_mul(factor["left_rows"], rows), factor["right_rows"]) + for t, rows in coefficients.items()} + need(wrong != expected, "Omitted physical bridge rejected") + rejected.append(missing) + controls = dict(omitted_bridges_rejected=rejected, + rank14_child_under_rank8_job_rejected=not(14 < 8), + full_rank8_helper_downgrade_to_rank7_rejected=(8 != 7), + all_idle_removed_p2_is_not_constant_monomial_diagonal=( + simultaneous_monomial_factor(physical_controller(2, 0)[0]) is None)) + pins = [Path(__file__), source, source.parent/"BASE.json.gz", + source.parent/"XCHECK.json", source.parent/"records/249-records.bin", + source.parent/"records/249-states.json", source.parent/"records/frames.json", + ROOT/"research/e8-bit-p111-tuned/code/gen_p3.py", + ROOT/"research/e8-bit-p111-tuned/code/xcheck_p.py", + ROOT/"research/e8-bit-p111-tuned/tune/apply.py", + ROOT/"research/e8-bit-p111-tuned/tune/wlib.py", + ROOT/"research/e8-bit-p111-tuned/tune/EXPECTED.json", + ROOT/"research/e8-bit-carrier-skeleton/code/bit/export_records.py", + REFERENCE/"joint_pair_dag.py"] + return dict(schema="finite-bit-mixed-productive-controller/1", + status="PASS_EXACT_FINITE_OPERATOR_AND_DISPLAYED_MIXED_INVOICE", + source_recovery="PR589 source regenerated byte-for-byte; not the missing stronger PR4085 BIT word", + local=local, finite_idle_menu=counts, candidates=cases, + strongest_pairs=strongest["pairs"], controls=controls, + exact_algebra="F2[(Z/2)^(2p+2)], represented by every monomial coefficient; no numerical character sampling", + physical_generator_ranks="D_P rank1, mutually perpendicular D_Bs rank7; helper endpoint D_(P+Bs) rank8", + not_proved=["Cover routing for these changed independent target projectors", + "Canonical weighted BIT output normalizers and their incoming-weight compatibility", + "Mixed-target all-size recursion or its fixed uniform precompilation", + "Physical tape, row stock, rounding/precision and complete outer multiplication transfer"], + source_sha256={str(path.relative_to(ROOT)):sha256(path.read_bytes()).hexdigest() for path in pins}, + runtime=dict(python=platform.python_version(), seconds=time.monotonic()-start), + new_multiplication_kappa=False) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--max-p", type=int, default=5) + parser.add_argument("--output", type=Path, default=HERE/"MIXED-PRODUCTIVE-BIT.json") + args = parser.parse_args() + need(1 <= args.max_p <= 6, "Bounded finite controller menu") + result = run(args.max_p) + args.output.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(json.dumps(dict(status=result["status"], strongest_pairs=result["strongest_pairs"], + roots={c["pairs"]:c["bare_mixed_moment_root_bracket"]["lower_display"] + for c in result["candidates"]}, runtime=result["runtime"]), sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/complex/fresh-certificates/THREE-base-HELPER-BOUNDARIES.json.gz b/research/pr4359-p7-padding/source/research/kappa-rebuild/complex/fresh-certificates/THREE-base-HELPER-BOUNDARIES.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..1dae5193bad6e7467eb13434fd1a2e971f2a4cba GIT binary patch literal 25720 zcmd3ObySpH*S8{|0*XpWOGr1;B_N123=KnfcZYz8(nt&)(%m(b(w#GONOuo0+ zv)=D}*ShEV<5|xipKE#T6LZa6=Q{iB{X4(C59Faw9^C&!d9>FIj9is+&4sIDxYS_2 zz`V+>I4?9C`HcGH2U|%eiolCk)4=I@J_glOW7U#(jGL`xq*U{%`|?B<&e-vs$D*bm zRzLE#&+V>x?JltkoRKfy9(C*aUchG;dGV6%TD>n!B6k<<3deOK-q$Ow*R$QMi>H3K$6M_n1reXyeNg10-^Efl 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Substantial OpenAI assistance. The full-identity ancestor supplies +the original center cuts and compensation; the independently retained later +cleanup supplies a legal scheduled alias of all91 old buffers. A fresh native +replay checks their actual composition. Eight sequential center fields reuse +one explicitly cleared C0. Each rank8 center is optionally split into rank5 +and rank3 with exact phase decoding, keeping a strict child-rank ceiling5. +""" +from collections import Counter +from copy import deepcopy +from pathlib import Path +import argparse +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import rebuild_native as N +import native_extensions as X + +INTEGRATED = N.ROOT/'research/kappa-global-routing/integrated-complex' +INTEGRATED_RECEIPT_SHA = '70c3d5b1c1d6a18afb29ea1febec3c619ff2b1e38a09c44db7828794ea095429' + + +def reuse_centers(words): + words = deepcopy(words) + for program in words.values(): + for event in program: + if event[0] == 'center': + event[1] = 0 + elif event[0] == 'scalar': + g = event[1] + for role in (g[1:3] if g[0] in ('add', 'copy') else g[1:2]): + if role[0] == 'C': + role[1] = 0 + return words + + +def compose_full_identity(v, tag, integrated_receipt): + source = v.CORE/'sources'/(tag+'-CANONICAL.json.gz') + scheduled = INTEGRATED/(tag+'-CANONICAL.json.gz') + N.need(N.digest(scheduled) == integrated_receipt['providers'][tag]['artifacts'][scheduled.name], + 'Authenticated scheduled cleanup input') + original = N.read(source); newer = N.read(scheduled) + changes = {k for k in set(original) | set(newer) if original.get(k) != newer.get(k)} + N.need(changes == {'centers', 'center_frames', 'cut', 'compensation', 'cleanup', 'local_profile', 'zero_buffers'}, + 'Exact ancestor-to-clean-J change inventory') + c = deepcopy(original) + c['cleanup'] = deepcopy(newer['cleanup']) + c['zero_buffers'] = [] + N.need(len(c['centers']) == 8 and len(c['cut']) == 176, 'Retained full-identity center response') + words = reuse_centers(v.emit_original(c)) + return c, words, dict(original_canonical_sha256=N.digest(source), scheduled_canonical_sha256=N.digest(scheduled), + changed_fields_from_original=['cleanup', 'zero_buffers'], + ordinary_compensation_and_all_eight_center_cuts_retained=True) + + +def split_centers(p, ce, canonical, words): + c = deepcopy(canonical); result = {}; phases = {}; profile = Counter({int(k): n for k, n in c['local_profile'].items()}) + N.need(profile[8] == 8, 'Eight old rank8 children') + del profile[8]; profile[3] += 8; profile[5] += 8 + c['local_profile'] = {str(k): n for k, n in sorted(profile.items())} + for direction, program in words.items(): + out = []; detail = [] + for event in program: + if event[0] != 'center': + out.append(deepcopy(event)); continue + _, role, old, new, rank = event + N.need(role == 0 and rank == 8 and {len(c['frames'][old]), len(c['frames'][new])} == {0, 8}, + 'Single eight-dimensional old center transport') + high = old if len(c['frames'][old]) == 8 else new + basis = c['frames'][high][:3] + if basis not in c['frames']: + c['frames'].append(basis) + mid = c['frames'].index(basis) + path = [old, mid, new]; pieces = []; recipes = [] + for a, b in zip(path, path[1:]): + width = abs(len(c['frames'][b])-len(c['frames'][a])) + part = ce.canonical_frame(9, c['frames'][a]).adjoint().then(ce.canonical_frame(9, c['frames'][b])) + if direction == 'backward': + part = p.conjugate(ce, part) + recipe = N.lower_exact(p, ce, part) + N.need(recipe['rank'] == width and width in (3, 5), 'Split child exact rank') + out.append(['center', 0, a, b, width]); pieces.append(part) + recipes.append(dict(old_frame=a, new_frame=b, recipe=recipe)) + whole = ce.canonical_frame(9, c['frames'][old]).adjoint().then(ce.canonical_frame(9, c['frames'][new])) + if direction == 'backward': + whole = p.conjugate(ce, whole) + product = pieces[0].then(pieces[1]) + N.need(product.tab == whole.tab and product.zero_state() == whole.zero_state(), + 'Two split children equal old center including absolute phase') + detail.append(dict(old_frame=old, intermediate_frame=mid, new_frame=new, + intermediate_basis=basis, pieces=recipes, product_exact_including_phase=True)) + N.need(len(detail) == 8, 'All eight center paths split') + result[direction] = out; phases[direction] = detail + return c, result, phases + + +def bind_helper_boundaries(c, tag): + source = HERE/'fresh-certificates'/(tag+'-HELPER-BOUNDARIES.json.gz') + receipt = N.read(HERE/'fresh-certificates/RESULT-helpers.json') + expected = receipt['providers'][tag]['helper_boundaries']['sha256'] + N.need(N.digest(source) == expected, 'Fresh helper boundary certificate pin') + helper = N.read(source) + for r in helper['recipes']: + role = r['role'] + N.need(c['frames'][c['start'][role]] == r['certificate']['start_basis'] and + c['frames'][c['final'][role]] == r['certificate']['end_basis'], + 'Full-identity helper has identical exact endpoint references') + return dict(certificate_sha256=expected, certificate=str(source.relative_to(N.ROOT)), + count=408, widths=helper['widths'], total_width=helper['total_width'], + both_orientations_and_global_phases_bound=True) + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--out', type=Path, default=HERE/'full-identity-certificates') + args = ap.parse_args(); args.out.mkdir(parents=True, exist_ok=True) + p, v, ce, predecessor, inherited = N.authenticated(); geo = N.geometry(v.PACKET) + N.need(N.digest(INTEGRATED/'RESULT.json') == INTEGRATED_RECEIPT_SHA, 'Pinned scheduled cleanup receipt') + scheduled_receipt = N.read(INTEGRATED/'RESULT.json') + result = dict(schema='fresh-full-identity-zero-bank-native-supplier/1', + generator_sha256=N.digest(Path(__file__)), reconstruction_source_sha256=N.digest(HERE/'rebuild_native.py'), + independent_interpreter_sha256=p.CHECKER_SHA, + independent_prefix_evaluator_sha256=N.digest(HERE/'native_extensions.py'), + integrated_cleanup_receipt_sha256=INTEGRATED_RECEIPT_SHA, + source_closure_verified=inherited, no_new_kappa_claimed=True, providers={}) + for tag in N.TAGS: + c, words, composition = compose_full_identity(v, tag, scheduled_receipt) + unsplit = {direction: v.replay(program, c, geo['R'], direction == 'backward', False) + for direction, program in words.items()} + c, split, phases = split_centers(p, ce, c, words) + checks = {} + for direction, program in split.items(): + checked = v.replay(program, c, geo['R'], direction == 'backward', False) + rows, prefixes = X.literal_replay(v, c, program, direction == 'backward') + N.need(all(rows['L', i] == v.expected(('L', i), geo['R'], direction == 'backward', False) for i in range(632)), + 'Second all632-column endpoint implementation') + N.need(checked['conservative_real_scalar_primitive_allowance'] == + unsplit[direction]['conservative_real_scalar_primitive_allowance'], 'Splitting adds no scalar macro') + N.need(max(checked['paid_profile']) == 5 and checked['explicitly_owned_C_fields_cleared'] == 1, + 'Child ceiling5 and one reusable owned C0') + checks[direction] = dict(independent_native_replay=checked, independent_prefix_and_endpoint=prefixes) + bad = deepcopy(split['forward']) + remove = next(i for i, e in enumerate(bad) if e[0] == 'scalar' and e[1][0] == 'add' and e[1][2] == ['C', 0]) + bad.pop(remove) + rejected = False + try: + v.replay(bad, c, geo['R'], False, False) + except ValueError as error: + rejected = 'operator mismatch' in str(error) + N.need(rejected, 'Dropped center response negative control rejected') + cp = args.out/(tag+'-FULL-IDENTITY-CANONICAL.json.gz') + wp = args.out/(tag+'-FULL-IDENTITY-NATIVE.json.gz') + result['providers'][tag] = dict(composition=composition, unsplit_replays=unsplit, split_replays=checks, + split_center_phase_recipes=phases, helper_boundary=bind_helper_boundaries(c, tag), + artifacts={cp.name:N.save(cp, c), wp.name:N.save(wp, split)}, + all_632_persistent_inputs_arbitrary=True, all_408_helpers_autonomous=True, + external_cleanup_fields=0, owned_C_fields=1, owned_C_input_arbitrary_and_erased=True, + max_child_rank=5, no_H_involution_or_query_controller_needed=True, + dropped_center_response_negative_control_rejected=True) + N.save(args.out/'RESULT.json', result) + print('PASS full identity', tag, checks['forward']['independent_native_replay']['paid_profile'], flush=True) + result['status'] = 'PASS_FULL_IDENTITY_ALL_FOUR_BOTH_DIRECTIONS_632_ARBITRARY_FIELDS_ZERO_EXTERNAL_BANK_CHILD_CEILING5' + result['scope'] = ('Complete ideal local native supplier and helper boundaries. Outer productive job ownership, ' + 'complete recurrence, scalar and storage charges, and rounded induction remain caller obligations.') + N.save(args.out/'RESULT.json', result) + + +if __name__ == '__main__': + main() diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/controller/P3-NATIVE-COVER.json.gz b/research/pr4359-p7-padding/source/research/kappa-rebuild/controller/P3-NATIVE-COVER.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..51a09b3952a491f06780bf6ce5f69b385f026b21 GIT binary patch literal 176694 zcmbrl1z42Z+BXh}fv9vyxd8zc7`n?tsvxK|GlU=^J#=GG0|Fu~C8&gybPUbVB?8hl zG}7Jt*9_|3=bZQbzUzN|`&!rIa;^Kh*B!rg$K&i9L6>ka|KXims?^P8SFmF_(BG<9 z{lLr2B()_ObLauTAx;guWVf5gS;{G(oM}b$W`8xhD1#ZYNM06nB}X;u*_DZx<;eWP z>m=7H@(gEMPY+g_s*h&;N3xFA+UAl@_S2HQkJ^Y%Hx{_OkGJ;yyTE48xYypgjrZX~ zlK08h+-lY7_U5=$rRVO{ocGZ}f0vZk$+*>?V!!%mS0$p=Xp z?PM!jMe5{exB8^Y#qDq+w=kyI0>F8#56qT21Xf~P0 zvi2`d>m=xAHWUrPGJ`A}H?x!>p)AoI;cc@m#+%dmu6E1srZ;2Q(jGW1=PhkGgCnDx 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zRqm#a!&<|}SHF+sHlv7%rUa+A`|o?_9dADj_MCq_iSm)EP06o~pFrqwwwqKw1b${} zOwrQym^9Rwv6eSXhX9%|WR}jfBdZ6;*QVLp^Gcj~G1K;b(lLzG9us%tjvVA5Fzmn{ dlWN-^*Vc9wANOec%e#Z)XI$DbY0#u&{|P9>Nu2-y literal 0 HcmV?d00001 diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/controller/p3_native_cover.py b/research/pr4359-p7-padding/source/research/kappa-rebuild/controller/p3_native_cover.py new file mode 100644 index 0000000000..8756693610 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/controller/p3_native_cover.py @@ -0,0 +1,274 @@ +#!/usr/bin/env python3 +"""Complete native ownership and phase binding for p3/keep43. + +This binds the exact Laurent controller to all 2,856 original helper roles, +whole-call adapters, arbitrary productive inputs, and the full recursive +invoice. Apache-2.0; substantial OpenAI assistance. Native source credits +and immutable hashes are inherited from the reconstruction receipts. +""" +from collections import Counter, defaultdict, deque +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +sys.path.insert(0, str(HERE)) +import global_identity_cover as G + +STAGES = ((0,'forward'),(0,'backward'),(0,'forward'),(1,'backward'), + (1,'forward'),(2,'backward'),(2,'forward')) +FORMAL = HERE.parent/'bit/COMPLEX-CONTROLLER-FACTOR.json' +TARIFF = HERE.parent/'architecture/P3-CONTROLLER-TARIFF-CERTIFICATE.json' +AUDIT = HERE.parent/'transfer-audit/P3-NATIVE-AUDIT.json.gz' +TARGETS = {6:192,7:56,8:93,9:1229,25:448,57:224} +PAID = {1:17623,2:5065,3:1738,4:714,5:254} + + +def need(condition, message): + if not condition: + raise AssertionError(message) + + +def stage_frame(n, stage, q): + if stage == 0: + return n.frame([(a,1) for a in n.AXES[:9]]+[(q,-1)]) + return n.frame((a,1) for a in n.AXES[9+8*(stage-1):9+8*stage]) + + +def contacts(n, F, phases): + result = [] + for stage,(pair,direction) in enumerate(STAGES): + sign = 1 if direction == 'forward' else -1 + spectator = n.frame((a,1) for a in n.AXES[9:9+8*stage]) + for port,recipe in enumerate(phases['recipes']): + q = recipe['q']; route = n.source_route(phases,stage,port) + need(all(route[i] == 1 << i for i in range(57,73)), 'No route touches outside ambient57') + need(all(axis < 1 << 57 for axis in route[:57]), 'All native views lie in ambient57') + input_x = n.frame([(q,1)]) if not stage else n.completed(stage-1) + input_y = () if not stage else n.frame(list(input_x)+[(q,-1)]) + local_x = n.frame(list(spectator)+[(q,sign)]) + local_y = spectator + end_x = n.frame(list(spectator)+[(a,sign) for a in n.AXES[:9]]) + end_y = n.frame(list(end_x)+[(q,-sign)]) + output_x = n.completed(stage) + output_y = n.frame(list(output_x)+[(q,-1)]) + maps = {'entry_X':F.between(n,input_x,route,local_x), + 'entry_Y':F.between(n,input_y,route,local_y), + 'exit_X':F.between(n,end_x,route,output_x), + 'exit_Y':F.between(n,end_y,route,output_y)} + delta = stage_frame(n,stage,q) + # References cancel as operators on arbitrary raw inputs. No + # historical assumption about which idles have run is needed. + need(n.polynomial(n.frame(list(output_x)+[(a,-c) for a,c in input_x])) + == n.polynomial(delta), 'Exact diagonal physical D_s on X') + need(n.polynomial(n.frame(list(output_y)+[(a,-c) for a,c in input_y])) + == n.polynomial(delta), 'Exact diagonal physical D_s on Y') + cross = n.frame(list(output_y if sign == 1 else output_x)+ + [(a,-c) for a,c in (input_x if sign == 1 else input_y)]) + wanted = n.frame(list(delta)+[(q,-1 if sign == 1 else 1)]) + need(n.polynomial(cross) == n.polynomial(wanted), 'Physical cross operator D_s Q^+-1') + result.append({'stage':stage,'pair':pair,'port':port,'direction':direction, + 'common_spectator_frame':list(spectator),'maps':maps}) + return result + + +def make_windows(n, phases, formal): + output = [] + for number,window in enumerate(formal['retained_idle_windows']): + stages = window['stages'] + patterns = [list(spec[1:]) for spec in (G.PAIRS if len(stages) == 2 else G.MIDDLE) + for _ in range(spec[0])] + need(len(patterns) == 224, 'Every retained window has224 distinct possible owners') + for index,widths in enumerate(patterns): + side,port = ('X' if index < 112 else 'Y'),index % 112 + recipe = phases['recipes'][port] + if 0 in stages: + need(stages == [0,1], 'The retained initial window is D0D1') + axes = recipe['idle_children'][0]['orthogonal_axes'] + shift = recipe['idle_children'][0]['translation_after'] + else: + axes = [axis for stage in stages for axis in n.AXES[9+8*(stage-1):9+8*stage]] + shift = 0 + desired = n.frame([term for stage in stages for term in stage_frame(n,stage,recipe['q'])]) + actual = n.frame([(axis,1) for axis in axes]+[(shift,2)]) + need(n.polynomial(actual) == n.polynomial(desired), 'Literal whole idle operator including phase') + need(len(axes) == window['rank'] and sum(widths) <= len(axes), 'Every hosted helper fits') + output.append({'family':number,'index':window['index'],'kind':window['kind'], + 'pair':window['pair'],'stages':stages,'side':side,'port':port, + 'owner':f"{side}{window['pair']}:{port}", 'widths':widths, + 'axes':axes,'translation_after':shift}) + return output + + +def helper_assignment(n, phases, formal, local, helper_recipes): + windows = make_windows(n,phases,formal) + pools = [] + for stage in range(7): + pool = defaultdict(deque) + for recipe in helper_recipes['THREE-base']['recipes']: + pool[recipe['width']].append(recipe['role']) + pools.append(pool) + bindings,residuals,fresh = [],[],[] + paid = Counter(); targets = Counter({25:448,57:224}) + for window in windows: + cursor = 0 + for stage,width in zip(window['stages'],window['widths']): + if not width: + continue + need(pools[stage][width], 'A real local helper of this width exists') + role = pools[stage][width].popleft() + axes = window['axes'][cursor:cursor+width]; cursor += width + bindings.append({'stage':stage,'role':role,'width':width,'owner':window['owner'], + 'axes':axes,'kind':'original_idle','window_index':window['index']}) + for axes in G.split_axes(window['axes'][cursor:]): + residuals.append({'owner':window['owner'],'after_stage':max(window['stages']), + 'axes':axes,'rank':len(axes),'kind':'idle_remnant'}) + paid[len(axes)] += 1 + for stage,pool in enumerate(pools): + for width,roles in sorted(pool.items()): + for role in roles: + owner = f'G{stage}:{role}'; target = max(6,width) + bindings.append({'stage':stage,'role':role,'width':width,'owner':owner, + 'axes':list(n.AXES[:width]),'kind':'fresh'}) + fresh.append({'owner':owner,'stage':stage,'native_width':width,'target_rank':target}) + targets[target] += 1 + for axes in G.split_axes(list(n.AXES[width:target])): + residuals.append({'owner':owner,'after_stage':stage,'axes':axes, + 'rank':len(axes),'kind':'fresh_topup'}) + paid[len(axes)] += 1 + coordinate_maps = {} + for stage,(pair,direction) in enumerate(STAGES): + native = local['providers']['THREE-base']['split_replays'][direction]['independent_native_replay'] + paid.update({int(rank):count for rank,count in native['paid_profile'].items()}) + selected = [row for row in bindings if row['stage'] == stage] + need(len(selected) == 408 and {row['role'] for row in selected} == set(range(224,632)), + 'All408 actual native helper roles are assigned exactly once') + need(len({row['owner'] for row in selected}) == 408, 'Every local helper has a distinct physical owner') + active = {f'{side}{pair}:{port}' for side in ('X','Y') for port in range(112)} + need(not active.intersection(row['owner'] for row in selected), 'No live main role is borrowed') + for row in selected: + key = ','.join(map(str,row['axes'])) + if key not in coordinate_maps: + coordinate_maps[key] = G.coordinate_map(row['axes'],57) + row['coordinate_map'] = key + row['whole_helper_boundary'] = {'provider':'THREE-base','direction':direction,'role':row['role'], + 'selector':'certificate.directions.direction.existing_native_boundary_normal_form'} + need(dict(sorted(paid.items())) == PAID, 'Full actual paid histogram') + need(dict(sorted(targets.items())) == TARGETS, 'All and only productive target fields') + need(len(fresh) == 1570 and len(bindings) == 2856, 'Complete field and helper census') + need(sum(k*v for k,v in targets.items())-sum(k*v for k,v in paid.items()) == 224, 'Rank-unit margin') + need(max(paid) < min(targets), 'Strict recursive separation') + return {'windows':windows,'helper_bindings':bindings,'owner_coordinate_maps':coordinate_maps, + 'paid_residuals':residuals,'fresh_outputs':fresh,'paid':PAID,'targets':TARGETS, + 'rank_margin':224,'productive_fields':2242,'owned_center_fields':1,'external_cleanup_fields':0} + + +def endpoint_normalizers(n, phases, formal): + output = []; histogram = Counter() + for role,term in enumerate(formal['exact_diagonal_monomials']): + q_power,selected = term[0],term[1:] + need(q_power in (-1,1) and set(selected) <= {0,1}, 'Exact Laurent endpoint alphabet') + for port,recipe in enumerate(phases['recipes']): + q = recipe['q'] + physical = n.frame([(q,q_power)]+[entry for stage,yes in enumerate(selected) if yes + for entry in stage_frame(n,stage,q)]) + axes = list(n.AXES[:9]) if selected[0] else [q] + axes += [axis for stage in range(1,7) if selected[stage] + for axis in n.AXES[9+8*(stage-1):9+8*stage]] + translation = q if q_power == -1 else 0 + repaired = n.frame(list(physical)+[(translation,2)]) + canonical_on_axes = n.frame((a,1) for a in axes) + need(n.polynomial(repaired) == n.polynomial(canonical_on_axes), 'Exact endpoint phase including constant') + if translation: + need(n.polynomial(physical) != n.polynomial(canonical_on_axes), 'Missing phase repair really fails') + rank = len(axes) + need(rank == 1+8*sum(selected), 'Earned endpoint rank') + matrix = G.coordinate_map(axes,57) + need(matrix['columns'][:rank] == axes, 'Literal target-rank conjugation') + output.append({'original_input_role':role,'port':port,'target_rank':rank, + 'input_coordinate_columns':matrix['columns'], + 'output_coordinate_inverse_rows':matrix['inverse_rows'], + 'output_translation_before_inverse_map':translation, + 'physical_frame':list(physical),'positive_axes':axes}) + histogram[rank] += 1 + need(histogram == Counter({25:448,57:224}), 'Main endpoint distribution') + return output + + +def scalar_invoice(local, formal): + native = sum(local['providers']['THREE-base']['split_replays'][direction]['independent_native_replay'] + ['conservative_real_scalar_primitive_allowance'] for pair,direction in STAGES) + adapters = formal['right_program']+formal['left_program'] + counts = Counter(row[0] for row in adapters) + need(counts == Counter({'ADD':4,'SWAP':6,'SCALE':2}), 'Literal boundary scalar word') + need(all(str(row[-1]) in ('1','-1') for row in adapters if row[0] in ('ADD','SCALE')), + 'Only unit scalar boundary coefficients') + # Ordinary swap: three additions followed by one negation. Signed swap + # needs three additions. No free whole-role movement is assumed here. + adapter_adds = 4+6*3; adapter_negs = 2+6 + bridges = sum(row[0] == 'ADD' for row in formal['physical_events']) + signed_swaps = sum(row[0] == 'SIGNED_SWAP' for row in formal['physical_events']) + need(bridges == 12 and signed_swaps == 3, 'Literal global bridge and swap census') + total = native+112*((adapter_adds+bridges+3*signed_swaps)*8+adapter_negs*2) + return {'native_real_scalar_allowance':native,'boundary_unit_ADD_per_port':adapter_adds, + 'boundary_negations_per_port':adapter_negs,'bridge_unit_ADD_per_port':bridges, + 'terminal_signed_swap_unit_ADD_per_port':3*signed_swaps, + 'conservative_real_scalar_primitive_allowance':total, + 'coordinate_and_phase_moves':'Explicit separate fixed movement operations; not scalar ADDs and not paid recursive calls.'} + + +def run(): + F = G.load(HERE/'frame_exchange.py','p3_contacts') + n = G.load(F.NATIVE,'p3_native_common') + packet,phases = n.load_sources() + local,pins,helpers = G.local_bindings() + formal_source = G.read(FORMAL); formal = formal_source['selected_p3_keep43'] + tariff = G.read(TARIFF); audit = G.read(AUDIT) + need(tariff['controller'] == formal, 'The native cover binds the exact priced controller') + for path,wanted in tariff['source_sha256'].items(): + need(G.digest(ROOT/path) == wanted, 'Pinned actual tariff source '+path) + for name,wanted in formal_source['source_sha256'].items(): + need(G.digest(FORMAL.parent/name) == wanted, 'Pinned formal word source '+name) + main_contacts = contacts(n,F,phases) + cover = helper_assignment(n,phases,formal,local,helpers) + endings = endpoint_normalizers(n,phases,formal) + scalar = scalar_invoice(local,formal) + need({int(k):int(v) for k,v in tariff['invoice']['paid'].items()} == cover['paid'], 'Independent complete paid invoice agrees') + need({int(k):int(v) for k,v in tariff['invoice']['targets'].items()} == cover['targets'], 'Independent productive credit agrees') + for path in (FORMAL,TARIFF,AUDIT,HERE/'global_identity_cover.py',HERE/'frame_exchange.py',F.NATIVE): + pins[str(path.relative_to(ROOT))] = G.digest(path) + return {'schema':'complete-native-p3-keep43-owner-phase-cover/1', + 'status':'PASS_COMPLETE_FINITE_NATIVE_CONTROLLER_OWNER_PHASE_INVOICE', + 'generator_sha256':G.digest(__file__),'sources':pins,'immutable_phase_sources':n.PINS, + 'main_contacts':main_contacts,'contact_count':3136,'main_endpoint_normalizers':endings, + 'cover':cover,'scalar_invoice':scalar,'root_bracket':tariff['invoice']['root_bracket'], + 'physical_order':'Endpoint input coordinate maps; R; literal serialized controller with whole-call helper adapters; L; endpoint translations; endpoint inverse coordinate maps.', + 'native_local_contract':{'forward':'D_s [[1,0],[Q^-1,1]]','backward':'D_s [[1,-Q],[0,1]]', + 'meaning':'Exact raw-input operators, valid for arbitrary prior histories and after every boundary scalar basis change.'}, + 'arbitrary_productive_input_fields':2242,'all_2856_original_helper_roles_assigned':True, + 'one_owned_center_reused_sequentially':True,'owned_center_arbitrary_at_entry_zero_at_return':True, + 'helpers_normalized_only_around_whole_native_invocations':True, + 'new_kappa':False, + 'remaining_transfer_obligations':['Finite mixed-to-uniform precompilation and ordinary supplier instantiation.', + 'Replacement precision, stock, scalar and movement constants for the resulting finite template.', + 'A compatible BIT supplier and the inherited outer analytic transfer.']} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out',type=Path,default=HERE/'P3-NATIVE-COVER.json.gz') + args = parser.parse_args() + receipt = run() + args.out.write_bytes(gzip.compress(json.dumps(receipt,sort_keys=True,separators=(',',':')).encode(),mtime=0)) + print(json.dumps({'status':receipt['status'],'targets':receipt['cover']['targets'], + 'paid':receipt['cover']['paid'],'scalar':receipt['scalar_invoice'], + 'root_bracket':receipt['root_bracket'],'sha256':G.digest(args.out)},sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/FINITE-TEMPLATE-CLOSURE.md b/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/FINITE-TEMPLATE-CLOSURE.md new file mode 100644 index 0000000000..9917ac5543 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/FINITE-TEMPLATE-CLOSURE.md @@ -0,0 +1,339 @@ +# Native closure and explicit constants for the finite uniform template + +Status: independently audited, conditional on the retained native movement, +fixed-tape, and analytic interfaces stated below. This note supplies the new +finite-template constants; it does not reuse the old supplier's scalar cap, +row reserve, or obsolete pathwise precision exponent. It complements +`AUDIT.md`, `P3-NATIVE-AUDIT.json.gz`, and `P3-COVER-AUDIT.json`. + +Apache-2.0. Substantial OpenAI assistance. The semantic completed-child +argument is the attributed argument in +[`references/semantic-bulk/pr23/semantic-bulk-17-note.tex`](../../../references/semantic-bulk/pr23/semantic-bulk-17-note.tex), +section “Linear semantic precision for this actual circuit.” Its later +explicit-constant application is also in +[`notes/stopped-product-complex.tex`](../../../notes/stopped-product-complex.tex). +The paths in the machine-readable receipt are relative to the repository +root and bind the exact reviewed versions by SHA-256. + +## 1. What has actually been instantiated + +The p3 complex unit is a complete native word, not just a histogram. The +independent audits verify its serialized scalar controller, 3,136 physical +main-contact maps and their absolute phases, 672 complete main endpoints, +2,856 actual local helper roles, causal idle windows, every paid completion, +and the final order of whole-field normalizers. Its productive targets are + +``` +{6:192, 7:56, 8:93, 9:1229, 25:448, 57:224}. +``` + +There are 2,242 independent productive fields, one explicitly owned center, +and paid children + +``` +{1:17623, 2:5065, 3:1738, 4:714, 5:254}. +``` + +All productive inputs are arbitrary. The owned center is initialized and +cleared; it is never an additional credited output. Every helper endpoint +is autonomous at the completed local boundary. Independent normalizers +therefore surround an entire local call, without changing the frames of +internal ADD instructions. + +The exact integer precompiler in `AUDIT.md` turns this unit into a finite +uniform word with parameters + +* ambient rank `N >= 2`; +* `W` productive arrays, each receiving the **full** rank-`N` transform; +* `P` rank-one paid children; +* `U` copies of the mixed unit in the completely expanded finite word; +* at most `O=U` owned centers, conservatively one per mixed-unit instance. + +For every rational `z` strictly above the mixed root and below one, the +constructive count argument provides an `N` with `P < W*N^z`. +“Finite” here means fixed before the eventual multiplication input grows. +It can be astronomically large. Neither this note nor the receipts claim +to have materialized the winning near-threshold instance. The later +`../controller/EXPLICIT-TEMPLATE-BOUNDS.md` strengthens the existence +argument to the specified complex rank `N=2^276540184361`, with uniform +saving `0.002304`; no search for a successful rank is left unperformed. +The integer recursion defines its exact finite `W,P,U`, and the constants +below are computable functions of that finite result. + +The fully materialized, depth-zero `N=57` example has `W=2242`, `P=127570`, +and `U=1`. It is a useful independent check that complementary source jobs +are really paid: `57*2242-127570=224`. This small example is not claimed to +attain the limiting mixed exponent. + +## 2. Every column count and every complete spectator field + +The local logical identities were replayed in a free noncommuting operator +word algebra. Apart from rational scalar arithmetic, the checker uses only +composition and cancellation of an operator with its recorded inverse. +For any positive integer `f`, substitute the `f`-column physical operator +for each such generator. This extends to an algebra homomorphism on the +free word algebra and preserves the checked identities. + +This is not the false assertion that tensor power is additive on arbitrary +matrix sums. The role-level scalar word is unchanged. Each physical address +generator is replaced by its column lift, while its formal products and +linear combinations are evaluated on the same independent role arrays. + +A rank-zero native monomial has the form + +``` +|x> -> i^(a+q(x)) |M*x+b>, +``` + +with invertible binary `M` and a permitted quadratic phase `q`. Its column +lift has blockwise address map `M`, translation `b` in every column, and +phase `a*f + sum_j q(x_j)` modulo four. This explicitly retains the absolute +phase. A fixed coordinate matcher in the precompiler becomes the same +fixed permutation of `f`-axis blocks. All untouched axes remain complete +spectator fields. A rank-one leaf becomes the standard rank-`f` child. + +The retained exact Clifford normal form supplies the monomial factors +around each child. The independent p3 audit checks the whole main boundary, +including the output translations required by negative powers of `C_q`. +The fixed THREE/base selection is valid for every column count: THREE/base +and THREE/extra have identical entrance and exit operators; their difference +is an internal frame and its associated warps. No layer-dependent selector +is required for the endpoint contract. + +For any integer input width `e=N*f+r`, first apply the `r=2`, `B=P+E`, and `E>=64`, + +``` +2*B*(N-1) >= P+E, +2*B*f+P*f+E <= 2*B*N*f <= 2*B*e. +``` + +Induction gives `A(e)<=2B e`. Completed disjoint selected-axis pieces have +total width at most `d`. The retained prefix kernels, outer phases and +normalization add at most `18d`, giving + +``` +A_layer <= (2*B+18)*d < C0*d. +``` + +Every calculation remains on one fixed fine grid. A child is never rounded, +compressed, or re-encoded at return. The change is to the proof's bound on a +completed value, not to its stored representation. Other fields remain +parked while the child executes. This is why the linear semantic bound +survives a huge scalar word and why the older pathwise `C1>1` estimate is +unnecessary. + +The stopping rule can be any fixed rational `0=2N`, every internal call has the required positive `f`; +the completed-leaf estimate remains `8e` at the stopping leaves. No old +numerical cutoff is carried over. + +### An effective threshold, including enormous constants + +Suppose `d<=c*p^epsilon`, with fixed `c>=1` and rational +`epsilon=a/b` in `(0,1)`. Let `L` be the binary bit length of +`4*C0*ceil(c)` and choose + +``` +t = max(4, ceil(b*L/(b-a))), p0 = 2^t. +``` + +For all `p>=p0`, `p^(1-epsilon)>4*C0*c`, so the integer guard +`Delta=C0*d` is at most `p/4`. Signed components with `p+Delta` fractional +bits and `Delta+3` magnitude/sign bits have width + +``` +p+2*Delta+3 <= 2p. +``` + +The audit emits `p0` as a compressed power of two. It does not try to +allocate that many bits. This construction proves the eventual `O(p)` word +bound for the new finite template, including the current outer choice +`epsilon=99999/100000`. Huge fixed constants change `p0`, not `C1` or the +power in the final exponent inequalities. + +## 5. Productive stock, owned storage, and native tape closure + +For the ordinary uniform complex word, let + +``` +D(e)=0 if e=W^D(d)` for `K>=1`. Pad complete rows once to the next multiple +of `W^D(d)`. The padding factor is below two. Every descendant then has +exactly `1/W` of its parent's productive volume and enough divisibility for +its remaining depth, with complete active, control and spectator fields. +All-row endpoint correctness restores appended zero rows to zero. + +Owned storage contributes no factor to productive output credit. A safe +choice is one full center field per finite mixed-unit instance, namely +`O=U`. At an ordinary recursion node each such field has the same shape as +one productive role stream, of volume `V/W`. Initialize, retain and clear +it as its actual word prescribes. If simultaneously suspended units keep +live centers, they receive distinct banks. Reusing one bank per recursion +depth would not suffice. Owned-space scans and parking cost fixed multiples +of volume; paid calls on those banks are already in `P`. + +The integer audit checks row divisibility and one-time padding at several +floor-depth boundaries. It also gives an explicit sufficient threshold +for `q00`. Concavity shows that the source complements leave at least +`eta*sum_s w_s*s^z0`, where `eta=z0*m^(z0-1)>1/4`. Choose + +``` +H0 = ceil((3+4*delta)/(h*delta)), +n0 = 2^H0, +A = n0^(1-z0). +``` + +Then the exit coefficient is at most `1/8` for every `n>=n0`. The base +bound `L(n)<=n` covers `n<=n0`; strong induction gives `L(n)<=A*n^z0` +for every rank. Finally + +``` +H1 = floor(H0*(1-z0)/(z-z0))+1, +N = 2^H1 +``` + +ensures `L(N) -> i^(a+q(x)) |M*x+b>` lifts to the same address recipe on each column, +with phase `a*f+sum_j q(x_j)` modulo four. Complete spectator coordinates +remain present. This substitutes physical operators in the already checked +role-level linear identity; it does not assume tensor power is additive. +The final normalizers make every productive endpoint the canonical +positive tensor job. Coordinate permutations place these on any required +disjoint axes. Remainder axes at an arbitrary width receive individual +paid kernels and remain completed spectators of the lifted word. + +[`FINITE-TEMPLATE-CLOSURE.md`](FINITE-TEMPLATE-CLOSURE.md) supplies fresh +coefficient, owned-space, row and precision constants. In particular, for +the completely expanded word with rank `N`, productive width `W`, rank-one +paid count `P`, unit count `U`, and conservative owned count `O=U`, put + +``` +Z = W+O, +G = 1494376*U, +E = 64*(Z+N+P+G+1)^3, +B = P+E, +C0 = 32*N*B^2, +C1 = 1. +``` + +The completed-child semantic recurrence is +`A(e)<=A(floor(e/N))+P*floor(e/N)+E`. It gives `A(e)<=2B*e`; completed +disjoint outer pieces and retained phases fit below `C0*d`. This measures +completed returned values without rounding or re-encoding children. +The large temporary values inside a child are not also unfinished parent +operands. All storage stays on one common fine grid. + +For `d<=c*p^epsilon` with `epsilon<1`, the explicit threshold in that note +ensures `C0*d<=p/4`, hence total component width at most `2p`. The new `C0` +may be enormous, but it is fixed. There is no inherited small numerical +guard constant and no appeal to the obsolete pathwise precision exponent. + +## 4. BIT uses one delayed ambient cover and one common weight + +The argument reviewed is +[`../bit/DELAYED-COVER-BRIDGE.md`](../bit/DELAYED-COVER-BRIDGE.md). +`BIT-BRIDGE-AUDIT.json` supplies a separate exact implementation audit. +The essential order is to precompile the entire finite projector program +first, and only then apply a single whole-ambient `GL_N` cover and external +weight. Internal jobs are not prematurely lowered to differently weighted +canonical children. + +For a rational idempotent `P` in ambient dimension `N`, write + +``` +D_P = [[I-P, P*C_N], [C_N*P, I-C_N*P*C_N]], +Q_S = diag(S, C_N*S*C_N). +``` + +Direct multiplication gives `Q_S D_Q Q_S^-1=D_(SQS^-1)` and +`D_P D_(I-P)=D_I`, including nonsymmetric projectors. Equal-rank rational +idempotents admit a fixed rational matcher `S` by matching image and kernel +bases. After the finite program is fixed, choose an odd prime avoiding all +its finitely many denominators, determinants and rank witnesses. All lifts +use these same rational matrices, so this choice is independent of the +eventual column multiplicity. + +Use the full cover `g in GL_N(Z/q^w Z)`. To match a parent request `P` to a +child endpoint `Q`, route that child's complete role fiber by `g -> gS`, +execute the entire child, and undo the route. Its autonomous endpoint is +exactly `D_(gPg^-1)`. Separate target roles may use separate matchers: each +route is a bijection of a full fiber carrying arbitrary data. Native port +charts and local helper ownership remain inside the schematic program; +they are not silently discarded when the ambient dimension grows. + +This is a paired whole-job construction. It does not implement arbitrary +isolated dense address maps by renaming rows, and it does not assume a +generic RAM-to-tape simulation. + +The inherited weight `A` is common to all fresh roles and independent of +the current complete cover field. Consequently `Lambda_A=diag(A,I)` +commutes with every internal role route and every pointwise scalar/COPY +operation. The completed source/complement endpoint is therefore the +required weighted full interchange. Only final rank-one leaves are lowered +to weighted canonical children. Their pivot weights depend on this parent +cover row, which is ancestor data when the child's fresh fields are exposed. +Different leaves can have different weights without violating the common +weight requirement inside any one child. + +At `f` columns the inherited reversed pairing is essential. The actual +lift uses `P tensor I_f` with full tail reversal `C_(Nf)`, or equivalently +conjugates the straightforward tensor lift by the blockwise `C_f` reversal. +The independent audit checks this on nonsymmetric rational projectors and +rejects dropping that reversal. It also checks arbitrary common external +weights depending on axes and columns. Current-cover-dependent weights +remain forbidden. + +The independent native replay covers all 636 rational frames, 2,386 nested +MOVE pairs, both 661-column local words, 111 ports and 666 embedded charts, +3,073 helper owners, and all 63 paid COPY-center calls. The rank-50 full-job +example has `W=3739`, `P=186725` and surplus `50*3739-186725=225`. +Additional checks include nonsymmetric rational matchers, a genuine +non-field ring, and 7,776 inverse/carry tests over `GL_2(Z/9Z)`. The last +tests retain all q-adic digits of the matcher; dropping its higher digits +has an explicit failing control. + +### Paid cover, atom conversion, and ordinary endpoint + +Right multiplication on `g=g0+qG1` is a finite low-type permutation plus a +fixed affine high-matrix map with its correct carry. The retained native +cover-routing lemma charges it as `O(V*w^(1-a_old))`. The finite number of +routers changes the constant, not this exponent. All bad generic classes +receive their actual fallback. With the explicit choice + +``` +q > 25,600,000*N^5 +``` + +and the finite denominator exclusions, the complete covered moment is at +most `400001/400002<1`. This includes the full fallback bill without +subtracting the good-class calls or assuming bad classes are independent. + +Use atom width `w=ceil(e^0.003)` and the retained old ordinary saving +`a_old=384599/10^10`. The resulting saving is + +``` +(1-0.003)*0.002750 + 0.003*a_old + = 27418653797/10^13 + > 0.0027. +``` + +The linear adapters are paid because `0.003` exceeds this saving. The +borrowed row stock satisfies `log S(e)=O(e^0.003 log e)` and is lower order +because `0.003<1-a_BIT`. Its complete borrowed field is restored. Padding +of full rows is performed once for the whole invocation and removed after +the completed endpoint. Numeric padding to atom lengths costs only a +fixed `q`-dependent factor. + +The ordinary wrapper uses two completed reversed calls and three charged +bank additions, in chronological order: + +``` +D <- D-H; F_n; D <- D+H; F_n; D <- H-D. +``` + +For `(H,D)` this gives successively `(H,D-H)`, `(C(D-H),CH)`, +`(C(D-H),CD)`, `(D,D-H)`, `(D,H)`. Thus it really supplies the ordinary +interchange, at constant multiplicative overhead and `O(Vn)` extra work. +No unshown batch or free half-swap is required. + +## 5. The changed row reserve fits the support-local outer wrapper + +This is an essential functional obligation, not another numerical moment +test. The applicable retained wrapper is the global support-local wrapper +in `vendor/pr1673/capped-phase-fusion/SUPPLIER-SUPPORT-AUDIT.md` and its +`SUPPORT-ADVERSARIAL-AUDIT.md`, under the current outer package. Its completed +supplier calls cover the **whole global dyadic tensor**. Calling separately +inside fixed coarse-label microboxes would not satisfy the interface. + +For a phase with `h` selected bits, take `G=4*ceil(log2 p)+6` and complete +neighborhoods of width `K=128G`, one inside each selected original axis. +The axis length grows like `p^(1-epsilon)`, so every fixed multiple of +`log p` fits eventually. Exposing the complete neighborhoods moves at most +`2hK` bit positions. Native binary matrices have fixed rank, so their +column lifts factor into finitely many parallel row additions on these +selected bits. Unit phases have fixed formulas of the same selected-bit +support. They do not introduce dependence on unrelated coarse labels. + +Reserve whole selected chunks for the two front controls, back control and +row prefix. **Do not first transform their selected bits.** The completed +active invocation is identity on every reserved coordinate for arbitrary +contents; those selected-axis kernels can be completed in later shrinking +phases. The finite guard condition used by the retained router is directly +satisfied by `K=128G`; no claim is made that this constant ratio satisfies +the older, stronger wording `K/log p -> infinity`. + +The new BIT stock cannot simply be inserted into the old statement +`O(log h)` for all nested reserves. Its own ordinary full-field interface +supplies its rows internally. Alternatively, the following conservative +external product bound explicitly covers simultaneous stock. A BIT call +has width at most `C*h*(log p)^2`. Its logarithmic stock is +`O(h^0.003*(log p)^(2*0.003+1))`. Including a further `O(log h)` nesting +factor and the complex stock gives, after enlarging one fixed constant, + +``` +q0(h,p) <= C*(log2 h + h^0.003*(log2 p)^3 + 1) +``` + +reserved complete chunks. This bound retains the **product** of stock +requirements; using their maximum would be invalid. Since `0.003<1`, there +is an explicit fixed polylogarithmic threshold `H(p)` above which +`q0(h,p)+O(1)<=h/64`. For example one may enlarge a fixed multiple of +`[1024*C*(log2 p)^3]^(1/(1-0.003))` to cover the logarithmic term and all +finite-template base thresholds. Consequently + +``` +R(h) <= 3h/128 + q0(h,p) + O(1) <= h/16 +``` + +for all sufficiently large active phases. The remaining `h<=H(p)` bits are +handled individually in `O(V*polylog p)` time. Thus successive active +widths shrink by at least a factor 16, and their sublinear costs sum to a +constant multiple of the first phase's cost. + +Each phase pads its complete row count once by a factor below two. Its +completed endpoint preserves the row coordinate, so appended zero rows +can be deleted before inverse exposure and before the next phase. This +prevents an accumulating factor of two per phase. The exposure is restored +before any next diagonal depending on coarse labels is applied. + +The support router's additional control reservoirs occupy +`O(h*(log p)^2)` positions and fit the full `Theta(p)`-bit tensor because +`group_beta<1`. A complete untouched `log^2 p` suffix is chosen and placed +first for short-record grouping; all subsequent reservoirs and routers +stay in its complement. The retained full-span route handles the bounded +regime where this gap argument fails. A single original axis is never +asked to hold all of the `hG` control bits. + +## 6. Fresh constants satisfy every changed outer interface + +The actual parameter point is in +[`../controller/OUTER-PARAMETERS.json`](../controller/OUTER-PARAMETERS.json). +The independent audit reproduces its nine cost rows directly, without +importing either outer ledger. It also checks the functional inequalities +needed above, including + +``` +epsilon = 0.99999 < 1, +group_beta = 0.99997 < epsilon, +1-epsilon-r0 > 0, +1-(2*xi-2)-r0-group_beta > 0, +group_beta*(1-0.003) > 0. +``` + +The first two absorb every new fixed semantic, movement and row constant; +the next two retain the precision and fine-prime spare powers. The last +ensures the changed BIT reserve is sublinear in the active grouped width, +even after the polylogarithmic factors above. The stopped supplier's +internal and leaf exponents are strictly below the selected `lambda` and +`lambda_prime`, respectively. The effective BIT saving is below both the +actual ordinary BIT saving and the selected complex saving. + +Every compiled-word constant, rational denominator and description degree +is fixed before the input length varies. Polynomial description/preparation +costs are absorbed by the retained complete superpolynomial record fibers +when `epsilon<1`, after increasing an effective threshold. A finite program +on fixed tapes remains a native program on fixed tapes; this argument does +not hide random-access gathering inside the coefficient allowance. + +The nearly critical halo calculation uses the retained explicit-metadata +branch with `halo_power=48` and `core_power=128`. It does not use the old +`K0^2=o(p)` shortcut, which is unavailable near this parameter point. The +boundary exponent uses the exact Strassen comparison `7^16<2^45`; no new +unstated stable-matrix algorithm is required. + +The outer analytic decomposition, ordered movement implementations, +fixed-tape model, prime padding, and exact integer recovery are the same +conditional hypotheses as in the reviewed outer package. The changed +mixed-job, native adapter, weighted-child, row-stock and semantic-precision +obligations have been supplied explicitly here. The conclusion is therefore +a source-bound **conditional research result** at `kappa=0.0023` under +those inherited hypotheses. It is not a claim of practical constants or of +an unconditional theorem. + +## 7. Reproducible independent checks + +From the repository root: + +```sh +python3 -B research/kappa-rebuild/transfer-audit/bit_bridge_audit.py +python3 -B research/kappa-rebuild/transfer-audit/outer_transfer_audit.py +``` + +The first binds the independent BIT checks to the exact current native and +bridge sources. The second uses its own 256-bit directed rational grid, +finite-series logarithm/exponential bounds, exact rank comparisons, and +fresh outer equations. `OUTER-TRANSFER-AUDIT.json` records all source hashes, +strict intervals, compressed ranks, nine outer savings and functional gaps. +The directory manifest binds this written audit and the complete source set. diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_cover_audit.py b/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_cover_audit.py new file mode 100644 index 0000000000..d9b44b662a --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_cover_audit.py @@ -0,0 +1,163 @@ +#!/usr/bin/env python3 +"""Adversarial replay of p3 physical ownership, normalizer order and invoice. + +Apache-2.0; substantial OpenAI assistance. Separate from the cover producer. +""" +from collections import Counter, defaultdict +from fractions import Fraction +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +from finite_dag_audit import Rule, Compiler + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +INPUT = HERE.parent/'controller/P3-NATIVE-COVER.json.gz' + + +def need(test, message): + if not test: + raise AssertionError(message) + + +def digest(path): + return sha256(Path(path).read_bytes()).hexdigest() + + +def read(path): + raw = Path(path).read_bytes() + return json.loads(gzip.decompress(raw) if str(path).endswith('.gz') else raw) + + +def main(): + receipt = read(INPUT) + need(digest(HERE.parent/'controller/p3_native_cover.py') == receipt['generator_sha256'], 'Exact cover generator') + for path, expected in receipt['sources'].items(): + need(digest(ROOT/path) == expected, 'Pinned source '+path) + independent = read(HERE/'P3-NATIVE-AUDIT.json.gz') + formal = read(HERE.parent/'bit/COMPLEX-CONTROLLER-FACTOR.json')['selected_p3_keep43'] + ours = {(row['stage'],row['port']):row for row in independent['contacts']} + for row in receipt['main_contacts']: + other = ours[row['stage'],row['port']] + need(all(row[key] == other[key] for key in ('maps','pair','direction')), 'Independent actual contact recipes agree') + ours_ends = {(row['output_role'],row['port']):row for row in independent['endpoint_normalizers']} + main_ranks = {} + for row in receipt['main_endpoint_normalizers']: + key = row['original_input_role'],row['port'] + other = ours_ends[key] + need(row['target_rank'] == other['rank'] and row['positive_axes'] == other['target_axes'], 'Independent target axes') + need(row['output_translation_before_inverse_map'] == other['physical_translation_after'], 'Translation precedes output inverse') + columns, inverse_rows = row['input_coordinate_columns'],row['output_coordinate_inverse_rows'] + need(columns[:row['target_rank']] == row['positive_axes'], 'Input conjugation has exact required columns') + for j, column in enumerate(columns): + decoded = sum(((r & column).bit_count() & 1) << i for i,r in enumerate(inverse_rows)) + need(decoded == 1 << j, 'Output map is inverse of actual input map') + role,port = key + main_ranks[f'{"Y" if role%2 else "X"}{role//2}:{port}'] = row['target_rank'] + need(receipt['physical_order'] == 'Endpoint input coordinate maps; R; literal serialized controller with whole-call helper adapters; L; endpoint translations; endpoint inverse coordinate maps.', + 'The emitted order realizes G^-1 X L M R G') + cover = receipt['cover'] + helpers_path = HERE.parent/'complex/fresh-certificates/THREE-base-HELPER-BOUNDARIES.json.gz' + helper_width = {row['role']:row['width'] for row in read(helpers_path)['recipes']} + stage_table = {event[1]:(event[2], 'backward' if event[3] else 'forward') + for event in formal['physical_events'] if event[0]=='LOCAL'} + by_stage = defaultdict(list) + by_window = defaultdict(list) + for row in cover['helper_bindings']: + stage = row['stage'] + need(helper_width[row['role']] == row['width'] == len(row['axes']), 'Actual native helper width, not a rank-only substitute') + contract = row['whole_helper_boundary'] + need(contract['direction'] == stage_table[stage][1] and contract['role'] == row['role'] and + contract['provider'] == 'THREE-base', 'Exact oriented helper normalizer') + by_stage[stage].append(row) + if row['kind'] == 'original_idle': + by_window[row['window_index'],row['owner']].append(row) + matrix = cover['owner_coordinate_maps'][row['coordinate_map']] + need(matrix['columns'][:row['width']] == row['axes'], 'Helper conjugation reaches actual idle axes') + for j,column in enumerate(matrix['columns']): + decoded = sum(((r & column).bit_count() & 1) << i for i,r in enumerate(matrix['inverse_rows'])) + need(decoded == 1 << j, 'Helper route inverse') + for stage, rows in by_stage.items(): + need({row['role'] for row in rows} == set(range(224,632)) and len(rows)==408, 'All local helper roles used exactly once') + need(len({row['owner'] for row in rows}) == 408, 'Helper physical owners injective') + active_pair = stage_table[stage][0] + active = {f'{side}{active_pair}:{port}' for side in ('X','Y') for port in range(112)} + need(not active & {row['owner'] for row in rows}, 'No helper borrows a live main register') + events = formal['physical_events'] + paid_by_owner = defaultdict(list) + for row in cover['paid_residuals']: + need(row['rank'] == len(row['axes']) and 1 <= row['rank'] <= 5, 'Actual completion width') + paid_by_owner[row['owner'],row['after_stage'],row['kind']].append(row) + for window in cover['windows']: + stages, pair = window['stages'],window['pair'] + idle_index = next(i for i,event in enumerate(events) if event == ['IDLE',pair,stages]) + first_index = next(i for i,event in enumerate(events) if event[0]=='LOCAL' and event[1]==min(stages)) + for event in events[first_index:idle_index]: + if event[0] == 'LOCAL': + need(event[2] != pair, 'Owned idle field is never an active local input in the window') + elif event[0] == 'ADD': + need(event[1]//2 != pair and event[2]//2 != pair, 'No interleaved bridge reads or writes a partially completed idle') + elif event[0] == 'SIGNED_SWAP': + need(event[1]//2 != pair, 'No swap before idle completion') + assigned = sorted(by_window[window['index'],window['owner']], key=lambda row:row['stage']) + need([(row['stage'],row['width']) for row in assigned] == + [(s,w) for s,w in zip(stages,window['widths']) if w], 'Actual window slice assignment') + pieces = [axis for row in assigned for axis in row['axes']] + rests = paid_by_owner[window['owner'],max(stages),'idle_remnant'] + pieces += [axis for row in rests for axis in row['axes']] + need(pieces == window['axes'], 'Every idle axis is funded once in chronological order') + fresh = {row['owner']:row for row in cover['fresh_outputs']} + fresh_binding = {row['owner']:row for row in cover['helper_bindings'] if row['kind']=='fresh'} + need(len(fresh)==len(fresh_binding)==1570 and set(fresh)==set(fresh_binding), 'Every fresh field is an independent actual helper') + for name, row in fresh.items(): + pieces = list(fresh_binding[name]['axes']) + pieces += [axis for extra in paid_by_owner[name,row['stage'],'fresh_topup'] for axis in extra['axes']] + need(pieces == [1 << i for i in range(row['target_rank'])], 'Every fresh full target includes paid topup axes') + local_receipt = read(HERE.parent/'complex/full-identity-certificates/RESULT.json') + native = read(HERE.parent/'complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz') + rounds = [] + native_scalar = 0 + for stage in range(7): + pair,direction = stage_table[stage] + native_scalar += local_receipt['providers']['THREE-base']['split_replays'][direction]['independent_native_replay']['conservative_real_scalar_primitive_allowance'] + owner = {row['role']:row['owner'] for row in by_stage[stage]} + for event in native[direction]: + if event[0]=='climb': + role=event[2] + name = f'X{pair}:{role}' if role<112 else f'Y{pair}:{role-112}' if role<224 else owner[role] + rounds.append((event[-1],name)) + elif event[0]=='center': + rounds.append((event[-1],'owned-C0')) + rounds += [(row['rank'],row['owner']) for row in cover['paid_residuals'] if row['after_stage']==stage] + roles = tuple(sorted(main_ranks.items()))+tuple((name,row['target_rank']) for name,row in sorted(fresh.items())) + rule = Rule(roles,tuple(rounds)) + need(rule.targets == Counter({int(k):v for k,v in cover['targets'].items()}), 'All productive ranks independently counted') + need(Counter(rank for rank,name in rounds) == Counter({int(k):v for k,v in cover['paid'].items()}), 'Every paid child independently counted on its actual owner') + scalar = native_scalar+112*((22+12+9)*8+8*2) + need(scalar == receipt['scalar_invoice']['conservative_real_scalar_primitive_allowance'] == 1147304, + 'Complete arithmetic invoice includes all six swap negations') + compiler = Compiler(rule) + compiled = compiler.compile(57) + need(compiled['width']==2242 and compiled['leaves']==127570 and compiled['units']==1, 'Full rank57 completion including all partial-source complements') + result = {'schema':'independent-p3-owner-order-and-complete-tariff-audit/1', + 'status':'PASS_ALL2856_HELPERS_CAUSAL_WINDOWS_MAIN_NORMALIZER_ORDER_AND_COMPLETE_BILL', + 'source_sha256':digest(__file__),'input_sha256':digest(INPUT), + 'main_phase_audit_sha256':digest(HERE/'P3-NATIVE-AUDIT.json.gz'), + 'native_local_source_bound':True,'helper_bindings':2856,'independent_productive_fields':2242, + 'targets':dict(sorted(rule.targets.items())), 'paid':dict(sorted(Counter(r for r,n in rounds).items())), + 'owned_center_uncredited':1,'arithmetic_allowance':scalar, + 'uniform_rank57':{key:str(value) if isinstance(value,Fraction) else value + for key,value in compiled.items() if key!='ordered_requirements'}, + 'uniform_rank57_event_graph':compiler.trees[57].summary(), + 'limits':['Ideal native finite unit and finite integer compilation audit.', + 'The rank57 depth-zero supplier is not asserted to attain the mixed exponent.', + 'Large fixed-template existence, updated precision/stock and outer transfer are separate documented steps.']} + (HERE/'P3-COVER-AUDIT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({'status':result['status'],'targets':result['targets'],'paid':result['paid'], + 'scalar':scalar,'uniform_full57_paid1':compiled['leaves']})) + + +if __name__=='__main__': + main() diff --git a/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_native_audit.py b/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_native_audit.py new file mode 100644 index 0000000000..0f3a4067a4 --- /dev/null +++ b/research/pr4359-p7-padding/source/research/kappa-rebuild/transfer-audit/p3_native_audit.py @@ -0,0 +1,283 @@ +#!/usr/bin/env python3 +"""Independent exact p3 Laurent replay, native contacts, and output phases. + +Apache-2.0; substantial OpenAI assistance. This reads the proposed event and +adapter word, not its polynomial generator. Native local words are separately +authenticated. Helper placement and complete recursive tariffs are caller +obligations, not inferred from the main output factorization. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from itertools import combinations +from pathlib import Path +import gzip +import importlib.util +import json +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +INPUT = HERE.parent/'bit/COMPLEX-CONTROLLER-FACTOR.json' +NATIVE_COMMON = ROOT/'research/kappa-next-regime/direct-decoder/native_common.py' +LOCAL_RECEIPT = HERE.parent/'complex/full-identity-certificates/RESULT.json' +AXES = tuple(1 << i for i in range(73)) + + +def need(test, message): + if not test: + raise AssertionError(message) + + +def digest(path): + return sha256(Path(path).read_bytes()).hexdigest() + + +def read(path): + data = Path(path).read_bytes() + return json.loads(gzip.decompress(data) if str(path).endswith('.gz') else data) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + result = importlib.util.module_from_spec(spec) + spec.loader.exec_module(result) + return result + + +def add(a, b, coefficient=1): + out = a.copy() + for word, value in b.items(): + out[word] = out.get(word, Q(0))+coefficient*value + if not out[word]: + del out[word] + return out + + +def shift(polynomial, delta, coefficient=1): + return {tuple(a+b for a, b in zip(word, delta)):coefficient*value + for word, value in polynomial.items()} + + +def replay(case): + count = 2*case['pairs'] + variables = len(case['coefficient_variables']) + zero = (0,)*variables + matrix = [[{zero:Q(i == j)} if i == j else {} for j in range(count)] for i in range(count)] + # Right boundary is the first physical operation. + for event in case['right_program']+case['physical_events']+case['left_program']: + kind = event[0] + if kind == 'ADD': + _, destination, source, coefficient = event + matrix[destination] = [add(a, b, Q(coefficient)) + for a, b in zip(matrix[destination], matrix[source])] + elif kind == 'SCALE': + _, role, coefficient = event + matrix[role] = [{word:Q(coefficient)*value for word, value in row.items()} for row in matrix[role]] + elif kind == 'SWAP': + _, a, b = event + matrix[a], matrix[b] = matrix[b], matrix[a] + elif kind == 'SIGNED_SWAP': + _, a, b = event + matrix[a], matrix[b] = matrix[b], [{word:-value for word, value in row.items()} for row in matrix[a]] + elif kind == 'IDLE': + _, pair, stages = event + delta = (0,)+tuple(int(s in stages) for s in range(variables-1)) + for role in (2*pair, 2*pair+1): + matrix[role] = [shift(row, delta) for row in matrix[role]] + elif kind == 'LOCAL': + _, stage, pair, backward = event + x, y = 2*pair, 2*pair+1 + q_delta = (1 if backward else -1,)+(0,)*(variables-1) + destination, source, coefficient = (x, y, -1) if backward else (y, x, 1) + matrix[destination] = [add(a, shift(b, q_delta), coefficient) + for a, b in zip(matrix[destination], matrix[source])] + d_delta = tuple(int(i == stage+1) for i in range(variables)) + for role in (x, y): + matrix[role] = [shift(row, d_delta) for row in matrix[role]] + else: + raise AssertionError('Unknown actual event '+kind) + wanted = [[{tuple(case['exact_diagonal_monomials'][i]):Q(1)} if i == j else {} + for j in range(count)] for i in range(count)] + need(matrix == wanted, 'Every Laurent coefficient of the literal boundary/controller word') + return matrix + + +def act(columns, vector): + out = 0 + while vector: + low = vector & -vector + out ^= columns[low.bit_length()-1] + vector ^= low + return out + + +def normalize(terms): + result = Counter() + for axis, coefficient in terms: + result[axis] += coefficient + return tuple(sorted((axis, value % 4) for axis, value in result.items() if axis and value % 4)) + + +def evaluate(terms, address): + return sum(coefficient*((axis & address).bit_count() & 1) for axis, coefficient in terms) % 4 + + +def affine_contact(old, new, columns, points, cache): + moved = tuple((act(columns, axis), coefficient) for axis, coefficient in old) + delta = [(evaluate(new, axis)-evaluate(moved, axis)) % 4 for axis in AXES[:57]] + need(all(value % 2 == 0 for value in delta), 'Native contact has no missing Fourier rank') + translation = sum((value//2) << i for i, value in enumerate(delta)) + error = normalize(list(moved)+[(translation, 2)]+[(axis, -coefficient) for axis, coefficient in new]) + if error not in cache: + need(all(evaluate(error, point) == 0 for point in points), 'Complete native quadratic phase') + cache.add(error) + inverse = tuple(sum(((columns[j] >> i) & 1) << j for j in range(73)) for i in range(73)) + need(all(act(columns, inverse[i]) == act(inverse, columns[i]) == AXES[i] for i in range(73)), + 'Actual route is orthogonal and explicitly inverted') + inverse_translation = act(inverse, translation) + inverse_error = normalize([(act(inverse, axis), coefficient) for axis, coefficient in new]+ + [(inverse_translation, 2)]+[(axis, -coefficient) for axis, coefficient in old]) + if inverse_error not in cache: + need(all(evaluate(inverse_error, point) == 0 for point in points), 'Inverse contact absolute phase') + cache.add(inverse_error) + return {'owner_columns':list(columns), 'inverse_owner_columns':list(inverse), + 'physical_shift':translation, 'inverse_physical_shift':inverse_translation, + 'global_phase_Z4':0} + + +def extend(axes, dimension=57): + basis = {} + columns = [] + + def insert(vector): + value = vector + for pivot in sorted(basis, reverse=True): + if value >> pivot & 1: + value ^= basis[pivot] + if not value: + return False + basis[value.bit_length()-1] = value + columns.append(vector) + return True + + need(all(insert(axis) for axis in axes), 'Independent actual target axes') + for axis in AXES[:dimension]: + insert(axis) + need(len(columns) == dimension, 'Invertible endpoint coordinate extension') + return columns + + +def main(): + receipt = read(INPUT) + for name, expected in receipt['source_sha256'].items(): + need(digest(INPUT.parent/name) == expected, 'Actual proposed Laurent-source pin') + case = receipt['selected_p3_keep43'] + need(case['pairs'] == 3 and case['keep_idle_mask'] == 43, 'Selected actual controller') + replay(case) + native = read(LOCAL_RECEIPT) + provider = native['providers']['THREE-base'] + for name, expected in provider['artifacts'].items(): + need(digest(LOCAL_RECEIPT.parent/name) == expected, 'Authenticated actual native word') + need(provider['all_632_persistent_inputs_arbitrary'] and provider['all_408_helpers_autonomous'], + 'Native unit accepts arbitrary independent raw fields') + common = load(NATIVE_COMMON, 'p3_audit_native_source') + packet, phases = common.load_sources() + points = (0,)+AXES[:57]+tuple(a ^ b for a, b in combinations(AXES[:57], 2)) + phase_cache = set() + contacts = [] + stages = [(event[1], event[2], event[3]) for event in case['physical_events'] if event[0] == 'LOCAL'] + need([s for s, pair, backward in stages] == list(range(7)), 'All seven chronological native stages') + for stage, pair, backward in stages: + sign = -1 if backward else 1 + spectator = tuple((axis, 1) for axis in AXES[9:9+8*stage]) + previous = tuple((axis, 1) for axis in AXES[:9+8*(stage-1)]) if stage else () + completed = tuple((axis, 1) for axis in AXES[:9+8*stage]) + for port, data in enumerate(phases['recipes']): + q = data['q'] + route = tuple(common.source_route(phases, stage, port)) + need(route[57:] == AXES[57:] and all(x < 1 << 57 for x in route[:57]), 'Fixed ambient57 route') + need(all(act(route, route[i]) == AXES[i] for i in range(73)), 'Port route cancels on an identity shear') + raw_x0 = ((q, 1),) if stage == 0 else previous + raw_y0 = () if stage == 0 else previous+((q, -1),) + local_x0 = spectator+((q, sign),) + local_y0 = spectator + local_x1 = spectator+tuple((axis, sign) for axis in AXES[:9]) + local_y1 = local_x1+((q, -sign),) + old_new = {'entry_X':(raw_x0, local_x0), 'entry_Y':(raw_y0, local_y0), + 'exit_X':(local_x1, completed), 'exit_Y':(local_y1, completed+((q, -1),))} + maps = {name:affine_contact(old, new, route, points, phase_cache) + for name, (old, new) in old_new.items()} + contacts.append({'stage':stage, 'pair':pair, 'port':port, + 'direction':'backward' if backward else 'forward', 'maps':maps}) + endpoints = [] + ranks = Counter() + omitted_translation_rejected = 0 + for port, data in enumerate(phases['recipes']): + q = data['q'] + for output, term in enumerate(case['exact_diagonal_monomials']): + q_power, stages = term[0], term[1:] + terms = [(q, q_power)] + if stages[0]: + terms += [(axis, 1) for axis in AXES[:9]]+[(q, -1)] + for stage in range(1, 7): + if stages[stage]: + terms += [(axis, 1) for axis in AXES[9+8*(stage-1):9+8*stage]] + axes = list(AXES[:9]) if stages[0] else [q] + for stage in range(1, 7): + if stages[stage]: + axes += list(AXES[9+8*(stage-1):9+8*stage]) + translation = q if q_power == -1 else 0 + need(q_power in (-1, 1), 'Only exact free Q-square repair is used') + wanted = tuple((axis, 1) for axis in axes) + error = normalize(terms+[(translation, 2)]+[(axis, -1) for axis in axes]) + need(all(evaluate(error, point) == 0 for point in points), 'Full exact endpoint including phase') + if translation: + wrong = normalize(terms+[(axis, -1) for axis in axes]) + need(any(evaluate(wrong, point) for point in points), 'Missing Q-square repair changes the operator') + omitted_translation_rejected += 1 + columns = extend(axes) + endpoints.append({'port':port, 'output_role':output, 'rank':len(axes), + 'physical_translation_after':translation, + 'target_axes':axes, 'canonical_to_target_columns':columns, + 'exact_absolute_phase':True}) + ranks[len(axes)] += 1 + need(ranks == Counter({25:448,57:224}), 'Actual positive canonical main target inventory') + boundary_counts = Counter(event[0] for event in case['left_program']+case['right_program']) + need(boundary_counts == Counter({'ADD':4,'SWAP':6,'SCALE':2}), 'Literal scalar boundary inventory') + need(all(Q(event[-1]) in (1,-1) for event in case['left_program']+case['right_program'] + if event[0] in ('ADD','SCALE')), 'Boundary scalars are dyadic units') + output = {'schema':'independent-p3-native-Laurent-boundary-binding/1', + 'status':'PASS_LITERAL_LAURENT_NATIVE_CONTACTS_AND_ALL672_MAIN_OUTPUT_PHASES', + 'source_sha256':digest(__file__), 'proposed_factor_sha256':digest(INPUT), + 'native_local_receipt_sha256':digest(LOCAL_RECEIPT), + 'native_route_source_sha256':digest(NATIVE_COMMON), + 'immutable_phase_sources':common.PINS, + 'literal_Laurent_coefficient_replay':True, + 'native_local_contract':{'forward':'D_s * [[1,0],[Q^-1,1]]', + 'backward':'D_s * [[1,-Q],[0,1]]', + 'D0':'F9 * Q^-1', 'Ds_for_s_positive':'C on fresh eight axes', + 'arbitrary_raw_inputs':True, + 'derivation':'Native exact reference conjugation; equal involutive port routes cancel on the identity-response shear.'}, + 'contacts':contacts, 'contact_count':len(contacts)*4, + 'inverse_contacts_checked':len(contacts)*4, + 'phase_determining_addresses':len(points), 'unique_phase_patterns':len(phase_cache), + 'canonical_main_targets':dict(sorted(ranks.items())), 'endpoint_normalizers':endpoints, + 'missing_endpoint_translation_controls_rejected':omitted_translation_rejected, + 'boundary_scalar_inventory':dict(boundary_counts), + 'arithmetic_only_boundary_allowance_per_port':{'unit_ADD':22,'negate':8, + 'real_scalar_primitives':22*8+8*2}, + 'alternative_boundary_implementation':'Six whole-role permutations, four unit ADD, two negations, with fixed movement charged separately.', + 'limits':['Independent native local binding and main endpoint closure only.', + 'Helper owner windows, complete paid tariffs and outer precision are separate obligations.', + 'No new kappa is claimed.']} + destination = HERE/'P3-NATIVE-AUDIT.json.gz' + destination.write_bytes(gzip.compress(json.dumps(output, sort_keys=True, separators=(',',':')).encode(), mtime=0)) + print(json.dumps({'status':output['status'],'contacts':output['contact_count'], + 'targets':output['canonical_main_targets'],'endpoint_phase_controls':omitted_translation_rejected, + 'sha256':digest(destination)})) + + +if __name__ == '__main__': + main() diff --git a/research/pr4359-p7-padding/strictification.py b/research/pr4359-p7-padding/strictification.py new file mode 100644 index 0000000000..dd2ae4337a --- /dev/null +++ b/research/pr4359-p7-padding/strictification.py @@ -0,0 +1,133 @@ +#!/usr/bin/env python3 +"""Exact tensor-and-target-completion certificate for the native p7 word. + +Apache-2.0. Substantial OpenAI/Codex assistance. Native controller and interval +engine: zxv's PR4359. Integer compiler: Jacob Alan Sussman's Theorem 1G. +""" +from fractions import Fraction as Q +from hashlib import sha256 +import argparse +import importlib.util +import json +from pathlib import Path +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +EXPONENT = 30000 +CUTOFF = 7 +TARGET_FLOOR = 8 +TESTED_SAVING = Q('0.00268648') +ALPHA_UPPER = 1-Q(1,10**8) +GAMMA_UPPER = Q(1999,2000) +DELTA_UPPER = Q(1,2) +BLOCK = 2000 +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 need(ok, message): + if not ok: + raise AssertionError(message) + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name,path) + result = importlib.util.module_from_spec(spec) + spec.loader.exec_module(result) + return result + + +def run(source_root, native_result=None): + if native_result is None: + native_result = module('p7_native',HERE/'native_inventory.py').run(source_root) + targets = {int(k):v for k,v in native_result['targets'].items()} + paid = {int(k):v for k,v in native_result['paid'].items()} + need(targets == TARGETS and paid == PAID,'Exact reconstructed p7 native invoice') + need(native_result['p'] == 7 and native_result['keep'] == 232127, + 'Actual reconstructed controller selection') + need(native_result['dimension'] == 121,'Actual native ambient rank') + productive_count = sum(targets.values()) + paid_rank = sum(k*v for k,v in paid.items()) + target_rank = sum(k*v for k,v in targets.items()) + need(productive_count == 7688,'Every independent productive field') + need((target_rank,paid_rank) == (131723,131115),'Exact rank-one moments') + need(target_rank-paid_rank == native_result['rank_margin'] > 0, + 'Positive raw rank-one surplus, preserved by completion and splitting') + engine_path = source_root/'research/kappa-rebuild/architecture/mixed_target_probe.py' + E = module('p7_source_intervals',engine_path) + target_lo,target_hi = E.moment(targets,TESTED_SAVING) + paid_lo,paid_hi = E.moment(paid,TESTED_SAVING) + alpha_lo,alpha_hi = paid_lo/target_hi,paid_hi/target_lo + log_lo,log_hi = E.log_interval(CUTOFF) + power_lo = E.exp_interval(TESTED_SAVING*log_lo)[0] + power_hi = E.exp_interval(TESTED_SAVING*log_hi)[1] + gamma_lo = paid_rank/(power_hi*target_hi) + gamma_hi = paid_rank/(power_lo*target_lo) + delta_lo = productive_count*TARGET_FLOOR/(power_hi*target_hi) + delta_hi = productive_count*TARGET_FLOOR/(power_lo*target_lo) + need(0 < alpha_hi < ALPHA_UPPER < 1,'Certified alpha < 1-10^-8') + need(0 < gamma_hi < GAMMA_UPPER < 1,'Certified original-paid tail gamma < 1999/2000') + need(0 < delta_hi < DELTA_UPPER < 1,'Certified completion tail delta < 1/2') + need(GAMMA_UPPER**BLOCK < Q(1,2),'Exact finite rational block decay') + need(EXPONENT % BLOCK == 0,'Complete decay blocks') + blocks = EXPONENT//BLOCK + need(EXPONENT >= blocks,'Completion tail is below the conservative block bound') + bound = 1/(1+EXPONENT*(1-ALPHA_UPPER))+Q(4,2**blocks) + need(bound < 1,'Complete normalized paid moment, including all target completion') + need(1 < CUTOFF < TARGET_FLOOR < max(targets) and 0 < TESTED_SAVING < 1, + 'Completion fits the actual ambient space and restores strict rank separation') + need(CUTOFF**16 < TARGET_FLOOR**15,'theta < 15/16') + need(CUTOFF < 2**3 and max(targets) < 2**7,'Exact compiler power bounds') + need(1/(1+BLOCK*(1-ALPHA_UPPER))+Q(4,2) > 1, + 'One decay block is insufficient under these bounds') + need(1/(1+EXPONENT*(1-ALPHA_UPPER))+2 > 1, + 'An undamped completion tail is rejected') + # Without completion, every permitted cutoff is below minimum target five. + # Its rank-one tail is worse than this already failing boundary value. + _,ln5_hi = E.log_interval(5) + old_tail_lo = paid_rank/(E.exp_interval(TESTED_SAVING*ln5_hi)[1]*target_hi) + need(old_tail_lo > 1,'Unpadded rank-one tail condition fails even at cutoff base five') + return { + 'schema':'p7-paid-target-completion-tensor-certificate/1', + 'status':'PASS_EXACT_P7_TARGET_COMPLETION_STRICTIFICATION', + 'exponent':EXPONENT,'cutoff_base':CUTOFF,'target_floor_base':TARGET_FLOOR, + 'cutoff_encoding':'7^30000','target_floor_encoding':'8^30000', + 'tested_saving':str(TESTED_SAVING),'targets':targets,'paid':paid, + 'productive_fields':productive_count, + 'target_rank_one_moment':target_rank,'paid_rank_one_moment':paid_rank, + 'rank_one_surplus_encoding':str(target_rank)+'^30000-'+str(paid_rank)+'^30000', + 'alpha_upper':str(ALPHA_UPPER),'alpha_interval':E.show((alpha_lo,alpha_hi)), + 'gamma_upper':str(GAMMA_UPPER),'gamma_interval':E.show((gamma_lo,gamma_hi)), + 'delta_upper':str(DELTA_UPPER),'delta_interval':E.show((delta_lo,delta_hi)), + 'decay_block_length':BLOCK,'decay_block_count':blocks, + 'normalized_moment_upper_rational':str(bound), + 'strictification_gap_rational':str(1-bound), + 'strictification_gap':E.show((1-bound,1-bound)), + 'strict_moment_verified':True,'new_min_target_encoding':'8^30000', + 'new_max_target_encoding':'121^30000','theta_upper':'15/16', + 'native_inventory':native_result, + 'source_sha256':{'research/kappa-rebuild/architecture/mixed_target_probe.py': + sha256(engine_path.read_bytes()).hexdigest()}, + 'controls':{'unpadded_rank_one_tail_rejected':True, + 'one_decay_block_rejected':True,'undamped_completion_rejected':True}, + 'materialized_tensor_or_completed_word':False, + '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.'} + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root',type=Path,default=HERE/'source') + parser.add_argument('--native-result',type=Path, + help='Use an already audited native receipt instead of rerunning its producer.') + parser.add_argument('--out',type=Path) + args = parser.parse_args() + native = json.loads(args.native_result.read_text()) if args.native_result else None + result = run(args.source_root,native) + if args.out: + args.out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({key:result[key] for key in + ('status','exponent','cutoff_encoding','target_floor_encoding', + 'tested_saving','strictification_gap')},sort_keys=True)) diff --git a/research/pr4359-p7-padding/verify.py b/research/pr4359-p7-padding/verify.py new file mode 100644 index 0000000000..53e2383639 --- /dev/null +++ b/research/pr4359-p7-padding/verify.py @@ -0,0 +1,101 @@ +#!/usr/bin/env python3 +"""Authenticate and verify the conditional p7 native tensor and paid-target-padding construction. + +Apache-2.0. Substantial OpenAI Codex assistance; source notices are retained. +""" +import argparse +from fractions import Fraction as Q +import hashlib +import importlib.util +import json +from pathlib import Path, PurePosixPath + +HERE = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + value = importlib.util.module_from_spec(spec) + spec.loader.exec_module(value) + return value + + +def verify(): + manifest = json.loads((HERE / 'EXPORTED-SOURCES.json').read_text()) + seen = set() + for row in manifest['files']: + rel = PurePosixPath(row['path']) + need(not rel.is_absolute() and '..' not in rel.parts and str(rel) == row['path'], + 'Canonical source path') + need(row['path'] not in seen, 'Unique source path') + seen.add(row['path']) + path = HERE + for part in rel.parts: + path /= part + need(not path.is_symlink(), 'No source aliases') + data = path.read_bytes() + need(len(data) == row['bytes'] and hashlib.sha256(data).hexdigest() == row['sha256'], + 'Exact exported source bytes: ' + row['path']) + need(hashlib.sha1(b'blob ' + str(len(data)).encode() + b'\0' + data).hexdigest() + == row['git_blob'], 'Exact original Git blob') + + source = HERE / 'source' + S = module('strictification', HERE / 'strictification.py') + E = module('endpoint', HERE / 'endpoint.py') + independent = module('independent_intervals', HERE / 'dependencies/compiler-refill/template_bound.py') + strict = S.run(source) + endpoint = E.run(source, strict) + targets, paid = strict['targets'], strict['paid'] + saving = Q(strict['tested_saving']) + tlo, thi = independent.moment_margin(targets, {}, saving) + plo, phi = independent.moment_margin(paid, {}, saving) + need(phi / tlo < Q(strict['alpha_upper']), 'Independent paid/target moment ratio') + cutoff = Q(strict['cutoff_base']) + loglo, loghi = independent.log_interval(cutoff) + base_power_lo = independent.exp_interval(saving * loglo)[0] + paid_mass = sum(k * v for k, v in paid.items()) + need(Q(paid_mass) / (base_power_lo * tlo) < Q(strict['gamma_upper']), + 'Independent original paid rank-one tail ratio') + productive_count = sum(targets.values()) + need(Q(productive_count * strict['target_floor_base']) / (base_power_lo * tlo) + < Q(strict['delta_upper']), 'Independent complete productive-padding tail ratio') + n = strict['exponent'] + block = strict['decay_block_length'] + need(n % block == 0 and Q(strict['gamma_upper']) ** block < Q(1, 2), + 'Independent exact rational block decay') + need(Q(strict['delta_upper']) <= Q(1, 2) and n >= n // block, + 'Independent complete padding tail decay') + upper = 1 / (1 + n * (1 - Q(strict['alpha_upper']))) + Q(4, 2 ** (n // block)) + need(upper == Q(strict['normalized_moment_upper_rational']), 'Exact charged-padding and cutoff bound') + need(upper < 1, 'Independent complete strictified moment') + need(cutoff < strict['target_floor_base'] < max(targets), + 'Completed target ranks exceed paid cutoff and fit the ambient rank') + bit = json.loads((source / 'research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json').read_text()) + need(Q(endpoint['outer']['parameters']['bit_saving']) == Q(bit['ordinary_saving_admitted']), + 'Unchanged admitted ordinary BIT saving') + return {'status': 'PASS_SOURCE_BOUND_CONDITIONAL_P7_PAID_PADDING_IMPROVEMENT', + 'source_files': len(seen), 'strictification': strict, 'endpoint': endpoint, + '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.'} + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write-result', action='store_true') + args = parser.parse_args() + result = verify() + normalized = json.loads(json.dumps(result)) + receipt = HERE / 'RESULT.json' + if args.write_result: + receipt.write_text(json.dumps(normalized, indent=2, sort_keys=True) + '\n') + else: + need(normalized == json.loads(receipt.read_text()), 'Exact saved certificate reproduction') + print(json.dumps({'status': result['status'], 'kappa': result['endpoint']['kappa'], + 'mixed_saving': result['strictification']['tested_saving'], + 'tensor_power': result['strictification']['exponent'], + 'uniform_rank_exponent': result['endpoint']['compiler']['H1']})) From e9058860b5c850760fdf970e796a96aefcdb1d98 Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 21 Oct 2026 12:24:13 -0500 Subject: [PATCH 2/2] Reduce p7 tensor power and record bounded controller follow-up --- research/pr4359-p7-padding/ENDPOINT.md | 46 +- research/pr4359-p7-padding/FOLLOWUP.json | 4623 +++++++++++++++++ research/pr4359-p7-padding/FOLLOWUP.md | 32 + research/pr4359-p7-padding/README.md | 18 +- research/pr4359-p7-padding/RESULT.json | 67 +- research/pr4359-p7-padding/TENSOR.md | 36 +- research/pr4359-p7-padding/VERIFY.json | 9 + research/pr4359-p7-padding/endpoint.py | 22 +- research/pr4359-p7-padding/scan.py | 99 + research/pr4359-p7-padding/strictification.py | 32 +- research/pr4359-p7-padding/verify.py | 4 +- 11 files changed, 4890 insertions(+), 98 deletions(-) create mode 100644 research/pr4359-p7-padding/FOLLOWUP.json create mode 100644 research/pr4359-p7-padding/FOLLOWUP.md create mode 100644 research/pr4359-p7-padding/scan.py diff --git a/research/pr4359-p7-padding/ENDPOINT.md b/research/pr4359-p7-padding/ENDPOINT.md index 47008a4b90..8667482f63 100644 --- a/research/pr4359-p7-padding/ENDPOINT.md +++ b/research/pr4359-p7-padding/ENDPOINT.md @@ -42,10 +42,10 @@ rank-one moment 131115, leaving surplus 608. Its raw paid ranks exceed its smallest target ranks. Moreover, a rank-one tail bound with cutoff below the raw minimum target rank does not suffice near this proposed saving. -The new construction tensors the native word `v=30000` times, completes -every productive endpoint of rank smaller than `8^v` to rank `8^v` on +The new construction tensors the native word `v=6240` times, completes +every productive endpoint of rank smaller than `11^v` to rank `11^v` on unused disjoint axes, and splits every paid call, including those endpoint -completions, into consecutive pieces of size at most `7^v`. Endpoint +completions, into consecutive pieces of size at most `10^v`. Endpoint completion occurs only after the whole native tensor word has finished. It uses the same arbitrary productive array, without new productive credit for copied inputs or work storage. The ambient rank `121^v` has room for @@ -56,30 +56,31 @@ the raw moments. The certificate proves ``` P_tau/T_tau < 1 - 1/10^8, -131115/(7^C_test*T_tau) < 9995/10000, -7688*8/(7^C_test*T_tau) < 1/2. +131115/(10^C_test*T_tau) < 4991/5000, +7688*11/(10^C_test*T_tau) < 2/3. ``` The first bound controls the original tensor word. The second pays for splitting its large calls. The third pays for completing small productive endpoints and splitting those completion calls. For a completion of rank -`D<8^v`, writing `D=q*J+r` with `J=7^v` gives, including `q=0`, +`D<11^v`, writing `D=q*J+r` with `J=10^v` gives, including `q=0`, ``` q*J^tau+r^tau <= D*J^(-C_test)+J^tau - < 2*8^v/J^C_test. + < 2*11^v/J^C_test. ``` Thus the complete normalized paid moment is bounded by `alpha^v+2*gamma^v+2*padding^v`, while the target moment only increases. -The exact block bound `(9995/10000)^2000<1/2`, with 15 blocks and -`padding<1/2`, gives the simpler sufficient inequality +The exact block bound `(4991/5000)^390<1/2` gives 16 decay blocks. The +completion tail satisfies `(2/3)^2<1/2`, giving 3120 blocks. Bounding both +tails by `2^-16` yields the simpler sufficient inequality ``` -1/(1+30000/10^8) + 4/2^15 < 1. +1/(1+6240/10^8) + 4/2^16 < 1. ``` -Every paid rank is now at most `7^v`, and target ranks lie between `8^v` +Every paid rank is now at most `10^v`, and target ranks lie between `11^v` and `121^v`. Rank-one surplus is unchanged: each endpoint completion adds the same rank to the paid and target totals, and paid splitting preserves rank. Hence it remains `131723^v-131115^v>0`. @@ -98,20 +99,20 @@ z0 = (t+z)/2, delta = z0-t = 1/1400000000. ``` -The source compiler now has `m=121^v`, `k_min=8^v`, and `r_max<=7^v`. -The exact integer inequality `7^16<8^15` gives exit exponent below -`15/16`, so use `h=1/16`. For ambient rank `x>=m`, +The source compiler now has `m=121^v`, `k_min=11^v`, and `r_max<=10^v`. +The exact integer inequality `10^26<11^25` gives exit exponent below +`25/26`, so use `h=1/26`. For ambient rank `x>=m`, ``` m E(x)/x < m^h*r_max*x^(-h) - < 2^B*x^(-h), B=(55/16)*v=103125. + < 2^B*x^(-h), B=(111/26)*v=26640. ``` -This follows from `7<2^3` and `121<2^7`. The exact complement coefficient +This follows from `10<2^4` and `121<2^7`. The exact complement coefficient is `eta=z0*m^(z0-1)`. Since `z0>1/2`, ``` --log2(eta) < 1+7*v*(1-z0) = 11303213/20000. +-log2(eta) < 1+7*v*(1-z0) = 147931769/1250000. ``` The entirely rational sufficient formulas @@ -124,9 +125,9 @@ H1 = floor(H0*(1-z0)/(z-z0))+1 therefore give ``` -H0 = 12659600210000, -H1 = 47613655221424910001, -N = 2^47613655221424910001. +H0 = 4307773805920, +H1 = 16201843136005340321, +N = 2^16201843136005340321. ``` The verifier checks `H0>=7*v`, covering the entire finite base range. @@ -141,7 +142,10 @@ the tensorized and padded word nor the uniform compiled word has been materialized. Their complete instructions, integer batch factors, paid leaves, scalar operations, and owned banks are defined by the finite recipes. The one-less-integer controls only concern these sufficient -formulas; no minimal-rank claim is made. +formulas; no minimal-rank claim is made. The initial sufficient choice +`v=30000`, paid cutoff `7^v` and target floor `8^v` gave +`H1=47613655221424910001`; the final parameters reduce both the tensor +power and this rank exponent while preserving the same tested saving. ## Outer parameters and changed constants diff --git a/research/pr4359-p7-padding/FOLLOWUP.json b/research/pr4359-p7-padding/FOLLOWUP.json new file mode 100644 index 0000000000..0ef5700a70 --- /dev/null +++ b/research/pr4359-p7-padding/FOLLOWUP.json @@ -0,0 +1,4623 @@ +{ + "all_fail_at_00268649": true, + "only_pass_at_00268648": [ + [ + 7, + 3, + 232127 + ] + ], + "p_range": [ + 2, + 20 + ], + "profile_count": 209, + "profiles": [ + { + "checks": { + "268649/100000000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-33.08421631324281616127622941108646453", + "upper": "-33.08421631324281616127622941108638910" + } + }, + "33581/12500000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-33.08361949023690802897326058458242010", + "upper": "-33.08361949023690802897326058458234467" + } + } + }, + "keep": 6, + "p": 2, + "prefix_initial_count": 0, + "suffix_terminal_count": 1 + }, + { + "checks": { + "268649/100000000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-33.08421631324281616127622941108646453", + "upper": "-33.08421631324281616127622941108638910" + } + }, + "33581/12500000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-33.08361949023690802897326058458242010", + "upper": "-33.08361949023690802897326058458234467" + } + } + }, + "keep": 3, + "p": 2, + "prefix_initial_count": 1, + "suffix_terminal_count": 0 + }, + { + "checks": { + "268649/100000000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-21.91407022171627546355834835915458999", + "upper": "-21.91407022171627546355834835915448394" + } + }, + "33581/12500000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-21.91315948129372699877782529668692062", + "upper": "-21.91315948129372699877782529668681457" + } + } + }, + "keep": 58, + "p": 3, + "prefix_initial_count": 0, + "suffix_terminal_count": 2 + }, + { + "checks": { + "268649/100000000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-18.79550615920431506927771474014746295", + "upper": "-18.79550615920431506927771474014735690" + } + }, + "33581/12500000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-18.79460689311865607148960594747233854", + "upper": "-18.79460689311865607148960594747223249" + } + } + }, + "keep": 43, + "p": 3, + "prefix_initial_count": 1, + "suffix_terminal_count": 1 + }, + { + "checks": { + "268649/100000000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-21.91407022171627546355834835915458999", + "upper": "-21.91407022171627546355834835915448394" + } + }, + "33581/12500000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-21.91315948129372699877782529668692062", + "upper": "-21.91315948129372699877782529668681457" + } + } + }, + "keep": 15, + "p": 3, + "prefix_initial_count": 2, + "suffix_terminal_count": 0 + }, + { + "checks": { + "268649/100000000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-15.39722429685476649580830585147576377", + "upper": "-15.39722429685476649580830585147562710" + } + }, + "33581/12500000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-15.39598254688533081846466438088117314", + "upper": "-15.39598254688533081846466438088103647" + } + } + }, + "keep": 490, + "p": 4, + "prefix_initial_count": 0, + "suffix_terminal_count": 3 + }, + { + "checks": { + "268649/100000000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": "-10.32799918023235761022721021775500057", + "upper": "-10.32799918023235761022721021775486390" + } + }, + "33581/12500000": { + "strict_moment": "FAIL", + "target_minus_paid": { + "lower": 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No exhaustive mask search, all-p barrier, global optimality claim, or physical admission of unverified profiles. The selected p7 profile is checked against the separate current native receipt.", + "selected_native_profile_matched": true, + "source_sha256": { + "research/kappa-rebuild/architecture/mixed_target_probe.py": "011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a", + "research/kappa-rebuild/complex/full-identity-certificates/RESULT.json": "943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6" + }, + "status": "PASS_EXACT_DECLARED_PROFILE_SCREEN" +} diff --git a/research/pr4359-p7-padding/FOLLOWUP.md b/research/pr4359-p7-padding/FOLLOWUP.md new file mode 100644 index 0000000000..60e4ae9c81 --- /dev/null +++ b/research/pr4359-p7-padding/FOLLOWUP.md @@ -0,0 +1,32 @@ +# Finite continuation over 209 algebraic profiles + +`scan.py` checks pair counts p=2,...,20 and every split a+b=p-1. Each +candidate retains every middle idle, the first a initial windows and the +last b terminal windows. It uses 2p+1 copies of the pinned THREE-base +helper and unsplit paid inventories. The selected p7 profile is compared +with the actual native inventory in this package's `RESULT.json` (or the +fresh native result supplied by a caller). + +The explicit candidate main profile has 224 outputs at rank16p+9 and, +for each l in {a,b}, 224 at every rank16j+25 for j=0,...,l-1. Whole idle +charges are 224 at rank8 for each of p-1 middle windows and 224 at rank16j +for j=1,...,l in each chain. This screen is arithmetic on these formulas; +it does not provide native admission for all 209 candidates. + +For fixed p and 0 131115^n; target padding adds equal paid and target rank, and splitting preserves rank", "t": "12466419/12500000", - "target_max_encoding": "121^30000", - "target_min_encoding": "8^30000", - "tensor_power": 30000, - "theta_upper": "15/16", + "target_max_encoding": "121^6240", + "target_min_encoding": "11^6240", + "tensor_power": 6240, + "theta_upper": "25/26", "z": "139623893/140000000", "z0": "1396238929/1400000000" }, @@ -145,7 +145,7 @@ "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": "b588dded720ca9063ddc3760de6864385e59cdb57bc2d866040fc73c551b3c3a", + "strictification_source_sha256": "1f3c2a38b34d9dad7266be212ca5d0225827d8e05bda4831e6c25c5713f624f0", "tested_saving": "33581/12500000" }, "independent_interval_crosscheck": true, @@ -158,26 +158,27 @@ "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": 7, - "cutoff_encoding": "7^30000", - "decay_block_count": 15, - "decay_block_length": 2000, + "cutoff_base": 10, + "cutoff_encoding": "10^6240", + "decay_block_count": 16, + "decay_block_length": 390, "delta_interval": { - "lower": "0.46868503106323215655720547807230369", - "upper": "0.46868503106323215655720547807230370" + "lower": "0.64382470915163933966321257464784307", + "upper": "0.64382470915163933966321257464784308" }, - "delta_upper": "1/2", - "exponent": 30000, + "delta_upper": "2/3", + "exponent": 6240, "gamma_interval": { - "lower": "0.99914863826508331502012871126187076", - "upper": "0.99914863826508331502012871126187077" + "lower": "0.99819171247300624373216957625759087", + "upper": "0.99819171247300624373216957625759088" }, - "gamma_upper": "1999/2000", + "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)", @@ -246,9 +247,9 @@ "8": 1344 } }, - "new_max_target_encoding": "121^30000", - "new_min_target_encoding": "8^30000", - "normalized_moment_upper_rational": "81930003/81944576", + "new_max_target_encoding": "121^6240", + "new_min_target_encoding": "11^6240", + "normalized_moment_upper_rational": "10240625039/10240638976", "paid": { "1": 37305, "16": 448, @@ -262,7 +263,7 @@ }, "paid_rank_one_moment": 131115, "productive_fields": 7688, - "rank_one_surplus_encoding": "131723^30000-131115^30000", + "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": { @@ -271,12 +272,12 @@ "status": "PASS_EXACT_P7_TARGET_COMPLETION_STRICTIFICATION", "strict_moment_verified": true, "strictification_gap": { - "lower": "0.00017783971449190242927121863440967", - "upper": "0.00017783971449190242927121863440968" + "lower": "0.00000136095023295546357907266586564", + "upper": "0.00000136095023295546357907266586565" }, - "strictification_gap_rational": "14573/81944576", - "target_floor_base": 8, - "target_floor_encoding": "8^30000", + "strictification_gap_rational": "13937/10240638976", + "target_floor_base": 11, + "target_floor_encoding": "11^6240", "target_rank_one_moment": 131723, "targets": { "121": 224, @@ -290,6 +291,6 @@ "9": 3195 }, "tested_saving": "33581/12500000", - "theta_upper": "15/16" + "theta_upper": "25/26" } } diff --git a/research/pr4359-p7-padding/TENSOR.md b/research/pr4359-p7-padding/TENSOR.md index 30cfe796c8..8ecfd3e4d0 100644 --- a/research/pr4359-p7-padding/TENSOR.md +++ b/research/pr4359-p7-padding/TENSOR.md @@ -134,37 +134,41 @@ saving C=0.00268648 the rational interval checker proves ``` alpha < 1-1/10^8, -gamma < 1999/2000 with c=7, -delta < 1/2 with b=8. +gamma < 4991/5000 with c=10, +delta < 2/3 with b=11. ``` -Take v=30000. The exact integer comparison -`(1999/2000)^2000<1/2` gives gamma^v<2^-15. Also delta^v<2^-15. +Take v=6240. The exact integer comparison +`(4991/5000)^390<1/2` gives gamma^v<2^-16. Also `(2/3)^2<1/2`, +so delta^v<2^-3120<=2^-16. Bernoulli's inequality bounds alpha^v by 1/(1+v/10^8), so ``` alpha^v+2*gamma^v+2*delta^v - < 1/(1+30000/10^8)+4/2^15 < 1. + < 1/(1+6240/10^8)+4/2^16 < 1. ``` This proves an explicit finite power. The checker separately rejects an undamped completion tail and an insufficient single decay block. It also checks the raw rank-one cutoff-base-five tail at this point: that simpler tail condition fails, explaining why target completion is needed here. -No smallest tensor power or optimal native controller is claimed. +The exact sufficient gap is greater than 0.00000136095023295546. +An earlier sufficient choice used v=30000, c=7 and b=8. The new parameters +reduce the finite tensor power and the derived uniform rank at the same +saving. No smallest tensor power or optimal native controller is claimed. ## 5. Effective uniform rank -The completed mixed unit has m_new=121^v, k_min=8^v and r_max<=7^v. -The exact comparison 7^16<8^15 gives theta<15/16; put h=1/16. +The completed mixed unit has m_new=121^v, k_min=11^v and r_max<=10^v. +The exact comparison 10^26<11^25 gives theta<25/26; put h=1/26. For ambient rank x>=m_new the inherited exit estimate gives ``` m_new*E(x)/x <= r_max*m_new^h*x^(-h) - < 2^((55/16)*v)*x^(-h), + < 2^((111/26)*v)*x^(-h), ``` -using 7<8=2^3 and 121<128=2^7. For a desired uniform exponent +using 10<16=2^4 and 121<128=2^7. For a desired uniform exponent z>t=1-C, put z0=(t+z)/2 and d=z0-t. The exact complement coefficient eta=z0*m_new^(z0-1), with z0>1/2, satisfies @@ -175,7 +179,7 @@ eta=z0*m_new^(z0-1), with z0>1/2, satisfies Thus rational sufficient choices are ``` -H0 = ceil((((55/16)*v)*d+1+7*v*(1-z0))/(h*d)), +H0 = ceil((((111/26)*v)*d+1+7*v*(1-z0))/(h*d)), H1 = floor(H0*(1-z0)/(z-z0))+1, N = 2^H1. ``` @@ -218,6 +222,16 @@ All these constants are finite and fixed before the multiplication input varies. Their absorption still requires the stated inherited physical, analytic, fine-prime, fixed-tape and exact-recovery hypotheses. +The related [PR4375 tensor-frame audit](https://github.com/CrocSwap/integer-mult-bounds/pull/4375), +read at head `9712f7cfc09723a557b3230a0d5e9826eaedcd2e`, concerns the +different PR4088/PR4100 profile. It distinguishes one rank-r*f child from +f scalar rank-r copies and leaves native frame realization and monomial +pricing open. The construction here requires the complete PR4359 all-column +contract: a paid position at column count f is one rank-r*f job, with every +whole-job route charged. Factorwise repetition is not a substitute for that +contract. The finite p7 geometry and moment checks do not independently +discharge this all-column native or tape-action premise. + Open next questions include reducing the sufficient tensor power, varying the target completion and paid cutoff, and extending the native controller only with independently verified contacts, phases and helper ownership. diff --git a/research/pr4359-p7-padding/VERIFY.json b/research/pr4359-p7-padding/VERIFY.json index 7948c564cf..b00ce132da 100644 --- a/research/pr4359-p7-padding/VERIFY.json +++ b/research/pr4359-p7-padding/VERIFY.json @@ -13,6 +13,15 @@ ], "timeout_seconds": 300, "checks": "Authenticate immutable source exports; regenerate one exact p7 factor and replay all native contacts, endpoints and phases; certify charged post-tensor target padding and independent interval bounds; specify the uniform rank and all outer margins with rejection controls." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/scan.py" + ], + "timeout_seconds": 180, + "checks": "Reproduce 209 explicitly defined algebraic rank-profile moments with exact intervals; bind selected p7 profile to the verified native receipt; compare the saved finite negative follow-up." } ] } diff --git a/research/pr4359-p7-padding/endpoint.py b/research/pr4359-p7-padding/endpoint.py index 06444a96fb..32d24821b0 100644 --- a/research/pr4359-p7-padding/endpoint.py +++ b/research/pr4359-p7-padding/endpoint.py @@ -42,17 +42,17 @@ def encode(value): def compiler_rank(exponent, tested, uniform): - """Explicit sufficient ambient rank after target padding to 8^exponent and paid cutoff 7^exponent.""" + """Explicit sufficient ambient rank after target padding to 11^exponent and paid cutoff 10^exponent.""" n = exponent t, z = 1-tested, 1-uniform - z0, h = (t+z)/2, Q(1, 16) + z0, h = (t+z)/2, Q(1, 26) delta = z0-t need(n >= 1 and Q(1, 2) < t < z0 < z < 1, 'Strict compiler exponents') - need(7**16 < 8**15, 'log(7)/log(8) < 15/16') - need(7 < 2**3 and 121 < 2**7, 'Exact power bounds for exit and complement') - # r_max=7^n, k_min=8^n, m=121^n. Thus m*E(x)/x is - # below 2^B*x^-h, with B=(3+7h)n. Also -log2(eta)<1+7n(1-z0). - B = (3+7*h)*n + need(10**26 < 11**25, 'log(10)/log(11) < 25/26') + need(10 < 2**4 and 121 < 2**7, 'Exact power bounds for exit and complement') + # r_max=10^n, k_min=11^n, m=121^n. Thus m*E(x)/x is + # below 2^B*x^-h, with B=(4+7h)n. Also -log2(eta)<1+7n(1-z0). + B = (4+7*h)*n debt = 1+7*n*(1-z0) ratio = (delta*B+debt)/(h*delta) H0 = -((-ratio.numerator)//ratio.denominator) @@ -63,10 +63,10 @@ def compiler_rank(exponent, tested, uniform): need(H1 > H0 and H1*(z-z0) > H0*(1-z0), 'Strict final uniform moment') need((H0-1)*h*delta < delta*B+debt, 'One lower H0 fails the stated sufficient bound') need((H1-1)*(z-z0) <= H0*(1-z0), 'One lower H1 fails the final strict bound') - return {'tensor_power': n, 'target_min_encoding': '8^'+str(n), + return {'tensor_power': n, 'target_min_encoding': '11^'+str(n), 'target_max_encoding': '121^'+str(n), - 'paid_max_bound_encoding': '7^'+str(n), - 'theta_upper': Q(15, 16), 'h': h, 't': t, 'z0': z0, 'z': z, + 'paid_max_bound_encoding': '10^'+str(n), + 'theta_upper': Q(25, 26), 'h': h, 't': t, 'z0': z0, 'z': z, 'delta': delta, 'exit_coefficient_log2_upper': B, 'negative_log2_eta_upper': debt, 'H0': H0, 'H1': H1, 'N_encoding': '2^'+str(H1), @@ -79,7 +79,7 @@ def run(source_root, strict_result=None): if strict_result is None: strict_result = module('tensor_strictification', HERE/'strictification.py').run(source_root) need(strict_result['strict_moment_verified'], 'Strict mixed moment was certified') - need(strict_result['cutoff_base'] == 7 and strict_result['target_floor_base'] == 8 + need(strict_result['cutoff_base'] == 10 and strict_result['target_floor_base'] == 11 and Q(strict_result['tested_saving']) == TESTED, 'Compiler inputs bind to the certified cutoff and saving') ledger_path = HERE/'dependencies/compiler-refill/endpoint.py' diff --git a/research/pr4359-p7-padding/scan.py b/research/pr4359-p7-padding/scan.py new file mode 100644 index 0000000000..bae64f0b66 --- /dev/null +++ b/research/pr4359-p7-padding/scan.py @@ -0,0 +1,99 @@ +"""Exact finite moment screen of declared balanced-prefix/suffix rank profiles. + +This checks 209 algebraic candidate profiles, not 209 native controllers. +Only selected cases have a separate exact Laurent/physical admission. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import importlib.util,json,sys +sys.dont_write_bytecode=True +HERE=Path(__file__).resolve().parent +PINS={ + 'research/kappa-rebuild/architecture/mixed_target_probe.py': '011c3c9d0cf81103dc84d709a0e36793eb7c5ae3f23c85eac27650ef13afa04a', + 'research/kappa-rebuild/complex/full-identity-certificates/RESULT.json': '943d5fad2fc529f470df05a35446e07ecaef7344abfce450d2c2eb2c9b3798f6', +} + + +def need(ok,message): + if not ok: + raise ValueError(message) + + +def profile(p,a,H,N): + b=p-1-a + targets=Counter({r:(2*p+1)*count for r,count in H.items()}) + paid=Counter({r:(2*p+1)*count for r,count in N.items()}) + targets[16*p+9]+=224 + for length in (a,b): + for j in range(length): targets[16*j+25]+=224 + for j in range(1,length+1): paid[16*j]+=224 + paid[8]+=224*(p-1) + mask=sum(1<=0 else 1] for r,count in signed.items()) + hi=sum(count*powers[C][r][1 if count>=0 else 0] for r,count in signed.items()) + need(lo>0 or hi<0,'Every tested moment has a strict interval sign') + checks[str(C)]={'target_minus_paid':E.show((lo,hi)), + 'strict_moment':'PASS' if lo>0 else 'FAIL'} + rows.append({'p':p,'prefix_initial_count':a,'suffix_terminal_count':p-1-a, + 'keep':mask,'checks':checks}) + passing=[[row['p'],row['prefix_initial_count'],row['keep']] for row in rows + if row['checks'][str(points[0])]['strict_moment']=='PASS'] + need(passing==[[7,3,232127]],'Only the selected p7 profile passes C=.00268648') + need(all(row['checks'][str(points[1])]['strict_moment']=='FAIL' for row in rows), + 'All declared profiles fail C=.00268649') + return {'schema':'finite-algebraic-balanced-profile-screen/1', + 'status':'PASS_EXACT_DECLARED_PROFILE_SCREEN','p_range':[2,20], + 'profile_count':len(rows),'only_pass_at_00268648':passing, + 'all_fail_at_00268649':True,'selected_native_profile_matched':True, + 'source_sha256':dict(PINS), + 'scope':'Finite exact arithmetic on the explicitly defined all-middle, initial-prefix, terminal-suffix rank-profile formulas. No exhaustive mask search, all-p barrier, global optimality claim, or physical admission of unverified profiles. The selected p7 profile is checked against the separate current native receipt.', + 'profiles':rows} + + +if __name__=='__main__': + import argparse + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root',type=Path,default=HERE/'source') + parser.add_argument('--write-result',action='store_true',help='Author the checked finite receipt.') + args=parser.parse_args() + result=run(args.source_root) + target=HERE/'FOLLOWUP.json' + if args.write_result: + target.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else: + need(result==json.loads(target.read_text()),'Exact replay agrees with checked FOLLOWUP.json') + print(json.dumps({k:v for k,v in result.items() if k!='profiles'},sort_keys=True)) diff --git a/research/pr4359-p7-padding/strictification.py b/research/pr4359-p7-padding/strictification.py index dd2ae4337a..a96c985535 100644 --- a/research/pr4359-p7-padding/strictification.py +++ b/research/pr4359-p7-padding/strictification.py @@ -14,14 +14,14 @@ sys.dont_write_bytecode = True HERE = Path(__file__).resolve().parent -EXPONENT = 30000 -CUTOFF = 7 -TARGET_FLOOR = 8 +EXPONENT = 6240 +CUTOFF = 10 +TARGET_FLOOR = 11 TESTED_SAVING = Q('0.00268648') ALPHA_UPPER = 1-Q(1,10**8) -GAMMA_UPPER = Q(1999,2000) -DELTA_UPPER = Q(1,2) -BLOCK = 2000 +GAMMA_UPPER = Q(4991,5000) +DELTA_UPPER = Q(2,3) +BLOCK = 390 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, @@ -69,18 +69,19 @@ def run(source_root, native_result=None): delta_lo = productive_count*TARGET_FLOOR/(power_hi*target_hi) delta_hi = productive_count*TARGET_FLOOR/(power_lo*target_lo) need(0 < alpha_hi < ALPHA_UPPER < 1,'Certified alpha < 1-10^-8') - need(0 < gamma_hi < GAMMA_UPPER < 1,'Certified original-paid tail gamma < 1999/2000') - need(0 < delta_hi < DELTA_UPPER < 1,'Certified completion tail delta < 1/2') + need(0 < gamma_hi < GAMMA_UPPER < 1,'Certified original-paid tail gamma < 4991/5000') + need(0 < delta_hi < DELTA_UPPER < 1,'Certified completion tail delta < 2/3') need(GAMMA_UPPER**BLOCK < Q(1,2),'Exact finite rational block decay') need(EXPONENT % BLOCK == 0,'Complete decay blocks') blocks = EXPONENT//BLOCK - need(EXPONENT >= blocks,'Completion tail is below the conservative block bound') + need(DELTA_UPPER**2 < Q(1,2),'Exact two-step completion-tail decay') + need(EXPONENT//2 >= blocks,'Completion tail is below the conservative block bound') bound = 1/(1+EXPONENT*(1-ALPHA_UPPER))+Q(4,2**blocks) need(bound < 1,'Complete normalized paid moment, including all target completion') need(1 < CUTOFF < TARGET_FLOOR < max(targets) and 0 < TESTED_SAVING < 1, 'Completion fits the actual ambient space and restores strict rank separation') - need(CUTOFF**16 < TARGET_FLOOR**15,'theta < 15/16') - need(CUTOFF < 2**3 and max(targets) < 2**7,'Exact compiler power bounds') + need(CUTOFF**26 < TARGET_FLOOR**25,'theta < 25/26') + need(CUTOFF < 2**4 and max(targets) < 2**7,'Exact compiler power bounds') need(1/(1+BLOCK*(1-ALPHA_UPPER))+Q(4,2) > 1, 'One decay block is insufficient under these bounds') need(1/(1+EXPONENT*(1-ALPHA_UPPER))+2 > 1, @@ -94,20 +95,21 @@ def run(source_root, native_result=None): 'schema':'p7-paid-target-completion-tensor-certificate/1', 'status':'PASS_EXACT_P7_TARGET_COMPLETION_STRICTIFICATION', 'exponent':EXPONENT,'cutoff_base':CUTOFF,'target_floor_base':TARGET_FLOOR, - 'cutoff_encoding':'7^30000','target_floor_encoding':'8^30000', + 'cutoff_encoding':'10^6240','target_floor_encoding':'11^6240', 'tested_saving':str(TESTED_SAVING),'targets':targets,'paid':paid, 'productive_fields':productive_count, 'target_rank_one_moment':target_rank,'paid_rank_one_moment':paid_rank, - 'rank_one_surplus_encoding':str(target_rank)+'^30000-'+str(paid_rank)+'^30000', + 'rank_one_surplus_encoding':str(target_rank)+'^6240-'+str(paid_rank)+'^6240', 'alpha_upper':str(ALPHA_UPPER),'alpha_interval':E.show((alpha_lo,alpha_hi)), 'gamma_upper':str(GAMMA_UPPER),'gamma_interval':E.show((gamma_lo,gamma_hi)), 'delta_upper':str(DELTA_UPPER),'delta_interval':E.show((delta_lo,delta_hi)), 'decay_block_length':BLOCK,'decay_block_count':blocks, + 'completion_decay_block_length':2, 'normalized_moment_upper_rational':str(bound), 'strictification_gap_rational':str(1-bound), 'strictification_gap':E.show((1-bound,1-bound)), - 'strict_moment_verified':True,'new_min_target_encoding':'8^30000', - 'new_max_target_encoding':'121^30000','theta_upper':'15/16', + 'strict_moment_verified':True,'new_min_target_encoding':'11^6240', + 'new_max_target_encoding':'121^6240','theta_upper':'25/26', 'native_inventory':native_result, 'source_sha256':{'research/kappa-rebuild/architecture/mixed_target_probe.py': sha256(engine_path.read_bytes()).hexdigest()}, diff --git a/research/pr4359-p7-padding/verify.py b/research/pr4359-p7-padding/verify.py index 53e2383639..e491e49d5a 100644 --- a/research/pr4359-p7-padding/verify.py +++ b/research/pr4359-p7-padding/verify.py @@ -68,8 +68,8 @@ def verify(): block = strict['decay_block_length'] need(n % block == 0 and Q(strict['gamma_upper']) ** block < Q(1, 2), 'Independent exact rational block decay') - need(Q(strict['delta_upper']) <= Q(1, 2) and n >= n // block, - 'Independent complete padding tail decay') + need(Q(strict['delta_upper']) ** block < Q(1, 2), + 'Independent complete padding tail block decay') upper = 1 / (1 + n * (1 - Q(strict['alpha_upper']))) + Q(4, 2 ** (n // block)) need(upper == Q(strict['normalized_moment_upper_rational']), 'Exact charged-padding and cutoff bound') need(upper < 1, 'Independent complete strictified moment')