From bb7fc427c79c26669a9e8de06e55f31cadaa992d Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Tue, 13 Oct 2026 20:05:08 -0500 Subject: [PATCH] Prove the complete cost obstruction for eight two-accumulator rewrites --- .../NATIVE-REPLAY.md | 102 + research/two-accumulator-saved-arms/NOTICE.md | 39 + research/two-accumulator-saved-arms/PROOF.md | 244 + research/two-accumulator-saved-arms/README.md | 148 + .../two-accumulator-saved-arms/RECIPES.json | 6030 +++++++++++++++++ .../RESEARCH-NOTES.md | 56 + .../two-accumulator-saved-arms/SOURCES.json | 204 + research/two-accumulator-saved-arms/TASK.json | 65 + .../two-accumulator-saved-arms/VERIFY.json | 64 + .../two-accumulator-saved-arms/audit_local.py | 171 + research/two-accumulator-saved-arms/build.py | 80 + .../check_sources.py | 48 + .../evidence/FAMILY-CHECK.json | 4907 ++++++++++++++ .../evidence/FRAME-CONTROL.json | 28 + .../evidence/PR1129-ROOT-ASSEMBLY.json | 344 + .../evidence/PR1129-ROOT-GEOMETRY-CHECK.json | 10 + .../evidence/all-eight-CLIFFORD-REVIEW.json | 19 + .../all-eight-INDEPENDENT-LOCAL-REPLAY.json | 71 + .../evidence/all-eight-LOCAL-CHECKS.json | 36 + .../all-eight-SCALAR-FRAME-AUDIT.json | 714 ++ .../evidence/all-eight-WRAPPER-CHECKS.json | 396 ++ .../selected1094-CANONICAL-WORD.json.gz | Bin 0 -> 84805 bytes .../evidence/selected1094-LOCAL-CHECKS.json | 36 + .../selected1094-SCALAR-FRAME-AUDIT.json | 712 ++ .../frame_control.py | 100 + .../inputs/CF0-FRAME-CONTROL.json.gz | Bin 0 -> 34277 bytes .../inputs/SEVEN-SLOT-WORD.json.gz | Bin 0 -> 57222 bytes .../inputs/notices/LICENSE | 201 + .../inputs/notices/PR1140-NOTICE.md | 36 + .../inputs/notices/UPSTREAM-NOTICE.md | 34 + .../inputs/notices/construction-NOTICE.md | 9 + .../inputs/notices/gauge44-slots-NOTICE.md | 24 + .../two-accumulator-saved-arms/intervals.py | 152 + .../two-accumulator-saved-arms/owner_bound.py | 150 + research/two-accumulator-saved-arms/verify.py | 134 + 35 files changed, 15364 insertions(+) create mode 100644 research/two-accumulator-saved-arms/NATIVE-REPLAY.md create mode 100644 research/two-accumulator-saved-arms/NOTICE.md create mode 100644 research/two-accumulator-saved-arms/PROOF.md create mode 100644 research/two-accumulator-saved-arms/README.md create mode 100644 research/two-accumulator-saved-arms/RECIPES.json create mode 100644 research/two-accumulator-saved-arms/RESEARCH-NOTES.md create mode 100644 research/two-accumulator-saved-arms/SOURCES.json create mode 100644 research/two-accumulator-saved-arms/TASK.json create mode 100644 research/two-accumulator-saved-arms/VERIFY.json create mode 100644 research/two-accumulator-saved-arms/audit_local.py create mode 100644 research/two-accumulator-saved-arms/build.py create mode 100644 research/two-accumulator-saved-arms/check_sources.py create mode 100644 research/two-accumulator-saved-arms/evidence/FAMILY-CHECK.json create mode 100644 research/two-accumulator-saved-arms/evidence/FRAME-CONTROL.json create mode 100644 research/two-accumulator-saved-arms/evidence/PR1129-ROOT-ASSEMBLY.json create mode 100644 research/two-accumulator-saved-arms/evidence/PR1129-ROOT-GEOMETRY-CHECK.json create mode 100644 research/two-accumulator-saved-arms/evidence/all-eight-CLIFFORD-REVIEW.json create mode 100644 research/two-accumulator-saved-arms/evidence/all-eight-INDEPENDENT-LOCAL-REPLAY.json create mode 100644 research/two-accumulator-saved-arms/evidence/all-eight-LOCAL-CHECKS.json create mode 100644 research/two-accumulator-saved-arms/evidence/all-eight-SCALAR-FRAME-AUDIT.json create mode 100644 research/two-accumulator-saved-arms/evidence/all-eight-WRAPPER-CHECKS.json create mode 100644 research/two-accumulator-saved-arms/evidence/selected1094-CANONICAL-WORD.json.gz create mode 100644 research/two-accumulator-saved-arms/evidence/selected1094-LOCAL-CHECKS.json create mode 100644 research/two-accumulator-saved-arms/evidence/selected1094-SCALAR-FRAME-AUDIT.json create mode 100644 research/two-accumulator-saved-arms/frame_control.py create mode 100644 research/two-accumulator-saved-arms/inputs/CF0-FRAME-CONTROL.json.gz create mode 100644 research/two-accumulator-saved-arms/inputs/SEVEN-SLOT-WORD.json.gz create mode 100644 research/two-accumulator-saved-arms/inputs/notices/LICENSE create mode 100644 research/two-accumulator-saved-arms/inputs/notices/PR1140-NOTICE.md create mode 100644 research/two-accumulator-saved-arms/inputs/notices/UPSTREAM-NOTICE.md create mode 100644 research/two-accumulator-saved-arms/inputs/notices/construction-NOTICE.md create mode 100644 research/two-accumulator-saved-arms/inputs/notices/gauge44-slots-NOTICE.md create mode 100644 research/two-accumulator-saved-arms/intervals.py create mode 100644 research/two-accumulator-saved-arms/owner_bound.py create mode 100644 research/two-accumulator-saved-arms/verify.py diff --git a/research/two-accumulator-saved-arms/NATIVE-REPLAY.md b/research/two-accumulator-saved-arms/NATIVE-REPLAY.md new file mode 100644 index 0000000000..79f2b2b3be --- /dev/null +++ b/research/two-accumulator-saved-arms/NATIVE-REPLAY.md @@ -0,0 +1,102 @@ +# Native local replay and source binding + +## Exact selected input + +The source word comes from PR1140 at +`8e2e18b93d8c6b302e540ad5edc767cb98cf1514`, path +`research/k8-frame-antichain/inputs/SEVEN-SLOT-WORD.json.gz`. +Its decompressed SHA256 is +`c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8`. + +It is also the exact decompressed input in the selected PR1094 replay +archive at the experiment base. The archive is +`research/community-frontier1094-audit/selected-replay.tar.gz`; its member +is `candidate/strict/global/base/providers/gauge44/FULL-WORD.json.gz`. +The sibling `CANONICAL-WORD.json.gz` has decompressed SHA256 +`4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c`. +The retained scalar/frame receipt binds both hashes and the local profile. +The package retains that receipt and the canonical word. Mask zero changes +only a research metadata field; all scalar gates, frames, endpoints, and +paid data are equal to the raw input. + +The source tree's old `evidence/local` files are historical R492 evidence. +They are not the selected rebuilt R480 word. The maintainer's +`docs/research/community-batch1099-review.md` already records this distinction. +This package binds to the selected replay archive. + +`audit_local.py` is copied without change from PR1238 at +`50a1c992ce28c95d83d11bc691353aaa289d9d65`, path +`research/end-cap-obstruction/inputs/repo/research/gauge44-slots/independent/audit_local.py`. +`intervals.py` is copied without change from PR1240 at +`1e136b8c4a552050820334ad113628775182f08c`, path +`research/complex-local-word-ceiling/ceiling.py`. +`SOURCES.json` gives their Git blobs and byte hashes. It also pins the native +entry points and the baseline attaining-table source. + +## Repeat the native run + +Use a checkout of the exact experiment base with the selected native source +directories present. The native source is read only. Put all new files in a +new work directory. The commands below use a Python environment that can run +the retained native tools. The recorded run used Python 3.14.7. The package's +standard-library family check was also run with Python 3.12. + +Set the three paths, then run from this repository root: + +```sh +NATIVE_ROOT=/absolute/path/to/base-checkout +PYTHON=/absolute/path/to/python +WORK=/absolute/path/to/new/two-accumulator-native +UP="$NATIVE_ROOT/research/complex-sw4-frame8/vendor/pr635/research/complex-571-cold14-st2" +SRC="$NATIVE_ROOT/research/complex-k492-owner-repair/vendor/multicold" +export MULTICOLD_SOURCE="$SRC" GAIN_PR564_SOURCE="$SRC" +export OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 +mkdir "$WORK" +"$PYTHON" -I -B research/two-accumulator-saved-arms/build.py --mask 255 --output "$WORK/RAW.json.gz" +"$PYTHON" "$UP/code/hpe_audit_and_transport.py" --raw "$WORK/RAW.json.gz" --routing "$SRC/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz" --out "$WORK/local" +"$PYTHON" "$UP/code/hpe_emit_local.py" "$WORK/local" +"$PYTHON" "$UP/code/hpe_audit_local.py" "$WORK/local" +"$PYTHON" "$SRC/code/run_portable.py" "$UP/code/hpe_adapters_local.py" "$WORK/local/CANONICAL-WORD.json.gz" "$WORK/local/RESIDUAL-ADAPTERS.json" "$WORK/local/WRAPPER-CHECKS.json" +"$PYTHON" "$SRC/code/run_portable.py" "$SRC/vendor/pr558/code/phases_full.py" "$WORK/local" "$SRC/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford" +``` + +The recorded all-eight run passes: + +- transport and exact 704-column maps in both orientations; +- 24,883 emitted events in each orientation and complete paid mass 5602; +- independent local replay and 25 rejected controls; +- exact residual wrappers and 17 rejected controls; +- all 2,900 directed frame/centre edges with exact global phases and 224 + endpoint adapters. + +The new canonical content SHA256 is +`0d5d90211bf938b59c1897589e379dfa16eadb0aa3e832f2b01b01a9ea40e50e`. +The Clifford recipe byte SHA256 is +`816fb074375279ed914f9cc7ca14da285fba8c76d133d8db69a60d9cbe74e293`. +Compressed hashes in inherited receipts describe the recorded environment; +content hashes are the comparison for regenerated compressed files. + +The native run is for the all-eight word. The all-256 check has the separate +coverage in the README. No complete global owner, physical operator stream, +or new kappa is constructed by these native commands. + +## Comparison with PR1319 + +The fresh PR1319 head is +`603defe58aac018c6a8457840481390a15846fe4`. Both its base and extra providers +use a different local bill and helper inventory. Each still contains all +the gate values removed from B by these eight recipes, but this does not +establish compatibility. The selected cleanup gates at indices 6794 in +recipe 6 and 6791 in recipe 7 are absent from both providers. Their width +inventories are, respectively, + +```text +{4:44,5:44,7:38,8:114,9:240} +{4:40,5:48,7:38,8:114,9:240} +``` + +Thus the recipes do not apply byte-for-byte to these providers, and the +baseline dual constants in this proof do not apply to their inventories. +The saved-arm restoration also touches the later reader helpers 592 through +599. A composition needs new dirty-input, frame, endpoint, and complete +cost checks. This package makes no claim about that composition. diff --git a/research/two-accumulator-saved-arms/NOTICE.md b/research/two-accumulator-saved-arms/NOTICE.md new file mode 100644 index 0000000000..311bab95bb --- /dev/null +++ b/research/two-accumulator-saved-arms/NOTICE.md @@ -0,0 +1,39 @@ +# Attribution and license + +The new saved-arm recipes, complete cost proof, builder, and check package +are by Ali Romman <226877337+aliromman@users.noreply.github.com>, with +substantial OpenAI Codex assistance. They are under Apache-2.0. + +The source word is Jeremy Kothe's seven-slot k8 construction in PR1074, +which retains the PR1018 step and credits Rohan Arun's PR987 search. This +package takes the exact retained word from the PR1140 input archive. It +does not claim authorship of the earlier scalar, frame, source-access, +wrapper, or phase construction. The source notices are retained under +`inputs/notices/`. + +The research question comes from the explicit two-accumulator escape in +PR1238. That work proves the monotone frame-ancestry obstruction and checks +the one-accumulator schedules. PR1140 gives the distinct 224-helper clean +formation lower bound. This package does not reprove or strengthen that +bound. PR1012 supplies the rank-mass accounting distinction. + +`audit_local.py` is an unchanged copy of the independent gauge44 local +auditor retained by PR1238. Its header credits icekylinx and OpenAI GPT-6 +Astra assistance. `intervals.py` is an unchanged copy of `ceiling.py` from +PR1240. Its header credits Douglas Colkitt and Claude (Anthropic) assistance. +Their source commits and file hashes are in `SOURCES.json`. + +The whole-helper prices and root comparison come from PR1129, by Ali +Romman with OpenAI Codex assistance. That proof credits Chafik Boukhalfa's +PR795 prices and the PR890/PR942 owner-bound chain. The present additional +550 units of dual demand per rewrite, the two majorization inequalities, +and the all-mixture conclusion apply to the changed local words here. +The sprint coordinator independently supplied and checked this dual +calculation during the current work. + +PR1198 makes the arbitrary-private-centre input obligation explicit. +PR1387 gives a separate warning that scalar invoices and owner checks alone +can miss a changed physical operator. This package proposes no changed +global owner and makes no operator-level claim for a new host assignment. + +No predecessor license, notice, or AI disclosure is replaced by this file. diff --git a/research/two-accumulator-saved-arms/PROOF.md b/research/two-accumulator-saved-arms/PROOF.md new file mode 100644 index 0000000000..c0859231ee --- /dev/null +++ b/research/two-accumulator-saved-arms/PROOF.md @@ -0,0 +1,244 @@ +# Complete cost of the eight saved-arm recipes + +## 1. Declared method and free choices + +Fix the source word and the eight gate recipes in this package. A call can +use any subset of the recipes. Different calls can use different subsets. +There are nine calls and 896 live data families per replica. Let `T` be any +positive integer number of replicas. Whole helpers can use any owner map +with the retained capacity stock. Helpers cannot be split. The stock per +replica is + +| Capacity | Number of bins | +| --- | ---: | +| 8 | 672 | +| 16 | 448 | +| 32 | 448 | +| 48 | 448 | + +The proof below even removes owner chronology, coordinate matching, and +per-call restrictions. Thus it gives a lower cost bound for all owners that +satisfy those additional restrictions. The method does not add physical +families, change the nine-stage schedule, or change the unpaid-coordinate +and centre law. The bit supplier and the outer recipe stay fixed. + +The claim is an optimum for use of these eight completed recipes, including +the zero-recipe choice. It does not optimize arbitrary rational gates, +partitions, frame choices, or schedules. No finite synthesis search is used +as evidence for an all-order impossibility statement. + +## 2. Local construction and exact finite bill + +The old hub helpers are 448 through 455. Each has one entrance direction +and a rank-eight final frame, so its width is 7. In recipe `g`, helper +`448+g` keeps one pair sum until the full packet can be formed. The recipe +routes the old hub uses through their original source and uses the saved +pair to complete the packet in the other accumulator. It keeps the later +packet copy. It does not reduce the total count of 480 helpers. + +The complete recipe includes 19 ordered core gates with explicit frames, +removal of two old entrance corrections, two changed cleanup operands, and +four final full-frame corrections. The new saved-pair helper starts at +frame zero and ends at the full rank-nine frame. It therefore has width 9. +Its arbitrary initial value is not assumed to be zero. The four final +corrections remove its dirt from the affected packet and later helper +columns. The normal frame-zero compensation also uses this helper. This +explains why retaining its former low endpoint is not a free option. + +The recipes have explicit pins to every replaced source gate. Their changed +gate sites and cleanup sites are disjoint. The check replays every one of +the 256 subsets with exact rational arithmetic. It checks the complete +704-column forward and inverse-transpose maps, source reads, monotone +frame paths, centre levels, helper entrances, and both low-end cones. The +native check separately verifies the emitted all-eight word, wrappers, and +Clifford phases. These are finite construction checks, not a formal proof +of the full multiplication theorem. + +Write `H_r` for one rank-`r` child. The exact local changes are + +```text +even g in {0,2,4,6}: -2 H1 + 2 H2, +odd g in {1,3,5,7}: H2. +``` + +Every recipe adds two local rank units and changes one width 7 to width 9. +The baseline local profile is +`{1:2412,2:418,3:432,4:142,5:82,8:8}`. Its rank mass is 5586. Its width +inventory, in width order `(4,5,7,8,9)`, is `(56,32,30,122,240)`. + +Let `E` and `O` now count individual even and odd recipe uses over all +`9T` calls, and put `Z=E+O`. These counts need not be uniform across calls. +The complete residual rank mass is + +```text +M = 14814 T - 2 Z. +``` + +The complete mass remains `73*896*T - 320*T`. This includes the eight +rank-eight centre paths per call. The saving cannot come from a new deficit. + +## 3. A necessary inequality for every owner + +Use the signed prices from the PR1129 whole-helper proof, which credits +PR795 and the PR890/PR942 proof chain: + +```text +width price at (4,5,7,8,9): (-1,-20,-8,-2,4), +capacity bonus at (8,16,32,48): (2,4,8,-13). +``` + +For residual rank `r`, let `u(r)` be the largest bonus plus price of any +legal bin pattern with that residual. There are 1,163 legal patterns. +Enumeration and an independent unbounded-fill recurrence give the same +table. In particular, + +```text +u(0)=0, u(1)=19, u(48)=-13. +``` + +The baseline total signed price is `-1084 T`. A width-7 to width-9 change +adds 12, so the changed total is `S=-1084 T+12 Z`. If `n_r` counts residual +bins, every whole-helper assignment satisfies + +```text +sum r*n_r = 14814 T - 2 Z, +sum u(r)*n_r >= -1084 T + 12 Z. +``` + +Set `v(r)=48*u(r)+13*r`. Then `v(0)=v(48)=0`, `v(1)=925`, and + +```text +sum_(0= 140550 T + 550 Z. (1) +``` + +The additional demand is `48*12-13*2=550` for each recipe use. The sign is +positive. A model that consumes arbitrary rank-one idle mass misses this +new packing restriction. + +## 4. Supporting inequality at the baseline optimum + +For a complex saving `b`, let + +```text +f_b(r) = (r/73)^(1-b), +c_b(r) = 48*f_b(r) - r*f_b(48), +lambda_b = c_b(1)/925. +``` + +The baseline whole-helper optimum has its root in + +```text +I = [0.001676905273619680861300, + 0.001676905273619680861301]. +``` + +The exact interval checker proves, for every `b` in `I`, + +```text +lambda_b > 0, +c_b(r) > lambda_b*v(r) + for each attainable 0= + T*((5622/37)*f_b(1) + (11302/37)*f_b(48)) + + Z*((22/37)*f_b(1) - (2/37)*f_b(48)). (3) +``` + +For example, the coefficient of `f_b(1)` is +`(140550*T+550*Z)/925 = (5622*T+22*Z)/37`. The coefficient of `f_b(48)` +is the remaining mass divided by 48. This proves the claimed residual +increment without assuming that the fractional counts can be attained. + +## 5. Every nonempty use has a larger complete moment + +Combine (3) with the exact local changes. The complete increment for one +even recipe is + +```text +Delta_even = (2/37)*(37*f_b(2)-26*f_b(1)-f_b(48)). +``` + +The complete increment for one odd recipe is + +```text +Delta_odd = (1/37)*(22*f_b(1)+37*f_b(2)-2*f_b(48)). +``` + +Both are strictly positive for every `00` after multiplication by +the positive factor `73^(-s)`. + +The same argument applies to + +```text +(48, 48, 0 repeated 57 times) +(2 repeated 37 times, 1 repeated 22 times). +``` + +Their common sum is 96. It gives `2*48^s < 37*2^s+22`, which proves +`Delta_odd>0`. The checker verifies every integer partial-sum inequality. +Strict concavity supplies the theorem for the whole open interval. + +At the baseline optimum root `b0` in `I`, the unchanged complete moment is +`896*T`. Every changed owner with `Z>0` has moment at least + +```text +896*T + E*Delta_even + O*Delta_odd > 896*T. +``` + +All complete moments increase with `b`. Thus every nonempty finite mixture +has a complex root strictly smaller than `b0`. The argument permits all +positive replica counts and all per-call subsets. The 256 finite checks +establish the recipe bills; they are not the reason that the number of +replicas can be unbounded. + +## 6. Attainment and kappa + +The zero-recipe choice retains the PR1129 local word and owner inventory. +PR1129 supplies an exact attaining whole-helper pattern table and a +literal time-compatible T37 owner map. Its root is `b0`. This package +rechecks the pattern counts and the root bracket. The existing native +global and independent owner receipts remain predecessor evidence with +explicit pins. The global owner construction is not rerun here. + +The retained bit endpoint is `0.001733427039589844234749`, above `b0`. +The retained outer recipe is monotone in the complex endpoint in this +range. Its seven updates have the form `a_next=s*(1-s+a_old)` with fixed +strict reserves. PR1129 checks all 47 inequalities and both endpoints +of `I` give the same outer grid value, + +```text +kappa = 0.001674097969905390. +``` + +It follows that no member of this method family improves that value. +The zero-recipe choice attains the family optimum under the inherited +admission contract. A very sparse nonempty mixture can tie the same rounded +grid value; the strict statement concerns the complex root, not every +rounded display value. There is no claim of a new kappa. + +This argument uses the actual changed helper widths and all residual mass. +It remains valid if a changed word has further owner or physical-admission +restrictions. Those restrictions cannot lower the cost below this relaxed +bound. It gives no obstruction for a new local bill outside these recipes. diff --git a/research/two-accumulator-saved-arms/README.md b/research/two-accumulator-saved-arms/README.md new file mode 100644 index 0000000000..39096151ae --- /dev/null +++ b/research/two-accumulator-saved-arms/README.md @@ -0,0 +1,148 @@ +# Two accumulators: eight exact rewrites and their complete cost + +This package gives eight explicit two-accumulator rewrites of the selected +seven-slot R480 local word. The second accumulator keeps one pair sum while +the first accumulator completes a packet. All 256 subsets pass the exact +local scalar, frame, entrance, and helper-cone checks. + +The complete cost gives a negative result for this method. Each rewrite +changes one helper width from 7 to 9. A whole-helper packing inequality then +shows that **every nonempty use of these rewrites has a smaller complex root +than the unchanged-word optimum in PR1129**. The theorem permits different +subsets in different calls, every positive replica count, and every whole-helper +owner assignment with the retained capacity stock. It does not assume that +the current owner map stays fixed. + +This is a construction and a scoped obstruction. It is not an impossibility +theorem for all two-accumulator programs. Arbitrary new partitions, rational +changes of basis, other schedules and frames, mixed encodings of several +packets, and the other eight packet roles remain outside the proved family. +The broader question in the initial research claim remains open. + +The exact base is `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. At that base, +the selected PR1094 result is `kappa = 0.001672660197076918`. The stronger +applicable comparison is PR1129 at +`a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21`: its unchanged-word whole-helper +optimum gives `kappa = 0.001674097969905390` under the inherited admission +and outer recipe. This package does not change the selected result. + +## Reproduce + +Use Python 3.10 or newer with the standard library. Run from the repository +root. The command takes several minutes and writes its receipt outside the +package. + +```sh +python3 -I -B research/two-accumulator-saved-arms/verify.py --output /tmp/two-accumulator-check.json +``` + +Expected last line: + +```text +PASS_TWO_ACCUMULATOR_SAVED_ARM_FAMILY +``` + +The command checks all 256 subsets on all 704 local input columns in both +orientations. It checks the all-eight word with eight extra independent +private centre inputs, for 712 columns. It checks the 1,163 legal bin patterns +by enumeration and an independent fill recurrence. Exact rational intervals +certify the supporting moment inequalities at the baseline root. Integer +partial sums check the two majorization relations used in the proof. +Three negative controls remove a required dirty-column correction, restore +an unpaid low helper end, and request a mask outside the declared family. + +The fast mathematical check is: + +```sh +python3 -I -B research/two-accumulator-saved-arms/owner_bound.py +``` + +Its status is `PASS_ALL_REPLICA_SAVED_ARM_OBSTRUCTION`. + +The source binding and the feasible raw CF0 frame control have separate +short commands: + +```sh +python3 -I -B research/two-accumulator-saved-arms/check_sources.py +python3 -I -B research/two-accumulator-saved-arms/frame_control.py +``` + +The frame control reproduces a feasible order after 57,478 states, then +checks the order with explicit binary spans. It is a local positive control, +not a complete supplier. The registered `VERIFY.json` runs these two checks +and the complete family check with Python 3.12. + +To produce the all-eight local word: + +```sh +python3 -I -B research/two-accumulator-saved-arms/build.py --mask 255 --output /tmp/two-accumulator-word.json.gz +``` + +The decompressed canonical JSON SHA256 is +`25e6b6b9de424b83795a4050ce065130d34826a9f217b4b61f2d591d3383dad2`. +Compression-container bytes do not define mathematical equality. + +## The paid change + +Let `E` and `O` count the even and odd selected recipe groups in one call. +Each is between 0 and 4. The local profile and width changes are + +```text +delta H1 = -2 E +delta H2 = 2 E + O +delta local rank mass = 2(E+O) +delta width-7 count = -(E+O) +delta width-9 count = (E+O) +``` + +All other local ranks, helper counts, centre paths, and data endpoints stay +fixed. The all-eight profile is +`{1:2404,2:430,3:432,4:142,5:82,8:8}`, with mass 5602. Its helper widths are +`{4:56,5:32,7:22,8:122,9:248}`. The total deficit remains 320 per replica. + +It is not valid to remove two arbitrary rank-one idle children for each +rewrite. The new width-9 helpers change the legal bin fills. The exact dual +forces the residual moment to increase by at least +`(22/37) H1 - (2/37) H48` per switched call. After the local change, both +recipe types have a strictly positive complete moment increment. See +[PROOF.md](PROOF.md). + +## Evidence and limits + +`RECIPES.json` contains the full gate replacements, source-gate pins, +frames, and cleanup corrections. `build.py` applies these data without a +search. The independent local checker does not import this builder. +`evidence/` retains the completed check receipts and the native local +admission receipts. `NATIVE-REPLAY.md` gives the native replay commands and +their source pins. Native phase and wrapper checks cover the all-eight +word. The subset matrix checks have the separate coverage stated above. + +No new global owner map or physical operator stream is claimed. The cost +obstruction already holds in a relaxation that removes owner chronology +and physical matching constraints. The unchanged zero-switch construction +uses the existing PR1129 owner map. Its earlier admission receipts are +source-bound predecessor evidence, not a new cold replay in this package. + +The local checks do not prove the all-size multiplication theorem. The +all-size/compiler, common-label/mutable-source, whole-call hosting, +precision/tape, exact-recovery, analytic-transfer, and bit H1-H5 obligations +remain inherited. A finite native check does not discharge these obligations. + +## Open next questions + +1. Can another two-accumulator schedule preserve a width-7 endpoint or + produce a better rank distribution? This can change the dual penalty. + Start with a complete dirty-input identity and new endpoint bill for one + selected packet. The present proof fixes the eight recipes and does not + constrain that synthesis problem. +2. Can mixed encodings across several packets use fewer paid versions? + Such an encoding can leave the independent-recipe class. Start with its + exact arbitrary-input map and reader interface. A clean-input identity + alone does not resolve the restoration and source-access costs. +3. Do the other eight correctly rebound packet roles admit a useful + reconstruction? Their selected carriers differ from the raw PR1238 + numbering. Start from the binding data described in `RESEARCH-NOTES.md`. + The missing step is an exact construction or an all-order lower bound. + +Prepared by Ali Romman with substantial OpenAI Codex assistance. The license +is Apache-2.0. 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The +initial target was the 16 packet-copy roles in PR1238. The broader class is +not closed by this package. + +1. A frame search on the raw CF0 cluster found a feasible 21-operation order + after 57,478 distinct states. This is a positive control against an + inference that PR1238 already excludes two accumulators. It does not give + a complete admitted supplier. The control keeps the source-version + precedence relations and target caps of that local cluster. +2. An attempted no-return argument for both partial packet versions did + not transfer to the selected word. The selected factorization can keep + one arm clean while its reader operations occur. Thus no rank-two + first-formation theorem or universal copy-necessity theorem is claimed. +3. The first selected saved-arm schedule passed the frame search but had + local change `+8 H2 -4 H3 +2 H4 -2 H5`. It lost even under a favorable + rank-51 idle relaxation. That calculation was a reason to change the + schedule, not evidence of an all-order obstruction. +4. A search that always chose the smallest immediate common frame excluded + useful choices. Moving some frame growth earlier gave the final paid + changes in `RECIPES.json`. The full arbitrary-input cleanup added four + full-frame corrections per group. These are part of the final word. +5. The local improvement looked favorable if each extra two units could + replace two rank-one idle units. The PR1129 signed-price inequality + rejects that credit. The new width-9 helpers lose some width-7 plus + width-9 fills. The resulting all-replica moment penalty is the theorem + in this package. +6. The raw and selected numbering of the other eight roles differ. Their + selected first-arm carriers are + `[482,483,506,507,518,519,494,495]`, the second-arm carriers are + `[554,555,530,531,542,543,566,567]`, and their later packet copies are + 696 through 703. A first attempt to treat 456 through 463 as the same + selected roles was rejected during source binding. Those labels must + not support a theorem about the selected word. + +The final construction family is eight explicit recipes, with all subsets +and arbitrary mixtures across calls. The completed coverage is 256 exact +local words and an all-replica cost proof. There is no randomness in the +final check. The stopping rule for the family proof is exact positivity of +both complete increments at the known optimal baseline root. Once this +holds, a search for a better owner of these words cannot help. + +The other eight roles, new partitions, arbitrary rational encodings, and +other frame schedules remain open. This is a change from the broader +initial research objective, not a proof that the larger class fails. The +eight completed rewrites and the exact obstruction are retained because +they show which local mechanism works and why its complete price loses. + +The all-eight word also passes a 712-column scalar check. The extra eight +columns are independent additive values at the private centre reads. This +check addresses arbitrary private input values. It is not an operator-level +test of a new global host assignment. 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"322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955" + }, + { + "commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "path": "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/code/phases_full.py", + "git_blob": "d68f097d5dfe79de2667727914330943ef66d219", + "sha256": "a273c325ffd6793d5b63b79a289a9d2bbc9292e6940fb5a926924f3708627af4" + }, + { + "commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "path": "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-local/inputs/phase-baseline/CANONICAL-WORD.json.gz", + "git_blob": "cbb49a627768c42e1ff752f43ccfcc56ffe2cb0b", + "sha256": "e070ae2c78b4a1b644b418774af62b40d8d16e6ba89602f0474afb557d507c37", + "content_sha256": "7c84ac65c8b37173aa4293934f041915895e8ec30595844cc1534e2a19ae0d25" + } + ], + "attaining_table_source": { + "commit": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21", + "path": "research/r480-owner-optimum/PROOF.md", + "git_blob": "5eed050bdc998a112df26d2908e27b9d6434b8c1", + "sha256": "ef9d835a15aee46d7c502644666d6221ca62a031c52352b00df5d3baa16efafb" + }, + "related_source_pins": { + "PR1238": "50a1c992ce28c95d83d11bc691353aaa289d9d65", + "PR1140": "8e2e18b93d8c6b302e540ad5edc767cb98cf1514", + "PR1240": "1e136b8c4a552050820334ad113628775182f08c", + "PR1012": "4ceaf380ed41b28dadcc41d2f974f025ac4d8c03", + "PR1198": "2abd7e92b7ad3cd769376244ce32dc7b3501c2b3", + "PR1129": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21", + "PR1319": "603defe58aac018c6a8457840481390a15846fe4" + }, + "generated_inputs": [ + { + "local_path": "inputs/CF0-FRAME-CONTROL.json.gz", + "sha256": "72ffed494e3c27c9d7ef400457325c4f523f4b053a6f735b2d3bbd21dcb963de", + "content_sha256": "2db62aac9cb9d55e8505d8257b64b4089c14f6ceac71020d7b7e2926cc724424", + "source_commit": "50a1c992ce28c95d83d11bc691353aaa289d9d65", + "source_package": "research/end-cap-obstruction", + "source_output": "work/o_cf0/FULL-WORD.json.gz", + "role": "Raw CF0 frame/precedence control, not the selected local word" + } + ], + "predecessor_receipts": [ + { + "local_path": "evidence/PR1129-ROOT-ASSEMBLY.json", + "sha256": "d2ef417968ea68bd5abc0ad8d2d27ba99bfcede6cff8743a25ec34358a54cb9b", + "source_commit": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21", + "scope": "Previously completed coordinator reproduction. Not rerun as a global cold check in this package." + }, + { + "local_path": "evidence/PR1129-ROOT-GEOMETRY-CHECK.json", + "sha256": "0ec7ec310c8448dfa286849a810e73006319a4f37983959d7d4a1527137d1eb1", + "source_commit": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21", + "scope": "Previously completed coordinator reproduction. Not rerun as a global cold check in this package." + } + ] +} diff --git a/research/two-accumulator-saved-arms/TASK.json b/research/two-accumulator-saved-arms/TASK.json new file mode 100644 index 0000000000..6476e3fcc3 --- /dev/null +++ b/research/two-accumulator-saved-arms/TASK.json @@ -0,0 +1,65 @@ +{ + "schema_version": 1, + "task_id": "complex-new-helper-inventory", + "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "original_card": { + "id": "complex-new-helper-inventory", + "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?", + "starting_points": [ + "research/heterogeneous-owner-assembly/README.md", + "certificates/selected-result.json" + ], + "methods": [ + "Propose a changed helper inventory and derive an optimistic exact moment.", + "Design a small completed instance and independently verify its endpoint and rank bill." + ], + "acceptance_gate": "A new physically realizable contract, not another mixture already covered by the frozen catalogue.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the frozen catalogue bound exclusions and select one genuinely different helper endpoint inventory.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write the complete optimistic child histogram and reject it immediately if even the relaxation has insufficient headroom.", + "bottleneck_link": "Helper inventory changes can improve the moment; repacking a covered cost interface cannot evade its scoped bound.", + "allowed_variations": [ + "Narrow to one changed boundary or helper type with explicit counts." + ], + "scope_change_triggers": [ + "Mixing only providers already inside the pinned catalogue." + ], + "overlap_terms": [ + "helper inventory", + "heterogeneous-owner", + "mutable leaver" + ] + }, + "assignment": "Two-accumulator packet formation and versioning in the five-route sprint.", + "scope_status": "refined", + "actual_scope": "Eight explicit saved-arm rewrites of the selected R480 word, all per-call subsets and mixtures, every positive replica count, and every retained whole-helper owner assignment.", + "scope_change_reason": "The broader initial all-partition and rational-synthesis problem remains open. A raw two-accumulator schedule refuted a simple obstruction. Eight completed selected-word recipes were then built and their use was fully optimized with the whole-helper dual.", + "bottleneck_link": "Each valid recipe changes a width-7 helper to width 9. The full packing penalty makes both local recipe types increase the complete moment at the applicable PR1129 optimum.", + "stop_rule": "Finish all 256 exact local words and native all-eight admission. Prove the sign of each complete moment increment for arbitrary mixtures. Do not interpret the finite search as a universal synthesis bound.", + "evidence": "PROOF.md, RECIPES.json, evidence/FAMILY-CHECK.json, the native receipts, the source archive binding, and the feasible raw CF0 frame control.", + "outcome": "negative-result", + "author": "Ali Romman <226877337+aliromman@users.noreply.github.com>", + "ai_assistance": "Substantial OpenAI Codex assistance. The sprint coordinator independently checked the dual and the proof.", + "open_questions": [ + { + "question": "Can a different partition, rational encoding, or frame schedule improve the complete local bill?", + "why_it_matters": "Such a bill can leave the proved fixed-recipe family.", + "first_step": "Build one complete arbitrary-input map with paid source access, endpoints, and cleanup.", + "blocked_by": "No all-order synthesis theorem or admitted better word is known here." + }, + { + "question": "Can the method compose with the changed PR1319 providers?", + "why_it_matters": "They have stronger local words and different width inventories.", + "first_step": "Rebind the two missing cleanup gates and prove the changed private-dirt map before deriving a new dual.", + "blocked_by": "The current recipes and dual constants do not apply byte-for-byte." + } + ] +} diff --git a/research/two-accumulator-saved-arms/VERIFY.json b/research/two-accumulator-saved-arms/VERIFY.json new file mode 100644 index 0000000000..df862fa558 --- /dev/null +++ b/research/two-accumulator-saved-arms/VERIFY.json @@ -0,0 +1,64 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/check_sources.py" + ], + "checks": "Copied source hashes and the exact selected1094 archive-to-word binding.", + "timeout_seconds": 30 + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/frame_control.py" + ], + "checks": "Feasible 57478-state two-accumulator frame schedule with an independent explicit-span replay.", + "timeout_seconds": 30 + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py", + "--output", + "/tmp/two-accumulator-saved-arm-check.json" + ], + "checks": "All 256 local words, meaningful mutations, 712-column all-eight scalar interface, exact owner dual, attaining pattern table, root bracket, and strict majorization data.", + "timeout_seconds": 600 + } + ], + "inputs": [ + "research/two-accumulator-saved-arms/RECIPES.json", + "research/two-accumulator-saved-arms/SOURCES.json", + "research/two-accumulator-saved-arms/TASK.json", + "research/two-accumulator-saved-arms/audit_local.py", + "research/two-accumulator-saved-arms/build.py", + "research/two-accumulator-saved-arms/check_sources.py", + "research/two-accumulator-saved-arms/evidence/PR1129-ROOT-ASSEMBLY.json", + "research/two-accumulator-saved-arms/evidence/PR1129-ROOT-GEOMETRY-CHECK.json", + "research/two-accumulator-saved-arms/evidence/all-eight-CLIFFORD-REVIEW.json", + "research/two-accumulator-saved-arms/evidence/all-eight-INDEPENDENT-LOCAL-REPLAY.json", + "research/two-accumulator-saved-arms/evidence/all-eight-LOCAL-CHECKS.json", + "research/two-accumulator-saved-arms/evidence/all-eight-SCALAR-FRAME-AUDIT.json", + "research/two-accumulator-saved-arms/evidence/all-eight-WRAPPER-CHECKS.json", + "research/two-accumulator-saved-arms/evidence/selected1094-CANONICAL-WORD.json.gz", + "research/two-accumulator-saved-arms/evidence/selected1094-LOCAL-CHECKS.json", + "research/two-accumulator-saved-arms/evidence/selected1094-SCALAR-FRAME-AUDIT.json", + "research/two-accumulator-saved-arms/frame_control.py", + "research/two-accumulator-saved-arms/inputs/CF0-FRAME-CONTROL.json.gz", + "research/two-accumulator-saved-arms/inputs/SEVEN-SLOT-WORD.json.gz", + "research/two-accumulator-saved-arms/intervals.py", + "research/two-accumulator-saved-arms/owner_bound.py", + "research/two-accumulator-saved-arms/verify.py" + ] +} diff --git a/research/two-accumulator-saved-arms/audit_local.py b/research/two-accumulator-saved-arms/audit_local.py new file mode 100644 index 0000000000..4744d8783c --- /dev/null +++ b/research/two-accumulator-saved-arms/audit_local.py @@ -0,0 +1,171 @@ +"""Independent exact scalar/frame audit of the changed forward supplier. + +This does not import a generator, builder, stored compensation, or price. +All claimed endpoint matrices are derived from the input word's gates. +Optional --main checks the transported boundary against the pinned parent. +Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0. +""" +import argparse,gzip,json,hashlib,time +from pathlib import Path +from fractions import Fraction as F +from collections import Counter + +def require(x,label): + if not x:raise RuntimeError(label) + +def basis(vs): + piv={} + for a in vs: + while a: + bit=a.bit_length()-1 + if bit in piv:a^=piv[bit] + else: + piv[bit]=a;break + for k in sorted(piv): + for j in piv: + if j>k and piv[j]>>k&1:piv[j]^=piv[k] + return tuple(piv[k] for k in sorted(piv,reverse=True)) + +def contained(a,b):return basis(a+b)==b + +def registers(e):return e[1:3] if e[0]=='add' else e[1:2] + +def apply(e,rows,dual=False): + if e[0]=='add': + t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add') + if dual:t,s,q=s,t,-q + dst=rows[t] + for k,x in list(rows[s].items()): + a=dst.get(k,F(0))+q*x + if a:dst[k]=a + else:dst.pop(k,None) + elif e[0]=='scale': + t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale') + if dual:q=1/q + rows[t]={k:q*x for k,x in rows[t].items()} + else:raise RuntimeError('unknown scalar primitive') + +def invert(e): + r=list(e) + if r[0]=='add':r[3]=-r[3] + else:r[2],r[3]=r[3],r[2] + return r + +def check_parent_interface(word,main): + # Read only the retained boundary data. No builder or local checker is imported. + relative="research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz" + path=main/relative;raw=path.read_bytes() + require(hashlib.sha256(raw).hexdigest()=="66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",'parent canonical input pin') + parent=json.loads(gzip.decompress(raw)) + tau=lambda x:x^(43 if (x&43).bit_count()%2 else 0) + ports=parent['ports'];v=word['report']['v'] + require(len(ports)==len(set(ports))==v,'parent port count') + require(set(map(tau,word['ports']))==set(ports),'transported source/target ports') + moved={i:ports.index(tau(p)) for i,p in enumerate(word['ports'])} + centers=[moved.get(r,r) for r in word['centers']] + actual=[list(basis([tau(x) for x in frame])) for frame in word['center_frames']] + expected=[parent['frames'][f] for f in parent['center_frames']] + require(len(centers)==len(set(centers))==len(actual)==8,'eight distinct centre carriers') + require(actual==expected and all(len(f)==8 for f in actual),'ordered centre frame interface') + return dict(parent_path=relative,parent_file_sha256=hashlib.sha256(raw).hexdigest(), + transport_tau=43,ordered_frame_bases_match=True,all_ports_match=True, + transported_centers=centers,source_centers=[r for r in centers if r=2*v} + for e in w['precondition']:apply(e,dirt) + compensation=[['add',y,k,-a.numerator,a.denominator,[]] for y in range(v,2*v) for k,a in sorted(dirt[y].items())] + entering=set(map(int,w.get('start_extra',{})));lowends=set(map(int,w.get('helper_final',{}))) + coldends=lowends-entering + require(not any(e[2] in entering for e in compensation),'nonzero entrance response') + require(not any(r in entering|coldends for e in w['precondition']+compensation for r in registers(e)), 'pre-wrapper touch of residual helper') + require(all(e[-1]==[] for e in w['precondition']+compensation),'nonzero frame precondition') + early=w.get('early_cleanup',[]);earlyids={i for i,U in early} + require(len(earlyids)==len(early),'duplicate early cleanup gate') + tail=[w['cleanup'][i][:-1]+[U] for i,U in early] + cleanup=[e for i,e in enumerate(w['cleanup']) if i not in earlyids] + prefix=w['precondition']+compensation+main + program=prefix+tail+cleanup + for dual in (False,True): + actual=ident() + for e in program:apply(e,actual,dual) + expected=ident() + for t in range(v):expected[t if dual else v+t][v+t if dual else t]=F(-1 if dual else 1) + bad=[i for i in range(n) if actual[i]!=expected[i]] + require(not bad,'all-column endpoint failure '+str((dual,bad[:8]))) + print('endpoint', 'dual' if dual else 'forward','PASS',flush=True) + full=basis([1<> r["group"] & 1] + removed, insertions, correction = set(), {}, [] + profile = Counter({int(k): v for k, v in word["report"]["local_profile"].items()}) + widths = Counter({int(k): v for k, v in word["report"]["width_inventory"].items()}) + for recipe in chosen: + for i, expected in recipe["remove_B"]: + if word["B"][i] != expected or i in removed: + raise ValueError("B gate pin or overlapping recipes") + removed.add(i) + at = recipe["insert_before_B"] + if at in insertions: + raise ValueError("overlapping insertion sites") + insertions[at] = copy.deepcopy(recipe["insert_B"]) + for i, expected, replacement in recipe["cleanup_changes"]: + if word["cleanup"][i] != expected: + raise ValueError("cleanup gate pin") + word["cleanup"][i] = copy.deepcopy(replacement) + helper = str(recipe["partial_helper"]) + if len(word["start_extra"][helper]) != 1 or len(word["helper_final"][helper]) != 8: + raise ValueError("helper endpoint pin") + del word["start_extra"][helper] + del word["helper_final"][helper] + correction.extend(copy.deepcopy(recipe["full_cleanup_corrections"])) + profile.update({int(k): v for k, v in recipe["local_delta"].items()}) + widths[7] -= 1 + widths[9] += 1 + gates = [] + for i, gate in enumerate(word["B"]): + gates.extend(insertions.get(i, [])) + if i not in removed: + gates.append(gate) + word["B"] = gates + word["cleanup"] = correction + word["cleanup"] + word["early_cleanup"] = [[i + len(correction), frame] for i, frame in word["early_cleanup"]] + word["report"]["local_profile"] = {str(k): v for k, v in sorted(profile.items()) if v} + word["report"]["local_rank_mass"] = sum(k * v for k, v in profile.items()) + word["report"]["width_inventory"] = {str(k): v for k, v in sorted(widths.items()) if v} + word["refactored_cleanup"]["saved_arm_groups"] = [r["group"] for r in chosen] + return word + + +def write(word, path): + raw = json.dumps(word, sort_keys=True, separators=(",", ":")).encode() + path.write_bytes(gzip.compress(raw, mtime=0)) + return hashlib.sha256(raw).hexdigest() + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--mask", type=int, required=True) + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + print(write(construct(args.mask), args.output)) diff --git a/research/two-accumulator-saved-arms/check_sources.py b/research/two-accumulator-saved-arms/check_sources.py new file mode 100644 index 0000000000..ca5513e6e6 --- /dev/null +++ b/research/two-accumulator-saved-arms/check_sources.py @@ -0,0 +1,48 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Check the copied input bytes and their selected replay bindings.""" +import gzip +import hashlib +import json +import sys +from pathlib import Path + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import build + + +def verify(): + if not __debug__: + raise RuntimeError("verification requires assertions; do not use -O") + sources = json.loads((HERE / "SOURCES.json").read_text()) + records = (sources["dependencies"] + sources["generated_inputs"] + + sources["selected_archive"]["members"]) + checked = 0 + for record in records: + if "local_path" not in record: + continue + data = (HERE / record["local_path"]).read_bytes() + assert hashlib.sha256(data).hexdigest() == record["sha256"], record["local_path"] + if "content_sha256" in record: + assert hashlib.sha256(gzip.decompress(data)).hexdigest() == record["content_sha256"] + checked += 1 + selected = json.loads((HERE / "evidence/selected1094-SCALAR-FRAME-AUDIT.json").read_text()) + assert selected["input_content_sha256"] == build.SOURCE_HASH + assert selected["canonical_content_sha256"] == "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c" + original, zero = build.source(), build.construct(0) + for key in original: + if key != "refactored_cleanup": + assert original[key] == zero[key], key + assert selected["local_profile"] == original["report"]["local_profile"] + assert selected["local_rank_mass"] == 5586 + changed = json.loads((HERE / "evidence/all-eight-SCALAR-FRAME-AUDIT.json").read_text()) + encoded = json.dumps(build.construct(255), sort_keys=True, separators=(",", ":")).encode() + assert changed["input_content_sha256"] == hashlib.sha256(encoded).hexdigest() + assert changed["canonical_content_sha256"] == "0d5d90211bf938b59c1897589e379dfa16eadb0aa3e832f2b01b01a9ea40e50e" + return {"status": "PASS_SELECTED_REPLAY_AND_COPIED_SOURCE_BINDINGS", "copied_files": checked, + "scope": "Byte pins and recorded selected/native bindings; no native replay is run by this command."} + + +if __name__ == "__main__": + print(json.dumps(verify(), indent=2)) diff --git a/research/two-accumulator-saved-arms/evidence/FAMILY-CHECK.json b/research/two-accumulator-saved-arms/evidence/FAMILY-CHECK.json new file mode 100644 index 0000000000..6ec08da7e4 --- /dev/null +++ b/research/two-accumulator-saved-arms/evidence/FAMILY-CHECK.json @@ -0,0 +1,4907 @@ +{ + "status": "PASS_TWO_ACCUMULATOR_SAVED_ARM_FAMILY", + "masks": [ + { + "content_sha256": "17b289e46cda795604a748bd15cd30c6fdc564676a0adf4542ba770de40d0f91", + "local_profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + }, + "width_inventory": { + 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This checks the scalar interface, not a new global physical stream." + }, + "owner_bound": { + "status": "PASS_ALL_REPLICA_SAVED_ARM_OBSTRUCTION", + "patterns": 1163, + "root_bracket": [ + "16769052736196808613/10000000000000000000000", + "1676905273619680861301/1000000000000000000000000" + ], + "minimum_support_margin": "67288680406911894814011510862786604492728432751002874662255421744838013605/16735575397580856369812993927036924181917927471205862771327853938643694518272", + "residual_increment_per_switch": { + "1": "22/37", + "48": "-2/37" + }, + "even_total_increment": { + "1": "-52/37", + "2": "2", + "48": "-2/37" + }, + "odd_total_increment": { + "1": "22/37", + "2": "1", + "48": "-2/37" + } + }, + "rejected_controls": { + "missing_dirty_column_restore": "all-column endpoint failure (False, [13, 14, 77, 78, 281, 283, 284, 285])", + "unpaid_low_helper_end": "pre-wrapper touch of residual helper", + "out_of_domain_mask": "mask must be an integer from 0 through 255" + }, + "elapsed_seconds": 164.03151004202664, + "scope": "All 256 fixed local recipes are checked. 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It does not classify all two-accumulator programs." +} diff --git a/research/two-accumulator-saved-arms/evidence/FRAME-CONTROL.json b/research/two-accumulator-saved-arms/evidence/FRAME-CONTROL.json new file mode 100644 index 0000000000..1230cabdfa --- /dev/null +++ b/research/two-accumulator-saved-arms/evidence/FRAME-CONTROL.json @@ -0,0 +1,28 @@ +{ + "status": "PASS_FEASIBLE_TWO_ACCUMULATOR_FRAME_CONTROL", + "states": 57478, + "order": [ + "r1", + "r3", + "a1", + "r4", + "a3", + "s1", + "r2", + "s3", + "s2", + "b7", + "s4", + "b9", + "W1", + "W2", + "e1", + "e2", + "q1", + "q2", + "W3", + "z1", + "z2" + ], + "scope": "Raw CF0 frame and precedence control only; no scalar or complete supplier admission is claimed." +} diff --git a/research/two-accumulator-saved-arms/evidence/PR1129-ROOT-ASSEMBLY.json b/research/two-accumulator-saved-arms/evidence/PR1129-ROOT-ASSEMBLY.json new file mode 100644 index 0000000000..0e696d96ee --- /dev/null +++ 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The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain." +} diff --git a/research/two-accumulator-saved-arms/evidence/PR1129-ROOT-GEOMETRY-CHECK.json b/research/two-accumulator-saved-arms/evidence/PR1129-ROOT-GEOMETRY-CHECK.json new file mode 100644 index 0000000000..a4f3de140d --- /dev/null +++ b/research/two-accumulator-saved-arms/evidence/PR1129-ROOT-GEOMETRY-CHECK.json @@ -0,0 +1,10 @@ +{ + "roles": 159840, + "idle": { + "0": 57668, + "1": 5622, + "48": 11302 + }, + "owner_content_sha256": "592dd6d5c3dc29a33472f75425f9652c73993a8e38bdc17c7372b321aaeefa03", + "status": "PASS_LITERAL_WHOLE_HELPER_GEOMETRY" +} diff --git a/research/two-accumulator-saved-arms/evidence/all-eight-CLIFFORD-REVIEW.json b/research/two-accumulator-saved-arms/evidence/all-eight-CLIFFORD-REVIEW.json new file mode 100644 index 0000000000..adf3ce24f2 --- /dev/null +++ b/research/two-accumulator-saved-arms/evidence/all-eight-CLIFFORD-REVIEW.json @@ -0,0 +1,19 @@ +{ + "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES", + "canonical_word_sha256": "6938e73de561f64bc456aef75d64db346b3d526018e0e9ee446da239996c19c9", + "frames": 1004, + "directed_edges": 2900, + "ranks": { + "1": 1920, + "2": 392, + "3": 408, + "8": 16, + "4": 124, + "5": 40 + }, + "endpoint_adapters": 224, + "all_child_equalities_include_global_phase": true, + "recipe_sha256": "816fb074375279ed914f9cc7ca14da285fba8c76d133d8db69a60d9cbe74e293", + "seconds": 117.40860829222947, + "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations." +} diff --git a/research/two-accumulator-saved-arms/evidence/all-eight-INDEPENDENT-LOCAL-REPLAY.json b/research/two-accumulator-saved-arms/evidence/all-eight-INDEPENDENT-LOCAL-REPLAY.json new file mode 100644 index 0000000000..106f11195e --- /dev/null +++ b/research/two-accumulator-saved-arms/evidence/all-eight-INDEPENDENT-LOCAL-REPLAY.json @@ -0,0 +1,71 @@ +{ + "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY", + "canonical_word_sha256": "6938e73de561f64bc456aef75d64db346b3d526018e0e9ee446da239996c19c9", + "local_programs_sha256": "b6968fcf8436bdd87537ca32fa3b2b35f8f92f052bf2af84cd35809ffe1fc48a", + "v": 112, + "helpers": 480, + "local": { + "forward": { + "all_exact_columns": 704, + "prefix_l1_upper": "11061381177932725185/4096", + "prefix_bits_upper": 52, + "charged_payload_bits": 192, + "private_work_erased": true + }, + "backward": { + "all_exact_columns": 704, + "prefix_l1_upper": "14824947804757647822141/64", + "prefix_bits_upper": 68, + "charged_payload_bits": 192, + "private_work_erased": true + } + }, + "paid_profiles": { + "forward": { + "1": 2404, + "4": 142, + "8": 8, + "3": 432, + "2": 430, + "5": 82 + }, + "backward": { + "1": 2404, + "4": 142, + "8": 8, + "3": 432, + "2": 430, + "5": 82 + } + }, + "entering_helpers": 184, + "cold_hyperplane_ended_helpers": 48, + "negative_controls_rejected": [ + "wrong_scale", + "missing_center", + "wrong_common_frame", + "wrong_child_rank", + "missing_pre_wrapper", + "missing_post_wrapper", + "wrapper_with_wrong_frame", + "wrapper_in_wrong_phase", + "wrapper_on_a_data_register", + "wrapper_on_a_target_register", + "wrapper_on_a_centre_register", + "hpe_pre_wrapper_resolved_to_full_recipe", + "hpe_post_wrapper_without_terminal_frame", + "hpe_post_wrapper_wrong_terminal_frame", + "hpe_tail_gate_at_full_frame", + "hpe_tail_climb_dropped", + "hpe_helper_exit_adapter_to_full", + "hpe_tail_gate_moved_into_full_cleanup", + "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter", + "cold_hpe_pre_wrapper_dropped", + "cold_hpe_post_wrapper_replaced_by_exit_adapter", + "cold_hpe_pre_wrapper_resolved_to_cold_full_convention", + "cold_hpe_wrapper_with_nonzero_entrance", + "cold_hpe_post_wrapper_wrong_terminal_frame", + "cold_hpe_premix_gate_before_pre_wrapper" + ], + "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate." +} diff --git a/research/two-accumulator-saved-arms/evidence/all-eight-LOCAL-CHECKS.json b/research/two-accumulator-saved-arms/evidence/all-eight-LOCAL-CHECKS.json new file mode 100644 index 0000000000..3e0dd22ce4 --- /dev/null +++ b/research/two-accumulator-saved-arms/evidence/all-eight-LOCAL-CHECKS.json @@ -0,0 +1,36 @@ +{ + "forward": { + "sha256": "a1524780b736219a103a3034692dc10fb0837df3edf6ba389278dbe01d536aaa", + "events": 24883, + "scalar_macros": 19805, + "real_component_primitive_bound": 200062, + "paid_profile": { + "1": 2404, + "2": 430, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + }, + "all_columns": 704, + "private_centers_cleared": true, + "private_coefficient_stream_cleared_after_each_macro": true + }, + "backward": { + "sha256": "250c4bdddcfbd1c7ab6b38f7eb5f9dd2c550b5332d11f1a05754b9373b4ef830", + "events": 24883, + "scalar_macros": 19805, + "real_component_primitive_bound": 200110, + "paid_profile": { + "1": 2404, + "2": 430, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + }, + "all_columns": 704, + "private_centers_cleared": true, + "private_coefficient_stream_cleared_after_each_macro": true + } +} diff --git a/research/two-accumulator-saved-arms/evidence/all-eight-SCALAR-FRAME-AUDIT.json b/research/two-accumulator-saved-arms/evidence/all-eight-SCALAR-FRAME-AUDIT.json new file mode 100644 index 0000000000..5f81e76998 --- /dev/null +++ b/research/two-accumulator-saved-arms/evidence/all-eight-SCALAR-FRAME-AUDIT.json @@ -0,0 +1,714 @@ +{ + "status": "PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES", + "input_content_sha256": "25e6b6b9de424b83795a4050ce065130d34826a9f217b4b61f2d591d3383dad2", + "routing_content_sha256": "7c84ac65c8b37173aa4293934f041915895e8ec30595844cc1534e2a19ae0d25", + "canonical_content_sha256": "0d5d90211bf938b59c1897589e379dfa16eadb0aa3e832f2b01b01a9ea40e50e", + "live_columns_each_orientation": 704, + "helpers": 480, + "compensation_additions": 7304, + "scalar_operations": 19781, + "center_rank_sum": 64, + "local_profile": { + "1": 2404, + "2": 430, + "3": 432, + "4": 142, + "5": 82, + "8": 8 + }, + "local_rank_mass": 5602, + "widths": [ + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 9, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 9, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 8, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 8, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 9, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 9, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 9, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 4, + 9, + 4, + 9, + 4, + 9, + 9, + 9, + 9, + 4, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 9, + 8, + 8, + 8, + 8, + 8, + 8, + 9, + 9, + 9, + 9, + 9, + 9, + 7, + 7, + 8, + 8, + 8, + 8, + 9, + 9, + 9, + 9, + 9, + 9, + 8, + 8, + 8, + 9, + 8, + 8, + 9, + 9, + 9, + 9, + 8, + 9, + 7, + 7, + 8, + 9, + 8, + 8, + 9, + 9, + 9, + 9, + 8, + 9, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 9, + 7, + 7, + 7, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 9, + 7, + 8, + 8, + 9, + 9, + 9, + 9, + 8, + 8, + 8, + 8, + 7, + 7, + 7, + 7, + 9, + 8, + 9, + 8, + 8, + 8, + 8, + 8, + 7, + 7, + 9, + 8, + 9, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5, + 8, + 8, + 8, + 4, + 8, + 4, + 4, + 4, + 8, + 8, + 8, + 4, + 8, + 4, + 4, + 4, + 8, + 8, + 8, + 4, + 8, + 4, + 4, + 4, + 8, + 8, + 8, + 4, + 8, + 4, + 4, + 4, + 8, + 8, + 8, + 4, + 8, + 4, + 4, + 4, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5, + 8, + 8, + 8, + 4, + 8, + 4, + 4, + 4, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5, + 8, + 8, + 8, + 5, + 8, + 5, + 5, + 5 + ], + "frames": 1004, + "directed_edges": 2900, + "tau": 43, + "target_port_order_matches_baseline": true, + "seconds": 0.9958857917226851, + "scope": "Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. 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591, 471, 483, 703) +OPERATIONS = { + "r1": (125, 231), "r2": (124, 231), "r3": (124, 283), "r4": (125, 281), + "a3": (591, 283), "a1": (591, 281), "s1": (149, 231), "s2": (148, 231), + "s3": (148, 299), "s4": (149, 297), "b9": (703, 299), "b7": (703, 297), + "W1": (283, 281), "W2": (299, 297), "e1": (471, 283), "e2": (483, 299), + "q1": (125, 299), "q2": (149, 283), "W3": (283, 299), + "z1": (124, 483), "z2": (148, 471), +} +PRECEDENCE = ( + ("r3", "W1"), ("a3", "W1"), ("W1", "e1"), ("W1", "q2"), + ("e1", "W3"), ("q2", "W3"), ("s3", "W2"), ("b9", "W2"), + ("W2", "e2"), ("W2", "q1"), ("W2", "W3"), ("e2", "z1"), + ("e1", "z2"), ("W1", "W3"), ("q1", "W3"), ("e2", "W3"), +) +CAPS = ((124, 12), (125, 13), (148, 36), (149, 37), + (591, 58), (591, 63), (703, 58), (703, 63)) + + +def verify(): + if not __debug__: + raise RuntimeError("verification requires assertions; do not use -O") + word = json.loads(gzip.decompress((HERE / "inputs/CF0-FRAME-CONTROL.json.gz").read_bytes())) + ports = word["ports"] + frames = {r: (p,) for r, p in enumerate(ports)} + frames.update({int(r): basis(f) for r, f in word.get("start_extra", {}).items()}) + for gate in word["A"] + word["B"][:239]: + for r in gate[1:3] if gate[0] == "add" else gate[1:2]: + frames[r] = basis(frames.get(r, ()) + tuple(gate[-1])) + frames[703] = () + initial = tuple(frames.get(r, ()) for r in REGISTERS) + names = list(OPERATIONS) + index = {r: i for i, r in enumerate(REGISTERS)} + gates = [tuple(index[r] for r in OPERATIONS[n]) for n in names] + predecessors = [sum(1 << names.index(a) for a, b in PRECEDENCE if b == n) for n in names] + seen = set() + + @lru_cache(None) + def join(a, b): + return basis(a + b) + + @lru_cache(None) + def admissible(r, frame): + return all(not ((v & ports[t]).bit_count() % 2) + for rr, t in CAPS if rr == r for v in frame) + + def search(done, current): + if done == (1 << len(names)) - 1: + return [] + key = done, current + if key in seen: + return None + seen.add(key) + for i, (a, b) in enumerate(gates): + if done >> i & 1 or predecessors[i] & ~done: + continue + frame = join(current[a], current[b]) + if not admissible(REGISTERS[a], frame) or not admissible(REGISTERS[b], frame): + continue + changed = list(current) + changed[a] = changed[b] = frame + tail = search(done | (1 << i), tuple(changed)) + if tail is not None: + return [names[i]] + tail + return None + + order = search(0, initial) + assert order is not None and len(seen) == 57478 + assert set(order) == set(names) + assert all(order.index(a) < order.index(b) for a, b in PRECEDENCE) + # Check the found order with explicit spans, without the cached joins. + spans = {r: {0} for r in REGISTERS} + for r, frame in zip(REGISTERS, initial): + for v in frame: + spans[r] |= {x ^ v for x in tuple(spans[r])} + for name in order: + a, b = OPERATIONS[name] + merged = {x ^ y for x in spans[a] for y in spans[b]} + spans[a] = spans[b] = merged + for r, target in CAPS: + assert all((v & ports[target]).bit_count() % 2 == 0 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zCl`wHJZT&{6fKxLM^6pC{+UZOe=a85H~l^OWp9&fKoKsSKxwpyO2F?g2Tg?CsHDZa zgc1|e-;_MDMuN+dz?GyYPU+(jiD22qOB13+eaF|qvliGEEk&8LPwLnpIli1DI*{lx zVyE=8T^HPX#6}ca`1oj8{kTN5Y7Tg3eN}mS?o22_R0j#QUtbM8B-Q2O2V=fsh`*?_ zVed!@D*l)HTW_@VgU^MKF2m-a`8mwiOvF+RW&tkc?Z^`wi`dK>=pK- z;s>efY&B5?M1$KSvl1HSy#bVg-}WJrFfiQL5U(NWbqX3j1iS_pzb1-{n3--MQIE zou7v4T^TKdbTYTiKhFt2u!T*DJZoToQYAL&e^yGE!G9_v>*btxyop!HYLIph%hkg- zGk?uxYm!4W#^Q9B71u|-WMi3FQfIccOcJwg6f=O1{-`4)=>vY^y~ZJ`CVVczMnPuhChNr&R!{wu5BlTXo`RMSr;gRlH^4bJ9n?kXZBp3HHRW 1 is a what-if for a changed coverage law only); + * the local word fixes its own paid child profile `local` (per call); + * every remaining unit of mass is an idle/remainder child of rank at most R, where the outer + recipe's halving guard m^2 > 2 R^2 bounds R (R = 51 for m = 73). + +Lemma. For a >= 0, a child of rank r costs (r/m)^(1-a) = r * c(r), with c(r) = r^(-a) m^(a-1) +non-increasing in r. Hence, with idle mass M fixed and idle ranks <= R, every idle histogram has +moment >= the relaxation that puts all of M into (possibly fractional) rank-R children: + + relax(a) = [ sum_local n_r (r/m)^(1-a) + (M/R) (R/m)^(1-a) ] / w (per call). + +The moment is increasing in a. So relax(a*) > 1 certifies that no hosting, owner packing or +idle-remainder change of the given local word, template and outer recipe certifies a saving +>= a*. Under the retained reduction kappa < a/(1+a) when the complex side binds, so +a*/(1+a*) also bounds kappa. This is a bound for the stated model, not for other local words, +templates, coverage laws or outer recipes. + +Exact rational intervals: ln k from atanh chains, exp by Taylor with Lagrange remainder, +outward rounding to 2^-PREC. Standard library only. Douglas Colkitt, with Claude (Anthropic) +assistance. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import isqrt + +PREC = 256 + + +def require(ok, why): + if not ok: + raise ValueError(why) + + +def down(x): + return Q((x.numerator << PREC) // x.denominator, 1 << PREC) + + +def up(x): + return -down(-x) + + +@lru_cache(None) +def atanh(t): + """Enclosure of atanh(t) for rational 0 < t <= 1/3.""" + require(0 < t <= Q(1, 3), 'atanh range') + s, p, k = Q(0), t, 0 + while True: + term = p / (2 * k + 1) + s += term + p *= t * t + k += 1 + tail = p / ((2 * k + 1) * (1 - t * t)) + if tail < Q(1, 1 << (PREC + 8)): + return down(s), up(s + tail) + + +@lru_cache(None) +def ln(k): + """Enclosure of ln k for an integer k >= 1: ln k = ln(k-1) + 2 atanh(1/(2k-1)).""" + require(isinstance(k, int) and k >= 1, 'ln domain') + if k == 1: + return Q(0), Q(0) + lo, hi = ln(k - 1) + a, b = atanh(Q(1, 2 * k - 1)) + return down(lo + 2 * a), up(hi + 2 * b) + + +def exp(lo, hi): + """Enclosure of exp([lo, hi]) for 0 <= lo <= hi <= 1/2.""" + require(0 <= lo <= hi <= Q(1, 2), 'exp range') + def series(y, upper): + s, t, k = Q(1), Q(1), 0 + while True: + k += 1 + t = t * y / k + s += t + if t * y < Q(1, 1 << (PREC + 8)): + return up(s + 2 * t * y / (k + 1)) if upper else down(s) + return series(lo, False), series(hi, True) + + +def child_cost(r, m, a): + """Enclosure of (r/m)^(1-a) = (r/m) exp(a ln(m/r)).""" + lm, um = ln(m) + lr, ur = ln(r) + e = exp(max(Q(0), a * (lm - ur)), a * (um - lr)) + return down(Q(r, m) * e[0]), up(Q(r, m) * e[1]) + + +def max_idle_rank(m): + """Largest R with m^2 > 2 R^2 (outer halving guard).""" + R = isqrt((m * m - 1) // 2) + while 2 * (R + 1) ** 2 < m * m: + R += 1 + while 2 * R * R >= m * m: + R -= 1 + return R + + +def model(local, m, families, stages, centre, R=None, unpaid=1): + """Per-call quantities. local: {rank: count per call (Fraction ok)}.""" + R = max_idle_rank(m) if R is None else R + require(2 * R * R < m * m, 'idle rank cap violates the halving guard') + require(all(0 < r < m for r in local) and all(n >= 0 for n in local.values()), 'local profile') + w = Q(families, stages) + require(1 <= unpaid < m, 'unpaid coordinates per family') + total = (m - unpaid) * w + centre + local_mass = sum(r * Q(n) for r, n in local.items()) + idle = total - local_mass + require(idle >= 0, 'local word pays more mass than the coverage law allows') + return dict(R=R, w=w, total_mass=total, local_mass=local_mass, idle_mass=idle, deficit=unpaid * w - centre) + + +def relax(local, m, families, stages, centre, a, R=None, unpaid=1): + """Enclosure of the per-call relaxation moment at saving a.""" + q = model(local, m, families, stages, centre, R, unpaid) + lo = hi = Q(0) + for r, n in local.items(): + c = child_cost(r, m, a) + lo, hi = lo + Q(n) * c[0], hi + Q(n) * c[1] + c = child_cost(q['R'], m, a) + k = q['idle_mass'] / q['R'] + lo, hi = lo + k * c[0], hi + k * c[1] + return down(lo / q['w']), up(hi / q['w']) + + +def ceiling(local, m, families, stages, centre, grid=Q(1, 10 ** 15), R=None, unpaid=1): + """Grid bracket [a_lo, a_hi]: relax(a_lo) < 1 < relax(a_hi), certified. a_hi is the ceiling.""" + lo, hi = Q(0), Q(1, 20) + require(relax(local, m, families, stages, centre, hi, R, unpaid)[0] > 1, 'search window too small') + require(relax(local, m, families, stages, centre, lo, R, unpaid)[1] < 1, 'relaxation has no positive saving') + while hi - lo > grid: + mid = Q(int((lo + hi) / 2 / grid)) * grid + if mid <= lo: + mid = lo + grid + v = relax(local, m, families, stages, centre, mid, R, unpaid) + if v[1] < 1: + lo = mid + elif v[0] > 1: + hi = mid + else: + raise ValueError('enclosure too wide to separate the grid point') + return lo, hi diff --git a/research/two-accumulator-saved-arms/owner_bound.py b/research/two-accumulator-saved-arms/owner_bound.py new file mode 100644 index 0000000000..a127547902 --- /dev/null +++ b/research/two-accumulator-saved-arms/owner_bound.py @@ -0,0 +1,150 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Check the whole-helper dual and the strict saved-arm moment increments.""" +from fractions import Fraction as Q +from pathlib import Path +import sys + +sys.path.insert(0, str(Path(__file__).resolve().parent)) +import intervals as I + +WIDTHS = (4, 5, 7, 8, 9) +PRICES = (-1, -20, -8, -2, 4) +CAPACITIES = {8: 672, 16: 448, 32: 448, 48: 448} +BONUS = {8: 2, 16: 4, 32: 8, 48: -13} +BASE_WIDTHS = (56, 32, 30, 122, 240) +LOCAL = {1: 2412, 2: 418, 3: 432, 4: 142, 5: 82, 8: 8} +ROOT = (Q("0.001676905273619680861300"), Q("0.001676905273619680861301")) +ATTAINING_BINS = ( + (8, (0, 0, 0, 1, 0), 24864, 0), + (16, (0, 0, 0, 2, 0), 3306, 0), + (16, (0, 0, 1, 0, 1), 9394, 0), + (16, (2, 0, 0, 1, 0), 3876, 0), + (32, (0, 0, 2, 0, 2), 298, 0), + (32, (0, 1, 0, 0, 3), 10656, 0), + (32, (1, 0, 0, 0, 3), 5622, 1), + (48, (0, 0, 0, 0, 0), 11302, 48), + (48, (1, 0, 0, 1, 4), 5274, 0), +) + + +def patterns(capacity, position=0): + if position == len(WIDTHS): + yield (), capacity, 0 + return + width, price = WIDTHS[position], PRICES[position] + for count in range(capacity // width + 1): + for tail, residual, value in patterns(capacity - count * width, position + 1): + yield (count,) + tail, residual, value + count * price + + +def price_table(): + table, count = {}, 0 + for capacity in CAPACITIES: + for _, residual, value in patterns(capacity): + value += BONUS[capacity] + table[residual] = max(table.get(residual, value), value) + count += 1 + # This recurrence has no pattern-count vectors. + fills = [None] * 49 + fills[0] = 0 + for filled in range(1, 49): + values = [fills[filled - w] + p for w, p in zip(WIDTHS, PRICES) + if filled >= w and fills[filled - w] is not None] + if values: + fills[filled] = max(values) + other = {} + for capacity in CAPACITIES: + for filled in range(capacity + 1): + if fills[filled] is not None: + residual = capacity - filled + value = BONUS[capacity] + fills[filled] + other[residual] = max(other.get(residual, value), value) + assert table == other + assert count == 1163 and (table[0], table[1], table[48]) == (0, 19, -13) + return table, count + + +def interval_sum(coefficients, endpoint_range=ROOT): + lower = upper = Q(0) + for rank, coefficient in coefficients.items(): + lo = I.child_cost(rank, 73, endpoint_range[0])[0] + hi = I.child_cost(rank, 73, endpoint_range[1])[1] + lower += coefficient * (lo if coefficient >= 0 else hi) + upper += coefficient * (hi if coefficient >= 0 else lo) + return lower, upper + + +def majorizes(left, right): + left, right = sorted(left, reverse=True), sorted(right, reverse=True) + assert len(left) == len(right) and sum(left) == sum(right) + a = b = 0 + for x, y in zip(left, right): + a += x + b += y + assert a >= b + assert left != right + + +def complete_bound(even=0, odd=0): + # Counts are per call. Fractional values give the all-call average. + total = Q(even) + Q(odd) + profile = {r: Q(9 * n) for r, n in LOCAL.items()} + profile[1] -= 18 * even + profile[2] += 18 * even + 9 * odd + n1 = Q(5622, 37) + Q(198, 37) * total + n48 = Q(11302, 37) - Q(18, 37) * total + profile[1] += n1 + profile[48] = n48 + assert sum(r * n for r, n in profile.items()) == 73 * 896 - 320 + return profile + + +def verify(): + if not __debug__: + raise RuntimeError("verification requires assertions; do not use -O") + table, count = price_table() + mass = sum(c * n for c, n in CAPACITIES.items()) - 9 * sum(w * n for w, n in zip(WIDTHS, BASE_WIDTHS)) + price = sum(BONUS[c] * n for c, n in CAPACITIES.items()) + 9 * sum(p * n for p, n in zip(PRICES, BASE_WIDTHS)) + assert (mass, price, 48 * price + 13 * mass) == (14814, -1084, 140550) + # One switched call replaces one width 7 with one width 9. + assert 48 * (PRICES[4] - PRICES[2]) - 13 * 2 == 550 + assert Q(550, 925) == Q(22, 37) + assert (2 + Q(22, 37)) / 48 == Q(2, 37) + margins = [] + for rank, value in table.items(): + if rank in (0, 1, 48): + continue + v = 48 * value + 13 * rank + coefficients = {rank: Q(48), 48: -rank + Q(v, 925), 1: -Q(48 * v, 925)} + lo, _ = interval_sum(coefficients) + assert lo > 0, (rank, lo) + margins.append(lo) + assert interval_sum({1: Q(48), 48: Q(-1)})[0] > 0 + majorizes([48] + [1] * 26 + [0] * 10, [2] * 37) + majorizes([48, 48] + [0] * 57, [2] * 37 + [1] * 22) + profile = complete_bound() + below = interval_sum(profile, (ROOT[0], ROOT[0])) + above = interval_sum(profile, (ROOT[1], ROOT[1])) + assert below[1] < 896 < above[0] + for capacity, stock in CAPACITIES.items(): + assert sum(n for c, _, n, _ in ATTAINING_BINS if c == capacity) == 37 * stock + for i, stock in enumerate(BASE_WIDTHS): + assert sum(p[i] * n for _, p, n, _ in ATTAINING_BINS) == 37 * 9 * stock + for capacity, pattern, _, residual in ATTAINING_BINS: + assert sum(w * n for w, n in zip(WIDTHS, pattern)) + residual == capacity + assert {r: sum(n for _, _, n, s in ATTAINING_BINS if s == r) + for r in (1, 48)} == {1: 5622, 48: 11302} + # Free removal of two rank-1 residuals contradicts the necessary dual. + false_n1 = Q(5622, 37) - 2 + assert 925 * false_n1 < 140550 + 550 + return {"status": "PASS_ALL_REPLICA_SAVED_ARM_OBSTRUCTION", "patterns": count, + "root_bracket": list(map(str, ROOT)), "minimum_support_margin": str(min(margins)), + "residual_increment_per_switch": {"1": "22/37", "48": "-2/37"}, + "even_total_increment": {"1": "-52/37", "2": "2", "48": "-2/37"}, + "odd_total_increment": {"1": "22/37", "2": "1", "48": "-2/37"}} + + +if __name__ == "__main__": + import json + print(json.dumps(verify(), indent=2)) diff --git a/research/two-accumulator-saved-arms/verify.py b/research/two-accumulator-saved-arms/verify.py new file mode 100644 index 0000000000..7377df1753 --- /dev/null +++ b/research/two-accumulator-saved-arms/verify.py @@ -0,0 +1,134 @@ +#!/usr/bin/env python3 +# SPDX-License-Identifier: Apache-2.0 +"""Check every recipe subset, arbitrary private centre inputs, and the owner bound.""" +import argparse +import contextlib +import copy +import io +import json +import sys +import tempfile +import time +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) +import audit_local as A +import build as B +import owner_bound as O + + +def augmented_program(word): + rows = [{r: Q(1)} for r in range(704)] + for gate in word["A"] + word["cut"] + word["B"]: + A.apply(gate, rows) + dirt = [{k: x for k, x in rows[r].items() if k >= 224} + if 112 <= r < 224 else {} for r in range(704)] + for gate in word["precondition"]: + A.apply(gate, dirt) + compensation = [["add", r, k, -x.numerator, x.denominator, []] + for r in range(112, 224) for k, x in sorted(dirt[r].items())] + cut = [] + for gate in word["cut"]: + cut.append(gate) + private = list(gate) + private[2] = 704 + word["centers"].index(gate[2]) + cut.append(private) + early = {i for i, _ in word["early_cleanup"]} + return (word["precondition"] + compensation + word["A"] + cut + word["B"] + + [word["cleanup"][i] for i, _ in word["early_cleanup"]] + + [gate for i, gate in enumerate(word["cleanup"]) if i not in early]) + + +def private_centres(base, changed): + for key in ("A", "cut", "centers", "center_frames"): + assert base[key] == changed[key] + for dual in (False, True): + maps = [] + for word in (base, changed): + rows = [{r: Q(1)} for r in range(712)] + for gate in augmented_program(word): + A.apply(gate, rows, dual) + maps.append(rows) + assert maps[0] == maps[1], ("private centre input map", dual) + return {"columns": 712, "orientations": ["forward", "inverse_transpose"], + "scope": "Each centre read has an independent arbitrary additive input. This checks the scalar interface, not a new global physical stream."} + + +def audit(word, directory, name): + path = directory / (name + ".json.gz") + digest = B.write(word, path) + receipt = directory / (name + "-AUDIT.json") + with contextlib.redirect_stdout(io.StringIO()): + A.run(path, receipt) + result = json.loads(receipt.read_text()) + assert result["content_sha256"] == digest + return {"content_sha256": digest, "local_profile": result["local_profile"], + "width_inventory": result["width_inventory"]} + + +def controls(directory): + controls = {} + word = B.construct(1) + missing = copy.deepcopy(word) + del missing["cleanup"][0] + missing["early_cleanup"] = [[i - 1, f] for i, f in missing["early_cleanup"]] + low = copy.deepcopy(word) + low["helper_final"]["448"] = B.source()["helper_final"]["448"] + for name, changed, reason in (("missing_dirty_column_restore", missing, "endpoint failure"), + ("unpaid_low_helper_end", low, "pre-wrapper touch of residual helper")): + try: + audit(changed, directory, name) + except RuntimeError as error: + assert reason in str(error), (name, str(error)) + controls[name] = str(error) + else: + raise AssertionError("accepted control " + name) + try: + B.construct(256) + except ValueError as error: + controls["out_of_domain_mask"] = str(error) + else: + raise AssertionError("accepted mask 256") + return controls + + +def main(): + if not __debug__: + raise RuntimeError("verification requires assertions; do not use -O") + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + begin = time.monotonic() + results = [] + with tempfile.TemporaryDirectory(prefix="saved-arm-check-") as scratch: + directory = Path(scratch) + rejected = controls(directory) + for mask in range(256): + word = B.construct(mask) + result = audit(word, directory, "mask-" + str(mask)) + result["mask"] = mask + even = sum(mask >> i & 1 for i in (0, 2, 4, 6)) + odd = sum(mask >> i & 1 for i in (1, 3, 5, 7)) + expected = dict(O.LOCAL) + expected[1] -= 2 * even + expected[2] += 2 * even + odd + assert result["local_profile"] == {str(k): n for k, n in expected.items()} + assert sum(int(r) * n for r, n in result["local_profile"].items()) == 5586 + 2 * (even + odd) + assert word["report"]["local_rank_mass"] == sum(int(r) * n for r, n in result["local_profile"].items()) + results.append(result) + if mask % 32 == 31: + print("checked", mask + 1, "of 256 exact local words", flush=True) + private = private_centres(B.source(), B.construct(255)) + bound = O.verify() + report = {"status": "PASS_TWO_ACCUMULATOR_SAVED_ARM_FAMILY", "masks": results, + "private_centres": private, "owner_bound": bound, "rejected_controls": rejected, + "elapsed_seconds": time.monotonic() - begin, + "scope": "All 256 fixed local recipes are checked. The proof permits arbitrary per-call mixtures and all positive replica counts. It does not classify all two-accumulator programs."} + args.output.write_text(json.dumps(report, indent=2) + "\n") + print(report["status"], flush=True) + + +if __name__ == "__main__": + main()