From 8f971e071c73836fc35e5407021c6cbbbcbe90a7 Mon Sep 17 00:00:00 2001 From: Rohan Arun Date: Sat, 10 Oct 2026 11:51:23 -0400 Subject: [PATCH 1/2] =?UTF-8?q?w3-stages-restore:=20438=20early=20restorat?= =?UTF-8?q?ions=20after=20PR312's=20kernel/target/plateau/reorder=20stages?= =?UTF-8?q?=20on=20the=20w3=20word=20(=CE=BA=207.55120411314104e-4)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit PR312's package with PR313's early-restoration stage inserted after the reorder stage: PR280's screen/emitter re-pinned to PR312's final word (438 of 440 helpers), endpoint-aware residual widths and a generic stock invariant in cohort-bank-review.cpp, an exact ILP tiling in stages/bank-tiling.json (105,377 banks per stage), legality against the candidate's declared endpoints, and re-pinned chart/price/finish literals (nine ordinary levels). +0.0756% over PR312, priced against PR304's supplier (bit side binds). 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b/.github/workflows/w3-stages-restore.yml @@ -0,0 +1,29 @@ +name: W3 with kernel, target-prefix, plateau and reorder stages +on: + push: + branches: [w3-stages] + paths: ['research/w3-stages-restore/**', '.github/workflows/w3-stages-restore.yml'] + pull_request: + paths: ['research/w3-stages-restore/**', '.github/workflows/w3-stages-restore.yml'] +permissions: + contents: read +jobs: + verify: + runs-on: ubuntu-latest + timeout-minutes: 60 + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: '3.11' + - run: sudo apt-get update && sudo apt-get install -y g++ libboost-dev + - run: python -m pip install -r research/w3-stages-restore/requirements.txt + - run: python -B research/w3-stages-restore/verify.py --output "$RUNNER_TEMP/w3-replay" --cxx g++ + - uses: actions/upload-artifact@v4 + if: always() + with: + name: w3-stages-receipts + path: | + ${{ runner.temp }}/w3-replay/*.json + ${{ runner.temp }}/w3-replay/logs + ${{ runner.temp }}/w3-replay/baseline/verification.json diff --git a/research/w3-stages-restore/.gitattributes b/research/w3-stages-restore/.gitattributes new file mode 100644 index 0000000000..fa1385d99a --- /dev/null +++ b/research/w3-stages-restore/.gitattributes @@ -0,0 +1 @@ +* -text diff --git a/research/w3-stages-restore/LICENSE b/research/w3-stages-restore/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/w3-stages-restore/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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-0,0 +1,16 @@ +# Attribution and provenance + +Publication and admission prepared for **utcorvusvolat-dotcom** with substantial OpenAI Codex assistance. The finite w3 word and its cube-layer/twin/line-pair redesign were supplied in `w3-bitword.zip`; their original README, frozen data, diagnostic checkers, receipts and builder provenance are retained in `supplied/`. The provided builders identify Agent A and Agent B; no additional personal authorship or priority is inferred. + +This package adds complete source binding, active-role deletion, concrete completed-bank allocation, changed-projector and annihilator admission, the full finite invoice, the stronger complex supplier's scalar/precision interface, and the source-bound orchestration. Original upstream license and assistance notices are preserved; credits do not imply endorsement or review. + +- eumemic: PR249/source527 word and machinery, the paired-cube physical emitter, transported dirty entries, exact arithmetic engines and prior PR168 lineage. The full unchanged PR249 package is in `vendor/pr249`. +- Dugongue: the multicut/cohort native checker and bank-admission lineage in PR254/259. Rohan Arun and Chafik Boukhalfa: subsequent PR263/266 composition and source-bound native packages. The supplied official legality and five-stage checkers are retained unchanged. +- Evan McKinney: completed-bank method (PR197); Rohan Arun: width-120 five-stage application (PR237). +- Henry Grant (hcg890) and Jacob Sussman: five-stage construction and certificate interfaces. Jacob Sussman's gcert reference checker is preserved within PR256. +- Chafik Boukhalfa with Anthropic Claude/OpenAI Codex assistance: PR256 explicit PR233 complex program and regeneration package. Its full `NOTICE`, proof and source pins are retained in `vendor/pr256`. +- icekylinx: paired-cube and flow/lift framework; Avi Eisenberg (ikeboy): complex supplier lineage; eumemic: modules and frame design. See the unchanged PR249/PR256 notices for their complete chains. +- utcorvusvolat-dotcom with OpenAI Codex assistance: PR270 source-bound connected-block work and PR280 changed-projector/finite-admission tools reused and adapted here. +- Niels Lohmann: `vendor/json.hpp`, MIT license in its header. The small `vendor/bits/stdc++.h` file is a portability include list. + +Apache-2.0 applies to the inherited Apache code and these admission additions, subject to the preserved third-party notices. Generated Python bytecode from the supplied archive is deliberately omitted; the supplied original SHA256SUMS remains provenance for the archive, while the root MANIFEST.json is the executable package's complete file manifest. diff --git a/research/w3-stages-restore/NOTICE.md b/research/w3-stages-restore/NOTICE.md new file mode 100644 index 0000000000..c6978f146a --- /dev/null +++ b/research/w3-stages-restore/NOTICE.md @@ -0,0 +1,41 @@ +# Attribution and scope + +`w3-stages-restore` is chafreaky's PR #312 package (utcorvusvolat-dotcom's #310 w3 word and admission chain; #312's +kernel, target-prefix/plateau and reorder stages; DreamingOfClouds' #304 supplier through #309's adapter) with one +more native stage from rohanarun's PR #313: utcorvusvolat-dotcom's PR #280 early-restoration screen and emitter +(`code/cleanup*.py`, re-pinned to this word, 438 of 440 helpers), the endpoint-aware residual widths and generic stock +invariant in `code/cohort-bank-review.cpp`, the exact tiling in `stages/bank-tiling.json`, `code/recompact.py`, and the +re-pinned chart/price/finish literals. Prepared by Rohan Arun (rohanarun) with Anthropic Claude assistance, +Apache-2.0; no exclusive priority is claimed. #312's notice follows unchanged. + +--- + +# Attribution and provenance + +Stages and composition prepared by **Chafik Boukhalfa** with Anthropic Claude assistance (Apache-2.0), on top of +utcorvusvolat-dotcom's PR #310 package. PR #310's full notice follows unchanged in `NOTICE-PR310.md` (also below). +Credits do not imply endorsement or review. + +- utcorvusvolat-dotcom (OpenAI Codex assistance) and the w3 archive's Agent A/Agent B: the w3 word and its complete admission (PR #310). +- Kernel mechanism: Dugongue (PR254/259 multicut kernel condensation, PR272 collective kernels), utcorvusvolat-dotcom (PR270 shared donors), Rohan Arun (PR269), Chafik Boukhalfa (PR266 composition); re-derived on w3 here. +- Target-prefix compression: eumemic (PR268), Rohan Arun (PR273/PR281 transcript stage, PR311 squares on w3); plateau/descent retiming: rohanarun (PR263), utcorvusvolat-dotcom (PR270). +- Reorder stage: Chafik Boukhalfa with Anthropic Claude assistance (PR299/PR306), after the toggle-detection view of Khattar–Gidney (arXiv:2407.17966). +- PR304 complex program: DreamingOfClouds; source-bound adapter archive `vendor/complex304.zip` and inventory from PR309 (Dugongue), used unchanged. +- Generic bank tiling input replaces PR #310's hard-coded census; the bank-review algorithm is unchanged. + +# Attribution and provenance + +Publication and admission prepared for **utcorvusvolat-dotcom** with substantial OpenAI Codex assistance. The finite w3 word and its cube-layer/twin/line-pair redesign were supplied in `w3-bitword.zip`; their original README, frozen data, diagnostic checkers, receipts and builder provenance are retained in `supplied/`. The provided builders identify Agent A and Agent B; no additional personal authorship or priority is inferred. + +This package adds complete source binding, active-role deletion, concrete completed-bank allocation, changed-projector and annihilator admission, the full finite invoice, the stronger complex supplier's scalar/precision interface, and the source-bound orchestration. Original upstream license and assistance notices are preserved; credits do not imply endorsement or review. + +- eumemic: PR249/source527 word and machinery, the paired-cube physical emitter, transported dirty entries, exact arithmetic engines and prior PR168 lineage. The full unchanged PR249 package is in `vendor/pr249`. +- Dugongue: the multicut/cohort native checker and bank-admission lineage in PR254/259. Rohan Arun and Chafik Boukhalfa: subsequent PR263/266 composition and source-bound native packages. The supplied official legality and five-stage checkers are retained unchanged. +- Evan McKinney: completed-bank method (PR197); Rohan Arun: width-120 five-stage application (PR237). +- Henry Grant (hcg890) and Jacob Sussman: five-stage construction and certificate interfaces. Jacob Sussman's gcert reference checker is preserved within PR256. +- Chafik Boukhalfa with Anthropic Claude/OpenAI Codex assistance: PR256 explicit PR233 complex program and regeneration package. Its full `NOTICE`, proof and source pins are retained in `vendor/pr256`. +- icekylinx: paired-cube and flow/lift framework; Avi Eisenberg (ikeboy): complex supplier lineage; eumemic: modules and frame design. See the unchanged PR249/PR256 notices for their complete chains. +- utcorvusvolat-dotcom with OpenAI Codex assistance: PR270 source-bound connected-block work and PR280 changed-projector/finite-admission tools reused and adapted here. +- Niels Lohmann: `vendor/json.hpp`, MIT license in its header. The small `vendor/bits/stdc++.h` file is a portability include list. + +Apache-2.0 applies to the inherited Apache code and these admission additions, subject to the preserved third-party notices. Generated Python bytecode from the supplied archive is deliberately omitted; the supplied original SHA256SUMS remains provenance for the archive, while the root MANIFEST.json is the executable package's complete file manifest. diff --git a/research/w3-stages-restore/PROOF-PR310.md b/research/w3-stages-restore/PROOF-PR310.md new file mode 100644 index 0000000000..4e2e1e6766 --- /dev/null +++ b/research/w3-stages-restore/PROOF-PR310.md @@ -0,0 +1,47 @@ +# w3 construction and admission argument + +## Finite word and geometry + +The supplied w3 word has 20,107 logical roles, 1,760 sources, 1,760 targets and 16,587 logical helper positions. It redesigns PR249's cube and line-pair layers while retaining the paired-cube decoder and five-stage interface. The original builders describe the design; this admission directly checks the frozen word and does not require missing discovery pickles. + +The official chronological checker replays every MOVE, common-frame ADD and copied-center lifetime. Initial source/target frames and source covectors equal those of the regenerated prerequisite. Changed helpers are disjoint from source-owned and donor roles. Each new frame has an integer full-rank basis B, an exact full-rank ordinary annihilator A, and B A^T = 0. Full rank modulo the auxiliary prime proves full rank over Q. Exact rational Gram inverses establish nondegeneracy for G = I − J/9. Thus the tested nested forward inclusions also give the reflected annihilator inclusions. + +The complete F₂ all-column identity is checked both on the logical word and on its compact physical word. The signed-integer endpoint of the parity word is not asserted to equal the original integer producer: the F₂ payload identity supplies the bit contract, as in source527. Signed coefficients are retained for exact inverse semantics and cancellation-free finite prefix bounds. The original producer's independent integer-decoder proof is freshly rerun as a prerequisite. + +For each helper whose initial frame is FULL24, no MOVE, ADD, COPY or ERASE may reference it. All 1,455 such positions satisfy this condition. Removing them by an explicit order-preserving register map preserves the entire active scalar map and chronology. The compact five-stage replay then checks all 22,172 physically present formal inputs; these deleted positions are not charged as live banks or selector assignments. + +## Exact bank packing + +The active residual ranks and populations are 4:2200, 6:22, 7:5, 11:24, 12:13, 23:810 and 24:12058. At 40 replicas per stage, use these width-120 patterns: + +| Pattern | Banks per stage | +| --- | ---: | +| four rank-23 blocks and seven rank-4 blocks | 8,100 | +| eight rank-11 blocks and eight rank-4 blocks | 120 | +| four rank-7 blocks and twenty-three rank-4 blocks | 50 | +| twenty rank-6 blocks | 44 | +| ten rank-12 blocks | 52 | +| thirty rank-4 blocks | 973 | +| five rank-24 blocks | 96,464 | + +These sum to 105,803 banks per stage. Every active role and replica receives exactly one slot of its residual width; every coordinate is covered once. Five separate stage inventories are enumerated. The literal stock is 4·1760·40 + 5·105803 = 810615, normalized by five to 162123. No divisibility heuristic or fractional bank is substituted for this allocation. + +The projector charts of all new frames are constructed exactly. The changed connector set is derived from the actual baseline and candidate words; every changed helper endpoint is included, including zero residuals used only to certify deletion. For each required projector E, the checker verifies E² = E, its exact rank, and an explicit invertible C with C⁻¹EC = diag(I,0). All 20,844 distinct changed projectors pass. At most 342 row factors are required; the retained conservative normalizer 787 dominates 342 + 119 + 120. All enumerated bank patterns are independently replayed on endpoint columns, with nonzero omitted and repeated block controls. + +## Stronger complex supplier and scalar costs + +PR256 regenerates both its control and the PR233 complex word from pinned source, runs gx.check1 including the exact scalar identity, reproduces the committed certificates byte for byte and certifies the PR233 five-stage saving 7547/10^7. We separately rerun the source527 label, scalar and splice interface on this actual replacement certificate. The live and physical stocks remain 14692 and 24127, with dimension 110, helper count 9412 and maximum child 46. + +The replacement contains coefficients beyond the original finite scalar lowerer's numerator bound of two. For q = a/b, 1 ≤ |a| ≤ 5 and b in {1,2,3,6}, the literal expansion copies the source to one disjoint work stream, halves and/or divides by three, performs |a| signed accumulations into the target, then clears the work stream. This preserves the source and uses no additional recursive child or odd divisor. Its exact Gaussian primitive count is 2 + |a| + [2 divides b] + [3 divides b]. Both orientations and every scratch lifetime are recounted, and forty exact recipe evaluations verify the identity and independent primitive counts. + +The newly counted local bound is below 2^48, global logical groups below 2^6050, routing below 2^30000, literal charge below 2^100000 and the semantic bound below 2^210000. The physical row coefficient 16171 fits the retained 20161 reserve. The original coefficients' stale numerical bill is not reused. + +## Finite bit invoice and exact assembly + +The normalized histogram equals 40 copies of the actual local MOVE/COPY histogram plus 28160 copies of each idle rank 4,23,46,50. It has 3,678,640 recursive calls, rank mass 19,419,560, stock 162,123, deficit 35,200 and maximum child 50. Literal counts are five times normalized counts. + +The invoice uses the 15,132 active helpers and actual banks, expands every signed ADD by its absolute integer coefficient, charges the full routing, primitive, coefficient, wrapper and selector costs, and retains the computed 94-bit signed prefix bound. The selector charge is 571950677600 < 2^40. The counted primitive coefficient is 58246212755400601 < 2^80. The source-owned selectors, new-frame and changed-projector finite bounds are all checked against the retained prime guard. + +The verifier proves q = 2^127 − 1 by its Lucas–Lehmer test, uses exact rare density 2·120^3/q with the full retained rank-one fallback, and evaluates the actual histogram with both unchanged rational moment engines. Eight positive-gap ordinary levels attain the 10^-27 grid cap. The exact assembly with the admitted PR233 supplier satisfies all 47 strict constraints and seven margins; the adjacent grid point fails for both the finite saving and coarse cap. + +For each positive minimum gap δ, the counted cutoff satisfies log₂ N ≥ max(1, ceil(36/δ²), ceil(2(4+ceil(log₂ C))/δ)). The all-size claim uses the same formula with C_full dominating the counted coefficient and every inherited primitive, wrapper, setup, row, routing and earlier-level constant. No recursive child is absorbed into a finite constant. The inherited uniform interfaces remain explicit assumptions. diff --git a/research/w3-stages-restore/PROOF-PR312.md b/research/w3-stages-restore/PROOF-PR312.md new file mode 100644 index 0000000000..28b8eadd64 --- /dev/null +++ b/research/w3-stages-restore/PROOF-PR312.md @@ -0,0 +1,16 @@ +# Stage argument (additions to PROOF-PR310.md) + +Every stage maps a word that passes PR #310's checks to a word that passes the same checks. The final word is +re-admitted by the unchanged native chain: legality, all-column F₂ (global and compact), exact charts, banks, price +and invoice. The stage checks below are extra evidence. + +1. **Kernels.** + - Let p be a pivot with donors d_i and odd integer coefficients a_i, where C_p + Σ a_i C_{d_i} ≡ 0 (mod 2) on the literal prefix responses up to the cut. + - p's prefix reads are omitted. Adding a_i·p into d_i after the cut and subtracting it at the end changes every target's prefix by C_p + Σ a_i C_{d_i}, which is 0 over F₂, and restores every donor. + - p enters at E. E is nondegenerate and contained in every member's first frame, so all chains stay nested. + - Entrance rank 840 ≡ 0 (mod 3). The residual census is tiled exactly, and the bank count equals 117,563 − (35,280 + 840)/3. + - Zero-response singles have no prefix reads (C_p = 0), so they enter at their first frame with no gates added. +2. **Target prefix.** The dependent's window response equals the signed sum of its retained targets' responses. This is checked exactly with integer fingerprints and over F₂. Removing the window reads and inserting setup and restore leaves every final value unchanged, as the integer replay confirms. +3. **Plateaus.** Each retimed component's gates commute as a block. The new frame is the exact intersection of the next frames, so it is contained in each of them, and the chains stay nested. +4. **Reorder.** A relocated ADD a += c·b crosses no read of a and no write of b. It therefore commutes over every commutative ring. MOVEs are rebuilt from the incidence frames as single nested climbs, with endpoints fixed. +5. **Price.** Rank mass and the deficit (35,200) are unchanged; stock is derived from the actual entrance frames. The exact price is computed against PR304's supplier at 7635/10⁷. At that value the 47 assembly constraints hold at the bit grid cap, and the adjacent grid point is rejected. PR233's supplier is still regenerated and guarded (PR256), but it is not the priced supplier. diff --git a/research/w3-stages-restore/PROOF.md b/research/w3-stages-restore/PROOF.md new file mode 100644 index 0000000000..e2a7d1fcf9 --- /dev/null +++ b/research/w3-stages-restore/PROOF.md @@ -0,0 +1,48 @@ +# w3 stages plus 438 early restorations — verification chain + +**Conditional κ = 151024082262820774685631 / (2·10²⁶) = 7.55120411314104·10⁻⁴**, +0.0756% over PR #312 +(7.54549816771013·10⁻⁴), +0.214% over PR #311, +0.296% over PR #310's w3 word; priced against PR #304's complex +supplier as #312 is (bit coarse binds; nine ordinary levels). + +This package is chafreaky's PR #312 package (`w3-bitword-stages`: utcorvusvolat-dotcom's #310 w3 word with the kernel, +target-prefix + plateau and reorder stages and #304's supplier admission) with **one more native transcript stage +after the reorder stage: PR #280's early restoration of cleanup helpers**, exactly as in PR #313 — the stage #312 +reports as blocked because #310's legality checker rejects endpoint changes. + +* **The stage** (`code/cleanup.py`, `cleanup_screen.py`, `cleanup_emit.py`, `cleanup_reference.py`: #280's own + screen/emitter re-pinned to this word). At the first `cleanup_gate` ADD (record 925,515) of #312's final word every + data target already has its scalar endpoints (checked on the exact F₂ prefix); 440 helpers `a` have a single later + scalar incidence `a −= b` with a donor unwritten in between, both at rank-22 frames whose rational span `E` is a + nondegenerate 23-dimensional frame. With 40 physical replicas 438 are moved (438·40 = 146·120 width-3 bank slots); + the write commutes over the integers with every crossed gate, `a` and `b` advance to `E`, the ADD runs there and `a` + retires at `E`. New-frame annihilators and cleared Gram determinants (mod 2¹²⁷ − 1), commutation, forward/inverse/ + roundtrip F₂ replays and an omitted-restoration control are checked. Local delta {1: +1314, 2: −876}; rank mass + 398,057 → 397,619; endpoint residual 316,569 → 316,131. +* **Admission of endpoints below the full frame.** `code/cohort-bank-review.cpp` (#312's plan-driven review) now takes + the candidate's `COHORT249-FINAL.json`: each helper's residual width is dim(endpoint) − dim(entrance), and the + stock invariant is the generic one (all slot coordinates fill the banks exactly). `stages/bank-tiling.json` carries + the new width census (438 at width 3, 1,762 at width 4, #312's kernel widths unchanged) and an exact integer tiling + (ILP over patterns of ≤ 3 widths; 105,377 banks per stage), which the C++ verifies in full as before (collision-free + tiling of all 3,026,400 slots, every bank a full 120-coordinate partition, per-pattern endpoint and + omission/repetition controls, exact charts: 4,703 new, ≤ 320 factors). Legality runs against the candidate's declared + endpoints with the export's base frame table; 23,870 changed projector charts (3,221 retired endpoints, ≤ 342 + factors). Literal stock 809,215 → 808,485 (normalized 161,697); finite coefficient 58,519,066,603,435,601 < 2⁸⁰; + selector charge 571,949,825,600 < 2⁴⁰. Re-pinned: `code/admit_geometry.py`, `code/price.py` (word hash `a972abfe…`, + 897,241 ADDs, 3,709,480 calls, mass 19,368,440, deficit 35,200, κ), `code/finish.py` (which also cross-binds the + restoration receipt and the pre-restoration word hash to #312's reorder output). + +## Reproduce + +```sh +python3 -m pip install -r research/w3-stages-restore/requirements.txt +python3 -B research/w3-stages-restore/verify.py --output /tmp/w3-stages-restore-proof --cxx g++ --boost-include /usr/include +``` + +About 12 minutes (both prerequisite source verifiers and #304's supplier admission fresh); prints `PASS conditional +kappa = 151024082262820774685631/200000000000000000000000000`. + +## Scope + +Exactly #310/#312's conditional interfaces; not a Lean certificate, an unconditional theorem or a benchmark. Not yet +composed on w3: sinks and the constructed-frame descent. #312's README/PROOF are kept as `README-PR312.md`, +`PROOF-PR312.md`. Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0; see `NOTICE.md`. diff --git a/research/w3-stages-restore/README-PR310.md b/research/w3-stages-restore/README-PR310.md new file mode 100644 index 0000000000..b1dc1f861e --- /dev/null +++ b/research/w3-stages-restore/README-PR310.md @@ -0,0 +1,37 @@ +# w3 bit word: source-bound completed-bank admission + +**Conditional κ = 94111687450666858500293 / 125000000000000000000000000 = 0.000752893499605334868002344.** + +This is **0.18551765% above PR309** (`0.000751499335697559705920828`), the leading public construction claim checked during preparation, and **3.96366336% above PR280**. These compare conditional asymptotic exponents, not measured multiplication speed. The frontier observation is separate from this offline certificate; no priority or global-optimality claim is made. + +The candidate is the supplied `w3-bitword.zip`: a cube-layer redesign, twin condensation and SAT-derived line-pair module on the PR249/source527 word. Its exact supplied word is preserved, SHA256 `a9501525563d3ec656ebf01aea9f2c9839e033563ea4a022500d68b12756ae86`. This package completes the missing source binding, bank allocation, endpoint/connector charts, finite invoice and stronger-complex-supplier admission. The retained original README and builders in `supplied/` describe the design and its initial partial-verification state; the builders are provenance only and are not required to verify the frozen word. + +## Reproduce + +Python 3.11+, a C++17 compiler and Boost headers are required. On Ubuntu: + +```sh +sudo apt-get install -y g++ libboost-dev +python3 -m pip install -r research/w3-bitword/requirements.txt +python3 -B research/w3-bitword/verify.py --output /tmp/w3-proof +``` + +Use a fresh output outside the package. The verifier is network-free. For a nonstandard Boost installation, add `--boost-include /path/to/boost/include`; select a compiler with `--cxx clang++` or `--cxx g++`. A small standard-header compatibility file supports the inherited `bits/stdc++.h` includes on macOS. + +Every mandatory proof stage executes. The two prerequisite source verifiers run concurrently in separate output directories. No saved PASS receipt or authenticated reuse option replaces execution. `CERTIFICATE.json` contains the mathematical admission; `VERIFICATION.json` binds it to all package source hashes and the actual fresh stages. Assertions must remain enabled, and the immutable source manifest is checked before and after the replay. + +## What is admitted + +- The complete eight-stage PR249/source527 prerequisite is rerun. Its actual raw word and frame table are regenerated and compared with the supplied base snapshot; the only ignored comparison field is nondeterministic elapsed seconds. The final w3 state word hash is recomputed. +- All 23,627 original global F₂ columns pass. The 1,455 freed helpers are proved absent from every actual record and are then deleted with an explicit register map; all 22,172 compact physical columns pass independently. The active helper count is 15,132. Sources and arbitrary remaining helper dirt are restored, 120 five-stage copies close, and six omitted-bridge controls are nonzero. +- All 3,473 new frame bases and ordinary annihilators have full rank and exact orthogonality. Their rational Gram inverses and complementary projector charts are computed. All 20,844 changed connector/endpoint projector charts are also constructed and checked; the maximum factor count is 342. All charged chart pivots and coefficients are below the retained 2^80 prime guard. +- Every one of the 3,026,400 active helper/replica/stage occurrences is assigned to a concrete width-120 bank slot without collision or padding. There are 105,803 banks per stage, 810,615 literal stock families and 162,123 normalized stock families. Bank endpoint tests and omission/repetition controls each cover 3,360 columns. +- The conservative normalizer remains 787. The complete bit-side selector charge is 571,950,677,600; the counted finite primitive coefficient is 58,246,212,755,400,601; the signed payload bound is 94 bits. Recursive children remain explicit. +- PR256 freshly regenerates and reference-checks the PR233 complex supplier at saving 7547/10^7. The complex label, forward/backward scalar, scratch-lifecycle, splice, router, precision and row guards are rechecked on that actual certificate. Coefficients with numerator up to five are expanded into paid repeated signed additions, with no new odd divisor. Forty exact coefficient recipes are checked. The resulting local bill is 238,393,708,927,310 < 2^48 and the physical row coefficient is 16,171 < the retained 20,161 reserve. +- The exact fixed prime q = 2^127 − 1, full rare-branch fallback, two independent rational moment engines, eight positive-gap ordinary levels, all 47 strict assembly inequalities and rejection of the adjacent 10^-27 grid point are admitted. + +## Scope + +This is a finite construction under the inherited all-size compiler, common weighted charts, restored rows, selectors, routing, prime supply, complex dirty-lifting, precision/recovery and analytic transfer interfaces. The checks do not establish these all-size hypotheses, a new Lean proof, an unconditional integer-multiplication theorem or a practical runtime result. + +The PR249 source package is pinned to `96495746c786d6d0339dbb38c7f553d4af3f88ed`; its manifest is `86e8bc5182079c00877077c8e4c7b2690ba2486bec385c0857f1794cd2e6bedb`. PR256 is pinned to `db3f75cdc5f03f3131d48fb220f6bf1958404ff3`. Original source, notices and licenses are retained. See `PROOF.md`, `SOURCE.json` and `NOTICE.md`. diff --git a/research/w3-stages-restore/README-PR312.md b/research/w3-stages-restore/README-PR312.md new file mode 100644 index 0000000000..b4d094c5bd --- /dev/null +++ b/research/w3-stages-restore/README-PR312.md @@ -0,0 +1,78 @@ +# w3 bit word with kernel, target-prefix, plateau and reorder stages, priced against PR304's complex supplier + +**Conditional κ = 377274908385506513145517 / 500000000000000000000000000 = 0.000754549816771013026291034.** + +That is +0.2200% over PR #310 (0.000752893499605334868002344, the w3 word's own admission), which this package +extends. It is +0.1382% over PR #311 (0.000753508664880762517753401, 209 target-prefix squares on the same word). +These are conditional asymptotic exponents, not measured multiplication speeds. No priority or optimality is claimed. + +This package is PR #310's `w3-bitword` package. It keeps the complete source binding, inert-role deletion, bank, chart, +finite and PR233/PR256 complex admission, and adds four transcript stages after the source binding plus one supplier +admission. Every native checker of PR #310 then runs fresh on the final word. + +| step | items | local Σφ change | κ after the step (exact grid) | +|---|---|---:|---| +| PR #310 w3 word | – | 1,068,458.57 | 7.52893499605e-4 | +| 1. kernel stage (`code/kernel_stage.py`) | 433 kernel families + 85 zero-response singles, entrance rank 840, 132 new frames | entrance change (stock 162,123 → 161,843) | 7.53675926616e-4 | +| 2. target-prefix + plateau stage (`code/target_plateau_stage.py`) | 45 F₂ target-prefix groups; 660 five-gate plateaus retimed into 660 new dim-15 frames | −1,025.22 | – | +| 3. reorder stage (`code/reorder_stage.py`) | just-in-time MOVE normalisation + 172 commuting ADD relocations (two rounds, fixed point) | −326.55 | bit cap 7.54549816771e-4 | +| 4. complex supplier | PR304's program via PR309's source-bound adapter, priced at 7635/10⁷ | – | **7.54549816771e-4** | + +With PR233's supplier (7547/10⁷) the complex side binds after step 3, at κ = 377065428344163231288117/5·10²⁶ = +7.541308566883e-4. Step 4 lifts that cap, so the bit side binds again. The bit coarse saving is 7.5512e-4, and the +complex supplier is 7.635e-4. + +## Reproduce + +Python 3.11+ with `requirements.txt` (NumPy, SciPy, SymPy, mpmath), a C++17 compiler and Boost headers: + +```sh +python3 -m pip install -r research/w3-bitword-stages/requirements.txt +python3 -B research/w3-bitword-stages/verify.py --output /tmp/w3-stages-proof --cxx g++ --boost-include /usr/include +``` + +It takes about 20 minutes. The PR249 source replay dominates the runtime. The PR256 complex source, the PR304 adapter and all stages +run fresh. Nothing is downloaded and nothing is published. + +## Stages + +- **Kernel stage.** This is the multicut kernel condensation of PR254/259/266/272, re-derived on the w3 word. + - The cut is the end of the initial target-correction prefix (record 819,879), and 12,058 helpers are eligible. + - The 433 families are twin pairs, integer and F₂ triples, and multi-donor families with shared donors allowed on nested E chains. They come from a multi-seed packing. + - For each family, the pivot's prefix reads are removed. The pivot enters at the nondegenerate E. Each donor receives `d += a·p` at E after the cut and `d −= a·p` at FULL at the end. + - The 85 zero-response helpers have no prefix reads in the w3 word, so they enter directly at their first frame. + - `code/kernel_checks.py` checks: + - exact rank and 9I−J Gram nondegeneracy of all 132 new frames; + - the F₂ kernel identity of every family on the original prefix responses; + - E inside every member's first frame; + - that no member is a source owner or donor key, and that pivots and donors are disjoint. + - `code/kernel_replay.py` checks: + - GF(2) replays with random dirty inputs: sources unchanged, targets t⊕x, helpers restored, all registers equal to #310's; + - controls that omit the Q (category 28) or Q⁻¹ (category 29) gates and are rejected. +- **Target-prefix and plateau stage.** This is the PR268/273 mechanism re-derived on the kernel word. + - At the global target cut, a dependent target t with an integer-exact window dependency R_t = Σ ±R_p (k ≤ 3) has its window reads replaced by setup at ZERO and restore at a common close frame. + - The 660 identical five-gate dim-13 components are retimed into the exact intersection of their four next frames (dim 15). + - Checks: + - nested chains; + - forward and inverse F₂ all-column replays; + - an integer replay mod 2⁶¹−1 equal on every register; + - the source-span rule (0 violations). +- **Reorder stage.** This is PR #299/#306's stage on the cohort word. + - The screen is re-run and must reproduce the frozen selection. + - Checks: the crossed-interval contract, an integer replay equal on every register, a nonvacuous omission control, and the fixed point. +- **PR304 supplier.** The PR309-vendored adapter archive is pinned by hash and its members by inventory. It is extracted fresh and runs gx.check1 on the actual PR304 program, together with its label, scalar, splice, cover, router, precision and row guards and two moment engines (7636/10⁷ rejected). The physical row coefficient 16,170 stays below the retained 20,161. + +The native chain then runs: +- legality (518 selections), and all 23,627 global and 22,172 compact F₂ columns (payload 97 bits < 104); +- the bank review, made generic: census and width-120 tiling read from `stages/bank-tiling.json`, 105,523 banks per stage, stock 809,215 / 161,843, 3,026,400 assignments; +- exact charts for all 4,265 new frames and 22,118 changed projectors (≤ 342 factors); +- price: two moment engines, eight levels, 47 strict constraints, adjacent grid point rejected; +- the finite invoice: coefficient 58,364,056,416,171,201 < 2⁸⁰, selector charge 571,950,117,600 < 2⁴⁰. + +PR #310's own README and PROOF are kept as `README-PR310.md` and `PROOF-PR310.md`. + +## Scope + +This is a finite construction under the same inherited all-size interfaces as PR #310: compiler, common weighted +charts, restored rows, selectors, routing, prime supply, complex dirty lifting, precision/recovery and analytic +transfer. No Lean proof, unconditional theorem or runtime result is claimed. diff --git a/research/w3-stages-restore/README.md b/research/w3-stages-restore/README.md new file mode 100644 index 0000000000..83dfd3f644 --- /dev/null +++ b/research/w3-stages-restore/README.md @@ -0,0 +1,48 @@ +# w3 word: #312's kernel, target-prefix, plateau and reorder stages plus 438 early restorations + +**Conditional κ = 151024082262820774685631 / (2·10²⁶) = 7.55120411314104·10⁻⁴**, +0.0756% over PR #312 +(7.54549816771013·10⁻⁴), +0.214% over PR #311, +0.296% over PR #310's w3 word; priced against PR #304's complex +supplier as #312 is (bit coarse binds; nine ordinary levels). + +This package is chafreaky's PR #312 package (`w3-bitword-stages`: utcorvusvolat-dotcom's #310 w3 word with the kernel, +target-prefix + plateau and reorder stages and #304's supplier admission) with **one more native transcript stage +after the reorder stage: PR #280's early restoration of cleanup helpers**, exactly as in PR #313 — the stage #312 +reports as blocked because #310's legality checker rejects endpoint changes. + +* **The stage** (`code/cleanup.py`, `cleanup_screen.py`, `cleanup_emit.py`, `cleanup_reference.py`: #280's own + screen/emitter re-pinned to this word). At the first `cleanup_gate` ADD (record 925,515) of #312's final word every + data target already has its scalar endpoints (checked on the exact F₂ prefix); 440 helpers `a` have a single later + scalar incidence `a −= b` with a donor unwritten in between, both at rank-22 frames whose rational span `E` is a + nondegenerate 23-dimensional frame. With 40 physical replicas 438 are moved (438·40 = 146·120 width-3 bank slots); + the write commutes over the integers with every crossed gate, `a` and `b` advance to `E`, the ADD runs there and `a` + retires at `E`. New-frame annihilators and cleared Gram determinants (mod 2¹²⁷ − 1), commutation, forward/inverse/ + roundtrip F₂ replays and an omitted-restoration control are checked. Local delta {1: +1314, 2: −876}; rank mass + 398,057 → 397,619; endpoint residual 316,569 → 316,131. +* **Admission of endpoints below the full frame.** `code/cohort-bank-review.cpp` (#312's plan-driven review) now takes + the candidate's `COHORT249-FINAL.json`: each helper's residual width is dim(endpoint) − dim(entrance), and the + stock invariant is the generic one (all slot coordinates fill the banks exactly). `stages/bank-tiling.json` carries + the new width census (438 at width 3, 1,762 at width 4, #312's kernel widths unchanged) and an exact integer tiling + (ILP over patterns of ≤ 3 widths; 105,377 banks per stage), which the C++ verifies in full as before (collision-free + tiling of all 3,026,400 slots, every bank a full 120-coordinate partition, per-pattern endpoint and + omission/repetition controls, exact charts: 4,703 new, ≤ 320 factors). Legality runs against the candidate's declared + endpoints with the export's base frame table; 23,870 changed projector charts (3,221 retired endpoints, ≤ 342 + factors). Literal stock 809,215 → 808,485 (normalized 161,697); finite coefficient 58,519,066,603,435,601 < 2⁸⁰; + selector charge 571,949,825,600 < 2⁴⁰. Re-pinned: `code/admit_geometry.py`, `code/price.py` (word hash `a972abfe…`, + 897,241 ADDs, 3,709,480 calls, mass 19,368,440, deficit 35,200, κ), `code/finish.py` (which also cross-binds the + restoration receipt and the pre-restoration word hash to #312's reorder output). + +## Reproduce + +```sh +python3 -m pip install -r research/w3-stages-restore/requirements.txt +python3 -B research/w3-stages-restore/verify.py --output /tmp/w3-stages-restore-proof --cxx g++ --boost-include /usr/include +``` + +About 12 minutes (both prerequisite source verifiers and #304's supplier admission fresh); prints `PASS conditional +kappa = 151024082262820774685631/200000000000000000000000000`. + +## Scope + +Exactly #310/#312's conditional interfaces; not a Lean certificate, an unconditional theorem or a benchmark. Not yet +composed on w3: sinks and the constructed-frame descent. #312's README/PROOF are kept as `README-PR312.md`, +`PROOF-PR312.md`. Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0; see `NOTICE.md`. diff --git a/research/w3-stages-restore/SOURCE.json b/research/w3-stages-restore/SOURCE.json new file mode 100644 index 0000000000..895833019d --- /dev/null +++ b/research/w3-stages-restore/SOURCE.json @@ -0,0 +1,38 @@ +{ + "comparison": { + "candidate_kappa": "377274908385506513145517/500000000000000000000000000", + "gain_percent": 0.13817384441295888, + "kappa": "753508664880762517753401/1000000000000000000000000000", + "note": "Public frontier checked during preparation on 2026-10-10; separate from offline admission.", + "pull_request": 311 + }, + "final_word_sha256": "7a4f847b197694466cbe92f4b98c9758ceab0715d9440ffe09ba6ceeb4733b65", + "input_archive": { + "name": "w3-bitword.zip", + "sha256": "c04c9987f30c7fe1a0d73d4d5cc2dff46cd6ecd916e7408d7020dd54f81c7afc" + }, + "pr249": { + "head": "96495746c786d6d0339dbb38c7f553d4af3f88ed", + "manifest_sha256": "86e8bc5182079c00877077c8e4c7b2690ba2486bec385c0857f1794cd2e6bedb", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/249" + }, + "pr256": { + "head": "db3f75cdc5f03f3131d48fb220f6bf1958404ff3", + "source_sha256": "9ce463476af549c04de4705b1bf0c8f7f18d473dc0817883066ad5e2136d90b5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/256" + }, + "pr309_complex304_adapter": { + "archive": "vendor/complex304.zip", + "archive_sha256": "0412e86f9c58cb6e3d93129c7a8bb7bb0fef6323f95a55d695f1d2dfa674a22d", + "head": "19d148bd7aa199378816cf1fb9ff746eb4d815da", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/309" + }, + "pr310": { + "branch": "utcorvusvolat-dotcom:codex/w3-bitword", + "head": "484b85f1d1fada27fda2ddab3ec952c1314d84c7", + "kappa": "94111687450666858500293/125000000000000000000000000", + "package": "research/w3-bitword", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/310" + }, + "word_sha256": "a9501525563d3ec656ebf01aea9f2c9839e033563ea4a022500d68b12756ae86" +} diff --git a/research/w3-stages-restore/code/admit_geometry.py b/research/w3-stages-restore/code/admit_geometry.py new file mode 100644 index 0000000000..65ada63837 --- /dev/null +++ b/research/w3-stages-restore/code/admit_geometry.py @@ -0,0 +1,64 @@ +#!/usr/bin/env python3 +"""Bind exact new-frame and changed-projector audits to the complete word.""" +import sys +if not __debug__:raise SystemExit('Assertions required') +sys.dont_write_bytecode=True +from pathlib import Path +from fractions import Fraction as Q +import argparse,json,hashlib,struct + +def read(p):return json.loads(Path(p).read_text()) +def rank_mod(rows): + if not rows:return 0 + p=2147483647;M=[[x%p for x in r] for r in rows];r=0 + for c in range(24): + pivot=next((i for i in range(r,len(M)) if M[i][c]),None) + if pivot is None:continue + M[r],M[pivot]=M[pivot],M[r];iv=pow(M[r][c],-1,p);M[r]=[(x*iv)%p for x in M[r]] + for i in range(r+1,len(M)): + if M[i][c]: + k=M[i][c];M[i]=[(a-k*b)%p for a,b in zip(M[i],M[r])] + r+=1 + if r==len(M):break + return r + +def frame(f): + d=f['dim'];B=f['B'];A=f['A'];assert len(B)==d and len(A)==24-d + assert all(len(r)==24 and all(isinstance(x,int) for x in r) for r in B+A) + # Full rank modulo a prime proves full rank over Q; exact orthogonality then proves A=B-perp. + assert rank_mod(B)==d and rank_mod(A)==24-d + assert all(sum(x*y for x,y in zip(a,b))==0 for a in A for b in B) + +def run(base,candidate,bank_dir,charts_dir,output): + base,candidate,bank_dir,charts_dir=map(Path,(base,candidate,bank_dir,charts_dir));nf=read(candidate/'COHORT249-FRAMES.json') + for f in nf.values():frame(f) + assert len(nf)==4703 + negative=[] + f=json.loads(json.dumps(next(iter(nf.values()))));f['A'][0]=[0]*24 + try:frame(f) + except AssertionError:negative.append('zero annihilator row rejected') + else:raise AssertionError('Bad annihilator accepted') + old=read(base/'249-states.json');ini=read(candidate/'COHORT249-INITIAL.json');fin=read(candidate/'COHORT249-FINAL.json');fs=read(base/'frames.json')['frames'];fs.update(nf) + def pairs(path):return {(b,c,r) for op,a,b,c,r,z in struct.iter_unpack('<6i',path.read_bytes()) if op==0 and r} + required=pairs(candidate/'COHORT249-RECORDS.bin')-pairs(base/'249-records.bin') + endpoints=0 + for i in range(3520,20107): + role=str(i) + if ini[role]!=old['initial'][role] or fin[role]!=old['final'][role]: + before,after=ini[role],fin[role];required.add((before,after,fs[str(after)]['dim']-fs[str(before)]['dim']));endpoints+=1 + audit=read(charts_dir/'COMBINED-CHART-AUDIT.json');charts=read(charts_dir/'COMBINED-CHARTS.json');bank=read(bank_dir/'BANK-REVIEW.json');full=read(bank_dir/'BANK-CHARTS.json') + assert {(x['before'],x['after'],x['rank']) for x in charts}==required and len(charts)==len(required)==23870 + assert audit['retired_endpoints']==endpoints==3221 and audit['unique_projectors_checked']==len(required) + assert audit['all_entries_below_two_to_80'] and audit['max_factors']==342 + assert int(audit['max_numerator'])<2**80 and int(audit['max_denominator'])<2**80 + assert {x['frame'] for x in full}=={int(k) for k in nf} and len(full)==4703 + assert bank['new_exact_charts']==4703 and bank['max_new_chart_factors']==320 + assert bank['actual_role_replica_stage_assignments']==3026400 and bank['actual_helper_roles']==15132 + assert bank['literal_stock']==808485 and bank['normalized_stock']==161697 + bank['new_frame_chart_max']=bank['max_new_chart_factors'];bank['max_new_chart_factors']=max(bank['max_new_chart_factors'],audit['max_factors']) + assert bank['max_new_chart_factors']+119+120<=bank['normalizer_factor_ceiling']==787 + bank.update(changed_projector_charts=23870,changed_helper_endpoints=3221,all_new_ordinary_annihilators_full_rank=True,geometry_controls=negative) + bank['geometry_input_hashes']={str(p.resolve()):hashlib.sha256(p.read_bytes()).hexdigest() for p in [candidate/'COHORT249-RECORDS.bin',candidate/'COHORT249-FRAMES.json',charts_dir/'COMBINED-CHART-AUDIT.json',charts_dir/'COMBINED-CHARTS.json',bank_dir/'BANK-REVIEW.json',bank_dir/'BANK-CHARTS.json']} + Path(output).write_text(json.dumps(bank,sort_keys=True,indent=2)+'\n');print('PASS all new frame ranks, exact annihilators and 22118 changed charts',flush=True) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('--base',required=True);ap.add_argument('--candidate',required=True);ap.add_argument('--bank',required=True);ap.add_argument('--charts',required=True);ap.add_argument('--output',required=True);a=ap.parse_args();run(a.base,a.candidate,a.bank,a.charts,a.output) diff --git a/research/w3-stages-restore/code/changed-charts.cpp b/research/w3-stages-restore/code/changed-charts.cpp new file mode 100644 index 0000000000..3b2c4ce776 --- /dev/null +++ b/research/w3-stages-restore/code/changed-charts.cpp @@ -0,0 +1,35 @@ +// Exact projector charts derived from the actual candidate and baseline words. +// Prepared with substantial OpenAI Codex assistance; Apache-2.0. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +using namespace std;using J=nlohmann::json;using Q=boost::multiprecision::cpp_rational;using Z=boost::multiprecision::cpp_int;using M=vector>; +J ld(string p){ifstream f(p);if(!f)throw runtime_error("missing "+p);J j;f>>j;return j;} +Q rat(J j){return j.is_string()?Q(j.get()):Q(j.get());}M eye(int n){M a(n,vector(n));for(int i=0;i(a.size()));for(int i=0;i(b[0].size()));for(int i=0;i=(Z(1)<<80)||d>=(Z(1)<<80))throw runtime_error("finite prime guard exceeded");} +M inverse(M a,int &ops,Q &det){int n=a.size();M b=eye(n);det=1;ops=0;for(int k=0;kpiv;for(int col=0;colv(n);v[free]=1;for(int i=0;i piv;M copy=a;for(int c=0;cpiv;for(int col=0;colv(n);v[free]=1;for(int i=0;iprojectors;auto proj=[&](int f)->M{if(projectors.count(f))return projectors[f];int d=fs.at(to_string(f))["dim"];if(d==24)return projectors[f]=eye(24);if(!d)return projectors[f]=M(24,vector(24));M B;for(auto row:fs.at(to_string(f))["B"]){vectorr;for(auto x:row)r.push_back(rat(x));B.push_back(r);}int ops;Q det;M BG=mul(B,G), gram=mul(BG,tr(B)), inv=inverse(gram,ops,det);return projectors[f]=mul(mul(tr(B),inv),BG);};set>pairs,oldpairs;int endpoints=0; +auto events=[&](string path){ifstream f(path,ios::binary);if(!f)throw runtime_error("missing word");f.seekg(0,ios::end);size_t size=f.tellg();f.seekg(0);if(size%sizeof(Ev))throw runtime_error("word shape");vectorv(size/sizeof(Ev));f.read((char*)v.data(),size);return v;}; +for(auto e:events(base+"/COHORT249-RECORDS.bin"))if(e.op==0&&e.r)oldpairs.insert({e.b,e.c,e.r}); +for(auto e:events(candidate+"/COHORT249-RECORDS.bin"))if(e.op==0&&e.r&&!oldpairs.count({e.b,e.c,e.r}))pairs.insert({e.b,e.c,e.r}); +J oldstate=ld(base+"/249-states.json");int v=oldstate["v"],n=oldstate["n"]; +for(int a=2*v;a()||after!=oldstate["final"][role].get()){int rank=fs.at(to_string(after))["dim"].get()-fs.at(to_string(before))["dim"].get();pairs.insert({before,after,rank});endpoints++;}} + +int maxops=0,checked=0;J charts=J::array();for(auto[before,after,r]:pairs){M E=sub(proj(after),proj(before));if(mul(E,E)!=E)throw runtime_error("not projector");M C=independent_columns(E);if(C[0].size()!=r)throw runtime_error("rank mismatch");M K=kernel_general(E);if(K.size()!=24-r)throw runtime_error("nullity mismatch");for(int i=0;i<24;i++)for(auto&v:K)C[i].push_back(v[i]);int ops;Q det;M inv=inverse(C,ops,det),want=eye(24);for(int i=r;i<24;i++)want[i][i]=0;if(mul(mul(inv,E),C)!=want||mul(C,inv)!=eye(24))throw runtime_error("chart identity");maxops=max(maxops,ops);charts.push_back({{"before",before},{"after",after},{"rank",r},{"basis",mj(C)},{"inverse",mj(inv)},{"factors",ops},{"determinant",det.str()}});checked++;if(checked%50==0)cout<<"checked "<548)throw runtime_error("factor budget exceeded");J receipt={{"status","PASS_EXACT_CHANGED_ENDPOINT_AND_MOVE_CHARTS"},{"retired_endpoints",endpoints},{"unique_projectors_checked",checked},{"max_factors",maxops},{"max_numerator",maxnum.str()},{"max_denominator",maxden.str()},{"all_entries_below_two_to_80",true}};ofstream(output+"/COMBINED-CHART-AUDIT.json")<idx +new=array('i');cols=[1<=0 + new.extend((0,role,before,f,rank,0));state[role]=f +def emit(r): + op,a,b,c,f,z=r + if op==1: + move(a,f);move(b,f) + if c%2:cols[a]^=cols[b] + elif op==2: + move(a,c);assert b==n and cols[b]==0;cols[b]=cols[a];state[b]=f + elif op==3: + assert cols[a]==cols[b] and state[a]==c and state[b]==f;cols[b]=0;del state[b] + else:raise AssertionError(r) + new.extend(r) +movedkeys={(e['role'],e['donors'][0],e['frame'])for e in edits} +for i in range(len(old)//6): + if i==cut: + for e in edits: + emit((1,e['role'],e['donors'][0],old[6*e['incidences'][0][0]+3],e['frame'],MOVED));assert cols[e['role']]==1< +#include +#include +using namespace std;using J=nlohmann::json;using Q=boost::multiprecision::cpp_rational;using Z=boost::multiprecision::cpp_int;using M=vector>; +J ld(string p){ifstream f(p);if(!f)throw runtime_error("missing "+p);J j;f>>j;return j;} +Q rat(J j){return j.is_string()?Q(j.get()):Q(j.get());}M eye(int n){M a(n,vector(n));for(int i=0;i(a.size()));for(int i=0;i(b[0].size()));for(int i=0;i=(Z(1)<<80)||d>=(Z(1)<<80))throw runtime_error("finite prime guard exceeded");} +M inverse(M a,int &ops,Q &det){int n=a.size();M b=eye(n);det=1;ops=0;for(int k=0;kpiv;for(int col=0;colv(n);v[free]=1;for(int i=0;iw;int count;}; +int main(int ac,char**av){if(ac!=8)throw runtime_error("args: baseline_export initial_json new_frames_json output_dir label tiling_json final_json");auto tiling=ld(av[6]),fin=ld(av[7]);string inp=av[1],out=av[4];auto st=ld(inp+"/249-states.json"),fj=ld(inp+"/frames.json")["frames"],ini=ld(av[2]),nf=ld(av[3]);int n=st["n"],v=st["v"];mapdims;for(auto it=fj.begin();it!=fj.end();it++)dims[stoi(it.key())]=it.value()["dim"];for(auto it=nf.begin();it!=nf.end();it++)dims[stoi(it.key())]=it.value()["dim"]; +M G=eye(24);for(auto&r:G)for(auto&q:r)q-=Q(1)/9;J charts=J::array();int maxops=0;for(auto it=nf.begin();it!=nf.end();it++){int d=it.value()["dim"];M U;for(auto row:it.value()["B"]){vectorr;for(auto x:row)r.push_back(rat(x));U.push_back(r);}if(U.size()!=d)throw runtime_error("dim");auto UG=mul(U,G);auto V=nullspace(UG);M B=tr(V);for(int i=0;i<24;i++)for(int j=0;j548)throw runtime_error("inherited factor budget exceeded"); +map>fam;int sumdim=0,changed=0,deleted=0; +for(int i=0;iexpected;for(auto it=tiling["census"].begin();it!=tiling["census"].end();++it)expected[stoi(it.key())]=it.value();int wantDeleted=tiling["deleted"],wantRank=tiling["entrance_rank"]; +if(fam.size()!=expected.size()||deleted!=wantDeleted||sumdim!=wantRank)throw runtime_error("actual residual census or saved rank"); +for(auto[r,k]:expected)if(fam[r].size()!=k)throw runtime_error("actual residual count"); +vectorpat;auto add=[&](vectorw,int count){if(count<0||accumulate(w.begin(),w.end(),0)!=120)throw runtime_error("pattern");if(count)pat.push_back({w,count});}; +auto rep=[](int r,int k){return vector(k,r);};auto mix=[&](int r,int k,int four){auto w=rep(r,k);w.insert(w.end(),four,4);return w;}; +for(auto pp:tiling["patterns"])add(pp["widths"].get>(),pp["count"]); +struct Slot{int bank,off,r,block;};map>slots;int banks=0;J pj=J::array();for(auto pp:pat){pj.push_back({{"widths",pp.w},{"count",pp.count}});for(int b=0;b>(8*j))&255;hash*=1099511628211ull;}};long long assignments=0,mass=0,columns=0,controls=0;for(int stage=0;stage<5;stage++){vector>occ(banks);for(auto[r,rows]:fam)for(int i=0;is{};s[col]=1;vector>bl;int o=0;for(int r:pp.w){bl.push_back({o,r});o+=r;}if(rev)reverse(bl.begin(),bl.end());for(auto[o,r]:bl)for(int j=o;js{};s[col]=1;int o=0;for(int b=0;b +#include "json.hpp" +#include +#include +#include +#include +#include +#include +using namespace std;using namespace boost::multiprecision;using J=nlohmann::json;using I=cpp_int;using Q=cpp_rational; +void need(bool x,const char*s){if(!x)throw runtime_error(s);}J load(string p){ifstream f(p);need(bool(f),"missing input");J j;f>>j;return j;} +Q rat(string s){auto p=s.find('/');return p==string::npos?Q(I(s)):Q(I(s.substr(0,p)))/I(s.substr(p+1));}I ceilQ(Q x){return (numerator(x)+denominator(x)-1)/denominator(x);}struct E{int op,a,b,c,f,z;}; +int main(int argc,char**argv){try{need(argc==6,"usage RECORDS ROOT_PRICE BANK_RECEIPT FIVE_STAGE_RECEIPT OUTPUT");ifstream f(argv[1],ios::binary|ios::ate);size_t bytes=f.tellg();need(bytes%sizeof(E)==0,"ABI");vectorev(bytes/sizeof(E));f.seekg(0);f.read((char*)ev.data(),bytes);J price=load(argv[2])["cohort_candidate"],bank=load(argv[3]),global=load(argv[4]);mapH;I adds=0,units=0,copies=0;for(auto e:ev){if(e.op==0&&e.f)H[e.f]++;else if(e.op==1){adds++;units+=abs(e.c);}else if(e.op==2){H[e.z]++;copies++;}}need(copies==24&&adds>0&&units>=adds,"actualword inventory");int m=120,v=1760,R=15132,T=40,N=2*m,d=m*m,stock=bank["literal_stock"];need(stock==bank["normalized_stock"].get()*5&&bank["actual_role_replica_stage_assignments"]==3026400,"actualbanks");need(bank["new_exact_charts"].get()>0&&bank["max_new_chart_factors"]<=548&&I(bank["max_intermediate_denominator"].get())<(I(1)<<80)&&I(bank["max_intermediate_numerator"].get())<(I(1)<<80),"newchart invoice");mapL;for(auto[r,n]:H)L[r]+=200*n;for(int r:{4,23,46,50})L[r]+=40*2*v;I Ecount=0,mass=0;J hh=J::object();for(auto[r,n]:L){Ecount+=n;mass+=r*n;need(r<60,"half-shrink");hh[to_string(r)]=n.convert_to();need(n==5*price["histogram"][to_string(r)].get(),"fullH versusnormalizedprice");}need(m*I(stock)-mass==176000,"physicaldeficit");need(price["stock"].get()*5==stock,"literalstock notnormalized");Q mu=rat(price["moment_upper"]);need(mu<1,"strict moment");Q c=rat(price["coarse"]),deltaTau=1-mu,deltaLin=1-Q(mass)/(m*stock)-Q(32*m)*Ecount/(I("10000000000000000")*stock);need(deltaLin>0,"linear fallback");I Jroute=T*(24*v+10*R),good=8*m*m+8,high=16*I(d+1)*(d+1),K=2*5*T*(I(stock-1)+I(R)*120*787),weighted=T*(5*adds+6*v),unit=T*(5*units+6*v);need(K==bank["selector_charge"].get()&&K<(I(1)<<40),"all selector factors");I F=I(global["signed_lift_prefix"][0]["cancellation_free_signed_row_l1_upper"].get()),B=I(global["signed_lift_prefix"][1]["cancellation_free_signed_row_l1_upper"].get()),payload=64*F*F*F*B*B;need(payload<(I(1)<<104),"payload prefix");I coeff=unit+Jroute*high+Jroute*(stock+24)+Ecount*good+Ecount*(128*I(N)*N*N)+16*I(m)*m*m+120*T+Ecount+K+1;need(coeff<(I(1)<<80)&&2*I(m)*m*m*I("10000000000000000")<(I(1)<<80),"fixed coefficient below prime threshold");need(I(stock+24)<(I(1)<<80),"stocklessprime");Q previous=rat("384599/10000000000");J cuts=J::array();for(int stage=0;stage<8;stage++){Q a=(1-c)*c+c*previous;vectorgaps={c-a,1-a-c,1-a-c*(1-previous),1-c};Q gap=*min_element(gaps.begin(),gaps.end());need(gap>0,"ordinary cutoff gap");I L1=ceilQ(36/(gap*gap)),L2=ceilQ(2*(4+msb(coeff)+1)/gap),cut=max(I(1),max(L1,L2));need(Q(cut)*gap*gap>=36&&Q(cut)*gap>=2*(4+msb(coeff)+1),"cutoff inequality");cuts.push_back({{"stage",stage+1},{"minimum_gap",gap.str()},{"counted_coefficient_cutoff_log2",cut.convert_to()},{"general_rule","For full inherited constants C_full>=counted coefficient, replace C by C_full in max(1,ceil(36/delta^2),ceil(2*(4+ceil(log2 C))/delta))."}});previous=a;} +J out={{"status","PASS_COHORT_LITERAL_FIVE_STAGE_FINITE_INVOICE_AND_POSITIVE_CUTOFFS"},{"physical_replicas",T},{"literal_stock",stock},{"normalized_stock",price["stock"]},{"positive_rank_children",Ecount.convert_to()},{"literal_rank_mass",mass.convert_to()},{"literal_deficit",176000},{"literal_histogram",hh},{"global_weighted_additions",weighted.convert_to()},{"global_unit_expanded_additions",unit.convert_to()},{"route_families",Jroute.convert_to()},{"normalizer_factor_bound",787},{"new_chart_factor_max",bank["max_new_chart_factors"]},{"extra_selector_calls",K.convert_to()},{"full_counted_primitive_coefficient",coeff.convert_to()},{"primitive_coefficient_bits",msb(coeff)+1},{"payload_signed_prefix_upper",payload.convert_to()},{"payload_bits",msb(payload)+1},{"internal_row_coefficient",14401},{"external_complex_row_coefficient",20161},{"simultaneous_extra_work_streams",1},{"strict_moment_slack",deltaTau.str()},{"linear_moment_slack",deltaLin.str()},{"ordinary_cutoffs",cuts},{"scope","Sufficient finite invoice for the literal new cohort word, 40 physical replicas and fully admitted bank stock; original 48dim route, retained odd-prime rational address grid, common-ancestor compiler and complex recovery interfaces are inherited unchanged. No Lean or independent certification of those underlying public theorems asserted."}};ofstream(argv[5])< +#include +using boost::multiprecision::cpp_int; +#include +#include +#include +#include +#include +#include +#include +using J=nlohmann::json; +struct E{int kind,dst,src,c;}; +void need(bool x,const char*s){if(!x)throw std::runtime_error(s);} +int main(int argc,char**argv){try{ +need(argc==5,"usage RAW6_RECORDS OUTPUT V HELPERS");std::string pre=argv[1];int v=std::stoi(argv[3]),r=std::stoi(argv[4]),loc=2*v+r,global=4*v+r,temp=global;need(v>0 && r>=0,"dimensions"); +struct Raw{int op,a,b,c,f,z;};std::ifstream f(pre,std::ios::binary|std::ios::ate);size_t sz=f.tellg();need(sz%sizeof(Raw)==0,"stream alignment");std::vectorp(sz/sizeof(Raw));f.seekg(0);f.read((char*)p.data(),sz);std::vectore;std::mapH;for(auto q:p){if(q.op==0){if(q.f)H[q.f]++;}else if(q.op==1)e.push_back({0,q.a,q.b,q.c});else if(q.op==2){H[q.z]++;e.push_back({1,loc,q.a,0});}else if(q.op==3)e.push_back({2,loc,q.a,0});else need(false,"opcode");} +J prefix=J::array();cpp_int largestF=0,largestB=0;for(int rev=0;rev<2;rev++){std::vectornorms(loc+1,1);cpp_int maxrow=1;bool isopen=false;for(size_t z=0;zmaxrow)maxrow=norms[q.dst];}else if(k==1){need(!isopen,"boundcopy");norms[loc]=norms[q.src];isopen=true;}else {need(isopen,"bounderase");norms[loc]=0;isopen=false;}}need(!isopen,"prefix copy closure");if(rev)largestB=maxrow;else largestF=maxrow;prefix.push_back({{"reverse",bool(rev)},{"cancellation_free_signed_row_l1_upper",maxrow.convert_to()},{"bits",boost::multiprecision::msb(maxrow)+1}});} +cpp_int payload=64*largestF*largestF*largestF*largestB*largestB;need(payload>0,"positive finite prefix"); // Exact width is reported and must be included in the separate finite invoice. +long long copies=0,adds=0,odd=0;bool open=false;int center=-1;long long reverseCopies=0; +for(auto q:e){need(q.kind>=0&&q.kind<=2,"kind");need(q.dst>=0&&q.dst<=loc,"local dst");if(q.kind==0){need(q.src>=0&&q.src<=loc&&q.dst!=q.src,"source distinct");need(q.dst!=loc,"copy immutable");need(q.src!=loc||open,"temp not open");if(open)need(q.dst!=center,"source changes inside copied-center block");adds++;odd+=q.c&1;} +else if(q.kind==1){need(!open&&q.dst==loc&&q.src>=0&&q.srca((size_t)(global+1)*words);auto row=[&](int i){return a.data()+(size_t)i*words;};for(int i=0;i=v&&i<2*v&&w==(size_t)(i-v)/64)want^=1ull<<((i-v)%64);need(x[w]==want,"local defining-decoder full formal column");}}} +if(stage==1||stage==2||stage==4){int b=stage==1?0:stage==2?1:2;for(auto q:bridges[b])for(int i=0;i(std::chrono::steady_clock::now()-t0).count()<<"s\n";} +for(int bank=0;bank<4;bank+=2)for(int i=0;i()},{"payload_prefix_bits",boost::multiprecision::msb(payload)+1},{"new_Q_categories",{28,29}},{"local_raw_H",H},{"negative_controls",controls},{"seconds",std::chrono::duration(std::chrono::steady_clock::now()-t0).count()}};std::ofstream(argv[2])<0,'row reserve gap') + need(2*(dim*(dim-1)+3*dim+dim+3*dim*(dim-1)//2+dim+1)+2*dim0 for o in ['forward','backward']),'fresh scalar expansion') + b['scratch_lifecycle_checks']=life;b['template_tests']=scalar.toy_checks() + b['five_invocation_scalar_primitives_per_vertex']=3*b['forward']['totals']['real_component_primitive_steps']+2*b['backward']['totals']['real_component_primitive_steps'] + b['scratch']=dict(live_roles=W,physical_roles_per_cover=W+R+h+1,additional_recursive_calls=0,extra_external_row_coordinate=False) + progress('Merging scalar events, exact frames and all final climbs.') + programs={};controls=[] + for orientation in ['forward','backward']: + events=list(splice.emit(c,orientation));programs[orientation]=splice.validate(events,c,orientation,m,b) + controls.extend(splice.controls(events,c,orientation,m,b)) + g=splice.global_contract(m);splice.validate_global(g,m) + mutations=[('wrong_helper_owner',lambda x:x['stage_recipe'][1].__setitem__('helper_owner','s1^(-1)(d)')), + ('rank_only_frame',lambda x:x['exact_frame_bindings']['x23'].__setitem__('declaration_line','same rank only')), + ('scratch_alias',lambda x:x['scratch_namespace'].__setitem__('centers',[14691,14713])), + ('wrong_live_normalization',lambda x:x.__setitem__('recursive_volume_denominator',24127)), + ('free_RAM',lambda x:x.__setitem__('primitive_policy','free_RAM')), + ('missing_tableau',lambda x:x.__setitem__('physical',14715))] + for name,fn in mutations: + bad=deepcopy(g);fn(bad) + try:splice.validate_global(bad,m) + except ValueError as error:controls.append(dict(name=name,rejected=True,reason=str(error))) + else:raise ValueError('global mutation accepted: '+name) + progress('Recomputing complex cover, router, precision and row inequalities.') + # Independently execute each literal coefficient expansion on exact rationals. + checked=0 + for a in range(-5,6): + if a==0:continue + for den in (1,2,3,6): + q=Q(a,den);event=splice.add(('L',0),('L',1),q) + values={('L',0):Q(3),('L',1):Q(7),('W',0):Q(11)} + ops=splice.lower_scalar(event) + for op in ops: + if op[0]=='copy':values[op[1]]=values[op[2]] + elif op[0]=='halve':values[op[1]]/=2 + elif op[0]=='divide3':values[op[1]]/=3 + elif op[0]=='accumulate':values[op[1]]+=op[3]*values[op[2]] + elif op[0]=='clear':values[op[1]]=Q(0) + else:raise ValueError('Unknown coefficient primitive') + need(values=={('L',0):3+7*q,('L',1):Q(7),('W',0):Q(0)},'exact scalar coefficient expansion') + need(len(ops)==scalar.coeff_steps(q),'two independent scalar primitive counters') + checked+=1 + precision=finite_guard(m,b,basis) + precision['new_coefficient_recipes_checked']=checked + precision['numerator_bound']=5 + + need(labels.scalar_word([(1,0,1),(0,1,-1),(0,2,1),(3,1,-1),(1,0,1),(3,1,1),(0,2,-1),(2,3,-1),(3,2,1),(1,3,-1),(2,0,1)])==[[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]],'global scalar signed exchange') + return dict(status='PASS_FRESH_COMPLEX_LABEL_SCALAR_SPLICE_PRECISION',five_stage_histogram=ledger['histogram'], + label_checks=checks,ledger=ledger,scalar_bill=b, + splice=dict(program=programs,global_contract=g,controls=controls,source_pin=PIN,certificate_sha256=cp['compressed_sha256']), + precision_guard=precision,input_pins=verified, + inherited_theorem_dependencies=[ + 'PR256 freshly regenerates the pinned PR233 gcert certificate and its complete gx.check1 scalar identity; no new Lean build is claimed.', + 'Pinned Lab.inv dirty lifting, exact gwinB/G0..G4 geometry, owner bijections and NetCert composition are inherited source theorems.', + 'Retained general Clifford synthesis, compact complete-stream tape primitives, common-grid precision and complete-row proofs remain analytic dependencies.', + 'The finite operational recipe is regenerated and checked; no astronomical cover enumeration or universal tape-machine execution is claimed.']) + +if __name__=='__main__': + result=run(package_root=Path(__file__).resolve().parents[1]/'vendor/pr249',progress=lambda text:print(text,file=sys.stderr)) + print(json.dumps(result,indent=2)) diff --git a/research/w3-stages-restore/code/complex_labels.py b/research/w3-stages-restore/code/complex_labels.py new file mode 100644 index 0000000000..ce18a1e5cc --- /dev/null +++ b/research/w3-stages-restore/code/complex_labels.py @@ -0,0 +1,174 @@ +"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction +Q=Fraction +from hashlib import sha256 +from pathlib import Path +from math import prod +import gzip,json,sys + +BASE = dict(h=22, v=1320, R=9412, cst=440, N=262944) +EXPECTED_H = {20: 22, 1: 29178, 10: 805, 11: 353, 12: 1141, 13: 168, 14: 725, 15: 605, 16: 81, 17: 39, 19: 1441, 2: 12667, 3: 9988, 4: 3839, 5: 1976, 6: 1491, 7: 642, 8: 1478, 9: 404, 18: 2640} +class Reject(ValueError): + pass + +def need(ok, msg): + if not ok: + raise Reject(msg) + +def digest(obj): + return sha256(json.dumps(obj, separators=(",",":"), sort_keys=True).encode()).hexdigest() + +def hist(counter): + return {str(k):v for k,v in sorted(counter.items()) if v} + +def role(r,v): + return "x" if r < v else "y" if r < 2*v else "s" + +def reduce_binary(x, frame): + for b in frame: + if x & (1 << (b.bit_length()-1)): + x ^= b + return x + +def coeff(a,b, where): + need(type(a) is int and type(b) is int and b>0, f"{where}: coefficient shape") + q=Fraction(a,b) + odd=q.denominator + while odd%2==0: + odd//=2 + need(odd in (1,3), f"{where}: literal coefficient outside dyadic/divisor-three grid") + return q + +def replay_label_counts(c): + """Full finite LABEL walk only. Never multiplies the 12,052-square scalar map.""" + need(c.get("format")=="gcert/1", "format") + need(all(c.get(k)==v for k,v in BASE.items()), "baseline parameter/count mismatch") + h,v,R=c["h"],c["v"],c["R"]; n=2*v+R + need(c.get("ext")==[], "baseline has no exterior-gauged helper inputs") + frames=c["frames"]; dim=list(map(len,frames)) + need(len(frames)==18248, "baseline frame-table count") + need(frames[0]==[] and frames[1]==[1<piv[i+1] for i in range(len(piv)-1)), "frame pivot order") + need(all(not(b>>p&1) for i,b in enumerate(f) for j,p in enumerate(piv) if i!=j), + "frame is not reduced echelon") + ports=c["ports"] + need(len(ports)==v==len(set(ports)), "port count/uniqueness") + need(all(type(p) is int and 0=4 and g[0] in ("out","in"), where+": gate shape") + tag,f,pivot,terms=g[:4] + need(len(g)==(5 if tag=="out" else 4), where+": gate arity") + need(type(f) is int and 0<=f{tr}"]+=1 + totals[phase]["scalar_additions"]+=1 + if sr==tr=="y": + ybracket[(source,target)]+=q;ypiv.add(source);ytarget.add(target) + for r in regs: + climb(r,f,phase) + if phase=="A": + cut=cur.copy() + need(all(cur[v+t]==0 for t in range(v)), "scatter: Y role moved too early") + for k,r,f in c["ret"]: + need(type(r) is int and 2*v<=r>k&1 else c["scat"]["outside"]),"scatter")) + for p in ports for k in range(22)) + return { + "frame_count":len(frames),"tested_distinct_nested_pairs":len(pairs), + "live_registers_per_invocation":n,"temporary_centers":22, + "ranked_live_transitions":transitions, + "phase_stats":totals,"role_histograms":measured, + "phase_histograms":{p:hist(x) for p,x in by_phase.items()}, + "invocation_histogram":hist(combined),"invocation_calls":sum(combined.values()), + "invocation_rank_mass":mass,"retained_centers":c["ret"], + "phase_state_sha256":{"start":digest(start),"after_A":digest(cut), + "after_B":digest(before_final),"final":digest(final)}, + "literal_gate_coefficients":dict(sorted(literal.items())), + "scalar_role_directions":dict(sorted(kind.items())), + "scatter_coefficients":dict(sorted(scatter.items())), + "scatter_additions":sum(scatter.values()),"Cc_copy_additions":22, + "two_hosts_metadata_count":len(c.get("two_hosts",[])), + "two_hosts_note":"Metadata only; not an independent allocator or host-use proof.", + "Y_bracket_pairs":len(ybracket), + "literal_inverse":"Each nonself additive shear inverts by negating its coefficient; inverse phase reverses order; inverse transpose keeps chronological order and swaps source/target with negation.", + "limits":["No scalar all-column replay","No old-response or cleanup matrix formed", + "No generated Lean data comparison or kernel build","No physical stream compiler"] + } + +def scalar_word(ops): + matrix=[[int(i==j) for j in range(4)] for i in range(4)] + for target,source,q in ops: + matrix[target]=[a+q*b for a,b in zip(matrix[target],matrix[source])] + return matrix diff --git a/research/w3-stages-restore/code/complex_scalars.py b/research/w3-stages-restore/code/complex_scalars.py new file mode 100644 index 0000000000..c209381078 --- /dev/null +++ b/research/w3-stages-restore/code/complex_scalars.py @@ -0,0 +1,217 @@ +"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction +Q=Fraction +from hashlib import sha256 +from pathlib import Path +from math import prod +import gzip,json,sys + +V,R,H=1320,9412,22 +def need(x,msg): + if not x:raise ValueError(msg) + +def kind(r):return "X" if r>k&1 else c["scat"]["outside"])) + yield add(live(V+t),tmp(r),q) + yield from part(B) + +def old_word(orientation,K): + if orientation=="forward": + yield from (copy(("T",q),live(2*V+q)) for q in range(R)) + for e in K: + op,t,s,a,b=e + yield add(t,s,Q(-a if t[0]=="L" else a,b)) + else: + yield from (clear(("T",q)) for q in range(R)) + for op,t,s,a,b in reversed(K): + yield add(s,t,Q(a,b)) + yield from (add(live(2*V+q),("T",q),Q(1)) for q in range(R)) + yield from (clear(("T",q)) for q in range(R)) + +def cleanup(orientation,AB): + for t,s,q in reversed(AB): + if kind(t)=="Y":continue + if orientation=="forward":yield add(live(t),live(s),-q) + else:yield add(live(s),live(t),q) + +def main_scalar(orientation,A,B,c): + def phase(gs): + for t,s,q in gs: + if orientation=="forward":yield add(live(t),live(s),q) + else:yield add(live(s),live(t),-q) + yield from phase(A) + # Every center is a complete temporary stream and one rank20 child, + # initialized/read/discarded before the next center uses the work stock. + for k,r,_ in c["ret"]: + yield clear(center(k)) + if orientation=="forward":yield add(center(k),live(r),Q(1)) + for t,p in enumerate(c["ports"]): + q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"])) + if orientation=="backward":yield add(center(k),live(V+t),q) + yield ("recursive_center",k,20) + if orientation=="forward": + for t,p in enumerate(c["ports"]): + q=Q(*(c["scat"]["inside"] if p>>k&1 else c["scat"]["outside"])) + yield add(live(V+t),center(k),q) + else:yield add(live(r),center(k),Q(-1)) + yield clear(center(k)) + yield from phase(B) + +def inv_schedule(orientation,A,B,c): + K=list(old_positive(A,B,c)) + yield from ((p,e) for p,es in [ + ("old_response",old_word(orientation,K)), + ("main",main_scalar(orientation,A,B,c)), + ("cleanup",cleanup(orientation,A+B))] for e in es) + +def coeff_steps(q): + """Non-destructive coefficient expansion using one complete work stream. + Copy source, halve/divide by3, repeat signed accumulation for the numerator, clear. + Counts Gaussian operations; multiply by2 for real/imag component primitives.""" + a,b=abs(q.numerator),q.denominator + need(1<=a<=5 and b in (1,2,3,6),"unsupported new coefficient") + return 2+a+int(b%2==0)+int(b%3==0) + +def bill(schedule): + phases={p:Counter() for p in ("old_response","main","cleanup")} + coeffs={p:Counter() for p in phases} + tape=sha256() + for p,e in schedule: + tape.update((json.dumps((p,e),separators=(",",":"))+"\n").encode()) + phases[p]["all_macros"]+=1 + if e[0]=="recursive_center": + phases[p]["recursive_centers"]+=1 + phases[p]["recursive_rank_mass"]+=e[2] + continue + phases[p]["scalar_macros"]+=1 + phases[p][e[0]]+=1 + if e[0]=="add": + q=Q(e[3],e[4]);coeffs[p][str(q)]+=1 + phases[p]["Gaussian_primitive_steps"]+=coeff_steps(q) + phases[p]["scalar_log2_magnitude_charge"]+=1+(abs(q.numerator)-1).bit_length() + phases[p]["halving_exposure"]+=int(q.denominator%2==0) + phases[p]["divisor3_exposure"]+=int(q.denominator%3==0) + else:phases[p]["Gaussian_primitive_steps"]+=1 + for p in phases:phases[p]["real_component_primitive_steps"]=2*phases[p]["Gaussian_primitive_steps"] + total=sum((Counter({k:v for k,v in x.items() if k not in ["recursive_rank_mass"]}) for x in phases.values()),Counter()) + return {"phases":{p:dict(x) for p,x in phases.items()},"coefficient_histograms":{p:dict(x) for p,x in coeffs.items()}, + "totals":dict(total),"schedule_sha256":tape.hexdigest(), + "other_main_recursive_calls":"Actual independently replayed live-label transitions; not scalar macros"} + +def mm(A,B):return [[sum((x*y for x,y in zip(row,col)),Q(0)) for col in zip(*B)] for row in A] + +def lifecycle(schedule): + """Verify that new scalar-only work stock never survives into a child.""" + initialized=set();dirty=set();active_centers=set();seen_main=False;children=0 + for phase,e in schedule: + if phase=="main" and not seen_main: + need(not dirty,"old-response tableau survives into recursive main phase") + seen_main=True + need(e[0] in ("add","copy","clear","recursive_center"),"unknown or unpaid recursive operation") + if e[0]=="recursive_center": + k=e[1] + need(type(k) is int and 0<=k<22 and e[2]==20,"new temporary entered uncharged child") + need(phase=="main" and not dirty,"old-response temporary used during child") + need(active_centers<=set([k]),"other center was not discarded before next child") + children+=1 + continue + target=e[1] + source=e[2] if e[0] in ("add","copy") else None + if source and source[0]=="T":need(source[1] in initialized,"uninitialized temporary read") + if target[0]=="T": + need(phase=="old_response","scalar-only tableau touched after recursive phase begins") + initialized.add(target[1]) + if e[0]=="clear":dirty.discard(target[1]) + else:dirty.add(target[1]) + if target[0]=="C": + if e[0]=="clear":active_centers.discard(target[1]) + else:active_centers.add(target[1]) + if e[0]=="add": + # Coefficient expansion is deliberately local: copy into W, + # optionally double/halve/divide3, accumulate, and clear W. + expanded=["copy_work"]+["halve"]*int(e[4]%2==0)+["divide3"]*int(e[4]%3==0)+["accumulate"]*abs(e[3])+["clear_work"] + need(len(expanded)==coeff_steps(Q(e[3],e[4])),"literal expansion count") + need(expanded[-1]=="clear_work","coefficient work survived scalar macro") + need(not dirty and not active_centers,"temporary stock not erased at invocation end") + need(children==22,"center child count changed") + return {"tableau_cleared_before_entire_main_phase":True,"tableau_absent_from_all_children":True, + "coefficient_work_cleared_per_add":True,"center_children":children, + "new_recursive_children":0,"moment_live_width":14692, + "new_work_stock_only":9413,"complete_stream_fraction":"1/(14692*|Orth(110,2)|)"} + +def ident(n):return [[Q(int(i==j)) for j in range(n)] for i in range(n)] + +def matrix(n,gs): + a=ident(n) + for t,s,q in gs:a[t]=[x+q*y for x,y in zip(a[t],a[s])] + return a + +def toy_checks(): + # 2 X, 3 S, 2 Y. Explicit nontrivial X mixing is undone; helper map + # and K are otherwise arbitrary. Exact Fraction checks cover every column + # of THIS TINY TEMPLATE, not of the published 12052-register source. + n=7;X={0,1};S={2,3,4};Y={5,6} + gs=[(2,0,Q(1)),(3,2,Q(2)),(5,3,Q(-1,6)),(0,1,Q(1,2)), + (4,0,Q(2)),(2,4,Q(1,2)),(6,2,Q(1,3)),(0,1,Q(-1,2)), + (3,1,Q(-1)),(5,4,Q(1)),(6,0,Q(1))] + M=matrix(n,gs) + need(all(M[i]==ident(n)[i] for i in X),"toy source rows not restored") + Ugs=[e for e in gs if e[0] not in Y] + U=matrix(n,Ugs) + Uinv=matrix(n,[(t,s,-q) for t,s,q in reversed(Ugs)]) + need(mm(Uinv,U)==ident(n),"restricted inverse identity") + Mi=matrix(n,[(t,s,-q) for t,s,q in reversed(gs)]) + g8=[Mi[i] if i in S else ident(n)[i] for i in range(n)] + h8=[M[i] if i in S else ident(n)[i] for i in range(n)] + need(g8==Uinv and h8==U,"cleanup projection identities") + Ut=matrix(n,[(s,t,q) for t,s,q in reversed(Ugs)]) + need(Ut==[list(x) for x in zip(*U)],"backward cleanup transpose") + Kgs=[e for e in gs if e[1] not in X] + Kmat=matrix(n,Kgs) + need(all(Kmat[i][j]==M[i][j] for i in Y for j in S),"zero-source old response") + Kt=matrix(n,[(s,t,q) for t,s,q in reversed(Kgs)]) + need(all(Kt[i][j]==M[j][i] for i in S for j in Y),"old response adjoint") + bad=matrix(n,[(t,s,q) for t,s,q in reversed(Ugs)]) + need(bad!=g8,"wrong inverse sign must fail") + bad_order=matrix(n,[(s,t,q) for t,s,q in Ugs]) + need(bad_order!=Ut,"unreversed transpose must fail") + return {"tiny_exact_template_columns_checked":7,"checks_passed":7, + "wrong_inverse_sign_rejected":True,"unreversed_transpose_rejected":True, + "published_full_scalar_replay":False} diff --git a/research/w3-stages-restore/code/complex_splice.py b/research/w3-stages-restore/code/complex_splice.py new file mode 100644 index 0000000000..9300ef3af3 --- /dev/null +++ b/research/w3-stages-restore/code/complex_splice.py @@ -0,0 +1,276 @@ +"""Portable pure functions extracted from the reviewed complex checks; no historical receipt readers.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction +Q=Fraction +from hashlib import sha256 +from pathlib import Path +from math import prod +import gzip,json,sys + +V,R,H,N,W=1320,9412,22,12052,14692 +PHASES=["old_response","ad0","A","centers","B","final","adF","cleanup","done"] +def need(x,s): + if not x:raise ValueError(s) + +def blobhash(p):return sha256(p.read_bytes()).hexdigest() + +def digest(x):return sha256(json.dumps(x,separators=(',',':'),sort_keys=True).encode()).hexdigest() + +def role(r):return 'X' if r0 else -1)]*abs(a)+[clear(work)] + +def emit(c,ori): + """Construct the complete local parametric invocation, before cover routing. + One role stream is its full complete address rectangle. Frame labels denote + exact canonical representatives, never just rank or binary matrices. + """ + A=list(flat(c['A']));B=list(flat(c['B']));cur=c['start'].copy() + K=[] + for part in (A,None,B): + if part is None: + for t,p in enumerate(c['ports']): + for k,r,f in c['ret']: + K.append(add(L(V+t),T(r),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside'])))) + else: + for t,s,q in part: + if role(s)=='X':continue + K.append(add(T(t) if role(t)=='S' else L(t),T(s),q)) + yield ('phase','old_response') + if ori=='forward': + for q in range(R):yield scal('old_response',copy(('T',q),L(2*V+q)),'old0') + for _,t,s,a,b in K:yield scal('old_response',add(t,s,Q(-a if t[0]=='L' else a,b)),'old0') + else: + for q in range(R):yield scal('old_response',clear(('T',q)),'old0') + for _,t,s,a,b in reversed(K):yield scal('old_response',add(s,t,Q(a,b)),'old0') + for q in range(R):yield scal('old_response',add(L(2*V+q),('T',q),Q(1)),'old0') + for q in range(R):yield scal('old_response',clear(('T',q)),'old0') + yield ('phase','ad0') + for r,f in enumerate(c['start']):yield ('adapter','old_to_new',r,f) + for part in ['A','centers','B','final']: + yield ('phase',part) + if part in ['A','B']: + for g in c[part]: + regs=[g[2]]+[x[0] for x in g[3]]+(g[4] if g[0]=='out' else []) + for r in regs: + if cur[r]!=g[1]: + old=cur[r];cur[r]=g[1] + yield ('climb',part,r,old,g[1],len(c['frames'][g[1]])-len(c['frames'][old])) + for t,s,q in flat([g]): + e=add(L(t),L(s),q) if ori=='forward' else add(L(s),L(t),-q) + yield scal('main',e,g[1]) + elif part=='centers': + for k,r,f in c['ret']: + yield scal('main',clear(C(k)),f if ori=='forward' else 0) + if ori=='forward':yield scal('main',add(C(k),L(r),Q(1)),f) + else: + for t,p in enumerate(c['ports']): + yield scal('main',add(C(k),L(V+t),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0) + yield ('center',k,f if ori=='forward' else 0,0 if ori=='forward' else f,20) + if ori=='forward': + for t,p in enumerate(c['ports']): + yield scal('main',add(L(V+t),C(k),Q(*(c['scat']['inside'] if p>>k&1 else c['scat']['outside']))),0) + else:yield scal('main',add(L(r),C(k),Q(-1)),f) + yield scal('main',clear(C(k)),0 if ori=='forward' else f) + else: + for r,f in enumerate(c['final']): + if cur[r]!=f: + old=cur[r];cur[r]=f + yield ('climb','final',r,old,f,len(c['frames'][f])-len(c['frames'][old])) + yield ('phase','adF') + for r,f in enumerate(c['final']):yield ('adapter','new_to_old',r,f) + yield ('phase','cleanup') + for t,s,q in reversed(A+B): + if role(t)=='Y':continue + e=add(L(t),L(s),-q) if ori=='forward' else add(L(s),L(t),q) + yield scal('cleanup',e,'old1') + yield ('phase','done') + +def contains(U,V): + for u in U: + for v in V: + if u>>(v.bit_length()-1)&1:u^=v + if u:return False + return True + +def validate(events,c,ori,manifest,bill): + phase=None;seen=[];cur=c['start'].copy();cent={};dirty=set();initialized=set() + climbed=Counter();hist=Counter();projection=sha256();whole=sha256();counts=Counter();ad0=[];adF=[] + pairs=set();states={};all_frame_incidence=0;primitive=sha256();primitive_count=0 + for ev in events: + whole.update((json.dumps(ev,separators=(',',':'))+'\n').encode()) + tag=ev[0];counts[tag]+=1 + if tag=='phase': + if phase=='A':states['after_A']=digest(cur) + if phase=='B':states['after_B']=digest(cur) + if phase=='final':states['final']=digest(cur) + phase=ev[1];seen.append(phase) + need(seen==PHASES[:len(seen)],'strict old/A/copy/B/final/adapter/cleanup chronology') + if phase=='ad0':need(not dirty,'old-response tableau survived before label recursion') + if phase=='A':need(ad0==list(enumerate(c['start'])),'missing or reordered exact entry adapter') + if phase=='adF':need(cur==c['final'],'final climbs omitted before cleanup') + if phase=='cleanup':need(adF==list(enumerate(c['final'])),'missing or reordered exact final adapter') + continue + if tag=='adapter': + _,which,r,f=ev + if which=='old_to_new':need(phase=='ad0','entry adapter position');ad0.append((r,f)) + else:need(which=='new_to_old' and phase=='adF','final adapter position');adF.append((r,f)) + elif tag=='climb': + _,p,r,old,new,d=ev + need(phase==p and p in ['A','B','final'],'live child outside source label walk') + need(not dirty and not cent,'new work stock or center active during live child') + need(cur[r]==old and d==len(c['frames'][new])-len(c['frames'][old]) and d>0,'wrong exact child endpoints/rank') + pair=(old,new) + if pair not in pairs:need(contains(c['frames'][old],c['frames'][new]),'nonnested child');pairs.add(pair) + cur[r]=new;climbed[p]+=1;hist[d]+=1 + elif tag=='center': + _,k,old,new,d=ev + need(phase=='centers' and not dirty and set(cent)=={k},'center child ownership') + need(cent[k]==old and (k,c['ret'][k][1],c['ret'][k][2])==tuple(c['ret'][k]),'center input frame') + f=c['ret'][k][2] + need((old,new,d)==((f,0,20) if ori=='forward' else (0,f,20)),'center child direction/rank') + cent[k]=new;hist[d]+=1 + projection.update((json.dumps(('main',('recursive_center',k,d)),separators=(',',':'))+'\n').encode()) + elif tag=='scalar': + _,p,e,f=ev + need(p==('main' if phase in ['A','centers','B'] else phase),'scalar phase binding') + need(e[0] in ['add','copy','clear'],'unpaid scalar operation') + target=e[1];source=e[2] if e[0] in ['add','copy'] else None + for x in [target]+([source] if source else []): + bank,r=x + if bank=='T':need(phase=='old_response' and 0<=r1 and Q(price['second_next'][0])>1 + assert price['prime_lucas_lehmer_residue']==0 and price['prime_lucas_lehmer_steps']==125 + gaps=[];bits=(coefficient-1).bit_length() + for row in price['ordinary_gaps']: + gap=min(map(Q,row.values()));assert gap>0 + cutoff=max(1,ceilq(Q(36)/gap**2),ceilq(Q(2*(4+bits))/gap)) + assert cutoff*gap**2>=36 and cutoff*gap>=2*(4+bits) + gaps.append({'minimum_gap':str(gap),'counted_log2_cutoff':str(cutoff)}) + assert len(gaps)==9 and len(price['assembly']['strict_constraints'])==47 + assert min(map(Q,price['assembly']['strict_constraints'].values()))>0 and price['adjacent_rejected'] + result={'status':'PASS_SOURCE_BOUND_W3_STAGES_RESTORATION_CONDITIONAL_FINITE_CONSTRUCTION','kappa':price['kappa'],'word_sha256':binding['word_sha256'],'compact_word_sha256':binding['compact_word_sha256'],'source_regenerated':True,'kernel_families_and_singles':518,'kernel_entrance_rank':840,'reorder_relocations':172,'complex_binds':price['complex_binds'],'bit_grid_cap':price['bit_grid_cap'],'reorder_local_phi_delta':reorder['local_phi_delta'],'pre_reorder_word_sha256':binding['pre_reorder_word_sha256'],'complex_supplier_regenerated':True,'active_helpers':15132,'normalized_stock':161843,'bank_assignments':3026400,'new_frame_charts':4265,'changed_projector_charts':22118,'new_chart_factor_max':342,'normalizer':787,'finite_coefficient':coefficient,'selector_charge':selectors,'payload_bits':97,'finite_cutoffs':gaps,'complex_guard':cg,'full_constant_rule':'Replace the counted coefficient by C_full dominating every inherited primitive, wrapper, row, setup, routing and earlier-level constant in the same positive-gap cutoff formula. No recursive child is absorbed.','scope':'Conditional on inherited all-size compiler, weighted charts, restored rows, selectors, routing, prime supply, complex dirty lifting, precision/recovery and analytic interfaces. No unconditional multiplication theorem, new Lean build or runtime benchmark is claimed.'} + receipts=['baseline/verification.json','COMPLEX-GUARD.json','BANK.json','PRICE.json','INVOICE.json','COLUMNS.json','COMPACT-COLUMNS.json','LEGALITY.json','candidate/SOURCE-BINDING.json','candidate/REORDER-STAGE.json','complex304/COMPLEX304.json','complex304/replay/CERTIFICATE.json','complex304/replay/NATIVE.json','KERNEL-REPLAY.json','KERNEL-CHECKS.json','candidate-target/TARGET-PREFIX-W3.json','candidate-w3/SOURCE-BINDING.json','logs/complex-source.log'] + result['fresh_receipt_hashes']={name:sha(out/name) for name in receipts} + (out/'CERTIFICATE.json').write_text(json.dumps(result,sort_keys=True,indent=2)+'\n');print('PASS integrated construction',price['kappa'],flush=True) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('output',type=Path);a=ap.parse_args();finish(a.output) diff --git a/research/w3-stages-restore/code/kernel_checks.py b/research/w3-stages-restore/code/kernel_checks.py new file mode 100644 index 0000000000..fab8bab840 --- /dev/null +++ b/research/w3-stages-restore/code/kernel_checks.py @@ -0,0 +1,56 @@ +"""checks.py CAND_DIR OUT_DIR OUT_JSON : exact independent checks of a kernel candidate built by transform.py. + - every frame added to COHORT249-FRAMES.json beyond #310's: B full rank, A full rank 24-d, A.B=0, Gram under 9I-J nonsingular (exact) + - every selection family: F2 kernel identity on the ORIGINAL word's prefix responses (C_p + sum C_d = 0 mod 2, odd coefficients), + E contained in the actual first positive frame of every member, members are ZERO-initial FULL-final helpers, not source owners/donor keys + - zero-response singles: no prefix reads in the original word; initial frame = their first MOVE destination + - entrance rank total divisible by 3; 249-states.json record_sha256 matches the records""" +import sys,json,hashlib,collections +import numpy as np +from sympy import Matrix +C,O,OUTJ=sys.argv[1:4] +st=json.load(open(C+'/249-states.json')); n,v,ZERO,FULL=st['n'],st['v'],st['ZERO'],st['FULL']; H0=2*v +fr=json.load(open(O+'/frames.json'))['frames'] +old_nf=json.load(open(C+'/COHORT249-FRAMES.json')); nf=json.load(open(O+'/COHORT249-FRAMES.json')) +added={k:x for k,x in nf.items() if k not in old_nf} +G=Matrix(24,24,lambda i,j:(9 if i==j else 0)-1) +for k,f in added.items(): + B=Matrix(f['B']); A=Matrix(f['A']); d=f['dim'] + assert B.rows==d and B.rank()==d and A.rows==24-d and A.rank()==24-d and (A*B.T).is_zero_matrix, k + assert (B*G*B.T).det()!=0, ('degenerate',k) + assert fr[k]==f +rec=np.fromfile(C+'/COHORT249-RECORDS.bin',dtype='4 else C+'/../base-verify/export/249-DONOR-OWNERSHIP.json'))['donor_keys']) +ini={int(k):x for k,x in st['initial'].items()} +nini={int(k):x for k,x in json.load(open(O+'/COHORT249-INITIAL.json')).items()} +def contained(Bk,Fk): + return (Matrix(fr[str(Fk)]['A'])*Matrix(fr[str(Bk)]['B']).T).is_zero_matrix if fr[str(Fk)]['A'] else True +sel=json.load(open(O+'/COHORT249-SELECTION.json')) +er=0; piv=set(); par=set(); nf_=ns=0 +for s in sel: + p=s['a']; ms=[p]+s['partners']; E=s['new_frame_id']; er+=s['E_dimension']; assert fr[str(E)]['dim']==s['E_dimension'] + assert p not in piv; piv.add(p); par.update(s['partners']) + for h in ms: + assert H0<=h4 else 4 + res=dict(trials=T,bits_per_trial=64,registers=n) + bad=dict(old_target=0,new_target=0,old_helper=0,new_helper=0,source=0,old_vs_new=0) + for t in range(T): + rnd=random.Random(1000+t); x0=[rnd.getrandbits(64) for _ in range(n)] + yo=runF2(old,x0,n); yn=runF2(new,x0,n) + for y,tag in ((yo,'old'),(yn,'new')): + bad[tag+'_target']+=sum(1 for i in range(v) if y[v+i]!=x0[v+i]^x0[i]) + bad[tag+'_helper']+=sum(1 for s in range(2*v,n) if y[s]!=x0[s]) + bad['source']+=sum(1 for i in range(v) if y[i]!=x0[i]) + bad['old_vs_new']+=sum(1 for s in range(n) if yo[s]!=yn[s]) + if t==0: + for cat in (28,29): + yc=runF2(new,x0,n,omit=cat); res[f'control_omit_cat{cat}_wrong_registers']=sum(1 for s in range(n) if yc[s]!=yo[s]) + res['F2_failures']=bad + rnd=random.Random(7); x0=[rnd.randrange(P) for _ in range(n)]; zo=runZ(old,x0,n); zn=runZ(new,x0,n) + x1=list(x0) + for s in range(2*v,n): x1[s]=0 + zo1=runZ(old,x1,n) + res['Z_mod_2^61-1']=dict(old_targets_depending_on_helper_dirt=sum(1 for s in range(v,2*v) if zo[s]!=zo1[s]), + helpers_restored_old=sum(1 for s in range(2*v,n) if zo[s]==x0[s]),helpers_restored_new=sum(1 for s in range(2*v,n) if zn[s]==x0[s]), + nonhelper_equal_old_vs_new=sum(1 for s in range(2*v) if zo[s]==zn[s]),note='#310 word itself is not a Z-identity; F2 is the semantics') + res['status']='PASS' if not any(bad.values()) and res['control_omit_cat28_wrong_registers']>0 and res['control_omit_cat29_wrong_registers']>0 else 'FAIL' + json.dump(res,open(sys.argv[3],'w'),indent=1); print(json.dumps(res)) diff --git a/research/w3-stages-restore/code/kernel_stage.py b/research/w3-stages-restore/code/kernel_stage.py new file mode 100644 index 0000000000..be305b70e2 --- /dev/null +++ b/research/w3-stages-restore/code/kernel_stage.py @@ -0,0 +1,156 @@ +"""transform.py CAND_DIR PLAN_JSON OUT_DIR +Kernel condensation on the w3 word (#310). For every family (pivot p, donors d_i, integer coefficients a_i with +C_p + sum a_i C_{d_i} = 0 over Z, E = nondegenerate subspace contained in the first positive frames of p and all d_i): + - remove p's initial target-correction reads (cat 4 at ZERO, all before CUT); + - after CUT (last initial read): families in increasing dim(E): MOVE d_i -> E, ADD d_i += a_i * p at E (cat 28); + - p enters at E (initial frame), its first MOVE ZERO->F_p becomes E->F_p (deleted if E == F_p); + d_i's first MOVE ZERO->F_d starts from d_i's last entrance frame instead; + - at the very end (all helpers at FULL): ADD d_i -= a_i * p at FULL (cat 29). +Zero-response singles (C_p = 0, no reads): p enters at its first frame F_p, first MOVE deleted. +Writes COHORT249-RECORDS.bin (+249-records.bin copy), COHORT249-INITIAL.json, COHORT249-FRAMES.json (#310's + new), +COHORT249-SELECTION.json, COHORT249-FINAL.json, 249-states.json (initial, record_count, record_sha256), frames.json (merged).""" +import sys,json,hashlib,shutil,os +import numpy as np +from fractions import Fraction as Fr +from math import lcm,gcd +C,PLAN,OUT=sys.argv[1],sys.argv[2],sys.argv[3] +os.makedirs(OUT,exist_ok=True) +st=json.load(open(C+'/249-states.json')); n,v,ZERO,FULL=st['n'],st['v'],st['ZERO'],st['FULL']; H0=2*v +frames=json.load(open(C+'/frames.json')) +FR=frames['frames'] +newfr_310=json.load(open(C+'/COHORT249-FRAMES.json')) +plan=json.load(open(PLAN)) +rec=np.fromfile(C+'/COHORT249-RECORDS.bin',dtype='4 else C+'/../base-verify/export/249-DONOR-OWNERSHIP.json'))['donor_keys']) +dim=lambda f: FR[str(f)]['dim'] +def rref(rows): + m=[[Fr(x) for x in r] for r in rows]; piv=[]; rr=0 + for c in range(24): + p=next((i for i in range(rr,len(m)) if m[i][c]!=0),None) + if p is None: continue + m[rr],m[p]=m[p],m[rr]; pv=m[rr][c]; m[rr]=[x/pv for x in m[rr]] + for i in range(len(m)): + if i!=rr and m[i][c]!=0: + q=m[i][c]; m[i]=[a-q*b for a,b in zip(m[i],m[rr])] + piv.append(c); rr+=1 + return tuple(tuple(r) for r in m[:rr]),piv +def prim(vec): + L=1 + for x in vec: L=lcm(L,Fr(x).denominator) + iv=[int(Fr(x)*L) for x in vec]; g=0 + for x in iv: g=gcd(g,abs(x)) + return [x//g for x in iv] +def annih(B): + R,piv=rref(B); A=[] + for fc in range(24): + if fc in piv: continue + vec=[Fr(0)]*24; vec[fc]=Fr(1) + for i,pc in enumerate(piv): vec[pc]=-R[i][fc] + A.append(prim(vec)) + return A +def contained(B,f): # rows of B inside frame f + A=FR[str(f)]['A'] + return all(sum(x*y for x,y in zip(b,a))==0 for b in B for a in A) +# first-use MOVE index per helper after CUT +firstmove={} +for i in range(CUT+1,len(rec)): + k,a,b,c,f,z=rec[i] + if k==0 and a>=H0 and a not in firstmove: firstmove[a]=i + elif k in (1,2,3): + for s in (a,b): + if s>=H0 and s0 + chain.append(new);gaps.append(row) + if R.grid_kappa(new)==cap:break + else:raise AssertionError('No finite cap') + supplier=json.loads(Path(complex_path).read_text());assert supplier['status']=='PASS_FRESH_PR304_COMPLEX_SUPPLIER' + complex_saving=Q(supplier['priced_complex_saving']);assert complex_saving==Q(7635,10**7)<=Q(supplier['tensor_saving']);bit_cap=cap + # As in the retained kappa_w.py rule, the assembled leaf is + # capped strictly below (1-beta)*complex, and the grid kappa is the smaller of the bit cap and that leaf's grid point. + leaf=min(chain[-1],(1-R.BETA)*complex_saving-Q(1,10**30));complex_binds=leaf0 and min(assembly['margins'].values())>cap + try:outer.assembly(leaf,complex_saving,R.bridge_template(),cap+Q(1,R.GRID),eta=R.ETA,beta=R.BETA) + except AssertionError:pass + else:raise AssertionError('Adjacent grid point admitted') + assert not complex_binds and bit_cap==Q(151024082262820774685631,200000000000000000000000000) + assert cap==Q(151024082262820774685631,200000000000000000000000000) and level==9 + result={'status':'PASS_EXACT_W3_PRICE_TWO_ENGINES_47_CONSTRAINTS','source_word_sha256':st['record_sha256'],'complex_saving':complex_saving,'complex_supplier':supplier,'cohort_candidate':{'stock':stock,'calls':calls,'rank_mass':mass,'deficit':35200,'histogram':hist,'coarse':coarse,'moment_upper':first[1],'kappa':cap},'local_histogram':dict(H),'prime':q,'prime_lucas_lehmer_steps':125,'prime_lucas_lehmer_residue':res,'rare_density':R.RHO,'full_fallback_retained':True,'coarse_bracket':[coarse,nxt],'first_interval':first,'first_next':first_next,'second_interval':second,'second_next':second_next,'ordinary_chain':chain,'ordinary_gaps':gaps,'assembly':assembly,'kappa':cap,'bit_grid_cap':bit_cap,'complex_binds':complex_binds,'assembled_leaf':leaf,'adjacent_rejected':True,'scope':'Exact arithmetic; source, geometry, bank and finite invoice admission required separately.'} + Path(output).write_text(json.dumps(R.serial(result),sort_keys=True,indent=2)+'\n');print('PASS exact price',cap,float(cap),flush=True) +if __name__=='__main__': + ap=argparse.ArgumentParser();ap.add_argument('candidate',type=Path);ap.add_argument('--bank',type=Path,required=True);ap.add_argument('--output',type=Path,required=True);ap.add_argument('--complex',type=Path,required=True);a=ap.parse_args();run(a.candidate,a.bank,a.output,a.complex) diff --git a/research/w3-stages-restore/code/recompact.py b/research/w3-stages-restore/code/recompact.py new file mode 100644 index 0000000000..47d2ce51ff --- /dev/null +++ b/research/w3-stages-restore/code/recompact.py @@ -0,0 +1,23 @@ +#!/usr/bin/env python3 +"""Recompute the compact record stream and the candidate's binding receipts after a transcript stage (same freed-role map as prepare_candidate.py).""" +import hashlib,json,struct,sys +from pathlib import Path +if not __debug__:raise SystemExit('Assertions required') +out=Path(sys.argv[1]);read=lambda p:json.loads(Path(p).read_text());sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest() +if '--merge-frames' in sys.argv: + fs=read(out/'frames.json');nf=read(out/'COHORT249-FRAMES.json');fs['frames'].update(nf);(out/'frames.json').write_text(json.dumps(fs,sort_keys=True,separators=(',',':'))+'\n') +st=read(out/'249-states.json');ini=read(out/'COHORT249-INITIAL.json');FULL=st['FULL'];n=st['n'];assert n==20107 +freed={r for r in range(3520,n) if ini[str(r)]==FULL};assert len(freed)==1455 +ev=list(struct.iter_unpack('<6i',(out/'COHORT249-RECORDS.bin').read_bytes())) +for op,a,b,c,f,z in ev:assert a not in freed and (op==0 or b not in freed),'Freed role used after the stage' +live=[r for r in range(n) if r not in freed];mapping={r:i for i,r in enumerate(live)};mapping[n]=len(live);assert len(live)==18652 +compact=[(op,mapping[a],b if op==0 else mapping[b],c,f,z) for op,a,b,c,f,z in ev] +(out/'COMPACT-RECORDS.bin').write_bytes(b''.join(struct.pack('<6i',*r) for r in compact)) +wordsha=sha(out/'COHORT249-RECORDS.bin');st['record_sha256']=wordsha;st['record_count']=len(ev) +final=dict(st['final']) +for op,a,b,c,f,z in ev: + if op==0:final[str(a)]=c +assert all(final[str(i)]==st['final'][str(i)] for i in range(2*1760)),'data endpoints unchanged';st['final']=final;(out/'COHORT249-FINAL.json').write_text(json.dumps(final,sort_keys=True)+'\n') +(out/'249-states.json').write_text(json.dumps(st,sort_keys=True,separators=(',',':'))+'\n');(out/'249-records.bin').write_bytes((out/'COHORT249-RECORDS.bin').read_bytes()) +b=read(out/'SOURCE-BINDING.json');b.update(pre_restoration_word_sha256=b['word_sha256'],word_sha256=wordsha,compact_word_sha256=sha(out/'COMPACT-RECORDS.bin'),record_count=len(ev),stage_after_binding='PR312 kernel, target-prefix+plateau and reorder stages, then early restoration (438 helpers, code/cleanup.py)');(out/'SOURCE-BINDING.json').write_text(json.dumps(b,sort_keys=True,indent=1)+'\n') +print('PASS recompaction after the restoration stage:',wordsha,len(ev),'records',flush=True) diff --git a/research/w3-stages-restore/code/reorder_stage.py b/research/w3-stages-restore/code/reorder_stage.py new file mode 100644 index 0000000000..ba2f260c06 --- /dev/null +++ b/research/w3-stages-restore/code/reorder_stage.py @@ -0,0 +1,172 @@ +#!/usr/bin/env python3 +"""Reorder stage on the actual w3 word: just-in-time MOVE normalisation plus commuting-ADD relocation. + +Each register's frame path is rebuilt from the frames of its actual incidences (ADD operands, COPY/ERASE +centres): before every event each operand climbs directly to the event frame (one nested MOVE), and after the +last event to its final frame. A relocation takes an ADD a += c*b out of a frame that is a strict breakpoint of +an operand path and executes it immediately before/after a neighbouring ADD incidence of a or b, inside that +incidence's frame, when no crossed event reads a (ADD source, COPY, ERASE) or writes b; the ADD then commutes +with every crossed event over every commutative coefficient ring. Moves are priced on the rebuilt paths with +phi(r) = r ln(120/r) and kept greedily over disjoint operand sets; round k screens the word after round k-1. +The screen is re-run here and must reproduce the frozen selection exactly. Checks: crossed-interval contract of +every move, nested exact-integer frame chains, fixed initial/final frames, an integer replay modulo 2^61-1 with +pseudo-random dirty values for every register (identical final values to the input word), a nonvacuous omission +control, and the frozen local histogram delta. The F2 all-column, legality, chart, bank and price checks of the +package then run unchanged on the output word. +Port of PR #299/#306's reorder stage (Chafik Boukhalfa, Anthropic Claude assistance) to the PR249 cohort word; Apache-2.0. +""" +import sys +if not __debug__:raise SystemExit('Assertions required') +sys.dont_write_bytecode=True +import argparse,bisect,hashlib,json,math,random,shutil,struct +from collections import Counter,defaultdict +from pathlib import Path +sha=lambda b:hashlib.sha256(b).hexdigest() +def phi(r):return r*math.log(120/r) if r>0 else 0.0 + +class Word: + def __init__(s,cand): + s.st=json.loads((cand/'249-states.json').read_text());fr=json.loads((cand/'frames.json').read_text())['frames'] + s.n=s.st['n'];s.v=s.st['v'] + s.dim={int(k):int(f['dim']) for k,f in fr.items()};s.B={int(k):f['B'] for k,f in fr.items()};s.A={int(k):f['A'] for k,f in fr.items()} + s.init={int(k):x for k,x in json.loads((cand/'COHORT249-INITIAL.json').read_text()).items()} + s.final={int(k):x for k,x in s.st['final'].items()};s.raw=(cand/'COHORT249-RECORDS.bin').read_bytes() + s.ev=list(struct.iter_unpack('<6i',s.raw));s._sub={} + def sub(s,a,b): + k=(a,b) + if k not in s._sub:s._sub[k]=s.dim[a]<=s.dim[b] and all(sum(x*y for x,y in zip(r,q))==0 for r in s.B[a] for q in s.A[b]) + return s._sub[k] + +def hist(ev): + H=Counter() + for op,a,b,c,f,z in ev: + if op==0 and f:H[f]+=1 + elif op==2:H[z]+=1 + return H +def phisum(H):return sum(c*phi(r) for r,c in H.items()) +def strip(ev):return [e for e in ev if e[0]!=0] +def rebuild(W,events): + n=W.n;state=[W.init[r] for r in range(n)]+[None];out=[] + def mv(r,f): + if state[r]!=f: + assert W.sub(state[r],f),('non-nested MOVE',r,state[r],f) + out.append((0,r,state[r],f,W.dim[f]-W.dim[state[r]],0));state[r]=f + for e in events: + op,a,b,c,f,z=e + if op==1:mv(a,f);mv(b,f) + elif op==2:mv(a,c);state[n]=f + elif op==3:mv(a,c);assert state[n]==f + else:raise AssertionError('MOVE in event stream') + out.append(e) + for r in range(n):mv(r,W.final[r]) + return out +def replay(ev,n,seed=20261010): + P=(1<<61)-1;rng=random.Random(seed);val=[rng.randrange(P) for _ in range(n+1)] + for op,a,b,c,f,z in ev: + if op==1:val[a]=(val[a]+c*val[b])%P + elif op==2:val[n]=val[a] + return val[:n] + +def index(W,ne): + n=W.n;incf=defaultdict(list);reads=defaultdict(list);writes=defaultdict(list) + for i,(op,a,b,c,f,z) in enumerate(ne): + if op==1: + incf[a].append((i,f,True));writes[a].append(i) + if b!=n:incf[b].append((i,f,True));reads[b].append(i) + else:incf[a].append((i,c,False));reads[a].append(i) + return incf,reads,writes +def count(L,lo,hi):return bisect.bisect_left(L,hi)-bisect.bisect_left(L,lo) +def screen(W,ne,window=6): + n=W.n;incf,reads,writes=index(W,ne);inct={s:[t for t,f,x in L] for s,L in incf.items()} + def cost(fs):return sum(phi(W.dim[b]-W.dim[a]) for a,b in zip(fs,fs[1:]) if a!=b) + def legal(fs):return all(W.sub(a,b) for a,b in zip(fs,fs[1:])) + def path(r,dele=None,add=None): + L=[(t,f) for t,f,x in incf[r] if t!=dele]+([add] if add else []);L.sort() + return [W.init[r]]+[f for t,f in L]+[W.final[r]] + cands=[] + for i,(op,a,b,c,f,z) in enumerate(ne): + if op!=1 or b==n:continue + def bp(r): + L=inct[r];k=bisect.bisect_left(L,i);pf=incf[r][k-1][1] if k else W.init[r];nf=incf[r][k+1][1] if k+1 4 else dict(gates=[], new_frames={}) +H = 24; Q = (1 << 61) - 1; M = 120 +def phi(r): return r * math.log(M / r) if r > 0 else 0.0 + +st = json.loads((CAND / '249-states.json').read_text()); n, v = st['n'], st['v']; ZERO, FULL = st['ZERO'], st['FULL'] +cov = np.array(st['source_covectors'], dtype=np.int64) +frj = json.loads((CAND / 'frames.json').read_text())['frames'] +dim = {int(k): int(f['dim']) for k, f in frj.items()} +Bm = {int(k): np.array(f['B'], dtype=np.int64).reshape(-1, H) for k, f in frj.items()} +Am = {int(k): np.array(f['A'], dtype=np.int64).reshape(-1, H) for k, f in frj.items()} +del frj +newframes = json.loads((CAND / 'COHORT249-FRAMES.json').read_text()) +added = {int(k): fr for k, fr in PLAT['new_frames'].items()} +for k, fr in added.items(): + assert k not in dim and len(fr['B']) == fr['dim'] and len(fr['A']) + fr['dim'] == H + B_, A_ = np.array(fr['B'], dtype=np.int64), np.array(fr['A'], dtype=np.int64) + assert not np.any(B_ @ A_.T) and np.linalg.matrix_rank(B_.astype(float)) == fr['dim'] and np.linalg.matrix_rank(A_.astype(float)) == H - fr['dim'] + dim[k] = fr['dim']; Bm[k] = B_; Am[k] = A_ +for k in newframes: assert int(k) in dim +initial = {int(k): f for k, f in json.loads((CAND / 'COHORT249-INITIAL.json').read_text()).items()} +final = {int(k): f for k, f in st['final'].items()} +raw = (CAND / 'COHORT249-RECORDS.bin').read_bytes() +old = list(struct.iter_unpack('<6i', raw)) +sel = json.loads(SELP.read_text()); CUT = sel['cut_record'] +assert hashlib.sha256(raw).hexdigest() == sel['input_record_sha256'] == st['record_sha256'] and len(old) == sel['input_record_count'] +subc = {} +def sub(a, b): + if a == b: return True + k = (a, b) + if k not in subc: + subc[k] = dim[a] <= dim[b] and (Bm[a].shape[0] == 0 or Am[b].shape[0] == 0 or not np.any(Bm[a] @ Am[b].T)) + return subc[k] +istarget = lambda r: v <= r < 2 * v + +# ---------- groups ---------- +groups = sel['groups']; dep_of = {}; atclose = defaultdict(list); members = set(); retained = set() +for j, g in enumerate(groups): + t, ps, sg, c, F = g['dependent'], g['retained'], g['signs'], g['close_after_record'], g['frame'] + assert istarget(t) and all(istarget(p) for p in ps) and t not in ps and len(set(ps)) == len(ps) and len(sg) == len(ps) + assert all(s in (1, -1) for s in sg) and c > CUT and dim[F] == g['close_rank'] + assert t not in dep_of; dep_of[t] = j; atclose[c].append(j); members.update([t] + ps); retained.update(ps) + assert all(not np.any(Bm[F] @ cov[m - v]) for m in [t] + ps), 'close frame outside a member cap' +assert not (set(dep_of) & retained), 'a dependent is also retained' + +# ---------- literal responses (F2 columns + integer fingerprints) on the original word ---------- +K = 4; rng = random.Random(0x5EED310) +val = [[rng.randrange(Q) for _ in range(K)] for _ in range(n + 1)] +cols = [1 << i for i in range(n)] + [0] +resF = {m: 0 for m in members}; resI = {m: [0] * K for m in members} +state = dict(initial); center = None; cpos = None; deleted = 0 +for i, (op, a, b, c, f, z) in enumerate(old): + if op == 0: state[a] = c + elif op == 1: + if i > CUT: + if b in dep_of: assert i > groups[dep_of[b]]['close_after_record'], 'active dependent used as a source' + if a in members and (a not in dep_of or i <= groups[dep_of[a]]['close_after_record']): + if a in dep_of: assert not istarget(b), 'target source inside a dependent prefix'; deleted += 1 + resF[a] ^= cols[b]; resI[a] = [(x + c * y) % Q for x, y in zip(resI[a], val[b])] + cols[a] ^= cols[b] if c % 2 else 0 + val[a] = [(x + c * y) % Q for x, y in zip(val[a], val[b])] + elif op == 2: assert center is None; center = a; cols[n] = cols[a]; val[n] = list(val[a]); state[n] = f + elif op == 3: center = None; cols[n] = 0; del state[n] + if i == CUT: + assert center is None and all(state[m] == ZERO for m in members), 'cut not at ZERO' + resF = {m: 0 for m in members}; resI = {m: [0] * K for m in members} + for j in atclose.get(i, []): + g = groups[j]; t = g['dependent']; RF = resF[t]; RI = list(resI[t]) + for p, s in zip(g['retained'], g['signs']): + RF ^= resF[p]; RI = [(x - s * y) % Q for x, y in zip(RI, resI[p])] + assert RF == 0 and RI == [0] * K, ('window dependency fails', j) + assert center is None +print('dependencies checked', len(groups), 'groups; deleted dependent reads', deleted, flush=True) +assert deleted > 0 + +retime = {} +for gte in PLAT['gates']: + i = gte['record']; assert old[i][0] == 1 and old[i][4] == gte['old_frame'] and i not in retime and old[i][2] != n + retime[i] = gte['new_frame'] + members.update([old[i][1], old[i][2]]) +# ---------- emit ---------- +zmax = max(e[5] for e in old if e[0] == 1); SETUP, RESTORE = zmax + 1, zmax + 2 +out = []; state = dict(initial); inserted = 0 +def move(r, f): + if state[r] == f: return + assert sub(state[r], f), ('nonnested use', r, state[r], f) + out.append((0, r, state[r], f, dim[f] - dim[state[r]], 0)); state[r] = f +def need(r, f): + if r in members: move(r, f) +for i, e in enumerate(old): + op, a, b, c, f, z = e + if op == 0: + if a in members: continue + assert state[a] == b; out.append(e); state[a] = c + elif op == 1: + if a in dep_of and CUT < i <= groups[dep_of[a]]['close_after_record']: pass + else: + if i in retime: f = retime[i]; e = (op, a, b, c, f, z) + need(a, f); need(b, f); out.append(e) + elif op == 2: + need(a, c); out.append(e); state[n] = f + elif op == 3: + out.append(e); del state[n] + if i == CUT: + for g in groups: + for p, s in zip(g['retained'], g['signs']): + move(g['dependent'], ZERO); move(p, ZERO); out.append((1, g['dependent'], p, -s, ZERO, SETUP)); inserted += 1 + for j in atclose.get(i, []): + g = groups[j] + for p, s in zip(g['retained'], g['signs']): + move(g['dependent'], g['frame']); move(p, g['frame']); out.append((1, g['dependent'], p, s, g['frame'], RESTORE)); inserted += 1 +for r in sorted(members): move(r, final[r]) +assert state == final + +# ---------- independent checks ---------- +def legality(recs): + state = dict(initial); hist = Counter(); copied = False; cs = None + for (op, a, b, c, f, z) in recs: + if op == 0: + assert state[a] == b and sub(b, c) and dim[c] - dim[b] == f; state[a] = c + if f: hist[f] += 1 + elif op == 1: + assert state[a] == f and state[b] == f and a != b and c % 2 + if copied: assert a != cs and a != n + elif op == 2: assert not copied and b == n and state[a] == c and z == dim[c]; copied = True; cs = a; state[n] = f; hist[z] += 1 + else: assert copied and a == cs and state[a] == c and state[n] == f; copied = False; del state[n] + assert not copied and all(state[s] == final[s] for s in range(n)) + return hist +def f2_replay(recs, reverse=False): + columns = [1 << i for i in range(n)] + [0]; wanted = [1 << i for i in range(n)] + for t in range(v): wanted[v + t] ^= 1 << t + rng_ = range(len(recs) - 1, -1, -1) if reverse else range(len(recs)); center = None + for k in rng_: + op, a, b, c, f, z = recs[k] + if op == 1: + if c % 2: columns[a] ^= columns[b] + elif op == (3 if reverse else 2): assert center is None; center = a; columns[n] = columns[a] + elif op == (2 if reverse else 3): center = None; columns[n] = 0 + assert columns[:n] == wanted, 'F2 all-column endpoint failure' +def int_replay(recs, seed): + r = random.Random(seed); val = [r.randrange(Q) for _ in range(n)] + [0] + for (op, a, b, c, f, z) in recs: + if op == 1: val[a] = (val[a] + c * val[b]) % Q + elif op == 2: val[n] = val[a] + elif op == 3: val[n] = 0 + return val[:n] +def source_span(recs): + """every non-target ADD operand's exact integer source content lies in the gate frame""" + # exact source content: x-source i holds the basis vector of its (rank-1) initial frame; helpers/targets 0. + # The COPY temporary (role n, copied-center scatter in the ZERO frame) is the COPY mechanism's own + # projection and is exempt, exactly as in the input word. + content = np.zeros((n + 1, H), dtype=np.int64); checked = 0; maxabs = 0 + for i in range(v): + assert dim[initial[i]] == 1; content[i] = Bm[initial[i]][0] + Abad = 0 + for (op, a, b, c, f, z) in recs: + if op == 1: + for r in (a, b): + if istarget(r) or r == n: continue + if Am[f].shape[0] and np.any(Am[f] @ content[r]): Abad += 1 + checked += 1 + content[a] += c * content[b] + if abs(content[a]).max() > 1 << 40: raise OverflowError + elif op == 2: content[n] = content[a] + elif op == 3: content[n] = 0 + maxabs = int(abs(content).max()) + return checked, Abad, maxabs + +hist_old = legality(old); hist_new = legality(out) +print('legality ok', flush=True) +for recs in (old, out): f2_replay(recs); f2_replay(recs, True) +print('F2 forward/inverse ok', flush=True) +for seed in (1, 2, 3): + assert int_replay(old, seed) == int_replay(out, seed), 'integer final values differ' +print('integer replays equal (3 seeds, mod 2^61-1)', flush=True) +sp_old = source_span(old); sp_new = source_span(out) +print('source span old (checked, violations, maxabs)', sp_old, 'new', sp_new, flush=True) +assert sp_new[1] <= sp_old[1], 'new source-span violations' +delta = Counter(hist_new); delta.subtract(hist_old); delta = {r: c for r, c in sorted(delta.items()) if c} +dphi = sum(c * phi(r) for r, c in hist_new.items()) - sum(c * phi(r) for r, c in hist_old.items()) + +# ---------- write candidate ---------- +OUT.mkdir(parents=True, exist_ok=True) +outb = b''.join(struct.pack('<6i', *e) for e in out) +(OUT / 'COHORT249-RECORDS.bin').write_bytes(outb) +(OUT / '249-records.bin').write_bytes(outb) +nf = dict(newframes); nf.update({str(k): fr for k, fr in added.items()}) +(OUT / 'COHORT249-FRAMES.json').write_text(json.dumps(nf)) +if added: + fj = json.loads((CAND / 'frames.json').read_text()); fj['frames'].update({str(k): fr for k, fr in added.items()}) + (OUT / 'frames.json').write_text(json.dumps(fj)); del fj +else: + shutil.copyfile(CAND / 'frames.json', OUT / 'frames.json') +for name in ('COHORT249-INITIAL.json', 'COHORT249-FINAL.json', 'SOURCE-BINDING.json', 'base-frames.json'): + if (CAND / name).exists(): shutil.copyfile(CAND / name, OUT / name) +shutil.copyfile(CAND / 'COHORT249-SELECTION.json', OUT / 'COHORT249-SELECTION.json') +st['record_sha256'] = hashlib.sha256(outb).hexdigest(); st['record_count'] = len(out) +(OUT / '249-states.json').write_text(json.dumps(st)) +rec = dict(status='PASS_W3_TARGET_PREFIX_COMPRESSION', plateau_retimed_gates=len(retime), plateau_new_frames=len(added), groups=len(groups), members=len(members), dependents=len(dep_of), + retained_distinct=len(retained), cut_record=CUT, deleted_dependent_reads=deleted, inserted_setup_restore_adds=inserted, + records_in=len(old), records_out=len(out), local_histogram_delta={str(r): c for r, c in delta.items()}, + local_phi_old=sum(c * phi(r) for r, c in hist_old.items()), local_phi_new=sum(c * phi(r) for r, c in hist_new.items()), + delta_phi=dphi, predicted_delta_kappa=-6.45e-10 * dphi, + source_span_checked_operands=sp_new[0], source_span_violations=sp_new[1], source_span_violations_input=sp_old[1], + integer_replay='equal on all registers, 3 seeds mod 2^61-1', f2_all_columns='forward and inverse', + input_record_sha256=sel['input_record_sha256'], output_record_sha256=st['record_sha256'], + selection_sha256=hashlib.sha256(SELP.read_bytes()).hexdigest()) +(OUT / 'TARGET-PREFIX-W3.json').write_text(json.dumps(rec, indent=2) + '\n') +print(json.dumps(rec, indent=1)) diff --git a/research/w3-stages-restore/requirements.txt b/research/w3-stages-restore/requirements.txt new file mode 100644 index 0000000000..d084b095fb --- /dev/null +++ b/research/w3-stages-restore/requirements.txt @@ -0,0 +1,4 @@ +sympy==1.14.0 +numpy==2.3.5 +scipy==1.17.0 +mpmath==1.3.0 diff --git a/research/w3-stages-restore/stages/bank-tiling.json b/research/w3-stages-restore/stages/bank-tiling.json new file mode 100644 index 0000000000..95b68cc227 --- /dev/null +++ b/research/w3-stages-restore/stages/bank-tiling.json @@ -0,0 +1,608 @@ +{ + "census": { + "3": 438, + "4": 1762, + "6": 22, + "7": 7, + "9": 4, + "10": 1, + "11": 24, + "12": 17, + "13": 2, + "14": 2, + "15": 3, + "16": 1, + "18": 1, + "19": 3, + "20": 16, + "22": 43, + "23": 1246, + "24": 11540 + }, + "patterns": [ + { + "widths": [ + 7, + 7, + 4, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 11, + 7, + 7, + 7, + 7, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 12, + 7, + 7, + 7, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 13, + 13, + 13, + 6, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 2 + }, + { + "widths": [ + 16, + 7, + 7, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 12 + }, + { + "widths": [ + 19, + 19, + 19, + 19, + 11, + 11, + 11, + 11 + ], + "count": 1 + }, + { + "widths": [ + 19, + 19, + 19, + 19, + 19, + 14, + 11 + ], + "count": 2 + }, + { + "widths": [ + 23, + 18, + 18, + 18, + 18, + 18, + 7 + ], + "count": 7 + }, + { + "widths": [ + 23, + 23, + 4, + 4, + 4, + 4, + 4, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 23, + 23, + 23, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 3 + ], + "count": 5537 + }, + { + "widths": [ + 23, + 23, + 23, + 12, + 12, + 12, + 12, + 3 + ], + "count": 166 + }, + { + "widths": [ + 23, + 23, + 23, + 23, + 6, + 6, + 4, + 4, + 4, + 4 + ], + "count": 439 + }, + { + "widths": [ + 23, + 23, + 23, + 23, + 10, + 9, + 9 + ], + "count": 40 + }, + { + "widths": [ + 23, + 23, + 23, + 23, + 11, + 11, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 23, + 23, + 23, + 23, + 16, + 4, + 4, + 4 + ], + "count": 1 + }, + { + "widths": [ + 24, + 19, + 11, + 11, + 11, + 11, + 11, + 11, + 11 + ], + "count": 103 + }, + { + "widths": [ + 24, + 24, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 24, + 24, + 14, + 14, + 11, + 11, + 11, + 11 + ], + "count": 39 + }, + { + "widths": [ + 24, + 24, + 18, + 18, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 24, + 24, + 18, + 18, + 18, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "count": 1 + }, + { + "widths": [ + 24, + 24, + 19, + 19, + 19, + 15 + ], + "count": 1 + }, + { + "widths": [ + 24, + 24, + 23, + 23, + 23, + 3 + ], + "count": 10266 + }, + { + "widths": [ + 24, + 24, + 24, + 13, + 13, + 11, + 11 + ], + "count": 37 + }, + { + "widths": [ + 24, + 24, + 24, + 15, + 15, + 15, + 3 + ], + "count": 13 + }, + { + "widths": [ + 24, + 24, + 24, + 22, + 22, + 4 + ], + "count": 860 + }, + { + "widths": [ + 24, + 24, + 24, + 24, + 4, + 4, + 4, + 3, + 3, + 3, + 3 + ], + "count": 224 + }, + { + "widths": [ + 24, + 24, + 24, + 24, + 7, + 7, + 7, + 3 + ], + "count": 80 + }, + { + "widths": [ + 24, + 24, + 24, + 24, + 12, + 4, + 4, + 4 + ], + "count": 15 + }, + { + "widths": [ + 24, + 24, + 24, + 24, + 15, + 9 + ], + "count": 80 + }, + { + "widths": [ + 24, + 24, + 24, + 24, + 16, + 4, + 4 + ], + "count": 27 + }, + { + "widths": [ + 24, + 24, + 24, + 24, + 20, + 4 + ], + "count": 640 + }, + { + "widths": [ + 24, + 24, + 24, + 24, + 24 + ], + "count": 86777 + } + ], + "deleted": 1455, + "entrance_rank": 36120, + "note": "endpoint-aware residual widths (438 early-restored helpers at width 3); exact tiling from bank_plan.py (ILP over patterns of <=3 widths)" +} \ No newline at end of file diff --git a/research/w3-stages-restore/stages/kernel-plan.json b/research/w3-stages-restore/stages/kernel-plan.json new file mode 100644 index 0000000000..2e84619ad1 --- /dev/null +++ b/research/w3-stages-restore/stages/kernel-plan.json @@ -0,0 +1 @@ +{"cut": 819879, "singles": [3526, 3536, 3540, 3546, 3556, 3566, 3570, 3576, 3586, 3596, 3600, 3606, 3616, 3626, 3630, 3636, 3646, 3666, 3676, 3696, 3706, 3726, 3736, 3756, 3766, 3786, 3796, 3816, 3826, 3836, 3840, 3846, 3856, 3866, 3870, 3876, 3886, 3896, 3900, 3906, 3916, 3936, 3946, 3966, 3976, 4106, 4110, 5176, 5186, 5190, 5196, 5206, 5226, 5236, 5256, 5266, 5286, 5296, 5316, 5326, 5346, 5356, 5376, 5386, 5406, 5416, 5436, 5446, 5466, 6526, 6546, 6556, 6576, 6586, 6606, 6616, 6636, 6646, 6666, 7606, 7626, 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packaging time: #309 at 7.51499·10⁻⁴; #308 is at 7.51472·10⁻⁴ and #306 at 7.51459·10⁻⁴. + +The bit coarse saving is c = 7.5346077·10⁻⁴. The bit side binds with the complex supplier of PR #233 (7547/10⁷) and with that of PR #304 (7635/10⁷); both give the same κ. With the old #193 supplier (7.47455·10⁻⁴), the complex side binds and κ = 7.46897·10⁻⁴ (+4.98 %). + +## What changed + +The base is the PR249 / source527 local word: 20,107 roles, the five-stage layout of PR234, m = 120. Only the local bit word changes. The deficit stays at 4,400 per set (35,200 in the normalized 40-replica units). + +1. **Design T (cube layer).** + - The four 011 X-mixes of each cube happen at 2-dim mix frames M. + - Each of the 8 non-mix tetra edges {a,b} gets a new 2-dim frame T = span(χa, χb). Its Gram matrix under G = I − J/9 is 2I. + - At T, two line registers and one starter make the two block copies directly. The starter ends up holding x_a, which is exactly the K4 "partner single". So singles ride on registers that are needed anyway. + - This covers all 220 cubes and frees 795 cube-layer helpers. +2. **Twin condensation of plane leftovers.** + - At 810 planes whose two arrivals are both mix-frame starters, the rank-forced leftover enters at the 1-dim intersection line of the two mix frames (entrance rank σ = 1) and is absorbed by the block holder. + - This adds 480 new 1-dim frames. +3. **Line-pair / all-but-one module template, found by SAT.** + - It uses 20 registers per line: 10 plane block holders plus 10 fresh registers, with two copies per block. + - The rounds are copies at s{X} (dim 3) → 5 triple frames (dim 7) → 5 six-block frames (dim 13) → final merge at F_Z (dim 21). + - This adds 1,320 new frames (dims 7 and 13) and frees 660 helpers. + +**Totals** +- 1,455 helpers are freed. They are encoded as entrance FULL (σ = 24) with no records. +- New entrance rank relative to PR249 = 35,280 = 3 · 11,760. That matches the stock drop of 11,760. It is not 795·24 + 810 + 660·24, because 36 of the 660 LP helpers already had σ > 0. +- There are 3,473 new frames, and every one is exactly nondegenerate. +- Local D per stage goes from 1,138,396 to 1,068,458.6 (−6.1 %). +- Normalized stock (40 replicas): 173,883 → 162,123. + +## Verify (about 1 minute) + + apt-get install -y g++ libboost-dev ; pip install numpy mpmath + bash verify.sh /tmp/w3-verify-work + +`verify.sh` runs these steps: +1. Rebuild the word and the PR249 base snapshot from the gzipped files (`reconstruct.py`). +2. Compile the **unmodified** official PR266 checkers (`checkers/official/*.cpp`, copied byte for byte from research/multicut-kernel-condensation-883/code). +3. Run `cohort-legality-independent`. Expected: PASS, ADD 934,385, rank mass 398,897, 24 COPY / 24 ERASE. +4. Run `cohort-five-stage-columns`. Expected: PASS on 23,627 formal F₂ columns, payload prefix 2⁹⁴ < 2¹⁰⁴. +5. Run the independent checker `checkT`, which replays legality, checks nondegeneracy mod p for all 22,228 used frames and replays formal F₂ over all 20,107 columns. Expected: all zeros. +6. Run `exactnd.py` for exact rational nondegeneracy (Bareiss) and exact annihilators of all 3,473 new frames. +7. Price with `cost.py` (moment root). +8. Run `kappa_w.py`: PR265/#270's fixed-prime engine (`fixed_prime_math.py` with the retained moment, base_two_moment and outer engines), η = 10⁻²⁴, β = 10⁻⁹, grid 10⁻²⁷, all 47 outer constraints, and rejection of the adjacent grid point. It runs once per complex supplier. + +The output of every step is recorded in `receipts/`. `receipts/pr256-complex233-verify.txt` is a fresh PASS of PR #256's verifier, which re-checks PR #233's complex word at 7547/10⁷. + +Word SHA-256 (COHORT249-RECORDS.bin): `a9501525563d3ec656ebf01aea9f2c9839e033563ea4a022500d68b12756ae86`. + +## Files + +- `word/`: COHORT249-RECORDS.bin, COHORT249-FRAMES.json (new frames only, with B and exact annihilator A), COHORT249-INITIAL.json and an empty COHORT249-SELECTION.json (no kernel cohorts are selected). It also has the full w3 249-states.json and the frames.txt / states.txt exports used by checkT. +- `base/`: the PR249 snapshot (249-records.bin, 249-states.json, frames.json, donor ownership). The same snapshot is produced by `checkers/official/export249.py` from PR266's vendored pr249-source.zip. +- `checkers/official/`: the unmodified PR266 native checkers, plus json.hpp and export249.py. +- `checkers/independent/`: checkT.cpp + sub.hpp, exactnd.py, and exactprice.py (the PR234 certify() engine). +- `pricing/`: cost.py, kappa_w.py and the retained #270 engines. +- `builders/`: provenance only. + - Agent A's Design T builder (`build_v5.py`, `gather.py`, `addcomp.py`, `verify.cpp`) and twin step (`twin.py`). + - Agent B's LP builder (`build_lp.py`, `rebuild.sh`), the SAT design `sat/sol_z5_m3t6.json` with its models, and the census tools. + - The builders were written against local scratch paths and intermediate pickles that are not included. They show how the word was made; they are not needed to check it. + +## What is NOT done yet (for whoever publishes) + +The word-level checks pass with the unmodified official tools. The later native stages of the #270 pipeline hard-code facts about the PR249-derived word and must be generalized before an official replay. The exact items: + +1. **Bank review (`cohort-bank-review.cpp`).** + - It hard-codes the base residual census {4:2200, 6:22, 7:5, 11:48, 12:23, 15:2, 24:…} and expects the r = 24 count to be 14,287 minus the changed roles. + - w3's residual multiset is {0:1,455 (freed), 4:2,200, 6:22, 7:5, 11:24, 12:13, 23:810, 24:12,058}, with total residual 317,409, which is divisible by 3. + - A feasible width-120 tiling exists: mix(23,4,7)×8,100, rep(4,30)×973, rep(24,5)×96,464, and so on. Freed (r = 0) roles must be deleted rather than banked. +2. **Native price (`cohort-price.cpp`).** + - It hard-codes the old complex supplier 747454944651775/10¹⁸ and the PR266 baseline regression. + - Run it with w3's histogram and new_entrance_rank = 35,280, using the PR #233 or #304 complex constant. +3. **Finite invoice (`cohort-finite-invoice.cpp`).** + - It hard-codes R = 16,587 and `actual_role_replica_stage_assignments == 3,317,400`. + - With 1,455 freed roles these become 15,132 roles and 3,026,400 assignments. The bounds only shrink. +4. **Source binding.** + - Write a `verify.py` in the style of #270 that regenerates the base from the PR249 source. + - The w3 word itself can be shipped as data, as most open PRs do. Note that the `record_sha256` field inside 249-states.json is stale (inherited) and should be recomputed. +5. **Optional stacking.** The community's stage transforms (kernel entries, descent, target squares, restorations, sinks, reorder) were developed on PR249/gen5b words. Re-deriving them on w3 should add further small gains. + +The result is conditional on the same retained all-size interfaces as #270, #299 and the other open PRs: compiler, charts, selectors, routing, prime supply, precision/recovery and complex correctness. It is not a Lean certificate. diff --git a/research/w3-stages-restore/supplied/SHA256SUMS b/research/w3-stages-restore/supplied/SHA256SUMS new file mode 100644 index 0000000000..69c06a9e21 --- /dev/null +++ b/research/w3-stages-restore/supplied/SHA256SUMS @@ -0,0 +1,86 @@ +3388927f50aa03dd07ac8955f096a51fb3fb4bba7d79017c41be64a434df6a6c ./README.md +ab96904508a21ddd0c3d4d779974e5dcfdb1f19a3938ade647724cc317c3270b ./base/249-DONOR-OWNERSHIP.json +ded35ac806ab0f478265ef65d629ab3760771c84e44d00c7ec9995037e11960d ./base/249-records.bin.gz +c5f6d78de1a3b279ab05a263b80d1b25a587f20f39e1540134f4542e89e5530c ./base/249-states.json.gz +f68fa82180cd352421b8bc3f7a5c89d51bde74e74cd8d62c222c28b0f23fcf31 ./base/PR249-SOURCE-MANIFEST.json +0e92416f9525a6c6c14add4c73923916e6866aaf118180880e6cc5a2b7aa7d18 ./base/frames.json.gz +b9b33b797601d70d766b2d0ab86c95b36a8246ca10bbafd5ff40058daff3918d ./builders/agentA_designT/addcats.py +82e5ef0c7b6cf84c53bf6039330930242c9a5c8e8ea13183b2805cf9577f7129 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