From 947726d431438fd73ee4c96231eb88aba2692360 Mon Sep 17 00:00:00 2001 From: Ryan Shea Date: Sat, 10 Oct 2026 00:14:43 -0400 Subject: [PATCH] Add PR256 complex-program and Lean proof reproduction audit --- .github/workflows/pr256-fourier-audit.yml | 37 ++ research/pr256-fourier-audit/MANIFEST.json | 29 ++ research/pr256-fourier-audit/NOTICE | 28 ++ research/pr256-fourier-audit/README.md | 123 +++++ research/pr256-fourier-audit/VALIDATION.md | 42 ++ .../evidence/five_stage_lean_receipt.json | 135 ++++++ .../evidence/five_stage_openai_origin.json | 373 ++++++++++++++ .../five_stage_regeneration_receipt.json | 10 + .../evidence/logs/axioms.log.gz | Bin 0 -> 245 bytes .../evidence/logs/build.log.gz | Bin 0 -> 16262 bytes .../evidence/logs/compare_fourier.log.gz | Bin 0 -> 1251 bytes .../evidence/logs/compare_wht.log.gz | Bin 0 -> 989 bytes .../logs/regenerate_certificate.log.gz | Bin 0 -> 1765 bytes .../evidence/logs/regenerate_fourier.log.gz | Bin 0 -> 428 bytes .../evidence/logs/regenerate_program.log.gz | Bin 0 -> 521 bytes .../evidence/logs/toolchain.log.gz | Bin 0 -> 66 bytes .../evidence/pr256_source_files.json | 22 + .../evidence/proof_source_files.json | 458 ++++++++++++++++++ research/pr256-fourier-audit/expected.json | 81 ++++ .../pr256-fourier-audit/inputs/FOURIER_NOTICE | 290 +++++++++++ research/pr256-fourier-audit/inputs/LICENSE | 201 ++++++++ .../pr256-fourier-audit/inputs/SOURCE.json | 25 + .../inputs/fourier-proof-source.tar.gz | Bin 0 -> 6107281 bytes .../inputs/gcert-program-233/NOTICE | 35 ++ .../inputs/gcert-program-233/SOURCE.json | 47 ++ .../certificate/expected.json | 243 ++++++++++ .../gcert1-p11-pr233-flow.json.gz | Bin 0 -> 478851 bytes .../inputs/gcert-program-233/gx/gx.py | 296 +++++++++++ .../pr256-fourier-audit/network_contract.py | 33 ++ .../pr256-fourier-audit/rational_bounds.py | 52 ++ .../pr256-fourier-audit/reproduce_lean.py | 145 ++++++ research/pr256-fourier-audit/test_audit.py | 103 ++++ research/pr256-fourier-audit/verify.py | 250 ++++++++++ 33 files changed, 3058 insertions(+) create mode 100644 .github/workflows/pr256-fourier-audit.yml create mode 100644 research/pr256-fourier-audit/MANIFEST.json create mode 100644 research/pr256-fourier-audit/NOTICE create mode 100644 research/pr256-fourier-audit/README.md create mode 100644 research/pr256-fourier-audit/VALIDATION.md create mode 100644 research/pr256-fourier-audit/evidence/five_stage_lean_receipt.json create mode 100644 research/pr256-fourier-audit/evidence/five_stage_openai_origin.json create mode 100644 research/pr256-fourier-audit/evidence/five_stage_regeneration_receipt.json create mode 100644 research/pr256-fourier-audit/evidence/logs/axioms.log.gz create mode 100644 research/pr256-fourier-audit/evidence/logs/build.log.gz create mode 100644 research/pr256-fourier-audit/evidence/logs/compare_fourier.log.gz create mode 100644 research/pr256-fourier-audit/evidence/logs/compare_wht.log.gz create mode 100644 research/pr256-fourier-audit/evidence/logs/regenerate_certificate.log.gz create mode 100644 research/pr256-fourier-audit/evidence/logs/regenerate_fourier.log.gz create mode 100644 research/pr256-fourier-audit/evidence/logs/regenerate_program.log.gz create mode 100644 research/pr256-fourier-audit/evidence/logs/toolchain.log.gz create mode 100644 research/pr256-fourier-audit/evidence/pr256_source_files.json create mode 100644 research/pr256-fourier-audit/evidence/proof_source_files.json create mode 100644 research/pr256-fourier-audit/expected.json create mode 100644 research/pr256-fourier-audit/inputs/FOURIER_NOTICE create mode 100644 research/pr256-fourier-audit/inputs/LICENSE create mode 100644 research/pr256-fourier-audit/inputs/SOURCE.json create mode 100644 research/pr256-fourier-audit/inputs/fourier-proof-source.tar.gz create mode 100644 research/pr256-fourier-audit/inputs/gcert-program-233/NOTICE create mode 100644 research/pr256-fourier-audit/inputs/gcert-program-233/SOURCE.json create mode 100644 research/pr256-fourier-audit/inputs/gcert-program-233/certificate/expected.json create mode 100644 research/pr256-fourier-audit/inputs/gcert-program-233/certificates/gcert1-p11-pr233-flow.json.gz create mode 100644 research/pr256-fourier-audit/inputs/gcert-program-233/gx/gx.py create mode 100644 research/pr256-fourier-audit/network_contract.py create mode 100644 research/pr256-fourier-audit/rational_bounds.py create mode 100644 research/pr256-fourier-audit/reproduce_lean.py create mode 100644 research/pr256-fourier-audit/test_audit.py create mode 100644 research/pr256-fourier-audit/verify.py diff --git a/.github/workflows/pr256-fourier-audit.yml b/.github/workflows/pr256-fourier-audit.yml new file mode 100644 index 0000000000..db5cbe9732 --- /dev/null +++ b/.github/workflows/pr256-fourier-audit.yml @@ -0,0 +1,37 @@ +name: PR256 complex proof audit + +on: + push: + paths: + - 'research/pr256-fourier-audit/**' + - '.github/workflows/pr256-fourier-audit.yml' + pull_request: + paths: + - 'research/pr256-fourier-audit/**' + - '.github/workflows/pr256-fourier-audit.yml' + workflow_dispatch: + +permissions: + contents: read + +jobs: + finite-audit: + runs-on: ubuntu-24.04 + timeout-minutes: 10 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13', '3.14'] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Replay finite program, source bindings, and retained evidence + run: python3 -B research/pr256-fourier-audit/verify.py + - name: Reject corrupted programs, statements, and evidence + run: python3 -B research/pr256-fourier-audit/test_audit.py + - name: Require unchanged tracked artifacts + run: git diff --exit-code diff --git a/research/pr256-fourier-audit/MANIFEST.json b/research/pr256-fourier-audit/MANIFEST.json new file mode 100644 index 0000000000..d5aacb63ef --- /dev/null +++ b/research/pr256-fourier-audit/MANIFEST.json @@ -0,0 +1,29 @@ +{ + "description": "Immutable audit inputs and historical evidence; new audit code is reviewed through the PR diff.", + "files": { + "evidence/five_stage_lean_receipt.json": "195df11c9eb43f56a671bd5f90c96f810bac8ea954cde85dc44c100e04190604", + "evidence/five_stage_openai_origin.json": "ee6e89f2a099324c21da1e7385d2b5c82b64cdbfd225f91e076cd1c8320738c9", + "evidence/five_stage_regeneration_receipt.json": "a47ada8a3095ce1ffc58c43dac9d7dd564069caee184c6f0af4dd830af94a8e4", + "evidence/logs/axioms.log.gz": "c9811ae280c91401bf56660ca3d56fcda28ceee727fb7ab633925278aff0c25d", + "evidence/logs/build.log.gz": "d25a3cf89b770b7a0c7f0ad32adbf2a960d195eb557a3254103e07f39d6326c4", + "evidence/logs/compare_fourier.log.gz": "b379cde884336eb5139bbbd3ab46883e66bc9058390a9223b2c318d61a4c2598", + "evidence/logs/compare_wht.log.gz": "0fc07ebd9dfbaeb4ff419cb4e31a068a69a1075bf3af730d183e9a2e659dfbc1", + "evidence/logs/regenerate_certificate.log.gz": "fe780019ca79162cfcd68e284d73db0d79456715e9c55298e58449cf1954c7e2", + "evidence/logs/regenerate_fourier.log.gz": "6ed176c454f047733b22fed8c76c1f9966b630edd8f9e4c0291b3f0b36ad0a1c", + "evidence/logs/regenerate_program.log.gz": "3f2e7bae2862b423d3bdcf2b00f889763bde77a7aa79a1da14eef83f474adb8e", + "evidence/logs/toolchain.log.gz": "f0d1c3b28558d3555ba5e0322441cbcbcdc20b163d531a1ac14b5e0ace4bcf57", + "evidence/pr256_source_files.json": "3a8341035c7ef0ede3d8d43812aa4bb2ffc78287c8c3424d74b4b98cb8bb7103", + "evidence/proof_source_files.json": "6010ff79f3128533fddc076e223225d58b59d22761746b6119f7ccfd51071ac9", + "expected.json": "295a3f5c0e6843db7fec76b25609d93e0a7aeb60fb79c394e1851ebb6a8789f1", + "inputs/FOURIER_NOTICE": "9419dd03a2f52cf8bdfc4d18216ce29f263ab583b27f01ced8e420985bcb7c81", + "inputs/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "inputs/SOURCE.json": "00f5689fba8d1edc1741376c14a5ad6cdf5e0718dd24af9881949a6bc7cd2cf1", + "inputs/fourier-proof-source.tar.gz": "871f47a16d2571dbcebc2ef61914e85d96b7b44f6d59579da246e13294d5658b", + "inputs/gcert-program-233/NOTICE": "c1c95d22cfb0f455aca64b4bee4cab900829641b8f041280e7aa88034491c87d", + "inputs/gcert-program-233/SOURCE.json": "9ce463476af549c04de4705b1bf0c8f7f18d473dc0817883066ad5e2136d90b5", + "inputs/gcert-program-233/certificate/expected.json": "c0e3d245bf7e458ff86288eb47672491c9efee28181b570f1a3f17c8d915f766", + "inputs/gcert-program-233/certificates/gcert1-p11-pr233-flow.json.gz": "09ceba1c0ea17282da155b937c8463669b913443c20f45fe2a7e6e024cb2d33a", + "inputs/gcert-program-233/gx/gx.py": "6f3dc8bb639933227a8dae181ec4a542e85c7276be9c9e330f49518e7b630b95" + }, + "schema": 1 +} diff --git a/research/pr256-fourier-audit/NOTICE b/research/pr256-fourier-audit/NOTICE new file mode 100644 index 0000000000..124f7f2473 --- /dev/null +++ b/research/pr256-fourier-audit/NOTICE @@ -0,0 +1,28 @@ +PR256 program / Fourier-proof reproduction audit +Copyright 2026 Ryan Shea. New audit code and documentation: Apache-2.0. +Prepared with substantial OpenAI Codex assistance. + +This work adapts the checks and retains the original reproduction evidence from +shea256/fourier-transform-below-nlogn at a101b363b38e6bf7d309042c94ba5fa18a424fad. +It contributes source/program/proof consistency checks and a separate reproduction, +not a new exponent, network, formal framework, or proof of integer multiplication. + +OpenAI supplies the original exact arithmetic model and Fourier reduction. Doug +Colkitt supplies early parameter/network work and the community repository; Rohan +Arun and Swapnil Jain supply earlier community improvements and the research lineage. +Jacob Sussman supplies the five-stage geometry, frame formalization, certificate +format/checker, and formal Fourier framework. Chafik Boukhalfa supplies the PR200/233 +pairing, PR256 explicit program, and the stronger instantiation of that framework. +The circuit retains icekylinx's source-assisted construction, eumemic's v4 modules, +Avi Eisenberg's reconstruction/pairing, an664's sharing work, and the earlier +contributors named in the preserved source notices. The incoming package credits +SovereignSteak and hcg890 for five-stage composition and ledger work. + +inputs/gcert-program-233/NOTICE and inputs/FOURIER_NOTICE are retained byte for byte; +inputs/LICENSE accompanies them. The complete proof archive retains its licenses, +notices and source-specific OpenAI attribution. Do not reinterpret this audit as +authorship of the imported constructions or proofs. + +Metadata clarification: PR209 was contributed by Jacob Sussman and PR237 by Rohan +Arun. The PR256 notice groups those numbers with Rohan Arun; the original notice +is preserved unchanged. This note supplies the checked attribution alongside it. diff --git a/research/pr256-fourier-audit/README.md b/research/pr256-fourier-audit/README.md new file mode 100644 index 0000000000..530c4e05be --- /dev/null +++ b/research/pr256-fourier-audit/README.md @@ -0,0 +1,123 @@ +# PR256 complex program: reproduction and proof consistency audit + +This adds a separate reproduction of Chafik Boukhalfa's PR256 and its instantiation +of Jacob Sussman's Lean framework. **No new multiplication kappa, network, or +Fourier exponent is claimed.** The contribution is a reproducible audit linking +the two source packages, exact arithmetic checks, and retained build evidence. + +## Pinned sources + +| Source | Revision | Role | +| --- | --- | --- | +| [CrocSwap PR256](https://github.com/CrocSwap/integer-mult-bounds/pull/256) | `db3f75cdc5f03f3131d48fb220f6bf1958404ff3` | Explicit complex program and source regeneration | +| [Fourier proof PR2](https://github.com/jacobalansussman/wht-power-saving-lean/pull/2) | `fd19e46b728faa414cbfbf91b01a6a0b7903375d` | Sussman's framework with Boukhalfa's PR233 instantiation | +| [OpenAI formal sources](https://github.com/openai/math/tree/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean) | `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb` | Original model, Fourier reduction, and challenge | +| [Downstream reproduction](https://github.com/shea256/fourier-transform-below-nlogn/tree/a101b363b38e6bf7d309042c94ba5fa18a424fad) | `a101b363b38e6bf7d309042c94ba5fa18a424fad` | Ryan Shea's checks, source audit, and build receipts | + +The proof extends Sussman revision `f010392c923279e3dd59ef3aa5fedad23affc5fd`. +Lean is 4.34.1; Mathlib is `d13f23b723b8a846827a245b89c10fc7d3f11612`. +The complete 456-file proof source archive is included, without compiled objects. +Only the PR256 inputs needed for the finite audit are copied here; its complete +producer is available at the pinned revision above. Original notices are retained. + +## Offline finite audit + +From the repository root, using Python 3.11 or later and no third-party packages: + +```sh +python3 -B research/pr256-fourier-audit/verify.py +python3 -B research/pr256-fourier-audit/test_audit.py +``` + +The first command: + +1. Checks source pins and runs Sussman's unmodified `gx.check1` on the explicit + PR233 program: 12,052 registers, 18,248 frames, 52,300 gates, and 69,683 + invocation blocks. Exact scalar replay covers all source columns; restoration + of arbitrary dirty scratch is supplied by the Lean invocation theorem. +2. Reconstructs the five-stage histogram and checks `m=110`, `W=14692`, rank + 1613040, deficit 3080, 358975 children and maximum child width 46. +3. Independently bounds the normalized moment using exact rational logarithm and + exponential enclosures at `a=7547361/10^10`. It checks the Lean engine's + finite-fill correction at `s=40`, the positive Fourier gap + `a - delta = 1/10^10`, and failure at `7547365/10^10` for this histogram. +4. Requires the PR256 and Lean programs to agree in every mathematical field + (only the descriptive `derived_from` string differs), then checks the Lean + histogram and exponent literals. It compares the Fourier challenge with the + original after accounting for comments, seven renamed declarations and the + stronger exponent. +5. Checks all 89 imported OpenAI Lean modules, the original challenge and the + toolchain against the 91-file origin ledger. These were fetched separately + from the immutable OpenAI revision during the recorded source audit. +6. Binds the historical reproduction receipts to their compressed logs and all + 456 archived source hashes. Checking a recorded receipt does not rerun Lean. + +Optional full-checkout comparisons require no network: + +```sh +python3 -B research/pr256-fourier-audit/verify.py \ + --program-source /path/to/pr256-checkout \ + --proof-source /path/to/pinned-fourier-checkout \ + --openai-source /path/to/pinned-openai-checkout +``` + +They compare the 20 program-package files, 456 proof-source files and 91 original +OpenAI files with the pinned ledgers, irrespective of the checkout's branch name. The default audit +does not rerun the producer or a full Clifford/DFT computation. + +## Reproducing the Lean build + +Install `leanprover/lean4:v4.34.1`, then run: + +```sh +python3 -B research/pr256-fourier-audit/reproduce_lean.py \ + --work-dir /tmp/pr256-lean-rebuild --lake lake --threads 2 \ + --receipt /tmp/pr256-lean-rebuild-receipt.json +``` + +This extracts the complete pinned source (or checks existing source bytes), +downloads the pinned Mathlib cache, regenerates the 41 certificate and 14 +Fourier-chain files, builds the proof, audits axioms, and runs upstream +`tools/Compare.lean` for WHT, DFT and convolution. The two large scalar reductions +are staged sequentially to reduce peak memory. Allow several GB of storage and +substantial memory; the recorded reproduction used a 32 GiB macOS arm64 machine. + +The original fresh project build passed in 2625.5 seconds, with Mathlib's compiled +cache. The WHT and Fourier comparisons passed in 33.7 and 42.6 seconds. The three +audited final theorems used only `propext`, `Classical.choice`, and `Quot.sound`. +The original combined build temporarily paused one large scalar reduction until +the other completed; it then resumed successfully, without changing source. +The script now stages those targets sequentially. The receipt retains the actual +original commands and is not relabeled as a new run. + +The full PR256 producer regeneration also passed (188.6 seconds), using Python +3.11, NumPy 2.3.5 and SciPy 1.17.0. To rerun that separately: + +```sh +git clone https://github.com/chafreaky/integer-mult-bounds /tmp/pr256-source +git -C /tmp/pr256-source checkout --detach db3f75cdc5f03f3131d48fb220f6bf1958404ff3 +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \ + uv run --python 3.11 --with numpy==2.3.5 --with scipy==1.17.0 \ + python -B /tmp/pr256-source/research/gcert-program-233/verify.py +``` + +## What this establishes for multiplication + +| Evidence | Established scope | Multiplication obligations remaining | +| --- | --- | --- | +| Exact program and histogram checks | The pinned finite complex program and its five-stage accounting agree with the formal input | No bit-side construction or outer multiplication assembly is checked here | +| Lean project and statement comparisons | The upstream WHT and all-length exact DFT/convolution theorems in OpenAI's family-130 RAM model | Finite precision/recovery, bit costs, fixed-tape implementation and the inherited multiplication-specific all-size interfaces are not proved | +| OpenAI source comparison | Imported model/reduction files match the identified OpenAI revision | Human assessment of formal statements and assumptions remains separate | +| Receipt and log hashes | The recorded successful runs are bound to these sources | Hashes alone do not independently attest that an execution occurred | + +The Fourier theorem has `delta=7547360/10^10`. It is an exact-complex-arithmetic +result with supplied roots and unrestricted coefficients, not a multiplication +theorem or practical FFT benchmark. The historical reproduction ran neither the +official Linux comparator nor a second kernel and is not independent human +mathematical review. Boukhalfa later reported official-comparator success in +[`837dc313`](https://github.com/chafreaky/wht-power-saving-lean/commit/837dc3130adc79f7b7ab4ddd56c15576bbd766b0); +that documentation-only update is distinct from this pinned local reproduction. + +See [NOTICE](NOTICE) for attribution and [VALIDATION.md](VALIDATION.md) for the +checks of this contribution. The root selected result and all existing witnesses +remain unchanged. diff --git a/research/pr256-fourier-audit/VALIDATION.md b/research/pr256-fourier-audit/VALIDATION.md new file mode 100644 index 0000000000..21e56afbf7 --- /dev/null +++ b/research/pr256-fourier-audit/VALIDATION.md @@ -0,0 +1,42 @@ +# Validation of this audit contribution + +Prepared against CrocSwap main `3b6b66891c0ac888521cf591fe306c6286601d4f`. +This is a separate AI-assisted reproduction, not independent human mathematical +review. The bound and proof remain the credited upstream authors' results. + +## Audit package + +- Offline finite verifier: passed on Python 3.11, 3.13 and 3.14. +- Eleven audit controls (two positive and nine negative): passed; altered stock/child counts, an unrecorded + exponent, a weakened quantifier, an extra axiom, a missing build, a wrong source + revision and a changed build log are rejected. Optimized Python is refused. +- Full-checkout comparison: all 20 pinned PR256 package files and all 456 proof + source files matched the separate checked-out revisions. +- OpenAI origin: all 91 ledger files were downloaded again from the immutable + OpenAI revision and matched, including all 89 imported OAI modules. +- Ported Lean reproduction wrapper: passed against the existing pinned build, + with `--cache-ready`. Both source generators reproduced their output; staged + scalar targets, combined build, axiom check, WHT comparison and Fourier + comparison all exited 0. This wrapper test reused the project build and is not + a second fresh build. The retained historical receipt records the earlier + successful fresh project compilation. +- Source syntax and whitespace checks passed. + +## Existing repository checks + +`make entrance-bank-verify` passed: selected-record validation, the complete +offline complex/bit construction, all 47 outer constraints, seven margins, +21 assembly controls, and the bank scheduling supplement. + +The full `make verify` regression run was invoked. At submission, its community, +producer, partial-gauge, three-stage-cover and paired-cube groups have passed; +the remaining groups are still pending. This is not a claim that the full suite +has passed. No existing source, certificate, selected-result pointer or root +documentation is changed by the contribution. + +## CI scope + +The added workflow repeats the offline finite audit and audit controls on +Ubuntu with Python 3.11, 3.13 and 3.14. It does not claim to run Lean or a second +kernel; full proof reproduction is the separate documented command. Configuring +the workflow does not itself constitute a successful CI run. diff --git a/research/pr256-fourier-audit/evidence/five_stage_lean_receipt.json b/research/pr256-fourier-audit/evidence/five_stage_lean_receipt.json new file mode 100644 index 0000000000..d5e42fb456 --- /dev/null +++ b/research/pr256-fourier-audit/evidence/five_stage_lean_receipt.json @@ -0,0 +1,135 @@ +{ + "axioms": { + "OAI.PowerSaving.RAM.hillsY_program": [ + "Classical.choice", + "Quot.sound", + "propext" + ], + "OAI.PowerSaving.convolution_mainY": [ + "Classical.choice", + "Quot.sound", + "propext" + ], + "OAI.PowerSaving.transform_mainY": [ + "Classical.choice", + "Quot.sound", + "propext" + ] + }, + "commands": [ + { + "command": [ + "/tmp/fourier-lean-toolchain/lean-4.34.1-darwin_aarch64/bin/lake", + "--version" + ], + "exit_code": 0, + "label": "toolchain", + "log_sha256": "36526a338068c343bedff5daa38fec328b4f722df1e8f0b5d026d4f0f908f3a3", + "seconds": 0.246 + }, + { + "command": [ + 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"Finite Python checks only; see five_stage_lean_receipt.json for the separately reproduced Lean build.", + "sources": { + "five_stage": { + "commit": "db3f75cdc5f03f3131d48fb220f6bf1958404ff3", + "repository": "https://github.com/chafreaky/integer-mult-bounds" + }, + "fourier_proof": { + "archive": "fourier-proof-source.tar.gz", + "base_commit": "f010392c923279e3dd59ef3aa5fedad23affc5fd", + "commit": "fd19e46b728faa414cbfbf91b01a6a0b7903375d", + "lean_toolchain": "leanprover/lean4:v4.34.1", + "mathlib_commit": "d13f23b723b8a846827a245b89c10fc7d3f11612", + "pull_request": "https://github.com/jacobalansussman/wht-power-saving-lean/pull/2", + "repository": "https://github.com/chafreaky/wht-power-saving-lean" + } + }, + "tensor_saving": "7547361/10000000000" +} diff --git a/research/pr256-fourier-audit/inputs/FOURIER_NOTICE b/research/pr256-fourier-audit/inputs/FOURIER_NOTICE new file mode 100644 index 0000000000..63aa295646 --- /dev/null +++ b/research/pr256-fourier-audit/inputs/FOURIER_NOTICE @@ -0,0 +1,290 @@ +Walsh-Hadamard power saving (wht-power-saving-lean) +Copyright 2026 Jacob Sussman + +Repository: https://github.com/jacobalansussman/wht-power-saving-lean + +This repository is not a project of OpenAI. OpenAI did not write, review or +endorse it. The package name "OAI" and the namespace "OAI.PowerSaving" are +those of openai/math and are kept only because the new files extend that +development. + +This repository is not a project of CrocSwap/integer-mult-bounds either. Its +authors did not write, review or endorse it. Section 6 says what is taken +from their repository. + +This repository contains files from, and files derived from, the repository +"openai/math" (https://github.com/openai/math), family 130, "Exact Fourier +transforms below n log n", at commit fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. +That repository is published under the Apache License, Version 2.0. A copy of +the licence is in the file LICENSE. The upstream repository has no NOTICE file +and its licence text names no copyright holder; the files are attributed here +to the authors of openai/math (OpenAI). + +1. Unmodified upstream files. + The 89 files under OAI/Computability/ are byte-for-byte copies of the files + with the same paths under lean/ in openai/math at the commit above. They + have not been changed. Modified copies of some of them are under + Work/Fourier/ and are listed in section 7. + One more file of openai/math is here unchanged, outside the Lean build: + third-party/openai-math/lean/ComparatorChallenges/UniformFourier.lean is a + byte-for-byte copy of lean/ComparatorChallenges/UniformFourier.lean at the + commit above (the statement of OpenAI's Fourier challenge). It is included + so that the modified copy named in section 2 can be compared with it. + +2. Files that contain upstream text. + - Work/CarrierCheck/ChallengeB2Ke16x.lean, + Work/CarrierCheck/ChallengeB2Ke16xR.lean, + Work/GCert/Data/ChallengeB2Gp193x.lean and the text template + tools/gen/templates/ChallengeB2L16x.lean.txt each contain, as their + lines 22-270, lines 9-257 of + lean/ComparatorChallenges/UniformFourier.lean of openai/math (the RAM cost + model), unchanged. Everything else in these files was written for this + repository. + - Work/Fourier/UniformFourierChallenge.lean is a modified copy of + lean/ComparatorChallenges/UniformFourier.lean of openai/math (the + statement of OpenAI's Fourier challenge, 336 lines). Changes: a comment + was added at the top; the exponent 1 - 1/(10^(13:ℕ)) was replaced by + 1 - 7474546/(10^(10:ℕ)); seven names received the suffix "Z" + (decimalExponent, decimalTime, TimeBounds, DFTGoal, ConvGoal, + transform_main, convolution_main). Everything else in the file is the + upstream text, unchanged. See section 7. + - Work/Scratch/Engine.lean and Work/Block/Engine.lean contain copies of + proofs of openai/math, changed for this repository: sections 1, 2 and 5 + of Work/Scratch/Engine.lean are upstream proofs with the batch layout + renamed, and both files contain a copy of the private upstream theorem + "hills_project" (lean/OAI/Computability/FourierTransform/ + TensorProgram.lean) with its envelope generalised. The comments in the + two files mark these places. + - lakefile.lean is adapted from lean/lakefile.lean of openai/math: the same + package name, toolchain, package option and Mathlib pin; every other + dependency was removed and the libraries of this repository were added. + lean-toolchain is a byte-for-byte copy of lean/lean-toolchain. + lake-manifest.json lists Mathlib and its dependencies at the revisions of + lean/lake-manifest.json. + - RELATED-WORK.md reproduces the BibTeX entries of two manuscripts of + openai/math. + +3. New files that build on upstream proofs. + The other files under WHTCheck/ and Work/ were written for this + repository. They import the upstream files, and several of them generalise + or adapt proofs of upstream files (for example Work/Block/Recursion.lean, + which says so in its header). They are changes and additions made for this + repository and are not part of openai/math. + +4. How the new files were made. + Jacob Sussman made the new files on 2026-10-08 and 2026-10-09 by directing + a team of AI agents (Claude). The agents wrote the new Lean files, the + certificate data and the generator scripts. See README.md, section 4. + +5. Ideas taken from other public work. + The network of the first result uses ideas published by others, among them + the helper circuit "NStar3" (Swapnil-jain/integer-mult-kappa, which credits + CrocSwap pull request #36 and Paureel for parts of it), its transfer to + family 130 (shea256/fourier-transform-below-nlogn), and "carrier links" and + "whole-residual batching" (pull requests to CrocSwap/integer-mult-bounds). + No file of Swapnil-jain/integer-mult-kappa or of + shea256/fourier-transform-below-nlogn is included here. One comment in + Work/Scratch/Engine.lean quotes three counts reported in + Swapnil-jain/integer-mult-kappa and names that source. The general frame + lemma that Work/GFrame proves is stated in + notes/general-clifford-frames.tex of CrocSwap/integer-mult-bounds; its Lean + proof was written for this repository. The credits, with links, are in + RELATED-WORK.md. + +6. Data derived from CrocSwap/integer-mult-bounds (second result). + The helper circuit of the second result is the paired-cube circuit of the + repository "CrocSwap/integer-mult-bounds" + (https://github.com/CrocSwap/integer-mult-bounds), in the state of its pull + request #193. It is the design of that community: icekylinx (pull requests + #144 and #184), eumemic (#168, and #117 behind its modules), ikeboy / + Avi Eisenberg (#191 and #193), with an664 (#128) credited there for the + workspace-sharing principle. That repository is published under the Apache + License, Version 2.0 (the same licence text as the file LICENSE). Its + NOTICE file begins "A sharper exponent for integer multiplication / + Copyright 2026 Douglas Colkitt" and says that the community release "is + not solely Douglas Colkitt's work". A complete copy of that NOTICE file, as + it is at the head of pull request #193, is in + third-party/CrocSwap-integer-mult-bounds/NOTICE. + + The data were taken from these files of that repository. They were loaded + as data by programs written for this repository; no program of that + repository was run, and none is included here. + - at the head of pull request #168 (eumemic), + 4a3c769e5c5430e7114c4d3e099ff34664677f17: + references/paired-cube/sources/local_L1.json + references/paired-cube/sources/tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json + references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json + references/paired-cube/sources/qmod_climb3u_best.json + references/paired-cube/selected-module/matching-arcs.json + references/paired-cube/physical/frames.json + - at the head of pull request #193 (ikeboy), + 187e1010ac8b259af8e9b5166f68b64bc27b4b47: + research/source-assisted-v4/data/physical-pairs.json + + Files of this repository that contain data derived from them: + tools/certificate/gcert1-p11-pr193.json.gz and the Lean data modules + generated from it, Work/GCert/Data/Gen/P193*.lean and the files they import + from Work/GCert/Data/Gen/P193/; its block counts are also in the generated + modules Work/GCert/Data/P193Price.lean, RateB2Gp193.lean, RateB2Gp193x.lean + and InstB2Gp193.lean. + Changes made: the circuit was rebuilt from those data as one explicit, + renumbered list of additions with a table of frames, in the certificate + format "gcert/1" of this repository; its 1,980 in-place steps were written + as pairs of additions with rescaled coefficients; the Lean data modules + were generated from that list. No file of that repository is included + unchanged, except the copy of its NOTICE file named above. + + Notices of that NOTICE file that pertain to these data, quoted: + + Paired-cube and shared-core extension, 9 October 2026 + Copyright 2026 icekylinx + + Source-assisted common-frame extension (2026-10-09) + Copyright 2026 icekylinx. Apache-2.0. + Substantial dependency: eumemic PR168, + fd25adb7fbaa12ee761d02c733c54d1d2a7687ee + + The full text of both notices, and the notices of the work they build on, + are in the copy named above. The credits, with links and with the words of + pull request #193 about its own sources, are in README.md ("Whose circuit + this is") and in RELATED-WORK.md, section 1. + +7. Modified copies of upstream files (third result). + The files listed below are copies of files of openai/math at the commit + above, changed for this repository. Each begins with a comment that names + the upstream file it is derived from and states what was changed. The + upstream originals under lean/OAI/Computability/ are in this repository + as well, unchanged (section 1), and the copies import them. The upstream + challenge file lean/ComparatorChallenges/UniformFourier.lean is in this + repository in both forms: unchanged under third-party/openai-math/ + (section 1) and modified (section 2). + + - Work/Fourier/ArbitraryLength.lean: modified copy of + lean/OAI/Computability/FourierTransform/ArbitraryLength.lean (224 + lines; 159 of them unchanged in the copy). Changes: identifiers renamed + on 64 lines (18 names: 15 with the suffix Z, 3 with Z inserted); 1 + import line replaced by 1; 15 comment lines added; no other change to + the code. + - Work/Fourier/Asymptotics.lean: modified copy of + lean/OAI/Computability/FourierTransform/Asymptotics.lean (187 lines; + 112 of them unchanged in the copy). Changes: identifiers renamed on 74 + lines (32 names: 26 with the suffix Z, 6 with Z inserted); 1 import + line replaced by 1; 15 comment lines added; no other change to the + code. + - Work/Fourier/Axioms.lean: written for this repository (not a copy of an + upstream file). + - Work/Fourier/ConvolutionProgram.lean: modified copy of + lean/OAI/Computability/FourierTransform/ConvolutionProgram.lean (100 + lines; 77 of them unchanged in the copy). Changes: identifiers renamed + on 22 lines (10 names: 9 with the suffix Z, 1 with Z inserted); 1 + import line replaced by 1; 15 comment lines added; no other change to + the code. + - Work/Fourier/Goal.lean: written for this repository; contains lines of + upstream files: of its 7 code lines, 6 are lines of + lean/OAI/Computability/FourierTransform/Goal.lean (original lines 35, + 75-77, 79, 81): unchanged: its lines 25; with identifiers renamed: its + lines 21, 24, 26, 28, 30. + - Work/Fourier/Main.lean: modified copy of + lean/OAI/Computability/FourierTransform/Main.lean (151 lines; 90 of + them unchanged in the copy). Changes: identifiers renamed on 59 lines + (40 names: 35 with the suffix Z, 5 with Z inserted); 1 import line + replaced by 2; 24 comment lines added; other code lines changed: 1 of + the original, 1 of the copy (copy line 59). + - Work/Fourier/Seam.lean: written for this repository; contains lines of + upstream files: of its 122 code lines, 15 are lines of + lean/OAI/Computability/FourierTransform/TensorProgram.lean (original + lines 36-37, 95-96): unchanged: its lines 93-94, 113-114, 141-142, + 163-164, 185-187, 194-196; with identifiers renamed: its lines 184; 3 + are lines of lean/OAI/Computability/FourierTransform/TensorSaving.lean + (original lines 83-84, 114): with identifiers renamed: its lines 45-46, + 59; 1 is a line of lean/OAI/Computability/FourierTransform/Main.lean + (original line 60): with identifiers renamed: its lines 213. + - Work/Fourier/SectorAlgorithm.lean: modified copy of + lean/OAI/Computability/FourierTransform/SectorAlgorithm.lean (224 + lines; 162 of them unchanged in the copy). Changes: identifiers renamed + on 61 lines (17 names: 13 with the suffix Z, 4 with Z inserted); 1 + import line replaced by 1; 15 comment lines added; no other change to + the code. + - Work/Fourier/SynchronizedAlgorithm.lean: modified copy of + lean/OAI/Computability/FourierTransform/SynchronizedAlgorithm.lean (126 + lines; 94 of them unchanged in the copy). Changes: identifiers renamed + on 31 lines (12 names: 10 with the suffix Z, 1 with Z inserted, 1 + other), the other being "canopy" to "Grove.canopy" (5 lines); 1 import + line replaced by 1; 16 comment lines added; no other change to the + code. + - Work/Fourier/TransformProgram.lean: modified copy of + lean/OAI/Computability/FourierTransform/TransformProgram.lean (146 + lines; 94 of them unchanged in the copy). Changes: identifiers renamed + on 51 lines (21 names: 19 with the suffix Z, 2 with Z inserted); 1 + import line replaced by 1; 15 comment lines added; no other change to + the code. + - Work/Fourier/UniformBounds.lean: modified copy of + lean/OAI/Computability/FourierTransform/UniformBounds.lean (183 lines; + 115 of them unchanged in the copy). Changes: identifiers renamed on 67 + lines (29 names: 25 with the suffix Z, 4 with Z inserted); 1 import + line replaced by 1; 15 comment lines added; no other change to the + code. + - Work/Fourier/UniformFourierChallenge.lean: modified copy of + lean/ComparatorChallenges/UniformFourier.lean (336 lines; 328 of them + unchanged in the copy). Changes: identifiers renamed on 7 lines (7 + names: 7 with the suffix Z); 12 comment lines added; other code lines + changed: 1 of the original, 1 of the copy (copy line 281). + - Work/Fourier/WorkingCompiler.lean: modified copy of + lean/OAI/Computability/FourierTransform/WorkingCompiler.lean (153 + lines; 104 of them unchanged in the copy). Changes: identifiers renamed + on 48 lines (14 names: 14 with the suffix Z); 1 import line replaced by + 1; 15 comment lines added; no other change to the code. + - Work/Fourier/WorkingPreparation.lean: modified copy of + lean/OAI/Computability/FourierTransform/WorkingPreparation.lean (212 + lines; 156 of them unchanged in the copy). Changes: identifiers renamed + on 55 lines (30 names: 28 with the suffix Z, 2 with Z inserted); 1 + import line replaced by 1; 15 comment lines added; no other change to + the code. + - Work/Fourier/WorkingTransform.lean: modified copy of + lean/OAI/Computability/FourierTransform/WorkingTransform.lean (119 + lines; 91 of them unchanged in the copy). Changes: identifiers renamed + on 27 lines (9 names: 8 with the suffix Z, 1 with Z inserted); 1 import + line replaced by 1; 15 comment lines added; no other change to the + code. + + Changes made to the eleven copied proof files: every declaration received + the letter "Z" in its name (as a suffix of its own name, or of the name + of the declaration it belongs to), so that it does not collide with the + upstream declaration of the same name; the upstream exponent "alpha" + (1 - 2/10^11) and the bound "hills" defined from it were replaced by + "alphaZ" (1 - 7474547/10^10) and "hillsZ", which are defined in + Work/Fourier/Seam.lean, and the single use of the upstream theorem + "hills_program" by "hillsZ_program"; the five definitions of the upstream + statement that contain its exponent (decimalExponent, decimalTime, + TimeBounds, DFTGoal, ConvGoal) were replaced by the versions of + Work/Fourier/Goal.lean, whose exponent is 1 - 7474546/(10^(10:ℕ)); + the import lines point to the copies; a header comment was added. + Two further changes: in the copy of Main.lean the same constant stands + once as the literal 2/10^11 and was replaced there too, and the two + final theorems of that copy received a documentation comment; in the + copy of SynchronizedAlgorithm.lean the name "canopy" was written out as + "Grove.canopy" in 5 places, because the short name is shadowed in the + larger environment of the copy. The script also renamed three names + inside upstream comments; the comments are otherwise the upstream ones + and describe the upstream network. + The proofs are those of openai/math. The copies were made by the script + tools/fourier/mkchain.py of this repository. + + Work/Fourier/Goal.lean contains copies of those five definitions of + lean/OAI/Computability/FourierTransform/Goal.lean, with the exponent + replaced and the suffix "Z" on the five names. + + Work/Fourier/Seam.lean was written for this repository. It repeats the + statement of the upstream theorem "hills_program" (TensorProgram.lean) and + the definition of "hills" (TensorSaving.lean) with the two names replaced; + its header says so. + + The work of others that the third result follows (danadran01, shea256, + eumemic) is credited in README.md ("Whose reduction this is") and in + RELATED-WORK.md, section 1. No file of their repositories is included + here. + +Not included in this repository and fetched by the build: Mathlib +(https://github.com/leanprover-community/mathlib4, Apache License 2.0) and its +dependencies. The comparator (https://github.com/leanprover/comparator) is a +separate tool and is not included. diff --git a/research/pr256-fourier-audit/inputs/LICENSE b/research/pr256-fourier-audit/inputs/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/pr256-fourier-audit/inputs/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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