Audit PR256’s complex program against its pinned Lean proof (no new κ)

[shea256]

PR256's explicit complex program and the corresponding Fourier Lean proof live in separate repositories. This adds a self-contained audit that checks their agreement and retains a separate reproduction of the pinned proof. No new κ, network, or Fourier exponent is claimed.

The contribution lives in research/pr256-fourier-audit/ and adds:

• Exact program, five-stage histogram, rational moment and finite-fill checks, plus agreement with the Lean input and exponent literals.
• Immutable source pins, a source-only proof archive, source-origin ledgers, and the original build/regeneration receipts with compressed logs.
• A Lean reproduction command, eleven audit controls (two positive and nine negative), and a Python 3.11/3.13/3.14 finite-audit workflow.
• An explicit dependency table distinguishing the formal exact-complex WHT/DFT result from the bit-side and implementation obligations still needed for multiplication.

The program is pinned to PR #256 at db3f75cdc5f03f3131d48fb220f6bf1958404ff3; the proof is pinned to wht-power-saving-lean PR #2 at fd19e46b728faa414cbfbf91b01a6a0b7903375d. This package can be reviewed before #256 merges. It leaves existing witnesses, selected-result pointers, and source files unchanged.

Credit belongs to Jacob Sussman for the formal framework and checker, Chafik Boukhalfa for the explicit program and stronger instantiation, and the underlying OpenAI/community construction. Original notices are preserved; the added notice credits OpenAI, Doug Colkitt, Rohan Arun, Swapnil Jain, and the other construction contributors. Ryan Shea contributes this separate reproduction and consistency audit, adapted from the pinned downstream project, with substantial OpenAI Codex assistance.

Validation

• Offline audit and all eleven controls pass locally on Python 3.11, 3.13 and 3.14.
• The new audit workflow passed on Ubuntu for all three Python versions.
• Separate checkout comparisons match all 20 PR256 package files and 456 proof-source files. All 91 OpenAI origin files were fetched again from the pinned revision and match.
• The retained historical fresh project build passed using the pinned Mathlib cache. The ported wrapper was also rerun successfully against that existing build: both generators, staged scalar targets, combined build, axiom check, and WHT/Fourier comparisons passed. That wrapper rerun is not described as another fresh build.
• make entrance-bank-verify passes.
• The broader Linux regression workflow passed all 52 jobs, including every make verify group on Python 3.11/3.13/3.14 and the existing formal packages. The local macOS make verify run stopped at the unchanged skip-suffix producer because Apple clang rejects -fopenmp; this platform limitation was not changed as part of the audit. The committed validation note records the earlier submission-time status; these CI results are the completed follow-up.

Receipt validation does not rerun Lean. The new CI runs the finite audit and audit controls; full Lean reproduction is a separate documented command. Our reproduction used the upstream local statement comparator, not the official Linux comparator or a second kernel, and is not independent human mathematical review.

[chafreaky]

Thank you for the independent audit of #256 against jacobalansussman/wht-power-saving-lean#2 — the agreement of the exact program, the five-stage histogram and the exponent literals with the pinned Lean inputs is exactly the cross-check that package could not give itself. For the record, the Lean side has since also passed the official comparator (leanprover/comparator with its real landrun sandbox, Linux) for both theorems; that is noted in the pinned PR's VERIFY.md section 10.

[Mister-Meeseeks]

Thank you @shea256. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Independent source and finite audit linking PR256 to the Lean Fourier development.

Review and limits: Fresh finite verifier and mutation tests passed. The 456-file Lean archive, 91-file OpenAI origin ledger and recorded build receipts are retained; no fresh full Lean rebuild or multiplication theorem is claimed here.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 947726d431438fd73ee4c96231eb88aba2692360. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.