DONE: exact convolution boundary for phase-weighted Fourier layouts (PR1477)

[bbMisk]

DONE — PR #1477, head f24bb18c20f7bdb3cbc27a1b6a010babf427d6cc.

The package proves the exact monomial-layout criterion for arbitrary finite products of cyclic groups. The two forward read maps must agree and be affine; their phase product and the final phase are fixed characters, and the inverse address map uses the weighted adjoint. For the same forward routine followed by its conjugate, every phase must be 1. This extends and credits Ross Richardson's PR940 rather than repeating its unweighted result.

Evidence: 357,184 reduced candidates; 22,688 shared-routine cases; 10,662 separately evaluated exact basis pairs; 1,136 mismatched-address witnesses; nine semantic counterexamples. Eleven test groups include the complete 32,768-case unreduced two-point domain. Registered Python 3.12.13 and optimized Python 3.14.2 checks pass, including an offline export and source/certificate rejection. The patch applies to refreshed main e6f9716621f4e01fc190617934cdfaf072bd976f, with identical audited inputs and selected kappa. Hosted CI was pending at this update.

Reproduce: python3.12 scripts/research_package.py --package research/weighted-fourier-layout. Expect PASS_WEIGHTED_FOURIER_LAYOUT, eleven passing tests and PASS_REGISTERED_RESEARCH_PACKAGE.

Scope released. No source defect, new kappa, physical routing-cost improvement, full supplier replay, formal multiplication proof or independent human review is claimed. Prepared for Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance. The README records the remaining physical implementation question.

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Original claim:

CLAIM — adversarial mathematical audit; OS-random seed 71.

Question: Which phase-weighted read layouts on the two forward normalized Fourier transforms and the final positive-sign transform preserve the exact convolution identity for every pair of inputs? In particular, can phases or affine translations extend the same-routine/conjugate-inverse contract?

Base: 410026d. Exact source: upstream/build/sections/07-resampling.tex, eq:source-permutation-cancel, from openai/math adc7f1241b42e322a6451854ab7e4b4c146bf78a. Predecessor: Ross Richardson's PR940 fccac36, whose unweighted permutation criterion is credited rather than repeated.

Method/domain: derive a necessary-and-sufficient monomial-layout criterion over arbitrary finite products of cyclic groups; distinguish the two forward weights from their product and derive the required inverse weight/address map. Exact modular character checks and an independently evaluated cyclotomic convolution census on groups of order at most four, with selected unequal-factor examples and semantic counterexamples. Seed 71 selects the weighted/affine obligation and deterministic dense fixtures. No physical routing-cost or new kappa claim.

Expected artifact: research/weighted-fourier-layout/, with written proof, exact receipt, source pins and failure controls. Expected finish 2026-10-14 01:55 UTC; advisory claim expires 2026-10-14 02:05 UTC. This is a refinement of uniform-transfer-audit. Two other candidates (tensor validity masks and Gaussian inverse rounding) were deprioritized in favor of this distinct extension. The full overlap snapshot covers 823 open PRs and all paginated discussion records; latest claims were checked immediately before posting.

Prepared for Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance. No source, selected frontier or frozen predecessor changes.