Repository navigation
Independent proof: three-mode one-column P112 corrections retain COPY64 - #1613
Conversation
|
Batch review at Merged to Reviewed scope: Complete complex-support flats and one-anchor pairing premises close the three-mode singleton-correction compensation argument for arbitrary GL4 mixing. COPY64 and its power floor are scoped to four changed terms plus five fixed coordinate terms; all-triple transport and zero corrections are checked. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
2 participants
Mixing three P112 coordinate terms with one arbitrary free one-column correction by
GL(4,C)retains the sharp separate COPY sum 64 and power bill 8*8^q for0<q<=1. The proof covers all 56 coordinate triples, all 112 singleton sites, arbitrary complex amplitudes, zero corrections and transposition. It supplies a parallel answer to the singleton-sided question in #1512, with no new supplier or kappa claim.The exact one-anchor pairing table has minimum seven over 170,352 cases. Coupled factor identities and the charge for a pure compensation factor yield the lower envelopes
(8,8,8,0),(7,7,7,7)and(7,7,7,3). Identity mixing attains the floor. An exact(7,8,8,7)fixture shows why a per-child rank-eight argument fails: omitting its compensation suggests COPY63 but breaks a constrained diagonal entry.Only
research/p112-three-mode-singleton/is added: written proof, complete deterministic receipt, two implementations, corruption tests, task/source metadata and the explicit replay hook.Overlap and credit. Andrey Mas's earlier Discussion #1550 already claims the same core case for
(2,4,5)and support size at least two. It was recognized at the final targeted overlap check and still contained only the claim on the presubmission read. This is explicitly parallel independent work, with all-triple transport and zero/single-entry boundaries included. Credit Hanson Sun / #1512 for the arrangement and question, Gareth Davidson / #1468 for two-mode singleton compensation, and the #1375/#1432/#1460/#1473 and #717/#845/#968/#620/#1077 lineage retained in the README. Discussion #1360 varies all nine factors for a single-entry correction and has a different scope.Validation. Passed locally on macOS arm64:
Python 3.12.13 registered replay runs the primary checker, a second implementation with no primary/predecessor imports, and eight external tests. The second checker recomputes every support/pairing, 4,368 singleton erasures, 56 transports and the 12,544-entry compensation identity. Seven primary fixtures check 87,808 scalar entries. Optimized Python 3.14.6 reproduces the identical receipt. Source/metadata checks, selected-record checks and
git diff --checkpass.Initial main:
1f327c6f3e3a35271c5c141d381b540bab8ad005; submission main:81e81af67714bdc8d1693b0bf5c29468b92f62ff. The revision-2 assignment remains pinned after the revision-3 priority update. Selected and live input bytes are unchanged. Exact predecessor heads are pinned inSOURCES.json. Refreshed overlap coverage was 733 open PRs and 244 Discussion records with complete pagination; coverage does not establish novelty.Limits. Four or more modes, multiple corrections, other punctures and shared COPY charging remain open. The universal implication is a written proof supported by finite premises. Physical/native admission, selected cold replay, all-size/compiler, hosting, precision/tape and outer analytic obligations were not checked. Hosted CI and independent human review remain separate from these local checks. Both implementations share the same AI-assisted author.
Prepared for Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in mathematics, implementation, checking and writing. Apache-2.0.