Research: solver-free P111 copied-rank certificate and source-order correction

[rseligm2]

Change and mathematical scope

Add a solver-free algebraic proof that the fixed label-functional copied-rank optimum is 63 for the actual bit P111 fixtures from #545 and #555. The model allows asymmetric factors, repeated terms and any finite number of totals: nine terms cost at least 63, ten at least 64, and eleven or more at least 66. Literal nine-term witnesses attain 63.

Credit #620 (Joel Pulikkan / GamingPuzzled) for the previously reported value and SAT obstruction. This contribution supplies an independent algebraic argument and exact source binding, not priority for the number 63. The archived sorted Hamming-root order differs from the published supplier order, so the same numeric deletion list selects a different puncture. The complete permutation and a rejection control are included; the corrected checks establish 63 on both actual published fixtures.

Only research/p111-copy-rank-certificate/ is added. No new kappa or global novelty is claimed. The result concerns this fixed binary label-functional factorization model, priced by rational pairing rank under the inherited #446 premise. Arbitrary port-subset rectangles, other decoder matrices, vector-valued labels, physical supplier realization, frames, restoration, hosting and the full multiplication theorem remain outside scope. The selected construction and upstream/ are unchanged.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. The pre-submission refresh inspected all-state P111 search results and recently updated PRs through #748. #717's complex decoders, #738's Gaussian geometry, #747's global stars and #748's source-representation circuit have different scopes. Exact references, predecessor attribution, the seed-41 structural-decoder assignment and the bounded fork-and-flush run are recorded in the package. Prepared for Russell Seligmann (@rseligm2) with substantial OpenAI Codex assistance; Apache-2.0. No independent human review is claimed.

Validation

From the repository root, using Python 3.9+ and only the standard library:

python3 -B research/p111-copy-rank-certificate/verify.py --check research/p111-copy-rank-certificate/RESULTS.json

Expected: PASS_P111_COPY_RANK: optimum 63 on two fixtures; exact geometry, independent minors, 18 negative controls.

• Exact checks cover all 511 nonzero supports per fixture, all 100 span-class pairs, all 12,321 live decoder entries, both witnesses, independent rank-three minor obstructions and 18 negative controls. Exhaustive three-dimensional projection controls support the mechanism; the all-length conclusion comes from the written proof.
• Python 3.9.6 and optimized Python 3.13.14 pass with byte-identical regenerated receipts. Clean relocated patch replay, source-byte and receipt-tamper rejection, selected-record integrity, local links and staged whitespace pass.
• Three fresh Astra/max branches and subsequent separate AI reviews checked the proof, source binding and independent finite obstructions. The initial archived-order inputs were corrected and re-evaluated; that distinction is explicit in METHOD.md.

The repository-wide make verify, full selected-supplier cold replay and proof-assistant verification were not run. Local exact checks are not formal verification of the full multiplication theorem. Hosted CI has not executed: all five upstream workflows report action_required with zero check jobs, requiring maintainer approval. The Verify research artifacts run is pinned to the submitted head e2ec7d7e719031e8f8b8012a4ab5b20faed074ce. No hosted CI pass is claimed.

[Mister-Meeseeks]

100-PR batch review at e2ec7d7e719031e8f8b8012a4ab5b20faed074ce.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Actual P111 source-bound label-factorization optimum 63; nine/ten/extra-total algebra and finite span certificates, with historical ordering mismatch documented.

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.