Independent verification: P112 root-star cost 64 via maximal-clique census

[bbMisk]

This independently verifies David Arias' #1236 result: masked P112 decoders whose paid supports are exactly the root stars C(alpha) or N(alpha) have minimum copy cost 64, at any finite term count. The coordinate decoder already attains it. No new theorem priority, kappa, physical supplier, or selected-frontier change is claimed.

The distinct evidence is a pivoted maximal-clique census: all 27,968 maximal cliques and their subsets recover all 482,577 cliques, with maximum size eight. This checks the nine-cost-seven obstruction by a different route from #1236's lattice/quadratic-form checker. A separate direct reconstruction computes all 57,600 binary atom ranks and 1,260 frames, then matches all five geometric sections of #1236's pinned certificate, including the full root, support, frame and atom-stream hashes. Neither new implementation imports predecessor executable code.

The package includes a written proof, every atom rank, exact source pins, semantic failure controls, and a path-scoped Python 3.12 workflow. Reproduce from the repository root:

python3 -I -O -B research/root-star-integer-cover-seed46/test_package.py

Expected: six test groups pass (Ran 6 tests, OK). The final package passed on CPython 3.14.6 and 3.12.13, including both complete implementations, five certificate mutations rejected by both, an injected nine-clique, altered support/decoder controls, source corruption, optimized standalone relocation, exact regeneration and overwrite protection. The pinned #1226 replay, selected-result integrity check and all five selected-result regressions also passed. Hosted CI and the full selected-supplier cold replay are not claimed.

Base: 49b3157d1d89adcef16df8be98445451672be5ba. Audited #1236: ee8437bd9879272094e20c024cd34a53c4e84cd8; predecessor #1226: 8b10989e4e45f0f9ce41004d7898a21a32f87e11. The refreshed main had no changes to the selected record, contribution instructions or this package's paths. Seed 46 assigned structural decoder research; the overlap refresh found the concurrent #1236 after the same endpoint argument was developed, so this submission is explicitly independent verification.

The theorem allows arbitrary real/complex coefficients and free cost-zero corrections, but excludes arbitrary proper sub-supports, further trims, unions, other punctures and changed copying/stage accounting. Compiler/all-size, mutable-source, hosting, precision/tape, analytic and bit-interface obligations remain inherited. The check does not certify #1236's execution-control claims or rerun its separate lattice receipt.

Credit David Arias / @DavidAriasC (#1236), Navinor (#1226), DreamingOfClouds (#717/#595), Joel Pulikkan / GamingPuzzled and the retained coordinate-decoder lineage. Prepared by Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in research, proof, both implementations, tests and writing. No independent human review claimed; Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 05a293a1055761b7ad7e929ac40acb341a6bf58d.

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

Reviewed scope: Independent PR1236 corroboration via maximal cliques and their complete subset closure, all57600 atom ranks and pinned geometric hashes; same scoped cost64 theorem, no priority or supplier claim.

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.