Independent verification: P112 root-star floor via Weyl and maximal-clique replays

[bbMisk]

Change and mathematical scope

Independent verification / scoped negative result; no new kappa. This package independently corroborates the cost-64 floor for P112 masked root-star decoders with exact C(alpha) / self-trimmed N(alpha) supports, arbitrary complex coefficients, any finite term count and free rank-zero corrections.

The final overlap refresh found David Arias's #1236, which had already submitted the same theorem while this work was underway. Credit belongs to that concurrent submission; this PR adds independent evidence, not a stronger theorem or priority claim. Navinor's #1226 supplies the preceding support-family census and assembly question.

The distinct implementation generates E8 roots by Weyl reflections, checks pairing ranks by column elimination and exhausts maximal cliques with pivoted Bron-Kerbosch. It imports neither predecessor code nor the new primary checker. The primary checker separately reconstructs roots, uses row elimination and enumerates every clique. Both reconstruct all 57,600 ordered support-pair costs and 1,260 frames, verify frame annihilation and extension, exclude nine compatible live normals, and check the cost-64 coordinate decoder on all 12,544 entries. The independent maximal-clique census is {3: 896, 7: 23040, 8: 4032}.

This also supplies a successful Python 3.12.13 registered-package replay of #1236 at ee8437bd9879272094e20c024cd34a53c4e84cd8, including all seven package tests. Its initial validation note recorded that environment as untested. Eight shared mathematical certificate fields agree exactly.

Task and overlap

Seed 36, complex-supplier track; base 49b3157d1d89adcef16df8be98445451672be5ba. Card complex-masked-decoder, refined to #1226's assembly gap and finally labeled independent corroboration after finding #1236. The initial local claim records three candidate tasks. No pinned sprint issue existed.

The refreshed overlap search covered 843 open PRs and 14 indexed discussion records with complete pagination, followed by a latest-PR check through #1240. Exact heads and source hashes are in SOURCES.json; the local claim was updated with the result and artifact link. #1212/#1213/#1191 and #1224 are credited as adjacent work and are not proof dependencies.

Validation

One offline replay command, Python 3.10+ with the standard library:

python3 -I -B research/masked-star-frame-compatibility/test_package.py

Expected final marker: PASS_MASKED_STAR_PACKAGE. The package passes on CPython 3.14.6 and through the repository's registered Python 3.12.13 runner. Seven semantic controls pass; both checkers reject three corrupted certificates. Optimized isolated relocation to a path containing spaces passes and preserves the certificate. The pinned #1226 census, package metadata/source pins, selected-record integrity and staged whitespace checks also pass. Exact commands, outputs and source hashes are in VALIDATION.json.

Only research/masked-star-frame-compatibility/ is added. The selected frontier, upstream and frozen predecessors are unchanged. No native supplier/cold replay, repository-wide historical suite, Lean proof or hosted CI success is claimed by the local receipt. All inherited physical/compiler, hosting, precision/tape and analytic obligations remain. Further trims, arbitrary subsets, other punctures and shared-copy pricing are outside this floor.

Credit and next questions

Prepared by Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance in proof development, both implementations, experiments and writing. Independent implementations within an AI-assisted contribution are not independent human review. Apache-2.0. README credits David Arias / #1236, Navinor / #1226, DreamingOfClouds, themilkman216, woklerx, GamingPuzzled and adjacent contributions individually.

README and TASK.json record the remaining question: whether an additional live-line trim changes the atom-rank and missed-frame constraints. That enlarged family has no favorable complete supplier budget or legal realization established here.

[Mister-Meeseeks]

100-PR batch review at 7f31a561787864f26eb2242ef35179d07223accf.

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

Reviewed scope: Independent corroboration of PR1236 using Weyl-generated roots, binary column elimination and complete pivoted maximal-clique census; same exact-support model, full coefficient identity and failure controls.

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.