Research: audit P104 tangent-to-orbit local regularity (no new kappa)

[1337isnot1337]

Status

Independent proof-step audit; no new κ, decoder construction, supplier, or selected-frontier change. This is a second review following the completed claim #1275 and PR #1292. It does not repeat the tangent-matrix census: it checks the local regularity implication and exhaustively verifies the displayed P104 kernel generators against the pinned reduced systems.

Finding

For each of the three P104 representatives, the pinned certificate gives tangent dimension 103 at K0 = 2G, equal to the dimension of the diagonal-torus orbit O. Since O is smooth and contained in the masked rank-eight variety X, dim_K0(X) >= 103; the certified tangent dimension gives dim(T_K0 X) <= 103. Thus the local ring is regular and X is smooth near K0. The inclusion O -> X has an isomorphism on tangent spaces between smooth 103-dimensional manifolds, so the inverse function theorem gives equality of their germs.

This supports the stated local conclusion. It does not rule out distant off-orbit P104 components or rank-nine costly parts and does not change the selected κ.

Reproduce

python3 -I -B research/seed38-p104-orbit-regularity-audit/verify.py
python3 scripts/research_package.py --package research/seed38-p104-orbit-regularity-audit --check-only

The verifier replays the pinned PR #1292 certificate, including its D4⊕D4 negative control and seeded sample, then checks all 168 gauge/torus generators against all 4,992 reduced rows in each of the three P104 classes modulo 2^31 - 1. It reports tangent/orbit dimension 103. The proof argument is in PROOF.md.

Pins and attribution

• Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f.
• Audited source: PR Research: masked rank-8 complex decoders are locally rigid on all P104 frame-pair punctures (no new kappa) #1292 head 7a8325f6c8e5a6830ce919965a2959ac459e010a; source files and base provenance files are SHA-256/Git-blob pinned in SOURCES.json.
• Local replay ran on Python 3.14.7 because Python 3.12 is not installed here; the package manifest registers the standard-library replay for the repository's Python 3.12 runner.
• Credit Navinor (with opencode assistance) for PR Research: masked rank-8 complex decoders are locally rigid on all P104 frame-pair punctures (no new kappa) #1292; DreamingOfClouds for PR Format limits part 2 (no κ claim): erratum to #595, exact invoice prices, frontier-word censuses, decoder floors, spec requirements, centre and fragmentation walls #717's mask model; themilkman216 for PR Research: frame-pair decoders and the exact 8-term complex copy-cost floor (no new kappa) #968's frame-pair floor; and burntout76 for PR Research: rank-8 complex decoders are gauge-rigid; E-graph eight-term floor (no new kappa) #1212's P112/P120 rigidity. This package was prepared with substantial OpenAI Codex assistance; no independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at dcd0b59e0a41e7952d826dfc2ead891a80af1967.

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

Reviewed scope: Independent audit of the P104 tangent-to-orbit implication: exact modular rank bounds meet rational gauge/torus directions, and matching local/tangent dimension gives a smooth locally open orbit. Local result only, not global rank-eight rigidity.

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.