Research audit: exact two-choice classification of six frame coalescences (no new kappa)

[adamgall]

Status: research audit / scoped negative result — no new kappa

Independently classify all frame replacements at the six historical A-gate sites in Chafik Boukhalfa's #583, with all neighbouring frames and the scalar word fixed.

Result

• Each site has exactly two legal frame-chain choices: the original line and the already selected plane. An explicit neighbour certificate and a short quotient-space proof exclude every other dimension, not only the enumerated planes.
• All 64 assignments pass independent full-word frame accounting. All 192 directed subset edges have delta {1:-2, 2:+1}. All 504 helper widths are unchanged.
• Exhaustive census: 255 containing planes/site, 1,530 total; exactly one admissible plane/site.
• 18 semantic negative controls: six omissions, six overpromotions, and six wrong planes of the same dimension that still contain the original line.
• No counterexample to Conditional κ = 0.001601661522127798: six paid-frame coalescences in the added-kernel provider #583 was found. This corroborates its accounting and adds an exact finite-class exclusion; it does not improve the selected bound.

The auditor represents binary subspaces as explicit vector sets, independently of the supplier's Gaussian elimination/profile code. The raw-word rebuild deliberately reuses unchanged credited predecessor constructors. No upstream, selected certificate, shared generator, or predecessor source is edited.

Reproduce

python3 -B research/coalescing-subset-audit/verify.py

Fresh cold run passed on Linux/Python 3.14.4 in 129.61 seconds:

PASS_SIX_COALESCENCES_ALL_SUBSETS_AND_CONTAINING_PLANES
64 subsets; 192 marginals; 1530 containing planes; 18 negative controls

RESULT.json contains every subset profile, the six exact incident-frame witnesses, the plane census, and negative-control failures. SOURCES.json authenticates the complete 314-file supplier manifest. VALIDATION.json records exercised checks and explicit non-checks. Two additional throwaway controls rejected scalar corruption at the source pin and frame-only recipe contract respectively.

Base, track and sources

• Exact base: ba82555c64e1879e4b7decce28186f208fcb8262.
• OS draw 2622477767, assignment seed 67: adversarial mathematical audit. Seed rotates exhaustive subset traversal; it is not the novelty claim.
• Conditional κ = 0.001601661522127798: six paid-frame coalescences in the added-kernel provider #583 source head: 89be768f0157f5a3d8e4db69cf1748768605eac9.
• Vendored Conditional κ = 0.001601260169988325: 48 added-kernel and 24 plain joint-prefix calls #579 head: 970d38a3862ee35064a827b671d196744ee2a928.
• Decoded source word: d339ebf52842f9ce01999106483eb59467b12ba6d13ce7757e7afdbaecbf98b7.
• Selected result at base remains Conditional κ = 0.001672188119205421: improved T16 owner packing on the seven-slot k8 word #1042, conditional kappa 0.001672188119205421.

No pinned coordination issue existed; the claim, three-task selection rationale, finite domain and stopping rule are recorded locally in CLAIM.md. PR metadata was refreshed through #1111 before submission. #815 (d8c8b40ab0a95b6d77389e6726d86dddb60fb53c) studies broader frame classes on different #626/#741 words with LP/CP-SAT. This audit is narrower, solver-free, and source-bound to #583; it does not duplicate or supersede those claims.

Scope and credit

The exclusion does not apply when neighbours, scalar gates, order, entrances, centres, or helper incidence change. Frame-chain legality is not native Clifford feasibility. No full phase/owner/assembly admission, repository-wide make verify, or selected-frontier replay is claimed: no shared construction changed. The all-size/compiler, realization, hosting, precision/tape, exact recovery, analytic and bit H1–H5 obligations remain inherited.

The chosen frames and gain belong to Chafik Boukhalfa (#583), with the unchanged #579/#575/#576/#571/#569/#568 and PR535 coalescer ancestry credited in the README and original notices. This contribution is by Adam Gall (@adamgall) with substantial OpenAI Codex assistance in research, implementation, verification and writing. New files are Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 1d6b61aeb268b1f918f16ff76a4bec57aa39eaa1.

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

Reviewed scope: Exact line-or-plane classification at six fixed coalescence sites; all 64 subsets, 192 marginals and containing-plane inventory, without unrestricted frame optimality.

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.