Scoped negative result: certify 33 fixed Clifford register words (no kappa claim)

[littleBro]

This adds a standalone, scoped negative result for the complex register search discussed in #288: 33 explicit words with m=3, W=3, s=8 have no full-rank coset endpoint in the formal projective Clifford group algebra, for any three invertible complex scalar mixing matrices at their specified locations. No new primitive or kappa is claimed. The words do not exhaust the three-block or full register model.

The checker combines necessary Boolean support conditions, invertibility/rank constraints and exact binomial torus equations. Twenty-nine words close by support/rank refutation; four require 78 exact support exclusions before the final Boolean contradiction. The package supplies the literal words, all proof traces, a written model/argument, source provenance and the complete standard-library implementation. It needs no author-local directory, historical checkout or external solver. It also gives four known nine-call solutions and distinguishes a surviving Boolean support from an arithmetic construction.

Validation

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60.

python -B -S research/clifford-relation-obstructions/verify.py

Expected result: PASS_FIXED_CLIFFORD_WORD_EXCLUSIONS, with 33 excluded templates and 78 exact torus refutations.

• Direct path enumeration agrees with sequential symbolic propagation; two constructions of the rank clauses agree.
• Literal Boolean proof replay, unimodular integer traces and direct Leibniz determinant identities pass.
• Exact dense checks cover all 33 skeletons, 150 Pauli conjugation identities, seven paid-gate square identities and eight executions of positive controls.
• Negative controls reject damaged traces, Boolean proofs, learned clauses, missing final refutations and an unsupported torsion exclusion. An eight-call word that passes the necessary Boolean filter but fails concretely is retained as a control.
• Fresh standalone-directory replay and alternate gzip compression reproduce identical mathematical output. Corrupt payloads and optimized-Python execution are rejected. Recorded local environment: native Windows, Python 3.14.4.

This addition changes only research/clifford-relation-obstructions/. The unchanged repository-wide suite and selected frontier replay were not rerun; no remote CI success is claimed.

Scope and attribution

The verifier shares the tableau/coset core between its two symbolic encodings; the separate dense matrix controls are finite checks. This is not a Lean proof, an all-size compiler/representation theorem or a bound for arbitrary Clifford words or integer multiplication. No bit-side construction or exponent invoice is supplied.

Credit: eumemic's #288 and its cited predecessors, including Swapnil Jain and the upstream Clifford-frame framework. This supplies additional finite evidence and does not claim priority for the general support, rank or torus methods. Prepared by littleBro with substantial OpenAI Codex assistance; Apache-2.0. Source pins, overlap context and the full assistance disclosure are in the package notices.

[Mister-Meeseeks]

Integrated at ee055dc44815497927ef618fc985b93c2dcbda2a in the 20-PR pilot, retaining your original commit, source notices and contributor credit.

Exact support/rank/torus refutations for 33 fixed formal projective Clifford words. Boolean traces, determinant identities and controls replayed. Formal group algebra only, not arbitrary finite representations or all eight-call words.

The scoped package check passed at c3a5b6b7afec35d259c29bc2d8bb8516e975ad31. This is research integration; the selected κ and inherited theorem assumptions are unchanged. Review, evidence and attribution. Thank you for the contribution.