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Research: arbitrary binary couplings preserve the dihedral rank tariff - #2716
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PR1911 already proves the infinite-dihedral tariff for rank-one idempotents. This extends the gate alphabet to every binary matrix N, including nilpotents and higher-rank nonprojectors, with each gate charged rank(N). The same sharp separate reflection tariffs hold for all finite register counts and all signed diagonal targets with restored dirty spectators.
The new step bounds every Laurent minor by the rank of the positive coefficient, without similarity to a projector. Exact rank factorization has no cross terms because ([g]+1)^2=0. A separate dirty-state implementation invoice records two address calls for nilpotent rank-one factors; the formal rank price is not an invocation count or a native child-rank claim.
Validation: registered Python3.12 optimized replay passed; all 530 binary matrices through R=3, 473690 Laurent minors, 530 formal factorizations, 284 rank-one dirty-input programs through R=4 (129 nilpotents), 4264 input columns, 34 signed targets and 5 controls. Four Git-free public-CLI groups cover read-only export, source corruption, Boolean/float receipts and actual code mutations. Independent agent proof/code review is recorded locally; no human or Lean proof review is claimed.
Credit Adam Gall PR1911, Arham Tahir PR1589, the finite-idempotent PR1941 and Cinna Davis PR2290. Only research/dihedral-arbitrary-couplings is added. Scientific pins 6bd33bc; actual base c3c94c2, refreshed guidance unchanged. Open-PR snapshot 767 records at 18:06Z; Discussion snapshot 1239 records at 15:22Z, supplemented by local merged notes and targeted REST; coverage is bounded. Claim: #1911 (comment).
No finite-quotient lower-bound transfer, selected cold replay, hosted CI, supplier adoption, or new kappa. Substantial OpenAI Codex assistance. Reproduce: python3.12 scripts/research_package.py --package research/dihedral-arbitrary-couplings.