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Exact two-row dirty-fanout tariffs over finite noncommutative rings - #5312
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Mister-Meeseeks merged 1 commit intoOct 23, 2026
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This scoped optimum extends the five-term finite-commutative tariff to every finite associative unital ring. It covers all positive, stationary, coefficient-independent directional prices and arbitrary finite gate words. Left-ideal principality and ordered coefficients determine the one-insertion terms. The complete kappa calculation is unchanged.
Proof and scope, exact checker, replay declaration, and source provenance are pinned to the reviewed commit. Base: canonical main
ff3cc58e370d0f678e529246f8c73e8094e18fcf, priority revision 7.CPython 3.12.14 registered normal and optimized replays passed: 320 exact minima over UT2(F2), with 46,604 settled states and 99,577 discovered states in five unrestricted shortest-word searches. Both print
PASS_NONCOMMUTATIVE_TWO_ROW_TARIFF; the launcher printsPASS_REGISTERED_RESEARCH_PACKAGE. All five package files match their committed bytes, and the base is an ancestor of the package commit.Use Python 3.12 and the standard library. No external runtime inputs or third-party Python packages are required. Hosted planning and the registered package replay passed on this exact head in run 39991018534. No predecessor scientific suite, selected cold replay, native replay, compiler, Lean or Docker build was run. The optional full-history preflight is unavailable in this shallow checkout. Finite checks corroborate the written proof; they do not constitute independent human or proof-kernel acceptance.
Price one triangular-ring realization under a complete physical cost model. Source preparation, native operations, precision, movement, and supplier/outer admission remain separate obligations.
Credit lee-phys's pinned finite-commutative formula, Krzysztof Wojt's PR #5045 for the source-count and return classification, Nick Petalas's PR #4916 for the noncommutative dirty-row contract, and Ross Richardson's PR #3121 for the dirty-cut lineage. Ali Romman's PR #5310 and pinned finite-module proof supply the finite left-module shortening extension, first recorded in Discussion #5300. This proof dependency is fixed at 77fef39; no executable is imported. Classical stable-range and module theory retain their credit.
Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.