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Exact determinant characters for truncated-polynomial multiplication tensors - #5316
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Mister-Meeseeks merged 1 commit intoOct 23, 2026
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This scoped proof answers the truncated-polynomial nilpotent case left open by PR #5252. For multiplication in F_q[t]/(t^n), it gives the full covariant stabilizer determinant image, three bounded character equations, and the exact splitting of its GL orbit into SL orbits. Extraction uses q and n under an explicit orbit promise. 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: 1,734 literal attaining maps, seven complete stabilizer domains with 260,985 input-map pairs and 1,729 autotopisms, and seven controls. Both print
PASS_TRUNCATED_TENSOR_CHARACTERS; 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 39992835239. 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.
Extend the character calculation to a specified multivariable local algebra or recognize the orbit promise. Source preparation, native operations, precision, movement, and supplier/outer admission remain separate obligations.
Credit Nick Petalas's PR #5252 for the finite-etale result, the inverse-input convention and the explicit nilpotent follow-up. Its pinned proof is context, not an imported algorithm. Credit David Ganz's PR #2849 for atlas A019 normalization, A029 character equations and A030 extraction. Classical isotopy, cyclic-group and truncated-polynomial-algebra facts retain their credit. No general literature-priority claim is made.
Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.