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Exact common-chart multiplicities for square-zero radical targets - #5313
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Mister-Meeseeks merged 1 commit intoOct 23, 2026
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This scoped counting proof answers the common-chart multiplicity question in PR #4766. It gives the complete distribution of admissible projective row/column pairs over every finite field and every radical dimension. A six-case table refines the existing reachable/unreachable count. 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: 1,065,033 target tuples, 1,928 independently enumerated subspaces and six controls. Both print
PASS_RADICAL_CHART_MULTIPLICITY; 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 39991699175. 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.
Bind a restricted common-chart policy to a physical caller and price its choice and emission. Source preparation, native operations, precision, movement, and supplier/outer admission remain separate obligations.
Credit Nick Petalas's PR #4766 for the all-field reachability count and explicit multiplicity question, and his PR #4745 for the arbitrary-word square-zero reachability theorem. The pinned reachability proof supplies the paid-cost interpretation: k>0 gives exact formal cost two, while k=0 is unreachable at any word length. That theorem is cited, not independently re-audited here. ToikY's PR #4334 supplies the shared-chart interface; Wentao Li's PR #4099 supplies the right-vector alphabet. The finite-geometry incidence counts are classical; no general literature-priority claim is made.
Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.