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Certify best-invoice regions across common-base power costs - #5768
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This was referenced Oct 27, 2026
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The new tool compares up to eight complete invoices across 0<t<1. It reuses the common-base polynomial reduction, then certifies minimizing candidates on open cells with exact Sturm and root-multiplicity counts. Rational boundary ties are evaluated exactly; extra isolated ties are counted; unresolved transition boxes remain explicit. This supports choosing among complete construction alternatives rather than sampling one exponent.
Eight new tests pass normally and under -O on Python 3.12: all 125 small quadratics against exact extrema, 64 endpoint/multiplicity combinations, three distinct winner regions, tangency, an irrational crossing, cancellation, budget limits, degree29/10^60 coefficients, and isolated CLI hashes. The existing polynomial suite also passes.
The guide states the exact open-endpoint argument and limitations. Box boundaries are rational x=b^t, not rounded exponents. Common-base differences are required; this does not prove native legality or κ. Latest main/priorities/overlap checked. Coordination: Discussion #5752.
Base:
de5ec2e7a6074068452f45b1a191b5c72832df4a. Verified head:5031b2cbd4c008fcffaeb1e8a7bc774169efcf5a.Prepared for Ali Romman with substantial OpenAI Codex assistance. Retained tool and mathematical predecessor credits apply. No selected-frontier change.
Validation closeout: the ten independent patches apply cleanly together. The combined Python 3.12.14 run passes all 69 new tests and 35 existing checks, normally and under
-O; the optional SymPy check is skipped. All 8 new tests in this PR also pass in the hosted planning log. The planning job reports eight failures and two errors in unchangedtest_research_current_assignment; the full unchanged module reproduces those same failures locally on priority revision 8. The downstream replay job is skipped. This is not a green hosted workflow. Combined evidence and remaining obligations are in Discussion #5752.The existing polynomial suite has seven passing checks and one skipped optional SymPy check.