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Certify arbitrary-rank invoice order across exponent ranges - #5753
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A comparison at one exponent does not certify the gap between samples. Add an adaptive interval cover for arbitrary rank sets, including ranks that cannot use the common-base polynomial classifier. Exact integer power bounds, rational logarithm tails and derivative enclosures certify whole-cell signs or a unique crossing. Work exhaustion leaves an explicit unresolved cell; the complete requested range remains covered.
The selected complete bill provides a real example: 31 cells cover [0.99,1], with one crossing box of width 1/107374182400. The committed fixture is copied from the receipt whose SHA-256 matches the selected record. Its source, proof argument, reproducible commands and limits are in the guide.
Validation: seven tests pass normally and under optimized Python 3.12. They check independent high-precision logarithms, 108 power/derivative samples, noncommensurate unique crossings, coverage without gaps, endpoint uncertainty, target debits, invalid budgets/contracts, exact input hashes and isolated optimized CLI execution.
git diff --checkpasses.This complements PR5732's fixed rational-power bounds and PR5746's complete common-base classification. It uses the retained signed-invoice interface and predecessor credits. It does not establish native legality, full charges, compiler closure or a new κ. Limits: 64 uncancelled ranks, 16..256 bits, 2047 boxes and depth 40; tangent and endpoint roots can remain unresolved.
Canonical claim: #5752. Fresh main, priority revision 8, open PR heads/bodies and recent Discussions were checked before work and submission. File-list truncation and API failures are recorded; overlap coverage is not a proof of novelty. Hosted CI and independent review remain pending.
Base:
de5ec2e7a6074068452f45b1a191b5c72832df4a. Verified head:875212cd80e5ab94256c6a05992da26b71344cad.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 7 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.