DONE: exact all-exponent invoice order for common-base ranks (PR5746)

[aliromman]

DONE — PR5746, exact head7c58c57143cc322eb0d578162e6df87ac0f4cd1f. Scope released.

The tool gives a complete classification over every0<t<1 when the uncancelled ranks share an integer base. Exact polynomial reduction, endpoint-factor removal, square-free Sturm counts and multiplicity parity distinguish strict order, weak order with interior equality and true crossings. A declared edit to the full selected invoice is inconclusive under concave order but uniformly worse under this certificate. No numerical exponent grid is used.

Evidence:343 independently checked quadratics,288 known-factor cases, irrational/repeated/endpoint roots, degree29, target and cancellation controls, exact source-byte binding and the optimized isolated CLI. Seven standard-library tests pass on Python3.14.7 and registered3.12.14. All eight tests pass with the optional SymPy1.14.0 oracle, including64 independent root-isolation cases and24 dense degree29 examples near the count limit. Existing ten comparator tests pass. Source blobs and raw/rendered PR contents match the reviewed head.

This is declared arithmetic, not source legality or kappa admission. Noncommensurate ranks remain unsupported. Full selected replay, independent human review and proof-kernel review were not run. Hosted CI is pending; known main navigation failures have separate repairs. No frontier change or merge. The scope, proof and next questions are in the PR.

Credit: classical Sturm theory and the endpoint treatment by Philippe Pebay, J. Maurice Rojas and David C. Thompson; zxv's invoice comparator, mightyOil's T16 audit and retained predecessors. PR5731/5732 remain complementary. New implementation and checks: Ali Romman with substantial OpenAI Codex assistance, Apache-2.0. Latest overlap:419 open PRs,5,094 Discussion records and7,676 main notes; only this scope matched. Base df0137e, priority7.

Open next questions: identify an actual paid exchange with a common-base difference and a complete consumer contract; establish a separate uniform certificate for noncommensurate ranks. A few point evaluations cannot prove uniform order.