feat: verify polynomial-coefficient recurrences - #902
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Summary
Adds bounded exact evaluation and independent verification for polynomial-coefficient linear recurrences.
combinatorics.recurrence.p_recursive.evaluatecombinatorics.recurrence.p_recursive.verifycompanionp_j(n)canonically in ascending rational powersPREFIXprojection, bound recurrence order, and every exact residual over the required consecutive rangeCloses #900.
Why
A held-out
gpt-5.4-miniaudit of Tong Niu's 2026 proof of Mathar's OEIS A176677 recurrence correctly refused Jacobian's constant-coefficient recurrence tool, then made an unsupported late arithmetic error and falsely reported that the recurrence failed at n=16. The new exact capability computes the correct final valuea(16)=3949969and independently verifies zero residuals over the declared finite range.This does not prove a recurrence for all indices or derive it from an external theorem. Production remains
COMPUTED; only the standard-libraryFractionchecker can returnVERIFIED.Validation
make check— 880 unit tests passed; Ruff, format, complexity, and mypy passedmake check-static— dependency, dead-code, architecture, typing, and package-build checks passedmake docs-linkcheckandgit diff --check— passedFocused adversarial coverage includes omitted, duplicate, out-of-order, out-of-range, and boolean result records; a corrupted late candidate; an exact A176677 regression through n=16; and rejection when the leading coefficient polynomial vanishes at a required step.