Independent verification: exact CRT resultants through radix 27

[swbiggart]

This independently checks the nonzero conjugate-reciprocal Sylvester determinant, complete Bezout identity and integral norm used in Ali Romman's incorporated #621 prime-power inverse proof. A new standard-library implementation evaluates every primitive embedding in split finite fields, then reconstructs exact integer coefficients using CRT and a proved coefficient bound. Integer polynomial replay and a separate Bareiss norm calculation check the reconstructed data.

Completed finite coverage: radices 3, 4, 5, 7, 8, 9, 11, 16, 25 and 27; 80 primitive embeddings; 193 split-prime runs; 2,918 determinant/adjugate evaluations. All eight published determinant/norm examples match exactly. This changes both arithmetic method and coverage beyond the rational-field/SymPy engines through radix 11. Concurrent #628's rounded inverse and radix-16 kernel evidence are credited; radix-25/27 exact resultant evidence and bounded CRT are distinct. No new kappa or uniform theorem is claimed.

Base: 17ce0c79b7b51c2634b439ea5a2b754f09909693. Reviewed #621 source head: 520774462b19b29af41554b74def31f9d01e997e. Upstream's refreshed 66849e1475c930fd7732b1a0067ffee7e1e95f60 changes only CONTRIBUTING.md. The selected frontier and upstream/ are unchanged. Assignment seed 83 and the local claim/result are retained.

Reproduce with Python 3.9+ and no external dependencies:

python3 -B research/prime-power-resultant-crt/verify.py --check research/prime-power-resultant-crt/RESULTS.json

Expected: PASS 80 primitive embeddings; 8 predecessor matches; 8 negative controls.

Validation: identical receipts on Python 3.9/3.11/3.13, including isolated optimized execution; six additional tests against permutation/minor determinants and all 1,000 trace dual-basis identities; meaningful CRT, conjugation, cofactor, source-pin and singular-root controls. The original primary checker, selected-record binding and complete historical make gen4-bank-verify pass. One full make verify passed its earlier groups and gen4, then stopped at the unchanged bit543 C++ cohort because Boost headers are missing locally; no full-suite pass is claimed. The scoped Linux Python 3.11/3.13 workflow passed on this exact commit: CI run. Wider inherited CI is separate. See VALIDATION.md for exact evidence and limits.

Changes are confined to one new research package and its scoped workflow. The finite checks do not prove the all-prime-power analytic theorem, paid preparation, rounding/restoration, tape/compiler interfaces or multiplication theorem. Preserves predecessor and kernel attribution under Apache-2.0. Contribution by Scott Woolsey Biggart (swbiggart), with substantial OpenAI Codex assistance. No delegated or human review is claimed.

[Mister-Meeseeks]

Thank you @swbiggart. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Independent CRT and Bareiss verification through radix27.

Review and limits: Exact finite determinant, Bezout and norm evidence across the stated embeddings. It does not prove paid preparation, rounded restoration or the all-prime-power analytic theorem by itself.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: b861542035d612ff844d0a9d1deaa0713329811a. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.