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Finite-field factorization assurance integration
Edition 9 October 2026 v2. Bounded conventional checker; defer source backend, low commercial confidence.
Research finding
The source new branch requires p>B^200000 and uniform all-field Hecke zero-free input; its numeric auxiliary-prime and bit-complexity bounds have extreme exponents. A separate classical checker can verify finite submitted factorizations.
Problem and buyer
A computer algebra or coding-theory software team may prefer reproducible finite-field factorization without randomized execution or conjectural assumptions, especially for difficult large-prime cases.
What the finding could enable
An exact backend could support deterministic symbolic workloads and reproducible build or verification pipelines. It would strengthen an existing algebra capability if its dependency chain and practical cost survive review.
Technical and commercial limits
No independent source proof or new backend acceptance. The checker is capped at degree 64 and p<=2^31-1; operation/byte limits yield explicit unknown outcomes. Multiplication alone does not establish irreducibility.
Minimal architecture
Validate prime and canonical coefficient/multiplicity contract; preserve producer result; independently multiply back and run classical Rabin checks; emit exact residues, hashes and limits.
Existing alternatives and differentiation
SymPy already factors and tests irreducibility; its installed 1.13.1 outputs passed 401 exhaustive tiny cases and three illustration inputs. FLINT documents an existing modular-polynomial surface.
Monetization hypothesis
No supported price or demand estimate. Earlier AUD 5,000-20,000 pilot range remains an unvalidated hypothesis; only pursue a specialist evidence integration after recurring buyer value is shown.
Validation experiment
456 passing controls, including an independent exhaustive divisor oracle on 401 monic polynomials, current-library outputs, malformed inputs, scan budgets and exact source-guard arithmetic.
Conditions to reject or defer
Defer direct source implementation until analytic/construction acceptance and a realistic workload advantage. Reject standalone-product scope without repeated evidence needs beyond current CAS tooling.
Next concrete action
Keep as an evidence-platform component; seek a permissioned specialist workload only when the user authorizes engagement. Continue other manuscript reviews without assuming buyer demand.
Detailed evidence
Source dependency/guard review, checker contract, comparisons and reading extent. 456 controls. Earlier dossier and original source links. The Facility Plan Auditor remains the first product experiment. No paid demand or profitability is established.