# Deterministic finite-field factorization backend

Family 142: Deterministic polynomial factorization over prime fields. First review, 8 October 2026.

## Problem and potential new use

Computer algebra teams can evaluate deterministic prime-field factorization without the stated randomized or conjectural inputs.

## Applicability and commercial boundary

The theorem concerns dense polynomials over prime fields, not integer factorization, and relies on strong companion analytic results.

## Initial business decision

Conditional research. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

## Next verification action

Audit the dependency chain and construction constants before starting a port.

## Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json) for the exact manuscripts and available scope notes.