feat(polynomial): admit exact rational factorization

[chasebryan]

Exact rational polynomial factorization admission

Clean rebuild from current main, salvaging only the viable exact Kronecker core and evidence from closed draft #344. No stale #344 admission ancestry is merged.

Mathematical contract

• complete exact irreducible factorization over explicit univariate Q[x]
• exact denominator-LCM/content normalization with positive-leading primitive integer representatives
• original leading coefficient retained as the canonical exact unit
• every returned nonconstant factor is monic and irreducible over Q
• repeated irreducible factors are grouped with exact multiplicity
• deterministic factor ordering
• exact candidate division and exact full multiply-back verification before success
• zero polynomial explicitly refused
• constants return unit-only factorization
• incomplete divisor/candidate search returns resource_limit, never a false irreducibility claim
• cooperative cancellation and request-wide exact work accounting

Public admission

• strict version-1 factorization protocol
• canonical JSONL mathematics gateway domain polynomial_factorization
• closed-schema MCP centl_math domain polynomial_factorization
• public capability discovery and inherited result/server ceilings
• no floating, approximate, heuristic, partial, multivariate, finite-field, or algebraic-extension fallback

Evidence

• direct exact regression suite from the feat(polynomial): admit exact rational factorization #344 core
• repeated/non-monic rational factor cases
• deterministic ordering and exact reconstruction checks
• explicit resource-boundary regressions proving incomplete search refuses
• independent constructed-factor oracle
• live test-only FLINT differential oracle, with no FLINT production dependency
• strict protocol tests including a canonical golden factorization
• JSONL and MCP route/schema/refusal/result-limit/cancellation tests
• docs/POLYNOMIAL-RATIONAL-FACTORIZATION.md freezes the contract

This remains draft until the refreshed native/CLI, dependency, and Actions security gates are green. It supersedes #344 rather than repairing or merging that stale branch.