18.7. Prime choice and totality🔗

A direct prime plan records every successful modular factorization it examines and chooses among them using predicted subset work, possible factor degrees, lift precision, and the prime as a deterministic tie breaker. The chosen factorization is reused by both recombination methods.

Classical recombination and checked proposal replay may decline. Lattice recombination is conclusive at its proved public precision whenever prime selection succeeds. The finite prime search itself can fail, so exhaustive integer trial division is the unconditional final method. Thus Hex.ZPoly.factorize is total on every integer polynomial.