Minimal Non-Units, Prime-Support Boundaries, and Batch Unit Testing: A Structural Reformulation and Open Decision Problem for Deterministic Integer Factorization

Abstract

This audit-corrected preprint consolidates research notes V0.2–V1.0 on deterministic integer factorization. It identifies the least prime factor of a composite integer as the first non-unit in natural order modulo N, separates prime-support information from evaluation circuit and bit complexity, proves an exact short-interval support identity under stated invariants, and formalizes a one-bit batch non-unit predicate whose efficient evaluation is polynomial-time Turing-equivalent to factorization. The preprint does not claim a polynomial-time factorization algorithm, a new deterministic complexity record, or priority over known prime-interval support formulas.