GADS MCL 26: Structural Difference Factorization Method (SDFM) in Primorial Rings.

This paper introduces GADS MCL 26, a deterministic evolution of modular filtering methods for integer factorization, designated as the Structural Difference Factorization Method (SDFM). Unlike traditional probabilistic sieving or brute-force approaches, SDFM utilizes the residue geometry within the primorial ring Z/42Z to identify families of integers sharing a common factor D = (42x + a). We resolve the historical circular dependency of the search variable x through a structural jump identity, enabling factor extraction in O (N) logarithmic time. Empirical results demonstrate an algebraic predictive capability that significantly accelerates the General Number Field Sieve (GNFS) or functions as a standalone structural factorization engine. The document details the algebraic foundation, complexity analysis, and practical implementation of this new paradigm in computational number theory.