Discrete model factorization 6n±1

This short paper presents a discrete arithmetic model describing the relationship between a natural number N = AB and its neighboring values N ± 2 through a compensated affine symmetry (A + a)(B − a) = AB − a². The model preserves the modular structure of the 6n ± 1 classes and defines a constant boundary variation ±2A between consecutive configurations. It provides a reversible, scale-consistent framework for reading integer factorization geometrically, connecting modular arithmetic with discrete affine transformations. Potential applications include structural analysis of factorization, computational reduction, and cryptographic modeling “This work is distributed under CC BY-SA 4.0 and is intended for non-commercial academic and educational use.” Earlier computational studies such as Riesel (1994) addressed algorithmic aspects of factorization, yet the discrete structural symmetry introduced here was not previously formalized.