Huahe Kernel Factorization: A Coordinate System for the Discrete State Space of Odd Integers

The Huahe Kernel Factorization is a complete coordinate system for the discrete state space of odd integers. It is built upon the central identity 2^i3^rR−2^j3^pQ=2 and is governed by three intrinsic constraints: r⋅p=0 (mod 3 orbit selection), (i−1)(j−1)=0 (mod 4 orbit selection), R,Q≡±1(mod6) (intrinsic 6m±1 orbit). The system assigns to every odd integer N>3a unique state vector (i,r,R). The state space is non-periodic, admits gradient directions determined by ln⁡2/ln⁡3, and contains non-differentiable cusps at the factor-2 boundary. Its generating function satisfies a qq-difference equation with a natural boundary term, and serves as a truncated projection of ζ(s) onto the discrete state space