A Fixed Modular Classification of Factor Residues for Semiprimes Modulo 90 (revised)

Version 2 (expanded and revised) — This preprint presents a deterministic modular classification of factor residues for semiprimes N = p·q (with distinct odd primes p, q > 5) modulo 90. The residue r = N mod 90 determines exactly 24 ordered residue pairs (a, b) from the fixed set C = (ℤ/90ℤ)×, with exactly one pair (up to order) corresponding to the true residues of p and q. Using digital-root (mod 9) and last-digit constraints (mod 10), the framework reduces the combinatorial search space to approximately 12 unique unordered pairs per r, achieving a reduction of ~96–98 % from 576 possible ordered pairs. The structure is universal, size-independent, and closed under multiplication (closed-circle property). Complete Master Inversion Tables for all 24 residues are provided, along with numerical verification examples. This offers a pre-computational filter for targeted verification in restricted factorization or semiprime generation.