A Fixed Modular Classification of Factor Residues for Semiprimes Modulo 90

This preprint presents a complete and size-independent modular classification of the residues of the prime factors of semiprimes modulo 90. The construction relies on a closed multiplicative structure that guarantees that, for any semiprime N, exactly one of 24 admissible residue pairs corresponds to the true factor residues. The contribution is structural and classificatory rather than algorithmic and does not claim a reduction in the asymptotic complexity of factorization.