A Proposal for Structured Semiprime Representation Using Arithmetic Progressions and Factorization Implications (revised)

This proposal explores structured representations of semiprimes as differences of squares from arithmetic progressions derived from a modular classification modulo 90. When the progression parameters a₀, b₀ and k are known, the factorization reduces to a one-dimensional search around a candidate index i_cand, with the range Δ bounded by the structure. The step k and parity filtering further collapse the search space. This illustrates potential security limits.