Additive Encoding of Primality Constraints and Local Obstruction Structure in a Symmetric Affine System

This preprint develops an exact finite residue-theoretic framework for a symmetric complementary affine system arising from an additive diagonal encoding of primality constraints. For a finite shift set H = {h_0, ..., h_k}, the paper studies the affine family formed by the complementary pairs i + h_j + 1, n - i - h_j + 1, 0 <= j <= k, and determines its congruence obstructions prime by prime. The main results include explicit forbidden residue classes, the finite support of full local obstruction, the collision discriminant controlling exceptional primes, an exact residue-overlap formula for the local obstruction count, an additive-energy interpretation of the overlap profile, exact admissible-class enumeration, and finite translation dynamics under n -> n + 2. The paper also identifies the local root-count data entering the corresponding Hardy-Littlewood singular series and formal Bateman-Horn local factors. The results are finite and residue-theoretic; no infinitude theorem or asymptotic estimate for prime-producing indices is claimed.