An Indexed CRT Assembly Lemma and Exact Admissibility in the Index Axis

We formalize a deterministic assembly principle for congruence obstructions on an abstract index axis. Given finitely many canonically anchored congruence classes modulo pairwise coprime moduli, we prove existence, uniqueness, and exact counting of admissible index classes via an explicit Chinese Remainder Theorem (CRT) construction. The result yields an exact characterization of permitted and forbidden indices, without recourse to density estimates, randomness, or asymptotics. This lemma provides the algebraic backbone of indexed sieve constructions and underlies later non--coverage and diagonal obstruction results.