A Structural Framework for Anchored Indexed Obstruction Systems

We formalize a structural framework for systems of congruence obstructions acting on an index axis, in which each modulus induces a uniquely determined periodic obstruction without translational freedom. The framework isolates the core objects, coverage notions, and structural consequences underlying indexed sieve constructions, exact CRT assembly, and archimedean non--coverage results. No new arithmetic results are proved. The purpose of this document is to make explicit the common structural assumptions already operating in several independent works, and to provide a unified and rigorous language in which those results naturally coexist.