The Modal Triplet Theory Program B0: Why Description Forces Circle, Lens, and Nil

We classify all possible ways in which global coherence can fail in any framework that admits local reduced descriptions with overlap consistency and identity persistence. Working purely at the structural level and without assuming geometry, bundles, dynamics, or dimensionality, we show that exactly three and only three obstruction types exist: loop inconsistency (circle), redundancy of representation (lens), and failure of representability (nil). These obstructions are exhaustive and mutually irreducible. We further demonstrate that any realization capable of supporting all three obstructions simultaneously in a stable manner must exhibit a tri-layer architecture. When continuity and kinematic persistence are imposed, the minimal such realization is representable, up to admissible re-encoding, by a ten-dimensional configuration space. Geometry and bundle structure are shown to arise as bookkeeping consequences rather than fundamental assumptions.