Coherence Capacity as the Invariant Admissibility Margin of Modal Triplet Theory

Across the Modal Triplet Theory (MTT) corpus, effective physical descriptions are shown to exist only within restricted admissible domains controlled by spectral gaps, projector regularity, and controlled truncation. In this paper we isolate and formalize the invariant structure underlying these conditions. We show that all MTT admissibility requirements define a single finite stability margin—coherence capacity—which measures how much projection-based effective description can be supported before truncation fails. Coherence capacity is not a new dynamical field but a scalar invariant that vanishes precisely at admissibility boundaries. We prove, in fully MTT-native language, that exhaustion of coherence capacity implies the nonexistence of a global measurable section of the coherent projection, yielding effective irreversibility as a structural necessity despite invertibility of the underlying dynamics. Spatial variation of coherence capacity induces a unique two-derivative geometric bookkeeping, reproducing Einstein gravity when the capacity is constant. The paper introduces no new dynamics and modifies no existing MTT constructions; it compresses them, making explicit which features of MTT are contingent and which are unavoidable in any projection-based theory with finite control margins.