Coherence Capacity as the Fundamental Resource of Effective Physics

We identify a single structural resource underlying effective physical descriptions: a finite coherence capacity, defined as the stability margin that allows a projection-based description to remain predictive under disturbance. Working under minimal axioms—invertible underlying dynamics, noninjective projection, and finite admissibility—we prove that exhaustion of coherence capacity necessarily induces noninvertibility of the effective evolution, forcing irreversibility despite reversibility of the underlying dynamics. Measurement collapse, thermalization, and black-hole information loss are shown to be instances of the same admissibility transition. We further show that spatial variation of coherence capacity requires a local geometric bookkeeping, yielding a gravitational response identical in form to Einstein gravity, with Newton’s constant emerging as a conversion factor between capacity and curvature units. The framework introduces no new dynamics or degrees of freedom and is independent of any specific microscopic model; Modal Triplet Theory is cited only as a concrete realization of the axioms. The results establish inevitability rather than existence: they classify what must follow if projection-based effective physics with finite stability margins exists.