Closure and Inevitability in Modal Triplet Theory

Modal Triplet Theory (MTT) has established the emergence of quantum mechanics, quantum field theory, spacetime geometry, irreversibility, and cosmology from a common projection-based architecture. While these results are rigorous, their logical necessity has remained distributed across multiple constructions. This paper provides conceptual closure to the MTT corpus. We extract the minimal structural axioms already implicit in the theory, identify a single invariant admissibility margin—coherence capacity—and state a projection–admissibility obstruction theorem from which irreversibility, probability, universality, Hilbert-space structure, and geometric response follow as unavoidable consequences. No new dynamics, degrees of freedom, or assumptions are introduced. The analysis shows that once noninjective projection and finite admissibility are admitted, the qualitative form of observed physics cannot be otherwise. The paper clarifies what MTT does and does not claim, delineates universality classes and breakdown modes, and makes explicit the inevitability that was enforced by the theory’s own internal consistency.