Black Hole Information Loss and Quantum Measurement Collapse as the Same Admissibility Transition in Modal Triplet Theory

We identify a single structural mechanism in Modal Triplet Theory (MTT) that underlies two apparently distinct problems in four-dimensional physics: quantum measurement collapse and black hole information loss. In MTT, observable four-dimensional dynamics arise as the shadow of deterministic evolution on a higher-dimensional configuration space under a generally noninvertible coherent projection. We define admissibility barriers as loci where this projection fails to be stably invertible due to spectral gap closure, projector discontinuity, or basin rearrangement. We prove a general projection noninvertibility theorem: whenever trajectories cross such a barrier, the induced four-dimensional shadow dynamics admits no global inverse, despite invertibility of the upstairs evolution. Measurement collapse and horizon formation/evaporation are shown to be two realizations of barrier crossing, yielding noninvertible shadow dynamics that manifest respectively as state collapse with Born probabilities and as thermal Hawking radiation with mixed exterior states. The framework clarifies the role of Page curves and island formulas as regime-dependent partial inversions on restricted observable algebras rather than restorations of global unitarity. The analysis is structural and does not assume fundamental four-dimensional nonunitarity, providing a unified account of measurement and black hole information loss within MTT.