We show that any effective physical theory capable of reproducing irreversible measurement, stable macroscopic records, relativistic locality, and finite predictivity must exhibit algorithmic undecidability at the level of observable dynamics. Within the coherent universality class realized explicitly by Modal Triplet Theory (MTT), noninvertible projection together with admissible basin structure forces the existence of well-posed physical decision problems that no algorithm can decide. The proof constructs a uniform many-one reduction from the halting problem for universal two-counter machines to the robust occurrence of selection events under admissibility, formulated entirely with finite encodings and stability margins. The relevant bound is not an external time horizon but a coherence budget determined by basin geometry, spectral gaps, damping rates, and gravity. Computational irreducibility is thus shown to be a structural consequence of viable physical theories, distinct from chaos or stochasticity, and explains why no globally valid effective laws can exist across measurement, spacetime structure, and ultraviolet completion.
Peter Nero (Thu,) studied this question.