Coarse-Grained Dynamical Inequivalence and the Emergence of Metastable Localized Matter

Observational equivalence is not, by itself, dynamical equivalence. A physical description is predictively complete only when every distinction it discards is irrelevant to the future conditional law it claims to reproduce. This paper makes that requirement exact. We define coarse-grained dynamical inequivalence: two preparations may share the same resolved observables---and even the same initial coarse response---yet evolve under one declared interaction into different conditional futures. An exact factorization criterion identifies when a reduction is legitimate, while preparation-relative conditional information quantifies the predictive loss when it is not. Within an information-projection account of physical genesis, this problem is formulated as event dynamics, in which occurrence, the state actually reached, physical exchange, and the retained history required by subsequent interactions form one law rather than separate annotations. Predictive closure, however, is not yet objecthood. We establish the conditional mechanics by which a dynamically relevant distinction can persist as a localized physical branch. Typed stochastic reduction, causal source completion, candidate selection, joint internal--boundary stationarity, constrained restoring spectra, finite-time survival, and retarded response must be compatible on the same preparation and the same branch. The source that restores balance is also the source charged in selection; the internal field and boundary are stationary for one energy; the same constrained modes govern recovery, survival, and response; and the actual first-entry distribution is carried forward instead of being replaced by equilibrium or a representative average. Continuous spatial and discrete molecular realizations show that equality of present observables does not determine equality of future law, that equilibrium preference does not entail formation or persistence, and that recorded success depends on the history actually realized. The resulting framework gives an operational meaning to causal persistence: a physical object persists when the distinctions that constitute it remain causally active in the laws of its future interactions.