Capacity-Gated Projection Dynamics: A Typed Hybrid Stochastic Model and Executable Specification

This paper turns the qualitative idea of capacity-gated projection into a complete model specification. The model contains finitely many particles, declared relational summary fields, normalized admissibility rows, a bottleneck reserve, within-mode drift and diffusion, flow and jump sets, and a deterministic reset map or Markov reset kernel. These data define a hybrid stochastic particle system. They are not consequences of a capacity scalar alone. The distinction repairs several ambiguities in the previous version. The logarithmic expression used there is a barrier potential, and its negative gradient is a genuine feedback force or penalty within the reduced model. A capacity-dependent speed cap and noise schedule are constitutive choices. Reaching a guard does not select a successor state until a reset law is supplied. Shared relational fields generally produce classical collective dependence, not quantum entanglement. The use of a Gaussian kernel also creates all-to-all mean-field coupling rather than strictly local interaction. We give a typed model record, a smooth rowwise barrier, a conditional well-posedness theorem up to guard accumulation, an explicit no-selection result for an unspecified reset, a generator criterion for classical nonfactorization, and an event-driven Euler–Maruyama specification that does not silently step through the guard. A two-particle circle model shows every object in closed form, including a translation-covariant reset kernel. A parameter and provenance ledger separates quantities inherited from an MTT admissibility problem from modeling choices and numerical controls. Boundary layers, hesitation, channels, sprouting, and persistent basins are therefore simulation observables to test under stated parameters, not inevitable consequences of projection. The result is a reproducible conditional model and a clear contract for promoting it to a physical application.