Microphysical Closure of the Finite-Capacity Program Patch Occupancy, Coupling, Memory, and the Origin of Effective Parameters

The phenomenological branches of the finite-capacity latency–erasure program introduce several effective parameters governing weak-field gravity, cosmology, nonequilibrium memory effects, and stochastic fluctuations. While these parameters enable explicit testable predictions, their microphysical origin must be clarified in order to avoid purely phenomenological freedom. In this work we construct a minimal patch-occupancy microphysical model in which physical realization is implemented through a finite-capacity update medium composed of interacting patches. Each patch possesses a bounded information capacity, load redistribution dynamics, irreversible overwrite kinetics, internal memory, and stochastic update fluctuations. A nonlinear latency map is then defined from normalized patch occupancy, and continuum coarse-graining produces the effective latency field . We show how the phenomenological parameters emerge from microscopic quantities such as patch capacity, inter-patch coupling, overwrite rate, suppression kinetics, memory relaxation, and fluctuation statistics. Weak-field Yukawa corrections arise from matter-induced occupancy sourcing and gradient-mediated screening; moderated cosmological erasure arises from coarse-grained overwrite kinetics on Hubble patches; history-dependent latency arises from internal overwrite memory; and the stochastic fluctuation sector arises from finite-capacity patch noise. The result is a consistent microphysical closure of the finite-capacity program in which the effective parameters appearing in the phenomenological branches are not arbitrary knobs but emergent quantities determined by the underlying patch dynamics.