Benchmark Atlas, Branch-Aware Inference, and Decisive-Island Search in the Finite-Capacity Latency–Erasure Program Admissible Parameter Geometry, Cross-Sector Forecast Design, and Synthetic-to-Operational Numerical Architecture for a Unified Finite-Capacity Theory

We develop the numerical and inferential architecture of the finite-capacity latency–erasure program by constructing a benchmark atlas, a branch-aware admissibility pipeline, and a decisive-island search framework spanning gravity, cosmology, nonequilibrium memory, and stochastic latency sectors. Earlier branches of the program established weak-field and screened gravity, moderated erasure cosmology, history-dependent clock effects, stochastic latency noise, microphysical parameter genealogy, unified source closure, and dynamical wave consistency. The present work turns that integrated theoretical backbone into a structured exploration program. We define the admissible parameter manifold by combining stability, sign, causality, source-closure, and regime-consistency requirements, then construct benchmark families corresponding to weak-field dominated, cosmology dominated, mixed gravity–cosmology, nonequilibrium-active, stochastic-active, and strong-field dynamical branches. A branch-aware solver architecture is introduced in which each trial point is mapped from microphysical parent space to effective sectoral observables only after admissibility filtering and regime classification. We define decisive islands as connected regions of admissible parameter space in which multiple sectoral observables are simultaneously informative, stable under perturbations of priors, and nondegenerate under cross-sector Jacobian analysis. Synthetic forecast tools are developed using Fisher-like information operators, decisiveness scores, cross-sector sensitivity matrices, and forecast residual maps. The resulting framework converts the finite-capacity program from a set of individually testable sectoral models into a computationally navigable research architecture with explicit benchmark logic, branch selection, and forecast hierarchy. This provides the numerical capstone of the finite-capacity program and a direct route from theory closure to operational parameter exploration.