Empirical Survival Corridor and Multi-Sector Data Viability in the Finite-Capacity Latency–Erasure Program From Multimessenger Timing and Solar-System Precision to Background Cosmology, Growth Safety, and Strong-Field Signature Windows

We develop the first empirical viability synthesis of the finite-capacity latency–erasure program by constructing a multi-sector survival corridor spanning gravitational-wave timing, solar-system weak-field precision tests, equivalence-principle constraints, cosmological background history, perturbative growth consistency, and strong-field compact-object signature windows. Earlier branches of the finite-capacity program established a unified source hierarchy, perturbative matter coupling, dynamical wave consistency, nonlinear hierarchy, thermodynamic closure, compact-object completion, and benchmark-oriented numerical inference. The present work does not add a new physical sector. Instead, it turns the existing theory into an explicitly data-aware framework by identifying the empirical bottlenecks that any viable branch must survive. We define a first-generation survival manifold whose members preserve far-zone luminal tensor propagation, suppress screened weak-field deviations to currently allowed levels, recover a background expansion history close to the observed corridor, and maintain controlled linear-growth response in weakly activated regimes. Distinctive finite-capacity physics is thereby localized to activated sectors including memory, stochastic timing, saturation shells, ringdown distortions, echo-like delayed structure, and other strong-field observables. We formulate theory-side inequalities for tensor-speed safety, solar-system screening, SEP-sensitive weak-field consistency, early-time cosmological suppression, and ordinary linear-growth control, and we show how these conditions embed naturally into the benchmark atlas and branch-aware inference program. The resulting framework converts the finite-capacity theory from a structurally unified program into a data-aware unified program with explicit first-pass empirical viability logic.