Unified Parameter Closure and Cross-Sector Constraints in the Finite-Capacity Program A Correlated Multiscale Architecture for Gravity, Cosmology, Nonequilibrium Memory, Stochastic Fluctuations, and Microphysical Realization

A multi-branch theoretical framework becomes scientifically stronger when its effective parameters cease to appear as disconnected sectoral constants and instead form a correlated architecture across scales. In the finite-capacity latency–erasure program, weak-field gravity, cosmological background evolution, nonequilibrium history-dependent clock effects, stochastic latency fluctuations, and microphysical patch-based closure have each introduced phenomenological parameters tailored to their own sectors. The central question addressed in the present paper is whether these parameters can be organized into a unified cross-sector closure structure, or whether the program remains only a loose aggregate of partially related models. We answer this question by constructing a correlated parameter-closure map for the finite-capacity program. A three-layer distinction is introduced between substrate-level quantities, effective coarse-grained constants, and directly observable sectoral combinations. We derive dimensional, structural, and asymptotic relations linking screening amplitudes, latency scales, cosmological moderation strengths, history-memory coefficients, stochastic transport amplitudes, and closure-support data. This makes it possible to identify which parameters are primary, which are derived, which combinations are degenerate, and which cross-sector inequalities must hold if the framework is to possess a common multiscale basis. The analysis is then strengthened mathematically by introducing the Jacobian of the closure map, local rank structure, null directions, singular-value based identifiability, and a Fisher-like observable information matrix. These tools allow the parameter architecture to be studied as a geometric object rather than merely a list of phenomenological constants. A reduced explicit closure matrix is analyzed to show that the theory possesses genuine but partial compression: the effective parameter image is lower-dimensional than naïve branch counting suggests, while observable degeneracies further restrict what can be inferred from measurement. Finally, the closure structure is subjected to a robustness analysis. Local Lipschitz stability, perturbation bounds, singular-gap rank stability, information-gap robustness, and closure-supported viability theorems are used to show that the multiscale architecture is not meaningful only in an exact symbolic sense, but can remain structurally coherent under controlled perturbations of substrate variables, coarse-graining coefficients, and observable weighting structure. The main result is a unified parameter architecture for the finite-capacity program. This architecture establishes an explicit micro-to-macro closure linking gravitational, cosmological, nonequilibrium, stochastic, and microphysical sectors through a common finite-capacity substrate. The framework therefore upgrades the program from a set of related effective branches to a correlated multiscale theory with identifiable substrate directions, closure-supported consistency relations, and a nontrivial but controlled observable geometry.