Criteria for Invoking Dark Matter in Late-Time Cosmology — State Dependence, Boundary Layers, and Interpretational Control —

This work presents an interpretational framework for assessing when the introduction of dark matter degrees of freedom is physically warranted in late-time cosmology. Rather than proposing a new particle model or modifying gravitational dynamics, this paper formalizes explicit criteria for distinguishing between genuinely global residuals and state-dependent, emergent effects associated with structure formation, environmental dependence, and boundary-layer regimes. The framework integrates state-dependent observables, extended diagnostics, and boundary-layer sensitivity into a logical decision structure, referred to as a Dark Sector Operating System (OS). This OS functions as an interpretational control layer applied prior to any model extension, clarifying when additional dark sector components are justified and when they are not. This publication constitutes an independent contribution that builds conceptually on earlier exploratory studies, while introducing a new level of interpretational responsibility and operational clarity. An official Japanese translation is included as supplementary material for accessibility; the English manuscript is the authoritative version for citation purposes. This work builds conceptually on earlier exploratory studies (v1, v2),but constitutes an independent contribution by formalizing explicit criteriafor invoking dark matter.