The Foundational Admissibility Framework

This paper presents a minimal structural framework for determining whether a state belongs to a system and whether system evolution may proceed. The framework isolates two necessary and sufficient conditions: admissibility and reachability. Admissibility specifies whether a generated state satisfies governing constraints, while reachability specifies whether the state lies on at least one permissible path from an initial condition. Together they define system membership and continuation without reference to domain-specific laws. This establishes a domain-neutral criterion for valid states applicable across formal, physical, computational, and dynamical systems.