Unified Structural Conditions for Persistence and Collapse

Scientific and formal disciplines routinely distinguish between persistence and collapse but typically treat them as domain-specific phenomena governed by separate mechanisms. This paper presents a unified structural account showing that persistence and collapse are complementary consequences of constraint-conditioned admissibility. Two previously established laws—the Constraint-Compatibility Persistence Law (CCSL) and the Constraint-Incompatibility Collapse Law (CICL)—are shown to jointly imply a general theorem: the Paton Constraint Corridor Theorem (PCCT). The theorem states that identity persistence is equivalent to the existence of at least one admissible identity-preserving trajectory within a constraint corridor. This result reframes stability, survival, and failure as boundary properties of admissible state space rather than dynamical accidents. The framework is domain-neutral and applies uniformly across physical, biological, cognitive, and formal systems.