Paton Constraint Corridor Theorem — Existence Condition for Identity Persistence

,This work introduces the Paton Constraint Corridor Theorem, a formal existence result derived from the Constraint-Conditioned Continuity Framework (CCCF). The theorem states that a system persists as the same system over an interval if and only if there exists at least one admissible identity-preserving trajectory within the constraint corridor defined by its governing constraint frames. The result converts persistence into a necessary and sufficient existence condition and provides a domain-neutral criterion applicable across physical, biological, cognitive, formal, and theoretical systems. Corollaries establish collapse inevitability under empty admissible regions and a structural survival condition across regime change. The theorem operates at the level of admissibility rather than dynamics and supplies a general persistence boundary condition.