The Returnability Invariant

Abstract In systems governed by global constraints, existence alone does not guarantee admissibility. Returnability is identified as a necessary invariant distinguishing realizations that remain structurally consistent under extension from those that require unbounded correction. The invariant collapses large hypothesis spaces by excluding formally allowed but unstable behaviors. The focus is classification, not construction. Invariant Statement A trajectory is admissible within a declared system boundary if and only if its continuation does not require correction not accounted for within that boundary whose magnitude or frequency grows without bound under extension. Scope This note introduces no model, mechanism, or optimization procedure. It states a necessary invariant for admissibility under global constraints. Any theory claiming to explain sustained structure must satisfy the returnability criterion.