Impossibility of Persistent Identity Without Irreversible Constraint

This work presents a structural impossibility result concerning persistence, identity, and constraint. It proves that no system can simultaneously maintain persistent identity under unbounded extension, admit infinite admissible continuation, enforce fully reversible constraint elimination, and remain globally definable. At least one of these conditions must fail. The result is independent of assumptions about time, computation, probability, agency, optimization, observers, or physical implementation. Identity is treated as an equivalence relation preserved under admissible transformation; constraint is treated purely eliminatively rather than preferentially. Under these minimal assumptions, irreversible exclusion of continuations (collapse) is shown to be structurally necessary for persistence. The theorem establishes a no-go boundary analogous in form to classical impossibility results in logic and computation, such as incompleteness and undecidability, but operating at a pre-computational, pre-physical level. It implies that forgetting, irreversibility, and collapse are not contingent failures but necessary structural features of any system that remains identifiable under unbounded transformation. Consequences apply across foundational ontology, computation, physics, artificial intelligence, and ethics, ruling out in principle any fully reversible, memory-complete, infinitely extensible persistence regime.