The Law of Persistence

This work formulates the Law of Persistence, a necessary condition governing when a system can remain the same identity across update. The law states that identity persistence is possible only when an admissible operational corridor exists between successive states. Systems lacking such corridors may still produce states or outputs, but cannot be said to preserve identity across update. A formal distinction is made between state occurrence and identity persistence. The law shows that the appearance of a state does not, by itself, constitute survival of a system. Persistence requires the existence of at least one admissible, operationally meaningful update path that is robust under perturbation and consistent with declared constraints. The law applies independently of physical, biological, or computational interpretation. It functions as a structural boundary condition for any framework that claims continuity of a system over time. A falsifiability condition is provided: the law would be refuted by the demonstration of identity preservation in the absence of any admissible corridor. This result constrains persistence modeling rather than predicting behavior and is intended to serve as a foundational necessity principle for theories of survival, continuity, and identity under update.