The Structural Persistence Principle: A Unified Statement of the Conditions for Organizational Identity Under Irreversible Dynamics

This working note states and derives the Structural Persistence Principle: a system maintains a distinguishable organizational identity under irreversible dynamics if and only if three conditions hold jointly — a strictly positive creation charge places the system inside a well-defined operational identity region, aggregate support flux exceeds passive depletion beyond passive first-exit time, and the support architecture spans the active constraint geometry at the operational boundary. The principle unifies three if-and-only-if results from companion papers under a single structural statement. The sufficiency direction of the persistence biconditional is derived from first principles via the chain rule on the joint distinguishability margin and Nagumo's invariance theorem, without additional regularity assumptions beyond smooth constraint functions and well-posed dynamics. The creation charge is identified as the structural dual of Landauer erasure, completing the cost triangle W_create ↔ W_maintain ↔ W_erase. The principle is domain-independent and applies across software systems, electrochemical systems, memory systems, quantum systems, and biological systems.