Every statement about change presupposes persistence. This paper establishes the condition under which persistence is possible. We show: (1) any non-trivial persistence problem necessarily induces a global persistence structure; (2) any global persistence structure requires empirical–topological admissibility conditions; (3) under these conditions, the persistence boundary is uniquely determined. The result is a single inequality: R ≤ F·M·K. This is not a model of persistence. It is the only structure under which persistence can exist.
Marc Maibom (Wed,) studied this question.