The Minimal Closure Theorem: A Structural Necessity for Persistent Systems

Persistent structures across physics, chemistry, biology, and computation exhibit a universal dependence on regulated loss. While this dependence is widely observed, it is rarely formalized as a structural necessity independent of mechanism, scale, or physical realization. This work introduces the Minimal Closure Theorem, a generator-level statement asserting that any system that persists under constraint must permit regulated detachment from its stabilized configuration. Sustained structure is shown to be incompatible with both complete closure and unconstrained divergence. The theorem is structural, scale-independent, and non-mechanistic. The result consolidates and formalizes a necessity already implicit in the author’s earlier constraint-level derivations within the ψ₀–OCM (Osborne Cosmological Model), providing a single canonical reference point without re-exposing underlying dynamics. Experimental systems are treated as realizations of the theorem’s consequences rather than as its source.