Closure of Complexity and Persistence

A minimal ontological framework is presented in which physical reality is described as an open correlational structure without fundamental closure. No primitive entities, spacetime, or fundamental dynamical laws are postulated at the base level. Existence is identified with structural persistence under admissible projections, while physical laws arise as regime-dependent manifestations of minimal structural complexity. In this work, we provide the operational closure of correlational approaches to emergent physics by formulating minimal correlational complexity as an inevitable principle of selection and persistence. A well-defined complexity functional is introduced, intrinsic to the correlational structure and constrained by viability conditions such as non-trivial evolution, decoherence-compatible projections, and emergent temporal ordering. We show that only correlational configurations minimizing this functional admit dynamically persistent solutions. A persistence theorem is established, demonstrating that any viable structure exceeding the minimal complexity threshold necessarily undergoes dynamical divergence, correlational collapse, or temporal freezing, and therefore fails to exist in a physical sense. Persistence and minimal complexity are shown to be equivalent criteria. Effective physical laws and action principles are not postulated but emerge as expansions around the minimal-complexity configuration. The resulting framework eliminates residual arbitrariness in kernel selection, removes hidden gauges of complexity, and renders the theory operationally closed. Physical reality is thereby characterized as the unique, dynamically stable realization of minimal correlational complexity within an open correlational ontology.