Corollary Axiom IX: Prime-Stabilized Topological Closure. Perelman's Theorem as Geometric Foundation for the Universal Model Framework

We introduce Prime-Selective Topological Closure (PSTC) as Corollary Axiom IX of the Universal Model Framework (UMF), a vertical information-theoretic ontology in which physical reality emerges from prime-indexed informational structure. PSTC formalizes a necessary global consistency condition on admissible prime-indexed information paths: only those configurations that are topologically closed under UMF admissibility constraints may persist across ontological layers. While earlier UMF axioms establish generative capacity—governing informational potential, selective actualization, and recursive self-localization—PSTC addresses a previously unresolved structural issue: the overgeneration of mathematically admissible but globally inconsistent realizations. The axiom functions as a non-dynamical closure principle, analogous in role to anomaly cancellation in gauge theories or renormalizability constraints in quantum field theory, enforcing global coherence without introducing additional empirical parameters. We show that PSTC is orthogonal to existing UMF axioms and is logically required to ensure uniqueness up to equivalence, bounded theory space, and observer-stabilizable realizations. The axiom restricts admissible universes to a measure-zero subset of prime-indexed configurations, thereby transforming UMF from an open generative framework into a self-consistent, self-selective ontology. Although PSTC is not directly empirical, its necessity is demonstrated through structural consistency arguments, improved convergence behavior in renormalization-group flows, and elimination of global contradictions otherwise permitted under prime-selective actualization alone. As such, PSTC strengthens the ontological closure of UMF while preserving falsifiability at the level of derived physical predictions. This work positions Prime-Selective Topological Closure as an essential axiom for any information-theoretic theory claiming necessity rather than contingency of physical law. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.