Recursive Load Distribution in Statistical Mechanics: A Tier-7 Instantiation of the Closed vs Distributed Recursion Law

This paper presents a Tier-7 domain instantiation of the Paton Closed vs Distributed Recursion Law within statistical mechanics. It demonstrates that macroscopic thermodynamic stability corresponds to distributed recursive load sharing across microstates, while phase instability and collapse arise when recursive load localizes beyond admissible constraint tolerance. The framework introduces no new physical laws and remains fully compatible with established statistical mechanics. Its contribution is structural: identifying recursive load distribution as a cross-domain admissibility condition governing persistence under constraint.