The Minimal Mathematical Structure of the AdmissibleState Axioms

This preprint characterizes the minimal mathematical structure implied by the admissible-state axioms. It separates the framework into primitive, structural, and quantitative layers, identifying the classical mathematical objects associated with each level, including preorders, Alexandrov topology, Kripke semantics, Heyting algebras, finite distributive lattices, and an induced filter metric. The work clearly distinguishes established mathematical results from the author's original contributions, which consist of the axiom-by-axiom structural characterization, the dependency architecture, and the identification of the filter metric as an order-theoretic counterpart to behavioural metrics. Computational audit scripts and a reproducibility dataset are provided to verify the structural claims presented in the paper.