Ontological Bridge: From Kaminsky's Duality Ontology to Khomyakov's KL-Geometric Observer Entropy

This paper constructs a rigorous mathematical bridge between Kaminsky's ontological duality framework and Khomyakov's KL-geometric theory of observer entropy. The central result establishes a canonical isomorphism between the statistical manifold (𝒫>₀(𝒳), D_KL) and the factor space of Kaminsky's ontological configuration space Ω_W = Subj × Subj under subjective-indistinguishability equivalence. Four theorems are proved: (T1) the ontological flow induces a Markov semigroup on the statistical manifold under an explicit fibre-uniformity assumption; (T2) the KL divergence is the unique f-divergence, up to positive scalar, whose Hessian recovers the Fisher–Rao metric; (T3) ontological observer entropy equals the expected within-fibre KL divergence from the uniform fibre prior; (T4) ontological observer entropy coincides with Khomyakov's observer entropy under a precise operator identification. A monotonicity theorem for subjective entropy is derived from the Shannon chain rule, yielding an entropic arrow of time consistent with physical time ordering. Version 1.2 introduces a new Parametric Realization assumption enabling a rigorous embedding of the ontological trajectory into a smooth parametric statistical family, together with a derived Fisher–Rao scaling theorem establishing the quadratic expansion of ontological observer entropy in terms of the Fisher information metric. These additions provide the missing structural link required to import the information-geometric scaling law into the ontological framework in a formally controlled manner.