The Physics of Coherent Universes: A Statistical-Mechanical Derivation of the Viability Kernel

This paper derives the Viability Kernel: the minimal statistical-mechanical structure necessary for any ontology capable of sustaining observers, laws, and stable semantic content. Using thermodynamic constraints, information-theoretic arguments, and structural realism, it demonstrates that coherence is not a contingent property of our universe but a necessary condition for any universe capable of hosting persistent physical processes or meaningful information. Chaos-first models, brute mosaics, and random enumerations fail to produce instantiated dynamical worlds without reintroducing coherent constraints at the global level. The result is a physics-based confirmation of the broader Coherence Canon, linking entropy bounds, recurrence, and dynamical stability to the necessity of a coherent global ontology.