Functional Stability Theory I: A Game-Theoretic Framework for the Thermodynamic Stability of Fundamental Parameters

This paper proposes a game-theoretic interpretive framework for the Standard Model of particle physics, grounded in thermodynamic optimization principles. We explore the hypothesis that the observed particle content and coupling constants are consistent with a Nash equilibrium of a multi-scale thermodynamic game, where the payoff function is the integrated entropy production over cosmological timescales. A semi-analytic stellar model demonstrates that the observed fine-structure constant lies within a broad plateau of near-maximal integrated stellar entropy production (S/S_max = 0.988), providing a first quantitative consistency check. Companion paper in the FST series; the programmatic overview is given in FST-IV (Concept-DOI 10.5281/zenodo.20130499). CHANGELOG Version 1.0 (May 2026) Initial release as part of the FST series. This is the v1 stage; future versions (v1.1, ...) will address remaining open items (Polettini 2013 reference on MEPP critique, DE-EN sync, design polish). Status: ~8.5/10 readiness per FST series audit.