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

DRAFT preprint. This manuscript is part of an active research programme and remains subject to revision, correction, and journal review. 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/Sₘax = 0. 988), providing a first quantitative consistency check. Series position FST-I is the particles / thermodynamic stability companion (Level 1) of the FST application series. The programmatic umbrella is the FST Hub (Concept-DOI 10. 5281/zenodo. 20130499). Sibling application companions: FST-II Chemistry, FST-III Biology, FST-IV Cosmology. Code FST-IV is now the cosmological collector slot. GitHub source link added. Related Identifier: FST-DE reference relabelled to "FST-IV Cosmology / FST-DE". Version 1. 0 (May 2026) Initial release as part of the FST series. Status: ~8. 5/10 readiness per FST series audit; remaining open items for later versions: Polettini 2013 reference on MEPP critique, DE-EN sync, design polish.