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. 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 & sources GitHub: research-line/functional-stability-theory, sub-path applications/fst-i-thermodynamic/. Changelog Version 1.7 (August 2026) Data presentation: Restored the multi-scale architecture and parameter-sensitivity matrix, and converted the envariance mechanisms and cosmological phase-transition summaries into captioned tables. Literature integrity: Preserved the corrected metadata for recent stochastic-thermodynamics sources and explicitly rejected an unsupported Active-Inference attribution. Disclosure: Updated the AI-assistance statement to describe the actual multi-system workflow and retained final human scientific and editorial responsibility. Claim boundary: No KKT certificate, resolvent certificate, or fundamental-parameter prediction is claimed. Bilingual synchronization: Rebuilt the English, German, and combined editions with a visible v1.7 candidate marker. Version 1.6 (July 2026) Alpha-tolerance gate: the manuscript adds a source-bound diagnostic based on the Oberhummer--Csoto--Schlattl +/-4% Coulomb-window experiment for carbon and oxygen production. The window is treated as a stress box, not as a universal viability law, active KKT equality, or probability distribution for alpha. Negative exact-selection result: within the current toy objective, the source window is strictly increasing, maximizes at alpha/alpha_obs = 1.04, and gives S(alpha_obs)/S_box,max = 0.998005599. The observed point remains near the top of a broad plateau, but it is not stationary and is not the box maximum. Claim boundary: no KKT certificate, independent parameter prediction, resolvent-stability proof, or completed multi-parameter selection claim is introduced. The result strengthens the guardrail: FST-I still needs independently specified active constraints, including an electron-mass constraint, before projected-gradient and tangent-Hessian evidence can count. Reproducibility: a dependency-free script and result ledger document the alpha-window evaluation, shifted-window controls, hashes, and explicit claim_upgrade_allowed=false status. DE/EN: English and German PDFs were rebuilt synchronously after the alpha-tolerance gate; the combined PDF was regenerated from the refreshed EN plus DE files. Version 1.5 (July 2026) Bibliographic maintenance: the self-citation to the RH Landscape / Atlas line was updated from the former working title The Riemann Hypothesis Part III: The Analytical Rank-Finite Certificate to the current DataCite/Zenodo title From Landscape to Atlas: Multi-Route Cartography of an Ongoing Expedition Toward the Riemann Hypothesis, v3.1, with unchanged Concept DOI 10.5281/zenodo.19035640. Citation preflight: the active EN/DE bibliography was rechecked after the July 2026 synchronization and style passes; both language versions remain synchronized at 52 cited items, with 15/15 DOI literals and 8/8 active arXiv anchors verified. Scope unchanged: no new FST-I claim, method, numerical result or stability certificate is introduced in this release; the existing v1.4 guardrail framing remains unchanged. DE/EN: English and German PDFs were rebuilt synchronously after the citation metadata fix; the combined PDF was regenerated from the refreshed EN plus DE files. Version 1.4 (June 2026) Strict-review guardrails: the manuscript now opens with an explicit evidence-status anchor: the 1D alpha scan is a consistency check, the 2D scan is a negative control against unconstrained single-scale MEPP, the local Hessian is a landscape diagnostic, and the multi-scale constraint hierarchy remains a hypothesis awaiting independent KKT validation. Constraint-leakage gate: the KKT ledger was extended with anti-post-hoc fields for raw payoff source, constraint identifiers, projected-gradient norm, tangent-Hessian status, residual-to-gap ratio, same-fit-reference risk and matched-control family. Minimum-gate wording: the proposed five-parameter / 80 percent test is now framed only as a minimum falsification gate, not as sufficient validation against cross-couplings or constraint leakage. Scope calibration: framework comparisons and stellar-model language were softened from parameter-selection evidence to candidate-level landscape diagnostics and proposed validation protocol. DE/EN: English and German PDFs were rebuilt synchronously after the strict-review edits; the combined PDF was regenerated from the refreshed EN plus DE files. Version 1.3 (May 2026) KKT/gradient guardrail: the 2D log-Hessian pilot is now explicitly a landscape diagnostic only. It does not certify stationarity, KKT optimality, or resolvent stability because the unconstrained gradient at the observed point is nonzero. MEPP scope corrected: unconstrained single-scale stellar MEPP is treated as falsified as a stand-alone selection principle by the two-dimensional scan (S(obs)/Smax2D = 0.47). Hierarchy claim reduced: the multi-scale constraint hierarchy is presented as an independently testable working hypothesis requiring projected-gradient, tangent-Hessian, and full multi-parameter validation. Language softened: Born-rule/game-theory, symmetry-breaking, sterile-neutrino, resolvent-stability and scale-transfer passages were recalibrated to conceptual reinterpretation, analogy or qualitative consistency, not new derivation or prediction. English style pass: the abstract, Pattern-A analogy, path-integral/payoff vocabulary and conclusion were editorially calibrated to maintain the manuscript's interpretive scope. Proof/paper math sync: EN/DE wording now treats envariance, high-entropy stability and multi-scale transfer as conjectural compatibility claims; the status table and stability protocol distinguish the existing raw 2D Hessian from a missing constrained tangent-Hessian/KKT certificate. Data presentation ledger: EN/DE now include a compact stellar-entropy/KKT status ledger separating the 1D alpha plateau, unconstrained 2D scan, local log-Hessian, missing constrained tangent test and matched controls. Citation metadata maintenance: the Higgs-VEV source now includes DOI 10.1140/epjc/s10052-024-13626-4, and the neutrino-oscillation review now includes pages 399--423 and DOI 10.1146/annurev-nucl-121423-100853. PDF text extraction: EN/DE sources now include lmodern and Unicode mapping so German text extraction preserves umlauts and avoids ligature artifacts. Version 1.2 (May 2026) MEPP caveat strengthened: Polettini (2013), DOI 10.3390/e15072570, added as a source for the limitations of Ziegler-style maximum entropy production beyond linear response. Self-citations updated: FST-II, RH, RFEP/Spectrum Duality and CRM references aligned to current Zenodo Concept-/Live-DOIs. Files refreshed: English, German and combined EN+DE PDFs generated from the v3 source set. Version 1.1 (May 2026) Hub-link corrected: "FST-IV Overview" references replaced by "FST Hub" (programmatic umbrella). The Hub paper holds Concept-DOI 10.5281/zenodo.20130499 and is no-numeral; 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.