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/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 1.6 (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.