Game-Theoretic Diagnostics for Chaperone Systems: A Potential-Game Test Maps the Goloubinoff Symmetry Landscape

We apply the potential-game test of Monderer & Shapley (1996) to chaperone–substrate interactions and show that Xu's (2022) fourth symmetry condition (S4) corresponds to the potential-game property for 2×2 games, sub-classifying the non-equilibrium chaperone class into kinetic and thermodynamic regimes. This paper is part of the Functional Stability Theory (FST) research program. It supersedes Section 3 (“Game-Theoretic Stability”) of the overview paper FST-III: Biological Stability and Nash Frustration (Geiger 2025, DOI: 10.5281/zenodo.20130573). The game-theoretic chaperone diagnostic is developed here as a standalone paper with extended results, including Extension B (hold-out validation and construction-conditioning demonstration). The central contributions are: (i) a mathematical correspondence between Xu's S4 condition and the potential-game property; (ii) a regime trinity (equilibrium / kinetic non-equilibrium / thermodynamic non-equilibrium) that sub-classifies 16 chaperone and fold-switching systems; (iii) one quantitatively validated prediction for XCL1/Lymphotactin salt-shift populations (23.7% Ltn40 at 150 mM NaCl, Tyler et al. 2012: ~24%); (iv) explicit construction-conditioning transparency via the Thermosome meta-demonstration. (i) External inputs: Xu (2022) symmetry conditions S1–S4; Monderer & Shapley (1996) potential-game definition; Goloubinoff et al. (2018) non-equilibrium chaperone framework.(ii) Structural component: S4–PG correspondence (Proposition 1); regime classification of 16 systems; Extension B hold-out results.(iii) Quantitative prediction: XCL1 salt-shift population at 150 mM (partially circular; calibrated input acknowledged).(iv) Honest limitations: All PG/non-PG results are construction-conditioned; the paper classifies rather than explains. This is a research preprint. The game-theoretic framework provides a diagnostic classification tool for chaperone thermodynamics, not a mechanistic explanation. All construction-conditioning caveats are stated explicitly in the paper. Changes in Version 1.2 (June 2026) Design maintenance: rebuilt the English, German and combined PDFs after the 2026-05-28 design check. Link presentation: shortened visible GitHub raw links on title and closing pages while preserving clickable targets. Quality checks: table, formula, margin, disclosure, bibliography and closing-page spot checks remained green; link annotation check returned no bad annotations and German text extraction preserved real umlauts. Changes in Version 1.1 (May 2026) Added German version: the paper is now available as an English PDF, a German PDF, and a combined English+German PDF. Improved PDF layout: repaired table design and float placement, especially the Chaperone Atlas and Thermosome tables. Improved publication metadata: added PDF metadata, separated title/abstract and table of contents, removed the visible version marker from the title page, and updated the public code link to https://github.com/research-line/fst-nash. Quality checks: rebuilt EN and DE LaTeX without overfull/underfull boxes or unresolved references, rendered representative pages for visual inspection, checked German umlauts from extracted PDF text, merged the bilingual PDF, and reran the core reproducibility scripts. Changes in Version 1.0 (May 2026) Initial release. S4–PG correspondence for 2×2 chaperone games (Proposition 1). Regime trinity: GG / kinetic NGG / thermodynamic NGG for 16 systems. XCL1 salt-shift quantitative prediction (Q9) with circularity caveat. Extension B: 4 hold-out systems (DnaJ, Hsp26, Hsp33, Hsc70) with pre-registered predictions. Thermosome meta-demonstration of construction-conditioning. Companion paper: FST-III Biological (DOI: 10.5281/zenodo.20130573). EN only: English PDF published. German translation planned for v1.1+.