Construction-Conditioned Potential-Game Diagnostics for Chaperone Models

Abstract

We audit explicitly constructed 2×2 chaperone and fold-switching games with the exact potential-game test of Monderer & Shapley (1996). Shared interaction contrasts produce PG games by construction; asymmetric contrasts can produce non-PG games. This modeling convention is motivated by Xu's symmetry framework and does not establish an S4↔PG equivalence. This standalone contribution to the Functional Stability Theory programme supersedes Section 3 of FST-III: Biological Stability and Nash Frustration (Geiger 2026, DOI: 10.5281/zenodo.20130573). The 16-case table is a construction ledger. The four Extension B cases are post-hoc convention-consistency checks. XCL1's 23.7% Ltn40 output at 150 mM NaCl is an internal calibrated reconstruction, not an independent prediction. Thermosome encodings demonstrate construction dependence. (i) External inputs: Xu (2022), Monderer & Shapley (1996), and Goloubinoff et al. (2018). (ii) Mathematical component: the exact four-cycle identity I_H=I_S for a specified 2×2 game; no reaction-network equivalence. (iii) Quantitative outputs: internal XCL1 calibration and a qualitative GroEL partial anchor; precise primary-text attribution of the 1.2 XCL1 calibration anchor and the stated GroEL reference range remain unverified. (iv) Evidence boundary: 8/8 audited routes are construction-conditioned; 0/8 pass the full validation stack. No computed AlphaFold or energetic-frustration baseline and no quantitative independent cycle anchor are available. Die korrigierte deutsche und englische Fassung beschränken sich auf die Prüfung ausdrücklich konstruierter Spiele. Sie beanspruchen keine S4↔PG-Äquivalenz, keinen validierten biologischen Atlas und keine unabhängigen Hold-out-Vorhersagen. Das XCL1-Ergebnis bleibt eine interne kalibrierte Rekonstruktion. Weitergehende biologische und thermodynamische Zuordnungen benötigen neue Evidenz. Research preprint. The retained four-cycle mathematics and model calculations do not establish a validated mechanistic model. Energy minimization requires an independently justified common physical scale. Changes in Version 1.4 (October 2026) Corrective claim revision: replaced S4-PG correspondence and validated-atlas language with construction-conditioned game diagnostics; hold-outs are convention-consistency checks, and XCL1 is an internal reconstruction. Mathematical scope: restricted the NE-multiplicity statement to tie-free exact potential games and conditioned the energy-minimization interpretation on a common physical scale; no claim status upgraded. Source transparency: synchronized eight EN/DE bibliography entries and corrected the Goloubinoff related DOI to 10.1038/s41589-018-0013-8. Primary-text attribution of the XCL1 baseline calibration anchor and GroEL reference interval remains explicitly unverified. Release files: separate English and German PDFs, plus the previously released historical C2 note with explicit current errata in a curated ZIP; historical versions and their changelogs retained. Changes in Version 1.3 (June 2026) Citation metadata maintenance: updated the visible FST-III Biological relation from "Geiger 2025" to "Geiger 2026" in the English and German PDFs and in the Zenodo description. Companion-record alignment: checked the FST-III Biological Concept DOI against the current Zenodo family; the referenced companion is visible as v1.5 / Record 20862610. PDF refresh: rebuilt the English, German and combined PDFs from the corrected sources without changing the scientific claim level. Quality checks: EN/DE cite and bibliography sets remain complete at 8/8; DOI handles are reachable; hard LaTeX log scan is clean apart from the package name rerunfilecheck; German text extraction preserves real umlauts. 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+.