Functional Stability Theory — Physical Instantiation via the Renormalized Free Energy Principle

NOTE: This is a preprint. Major revisions are not excluded. We present the physical master paper of Functional Stability Theory (FST): a framework that treats functional positivity under a gauge constraint as a shared structural challenge across number theory, mathematical physics, and cosmology. This v1. 8 release keeps the live v1. 7 Zenodo description design with the Five-Masters series structure, but updates the RFEP paper to the 2026-05-20 strict-review guardrail and the 2026-05-26 source-check refresh. Three ontological layers are distinguished: (1) the abstract RFEP as an organising stability meta-rule; (2) the Dissipative Selection Principle (DS1-DS3) ; and (3) domain-specific instantiations as verification targets rather than completed domain proofs. The v1. 8 text explicitly treats Zookeeper-MS2/C2 as a conditional microcluster normal form with open uniform gates and requires independent target-subspace or outer-gap certificates before a domain transfer can be read as more than posterior self-consistency. The Five Masters Zookeeper: The Spectral Zookeeper, Concept DOI 10. 5281/zenodo. 19673126. Zeta Zoo: Branch-Local Hilbert-Polya, Concept DOI 10. 5281/zenodo. 19673226. Dirichlet Atlas: Zoo-Mapping / character atlas, Concept DOI 10. 5281/zenodo. 19960809. Selberg: NE-B failure as Hilbert-Polya detection, Concept DOI 10. 5281/zenodo. 19962588. RFEP: this physical master paper, Concept DOI 10. 5281/zenodo. 19036190. CHANGELOG Changes in Version 1. 8 (May 2026) Critical: Reframed the Zookeeper import as a conditional microcluster normal form with explicit open uniform gates sₗambda -> 0, pₗambda -> 0, and g_* >= g0 > 0. Critical: Demoted the FST-7 equivalence language to a conditional compatibility schema and marked mass-defined effective gaps as posterior diagnostics unless independently certified. Major: Reorganised RFEP as the physical instantiation of FST rather than an appendix-like spectrum-zero route map; added branch locality, Zeta-Zoo separation, physics/cosmology proof-status mapping, and the CRM loop in the outlook. Major: Corrected the C2ca. 5 Laplace-gap justification: the values g_* approx 5--7 are numerical diagnostics of the full mass-defined cluster gap, not consequences of the rough potential-free lower bound. Minor: Removed the self-reference Bibitem RFEPFramework, aligned Zookeeper/Zeta-Zoo references with stable Concept DOIs, and anchored eight previously uncited bibliography entries in the EN/DE text. Source check: Corrected Connes 2026, CCM 2024, RH Landscape/Even-Dominance, Cornelissen--Marcolli 2010, and several DOI metadata fields against arXiv, DOI/Crossref, AMS, and Zenodo API records. DE/EN: English, German, and combined PDFs were rebuilt; the combined PDF follows the project convention English first, then German. Technical info Public GitHub project path: research-line/functional-stability-theory/tree/main/masters/spectrum-duality. Published in English and German versions; the combined PDF merges the two language versions. Keywords: Functional Stability Theory, RFEP, Pattern A, Dissipative Selection, Gauge Constraint, Spectrum Duality, Yang-Mills, Navier-Stokes, Dark Energy, CRM, Renormalized Free Energy