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

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 1.10 (July 2026) Maintenance release candidate for the local tangential certificate-ledger guardrail and expanded RFEP transfer-ledger data surface. This candidate does not promote RFEP to a completed domain proof; all physical and arithmetic transfers remain diagnostic unless their independent target, outer-gap, tangential-residual, normal-residual, scale/advice, and matched-control gates are separately satisfied. Tangential certificate ledger: the paper now separates raw total residuals from projected tangential evidence and records paid versus unpaid normal residuals before any residual/gap signal can be treated as certificate-like evidence. Data-surface expansion: the RFEP transfer table is expanded into explicit fields for target provenance, gap certificate, tangential residual, normal/escape account, scale and controls, and decision status. Claim hygiene: mechanical positive-control rows are identified as controls, not physical domain certificates; branch-level Yang--Mills, Navier--Stokes, turbulence, cosmology, and RH readings remain verification programmes. PDF hygiene: English, German, and combined PDFs were rebuilt from the active v0.9 source set after the June 2026 guardrail and design passes. DE/EN: English and German PDFs remain synchronized; the German PDF text extraction contains real umlauts, and the combined PDF merges English first, then German. Changes in Version 1.9 (June 2026) Maintenance release candidate after the post-v1.8 certificate-ledger guardrail and English-style pass. The release keeps RFEP as a framework and transfer-audit layer; it does not claim a completed domain proof for Yang-Mills, Navier-Stokes, turbulence, cosmology, or RH. Certificate-ledger guardrail: the post-v1.8 text makes independent target-subspace, outer-gap, spectral-exactness, detector-degree, advice-budget, and repair-certificate gates more explicit before any domain-transfer claim can be strengthened. Claim hygiene: the RFEP layer is framed as an organising stability meta-rule and diagnostic framework, not as an automatic closure theorem for the domain papers. Style maintenance: the English register was tightened and idiomatic wording was smoothed after the June 2026 style pass. PDF hygiene: the English, German, and combined PDFs were rebuilt from the active v0.9 source set; German PDF text extraction uses real umlauts. DE/EN: English and German PDFs remain synchronized in the local candidate set; the combined PDF merges English first, then German. Changes in Version 1.8 (May 2026) Critical: Reframed the Zookeeper import as a conditional microcluster normal form with explicit open uniform gates s_lambda -> 0, p_lambda -> 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