The Self-Referential Renormalization Group (SRRG)

We introduce the Self-Referential Renormalization Group: a gradient-flow theory on the space of self-referential physical theories. The flow maximises a net viability functional FS = RS - C_ S, where RS measures self-representation capacity and C_ S decomposes into closure, self-computation, and selector costs inherited from the NEMS/PSC framework. The main body establishes the core fixed-point structure: fixed-point existence via the Master Fixed-Point Theorem, monotonicity of F along the flow (an analogue of Zamolodchikov's c-theorem), linearised contraction rate 1/ where is the golden ratio, and minimal U (1) symmetry under the PSC cost condition. The Information Profit Threshold 1. 1309 arises as the efficiency ratio at the fixed point, conditional on the explicit PSC Landauer self-consistency hypothesis hₚsc\ₛc (grade A^-; Remark). The associated one-dimensional -flow has a candidate projected -function _ = (-) (-2), with an IR-stable fixed point at = and a UV-unstable separatrix at =2; the algebraic uniqueness and no-third-zero properties are machine-certified in Lean 4 (Vieta's theorem, zero sorry). Conditional physical applications — strong CP phase QCD=0, three fermion generations Ngen=3, multi-scale SM gauge structure, Higgs quartic recovery H = mH²/ (2v²), and structural exclusion of Planck-scale vacuum energy — are developed in Appendix, with all additional physical bridge hypotheses stated explicitly (Table). A negative diagnostic for the Weinberg angle via Haar-entropy ratios is included as Appendix. . . .