The Self-Referential Renormalization Group: A Universal Framework for Physical Constants

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 F[S] = R[S] - C_ [S], where R[S] 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 h_psc\_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 N_gen=3, multi-scale SM gauge structure, Higgs quartic recovery _H = m_H^2/(2v^2), 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 .... Round G1 update (2026-05-16): PSCEntropyDuality axioms discharged; one named open axiom remains (psc_ew_entropy_maximization); grade [A-] unchanged.