Universal Operator Scaling from Critical Spacetime: Linking Muon g−2 and FCNC in Granular Entropic Physics

We present a unified scaling framework within Granular Entropic Physics (GEP) that connects two persistent anomalies in particle physics — the muon anomalous magnetic moment deviation and the excess in the ultra-rare kaon decay K+ → π+νν̄ reported by NA62 — as distinct projections of a single critical network structure. Starting from the fluctuation exponent α = 8/3, derived independently from the requirement that the cosmological constant be scale-independent, we obtain a universal operator scaling dimension Δ_O = α/2 = 4/3 and an operator-dependent network stiffness κ_eff(O) ~ ξΔ_O, where ξ is the correlation length near the critical point K_crit. The dipole operator governing g−2 carries anomalous dimension Δ_D ≈ 3, arising from a topological chirality flip in the Möbius defect picture with energy cost E ~ 1/L. The FCNC four-fermion operator carries Δ_F ≈ 1, requiring no chirality flip. This hierarchy naturally yields κ_eff(dipole) ~ 10⁶–10⁷ and κ_eff(FCNC) ~ 10–100, reproducing δa_μ ~ 10⁻⁹ and δBR/BR ~ 10–20% without new particles. An enhancement factor Z₃ × Z₂ × log ξ ~ 50 for FCNC transitions is derived from the three inequivalent classes of edge-based loops in the tetrahedral network and the Möbius twist degeneracy — not fitted to data. The central result is a parameter-free master relation: δ_FCNC ~ (δa_μ)1/3, linking the kaon anomaly to the muon g−2 through a single critical exponent. This prediction is testable at Belle II, KOTO, and future precision experiments.