Paper II — UN Theory Non-Perturbative Scale Invariance and Functional Renormalization Group Fixed-Point Analysis of the Substrate Correlation Ratio α...

This paper provides a non-perturbative proof of scale invariance for the correlation scaling ratio alpha in UN Theory using the Functional Renormalization Group (FRG). Starting from the exact bi-local Wetterich flow equation defined on the admissible correlation manifold B_adm, a non-perturbative derivative expansion of the effective average action C_k[I] is constructed. Using a heat-kernel kinetic projection operator P_alpha, the exact non-perturbative beta function \beta(\alpha) \equiv k \partial_k \alpha is derived. The paper proves the existence of an unconditionally attractive, scheme-invariant non-Gaussian fixed point \beta(\alpha*) = 0 with a positive critical exponent \theta > 0. Evaluated in the optimized Litim regulator scheme, the fixed point yields strictly alpha* = 0.139. At this fixed point, the gravitational anomalous dimension vanishes (\eta_G(\alpha*) = 0), causing the running Newton constant to freeze (\partial_t G = 0), suppressing ultraviolet divergences, and establishing non-perturbative Asymptotic Safety for the emergent effective action.