Renormalisation Group Analysis of the KA Operational Universality Class: Fixed Points, Critical Exponents, and Lead-Time Scaling - From RG Analogy to Leading-Order Derivation (OP2)

The KA Operational Universality Conjecture predicts that systems satisfying axioms A1-A5 exhibit metric singularity precursor divergence dF_KA/dt -> +infinity as kappa -> kappa_c^-. Paper 2 proposed an RG-analog fixed-point structure and motivated lead-time scaling Delta_t ~ lambda⁻¹ ln(kappa_c/kappa_0) from an asymptotic argument. Open Problem 2 asked for a rigorous RG derivation. We provide this derivation at leading order. Starting from the Wilsonian effective action for fluctuations phi = det(A(kappa)) near the critical manifold M_c, we derive one-loop RG beta-functions and identify the Wilson-Fisher fixed point at r*=-epsilon/6+O(epsilon^2), u*=2*epsilon/3+O(epsilon^2) (dimensionless couplings). This gives the correlation length exponent nu = 1/2 + epsilon/12 + O(epsilon^2) and effective anomalous dimension eta(k) = tr(d_kappa Sigma*⁻¹ * d_kappa Sigma*)/k + O(1/k^2) for k >= 3 flows. The lead-time formula Delta_t = (nu/kappa_dot)*ln(kappa_c/kappa_0) is derived from RG flow, identifying the phenomenological constant of Papers 1-2 as the correlation length exponent nu. Simulation confirms nu_hat = 0.503-0.541 across k=2,3,4,5 flow regimes (R^2 > 0.98). Lead-time predictions match Paper 3 calibrated domains to within 2%. Full higher-loop calculations remain open (OP2b).