Rigorous asymptotic analysis of the Fisher information metric near criticality. Derives the d_R scaling exponent analytically via Brillouin zone mode decomposition and proves convergence properties.
Proves the Scaling Closure Theorem: d_R = (d*nu + 2*eta)/(d*nu + eta) from five structural assumptions (A1-A5) about the microscopic Fisher manifold at criticality. A1 (Ricci decomposition) and A2 (Z_2 fusion) and A4 (eigenvalue anisotropy) are proved as theorems. A3 (diagonal block cancellation) at 99.95%+ and A5 (triangle non-cancellation) at 99.9%+. Universality verified across 8 CFT classes including 2D Ising, Potts q=3,4, 3D Ising/XY/Heisenberg, BKT, and Gaussian. Companion proof paper for the Prediction Letter (arXiv:2603.07651).