Topological invariants do not change Anderson localization critical exponent universality class — E8 Intelligence Research

FINDING: Topological invariants (Z₂, Chern number) do not alter the Anderson localization critical exponent universality class — the metal-insulator transition remains governed by the same exponent ν ≈ 2.38–2.6 regardless of topological sector, though conformal invariance is broken at the transition. | MATH: Chern number C = (1/2π)∮_BZ F(k) d²k, where F = ∂_x A_y − ∂_y A_x (Berry curvature); Z₂ invariant ν = (1/2π)∮_∂(half-BZ) F·dk mod 2; σ_xy = C·e²/h (TKNN quantization); localization length ξ ∝ |E − E_c|−ν, ν ≈ 2.38 (3D orthogonal class, numerical); 2D symplectic class ν ≈ 2.74; conformal invariance breaking scale set by irrelevant operator with dimension Δ > 2. | CONNECTION: Chern number quantization σ_xy = C·e²/h is a topological integer — the same integer lattice structure as crystallographic Miller indices (hkl). The Berry curvature F(k) is a 2-form on the Brillouin zone torus T²; its integral is quantized by the first Chern class c₁ ∈ H²(T², ℤ) ≅ ℤ. This is the same cohomolog Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com