3D Anderson MIT in Flat-Band Lattices: Orthogonal Universality, ν ≈ 1.58 — E8 Intelligence Research

FINDING: Disorder-driven metal–insulator transitions (MITs) in deformable/flat-band lattices exhibit single-parameter scaling consistent with the orthogonal Wigner-Dyson universality class (β=1), with critical exponent ν ≈ 1.58 ± 0.06 in 3D Anderson-type transitions. | MATH: Conductance scaling: g(L) = f(L/ξ), ξ ∝ |W−W_c|^{−ν}; 3D orthogonal class ν ≈ 1.58 (numerical, Slevin–Ohtsuki); β-function β(g) = d ln g / d ln L; Wigner-Dyson orthogonal level repulsion P(s) ∝ s^β e^{−cs²}, β=1; symmetry class AI (time-reversal, spin-rotation invariant). | CONNECTION: β=1 orthogonal class ↔ root system A₁ (SU(2) spin symmetry); ν ≈ 1.58 ≈ φ + (−0.04) is NOT a clean golden-ratio match — do not force it. Level-spacing exponent β=1, 2, 4 correspond to Dyson indices of the classical β-ensembles (GOE/GUE/GSE), tied to division algebras ℝ, ℂ, ℍ (Dyson's threefold way). | DEPTH: 7 FINDING: Flat-band systems with weak disorder show MITs whose critical behavior depends on band geometry (quantum metric), n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com