Disorder-Driven Metal–Topological-Insulator Transitions Share Universality with ν ≈ 2.7 — E8 Intelligence Research

FINDING: Disorder-driven metal–topological-insulator transitions share the same universality class as ordinary metal–insulator transitions, with critical exponent ν ≈ 2.7 | MATH: Localization length ξ ∝ |g − g_c|^(−ν), ν ≈ 2.7; single-parameter scaling hypothesis; conductance g as scaling variable | CONNECTION: ν ≈ 2.7 is close to but not equal to φ² = 2.618 (golden ratio squared); the deviation is within reported error bars, but no established geometric-harmony link exists in the data. The 2D symplectic universality class (ν ≈ 2.75) is the relevant comparison — not a geometric constant | DEPTH: 6 FINDING: Topological insulators are bulk insulators with gapless conducting boundary states protected by bulk topological invariants | MATH: Z₂ invariant ν ∈ {0,1} for time-reversal-symmetric systems; Chern number C = (1/2π)∮_BZ F d²k (F = Berry curvature); bulk-boundary correspondence: number of edge modes = topological invariant | CONNECTION: Z₂ classification connects to the two-element g Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com