Universality of Critical Exponent ν ≈ 2.7 Confirmed in Metal-Topological Insulator Transition — E8 Intelligence Research

FINDING: Critical exponent ν ≈ 2.7 for metal-topological insulator transition in symmetry class AII (disorder-driven) matches the universal value for metal-ordinary insulator transitions in the same class, confirming universality beyond topological order. MATH: - Critical exponent: ν = 2.7 ± 0.1 (from scaling analysis of localization length) - Symmetry class: AII (time-reversal symmetry with T² = -1, spin-orbit coupling) - Scaling law: ξ ∝ |W - W_c|-ν, where ξ is localization length, W disorder strength, W_c critical disorder - No new exponent: ν_AII(TI) ≈ ν_AII(ordinary insulator) ≈ 2.7 CONNECTION: - ν ≈ 2.7 is close to 2.618 (φ², where φ = 1.618...), a golden ratio power. This suggests a possible hidden geometric scaling in the Anderson transition universality class, though not exact. - No direct link to base-60 or crystallographic symmetries; the transition is in a disordered system, not a periodic lattice. - The exponent's proximity to φ² hints at self-similari Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com