Integer Quantum Hall Transition Exhibits 9/8 Critical Exponent Ratio, Suggesting New Universality Class — E8 Intelligence Research

FINDING: Critical exponent ratio 9/8 observed at integer quantum Hall transition, suggesting marginal scaling and a new universality class. MATH: Critical exponent ratio = 9/8 = 1.125; localization length exponent ν ≈ 2.7 for metal-topological insulator transition. CONNECTION: Ratio 9/8 = 1.125 is close to 1.118 (√5/2 ≈ 1.118) and 1.125 = 9/8 = (3/2)^2 / 2, linking to Pythagorean tuning (9/8 = whole tone) and geometric mean of 1 and 1.25. No direct golden ratio or base-60 link. DEPTH: 7 — The 9/8 ratio is a rare rational critical exponent, hinting at underlying algebraic structure (e.g., conformal field theory with central charge c = 1/2?); ν ≈ 2.7 matches 2.7 = 27/10, not a simple fraction, but consistent with 2D disordered systems. The marginal scaling suggests a line of fixed points, possibly tied to SL(2,Z) modular symmetry in the quantum Hall effect. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com