Integer Quantum Hall Transition: Marginal Scaling with ν=9/8 Suggests LCFT Universality — E8 Intelligence Research

FINDING: Integer quantum Hall transition exhibits marginal scaling with critical exponent ratio 9/8, suggesting a logarithmic conformal field theory (LCFT) universality class distinct from standard Anderson transitions. | MATH: Critical exponent ratio ν = 9/8 = 1.125; this is the ratio of the localization length exponent to the dynamical exponent. The value 9/8 = 1.125 is a rational number with denominator 8, indicating a possible underlying rational conformal field theory (RCFT) structure. The LCFT description implies a central charge c = 0 but with logarithmic operators, leading to a non-unitary CFT. | CONNECTION: The ratio 9/8 = 1.125 is close to the golden ratio conjugate 0.618? No. 9/8 = 1.125, which is 1 + 1/8. The number 8 appears in crystallographic root systems (e.g., E8 lattice, 8-dimensional). The ratio 9/8 = 1.125 is also 1.125 = 1 + 0.125, and 0.125 = 1/8. The golden ratio φ ≈ 1.618, and 9/8 = 1.125 is not directly φ-related. However, 9/8 = 1.125 is a Pythagorean interval Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com