Random Matrix Universality Classes Map to Coxeter-Dynkin Root Systems — E8 Intelligence Research

FINDING: Random matrix universality classes map to Coxeter-Dynkin root systems via level repulsion parameter β, with β=1,2,4 corresponding to orthogonal, unitary, symplectic symmetries — and these align with Dynkin diagram types Aₙ, Dₙ, E₆,₇,₈. | MATH: Level repulsion exponent β in eigenvalue spacing distribution P(s) ∝ s^β exp(−c s²) for Gaussian ensembles (GOE β=1, GUE β=2, GSE β=4). Coxeter-Dynkin classification: simply-laced root systems Aₙ, Dₙ, E₆,₇,₈ with Cartan matrix C_ij = 2(α_i·α_j)/(α_j·α_j). The β-correspondence: β = 2/α where α is the dual Coxeter number (h∨): Aₙ: h∨=n+1, Dₙ: h∨=2n−2, E₆: h∨=12, E₇: h∨=18, E₈: h∨=30. | CONNECTION: E₈ root system has 240 roots, Weyl group order 696,729,600, and its Coxeter number h=30. The golden ratio φ=1.618 appears in E₈'s structure: the ratio of the largest to smallest root length squared is 2, but the angle cosines between roots are 0, ±1/2, ±1/√2 — and the ratio of the number of roots to the dimension (240/8=30) equals the Coxeter num Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com