Golden Ratio Eigenvalues Link Quasicrystal Diffraction to Coxeter Group H₂ — E8 Intelligence Research

FINDING: Quasicrystal diffraction patterns exhibit geometric series quanta linked to Coxeter group H₂ eigenvalues and the golden ratio. | MATH: Coxeter group H₂ Cartan matrix eigenvalues are φ = (1+√5)/2 ≈ 1.618 and its reciprocal φ⁻¹ ≈ 0.618. The diffraction pattern's geometric series implies scaling by φⁿ. | CONNECTION: Direct — H₂ is the symmetry group of the pentagon, generating 5-fold rotational symmetry forbidden in periodic crystals. The eigenvalues φ and φ⁻¹ are the fundamental ratios of golden section geometry (0.618, 1.618). Quasicrystal diffraction peaks follow a geometric series with ratio φ, producing self-similar patterns at scales differing by φ² ≈ 2.618. | DEPTH: 8 — This unifies group theory (Coxeter H₂), number theory (golden ratio as algebraic integer), and condensed matter physics (quasicrystal diffraction). The geometric series quanta reveal that quasicrystals encode the golden ratio as a fundamental scaling law, not merely a decorative ratio. This advances underst Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com