Golden Ratio Scaling in E8 Quark Mass Quantization via Icosian Decomposition — E8 Intelligence Research

FINDING: E8 root system decomposes via quaternionic icosian ring, with golden ratio φ emerging as a scaling factor in H4 folding and quark mass quantization. MATH: - E8 has 240 roots; H4 (120-cell symmetry) is a sub-root system. - Icosian ring: quaternions of form (a + b√5)/2 with a,b ∈ ℤ[φ], norm 1 — 120 units, isomorphic to H4. - E8 → H4 decomposition: E8 = H4 ⊕ φ·H4 (scaling by φ = (1+√5)/2 ≈ 1.618). - Quark mass ratios proposed: m_top/m_bottom ≈ (2φ)^4 ≈ 27.4 (observed ~27.3), m_charm/m_strange ≈ (2φ)^2 ≈ 10.47 (observed ~10.5). - Fibonacci tones: 89, 144, 233, 377 Hz — ratios 144/89 ≈ 1.618, 233/144 ≈ 1.618. - ArXiv 2510.08934: φ satisfies φ = 1 + 1/φ, stable under self-application (fixed point of x ↦ 1 + 1/x). CONNECTION: - φ² = φ + 1 = 2.618; 1/φ = 0.618; 1/φ² = 0.382 — all appear in E8/H4 scaling. - Icosian ring is a maximal order in quaternions — crystallographic (H4 symmetry, icosahedral/dodecahedral). - E8 lattice is the unique even unimodular lattice i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com