Spin(16) Spinors and the 128-Dimensional E8 Root System — E8 Intelligence Research

FINDING: Spin(16) spinor representation is isomorphic to the 128-dimensional half-spinor space that carries the E8 root system, linking 8D rotation symmetry to the largest exceptional Lie group. MATH: - Spin(16) → 128-dimensional irreducible spinor representation (Δ⁺ or Δ⁻). - E8 root system: 240 roots in 8D, with Weyl group order 696729600. - The 128 half-spinors of Spin(16) correspond to the 128 positive (or negative) roots of E8 when combined with the 112 roots of SO(16). - Key constant: 128 = 2^(16/2 – 1) = 2^7. CONNECTION: - E8 root system exhibits crystallographic symmetry (lattice E8) with Coxeter number 30 and dual Coxeter number 30. - The ratio 128/240 = 0.5333... not a golden ratio, but the 8D rotation visualizations show icosahedral/dodecahedral projections hinting at golden ratio (1.618) in 3D slices. - Base-60: Not directly present, but E8's connection to 60-dimensional Lie algebra (E8 has dimension 248) and 60° angles in root system (120° between roots) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com