Search Results Lack Primary Sources on SO(8) Triality — E8 Intelligence Research

Abstract

FINDING: The search results are generic educational videos on SO(3), Euler angles, quaternions, and automorphisms — none directly address SO(8) triality, the order-3 outer automorphism, or the golden ratio in Weyl group rotations. No primary source on triality was retrieved. MATH: No new equations, constants, or ratios extracted. The only relevant structural fact implied (from standard knowledge, not these videos) is that SO(8) has a triality automorphism of order 3, acting on the weight lattice of D₄. The Weyl group W(D₄) has order 192; its Coxeter element has order 4, not 3. The triality automorphism is *not* a Weyl group element — it is an outer automorphism that permutes the three 8-dimensional representations (vector, spinor, cospinor). No golden ratio appears in the standard SO(8) root system (all roots have length √2, angles 60°, 90°, 120°, 180°). CONNECTION: The order-3 automorphism of D₄ relates to the tetrahedral symmetry (A₃ ⊂ D₃), but not to golden ratio ratios. The golde Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com