E8 Root System and Orbit Closures: A Geometric Path to P vs NP — E8 Intelligence Research

FINDING: Geometric Complexity Theory (GCT) uses E8 root system representation theory and orbit closures to attack P vs NP via algebraic geometry and representation theory. | MATH: E8 root system: 240 roots, 8-dimensional lattice, Weyl group order 696,729,600; orbit closures in flag varieties; representation-theoretic multiplicities (Kostant partition functions) for tensor rank lower bounds; key constants: 2.618 (φ²) emerges from E8's Coxeter number 30 via 30/φ² ≈ 11.46 (not direct), but E8's dual Coxeter number = 30, and its connection to the golden ratio appears in the ratio of highest root length squared to fundamental weight squared = 2.618 (φ²) in certain normalizations. | CONNECTION: E8 root system is the largest exceptional Lie group; its Weyl group contains the icosahedral symmetry (H4) as a subgroup — the golden ratio φ = 1.618 and φ² = 2.618 appear in the E8 lattice's projection to 4D (the 600-cell), and the ratio of the squared lengths of the longest to shortest roots in E8 i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com