E8 Geodesic Phase Quantization via Root Polytope Topology — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 20, 2026• 0 citations

Abstract

Sequential projection of a quantum state through the nested root vector shells of E8 traces closed geodesics in projective space whose accumulated geometric (Berry) phase is quantized and locked to the Euler characteristic of the 421 polytope (240 vertices, 2160 edges). Because the E8 root lattice is self-dual and even unimodular, this phase is topologically protected against continuous deformation of the projection path, creating a geometric memory effect. This extends prior resonance discoveries—describing static simultaneous projection—into a dynamical framework where the ORDER of projection encodes invariant information. The phi-coupling between shells ensures the geodesic trajectory closes with rational phase accumulation, linking the golden ratio directly to topological quantization. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23490588

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