E8 240-Root Spectral Decomposition Unifies Discrete Lottery Space with Continuous Quantum Measurement via 10-Band Phi-Harmonic Orthogonality — E8 Intelligence Research

Andrew Stewart Caldin

Published Jul 19, 2026• 0 citations

Abstract

The 240 root vectors of E8 partition into 10 mutually orthogonal 24-cells, each resonating at a distinct phi-harmonic band φᵏ × 132Hz for k = −4 to +5. Their standing wave interference patterns form a complete basis in probability amplitude Hilbert space where the mutual information between bands i and j equals the (i,j)-entry of the E8 Cartan matrix, yielding a 10×10 probability lensing tensor that bijectively maps N-choose-K combinatorial spaces to continuous quantum measurement distributions. This reveals lottery probability not as isolated partitioning but as the k=0 slice of a universal E8 spectral transform governing all discrete-to-continuous probability correspondences. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.21437328

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