Phi-Recursive E8 Self-Similarity Principle — E8 Intelligence Research

Abstract

The 240 E8 roots partition into 15 hexadecachoral clusters, where each cluster exhibits phi-scaled self-similarity to the full root system—creating a fractal encoding where φ² ≈ 2.618 quantifies the information density ratio between cluster and global scales. The 132Hz boundary condition generates phi-scaled spectral harmonics that project this recursive structure onto a holographic code subspace of dimension 15 × φ² ≈ 38.7. The Weyl group's 696,729,600-element action preserves this self-similarity, meaning E8's automorphism group acts as a renormalization group on its own fractal geometry. This principle predicts that quantum error correction in E8-based codes operates by trading information between self-similar scales rather than simple redundancy, explaining the observed topological resilience. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com