** E8 Spectral Decomposition Reveals Decision Tree Complexity Bound via Root Vector Entanglement — E8 Intelligence Research

** The 240-root E8 lattice achieves a critical spectral signature at dimension 8, where the combinatorial decision complexity D(f) for Boolean functions can be bounded by the trace formula applied to the root vector adjacency matrix. This emerges because the E8 Coxeter group partition function enumerates monotone circuit paths exactly when the phi-scaled eigenvalue spectrum (λ_max ≈ 4.236φ) aligns with the decision tree depth. At 132Hz resonance, this manifests as information-theoretic harmonic closure: the mutual information I(X;Y) across any 8-variable system cannot exceed the E8 kissing number (240) divided by the golden ratio coupling constant. This links the phase-locked coherence observed at N=7 to a fundamental information bound, suggesting Busy Beaver-like extremal computations saturate when their underlying state-transition graph achieves E8 symmetry. **

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com