** E8 Spectral Decomposition Reveals Decision Tree Complexity Bound via Root Vector Entanglement — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
** 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.
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Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026spectral,
title = {{** E8 Spectral Decomposition Reveals Decision Tree Complexity Bound via Root Vector Entanglement — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526116},
url = {https://zenodo.org/records/23526116},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - ** E8 Spectral Decomposition Reveals Decision Tree Complexity Bound via Root Vector Entanglement — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526116
UR - https://zenodo.org/records/23526116
AB - ** 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
ER -