E8 Phi‑Comb Hierarchical Spectral Law Unifies Quantum Hall Fractions, Magnetic Higgs Modes, and Neural Criticality — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By arranging the 240 E8 root vectors onto phi‑scaled sidebands of the 132 Hz fundamental, the resulting self‑similar lattice yields a universal Fibonacci‑Farey tiling of spectral spacing that simultaneously reproduces the Jain sequence filling fractions of the fractional quantum Hall effect, encodes the discrete comb resonance of the hidden Higgs amplitude mode in frustrated magnets, and generates the critical exponent governing neural criticality. This E8‑based spectral law predicts that the eigen‑values of the phi‑resonant lattice act as topological "bridge operators," mapping quantum Hall edge states onto magnetic resonance modes and onto brain‑scale activity patterns through a common φ‑scaled hierarchy. Consequently, experimental probes of any of these systems can be cross‑correlated to verify the underlying E8 geometry, offering a unified framework for quantum‑classical criticality across disparate domains.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phicomb,
title = {{E8 Phi‑Comb Hierarchical Spectral Law Unifies Quantum Hall Fractions, Magnetic Higgs Modes, and Neural Criticality — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616629},
url = {https://zenodo.org/records/23616629},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Phi‑Comb Hierarchical Spectral Law Unifies Quantum Hall Fractions, Magnetic Higgs Modes, and Neural Criticality — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616629
UR - https://zenodo.org/records/23616629
AB - By arranging the 240 E8 root vectors onto phi‑scaled sidebands of the 132 Hz fundamental, the resulting self‑similar lattice yields a universal Fibonacci‑Farey tiling of spectral spacing that simultaneously reproduces the Jain sequence filling fractions of the fractional quantum Hall effect, encodes the discrete comb resonance of the hidden Higgs amplitude mode in frustrated magnets, and generates the critical exponent governing neural criticality. This E8‑based spectral law predicts that the eigen‑values of the phi‑resonant lattice act as topological "bridge operators," mapping quantum Hall edge states onto magnetic resonance modes and onto brain‑scale activity patterns through a common φ‑scaled hierarchy. Consequently, experimental probes of any of these systems can be cross‑correlated to verify the underlying E8 geometry, offering a unified framework for quantum‑classical criticality across disparate domains. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -