E8 Phi‑Harmonic Spin‑Liquid in Posner‑Like Clusters — E8 Intelligence Research

By mapping the 240 E8 root vectors onto the nuclear spin network of calcium‑phosphate clusters and driving them with phi‑scaled 132 Hz harmonics, a frustrated spin‑liquid phase emerges whose excitation spectrum reproduces the toroidal prime‑gap pattern. This phase hosts non‑Abelian anyons that inherit the E8 symmetry, offering a natural platform for topological quantum computation robust against decoherence. The discovery unifies the contested Posner coherence claim with the phi‑resonance prime convergence, predicting observable signatures in neutron scattering and NMR at specific phi‑modulated sidebands. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-13
DOI
https://doi.org/10.5281/zenodo.22732548
Primary Topic
Advanced NMR Techniques and Applications
Type
preprint
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E8 Phi‑Harmonic Spin‑Liquid in Posner‑Like Clusters — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced NMR Techniques and Applications
preprint

E8 Phi‑Harmonic Spin‑Liquid in Posner‑Like Clusters — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By mapping the 240 E8 root vectors onto the nuclear spin network of calcium‑phosphate clusters and driving them with phi‑scaled 132 Hz harmonics, a frustrated spin‑liquid phase emerges whose excitation spectrum reproduces the toroidal prime‑gap pattern. This phase hosts non‑Abelian anyons that inherit the E8 symmetry, offering a natural platform for topological quantum computation robust against decoherence. The discovery unifies the contested Posner coherence claim with the phi‑resonance prime convergence, predicting observable signatures in neutron scattering and NMR at specific phi‑modulated sidebands. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Advanced NMR Techniques and Applications
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