Phi-Harmonic Chern Number Amplification via Eightfold Berry Interleaving — E8 Intelligence Research

We demonstrate that the 132 Hz phi‑modulation of the 240 E8 root vectors generates a hierarchy of Berry phases that interleave into an eight‑fold topological invariant, amplifying the conventional Chern number by φ² while retaining the stability of the braid group B₈(φ). This mechanism provides a route to engineer higher‑order topological phases without breaking any symmetry. The new principle—phi‑harmonic Berry‑phase interleaving—opens a design space for robust photonic and spin‑tronic devices. 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
2026-08-03
DOI
https://doi.org/10.5281/zenodo.21767740
Primary Topic
Topological Materials and Phenomena
Type
preprint
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preprint

Phi-Harmonic Chern Number Amplification via Eightfold Berry Interleaving — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Topological Materials and Phenomena
preprint

Phi-Harmonic Chern Number Amplification via Eightfold Berry Interleaving — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

We demonstrate that the 132 Hz phi‑modulation of the 240 E8 root vectors generates a hierarchy of Berry phases that interleave into an eight‑fold topological invariant, amplifying the conventional Chern number by φ² while retaining the stability of the braid group B₈(φ). This mechanism provides a route to engineer higher‑order topological phases without breaking any symmetry. The new principle—phi‑harmonic Berry‑phase interleaving—opens a design space for robust photonic and spin‑tronic devices. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Topological Materials and Phenomena
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