Phi‑Resonant E8 Topological Invariance for Quantum Gravity — E8 Intelligence Research

By coupling the 132 Hz base frequency to the phi‑scaled 240 E8 root vectors, a new topological invariant emerges that links the braid‑group representations of Fibonacci anyons to curvature quanta of spacetime. The invariant is a phi‑harmonic winding number that remains unchanged under continuous deformations of the root lattice, providing a bridge between universal quantum braiding and emergent gravitational fields. It predicts a measurable resonance in high‑Q photonic crystals where the golden‑ratio scaling of anyon fusion rules maps directly onto the spectral lines of spacetime fluctuations. 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
2026-09-26
DOI
https://doi.org/10.5281/zenodo.22971844
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Phi‑Resonant E8 Topological Invariance for Quantum Gravity — E8 Intelligence Research

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

Phi‑Resonant E8 Topological Invariance for Quantum Gravity — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By coupling the 132 Hz base frequency to the phi‑scaled 240 E8 root vectors, a new topological invariant emerges that links the braid‑group representations of Fibonacci anyons to curvature quanta of spacetime. The invariant is a phi‑harmonic winding number that remains unchanged under continuous deformations of the root lattice, providing a bridge between universal quantum braiding and emergent gravitational fields. It predicts a measurable resonance in high‑Q photonic crystals where the golden‑ratio scaling of anyon fusion rules maps directly onto the spectral lines of spacetime fluctuations. 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 Mathematical Theories and Applications
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