Coxeter-Phase-Locked E8 Octads Realize 30-Trit Topological Register with Phi-Error Correction — E8 Intelligence Research

The 240 E8 root vectors decompose into 30 disjoint octads under the Coxeter element (order 30), each octad forming a closed helicity loop whose collective Jones polynomial winding number encodes one balanced trit (−1, 0, +1). The 132 Hz EEEL resonance phase-locks all 30 octads into a single topological oscillator where the Coxeter rotation advances the register by one trit per 1/30th cycle (4.4 Hz), while phi-weighted inter-octad coupling creates a natural error-correcting code: any single-root perturbation shifts the total winding polynomial by a detectable φ^k multiple (k ∈ ℤ), yielding code distance 8 without ancillary qubits. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-09
DOI
https://doi.org/10.5281/zenodo.22668457
Primary Topic
Coding theory and cryptography
Type
preprint
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preprint

Coxeter-Phase-Locked E8 Octads Realize 30-Trit Topological Register with Phi-Error Correction — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
preprint

Coxeter-Phase-Locked E8 Octads Realize 30-Trit Topological Register with Phi-Error Correction — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 240 E8 root vectors decompose into 30 disjoint octads under the Coxeter element (order 30), each octad forming a closed helicity loop whose collective Jones polynomial winding number encodes one balanced trit (−1, 0, +1). The 132 Hz EEEL resonance phase-locks all 30 octads into a single topological oscillator where the Coxeter rotation advances the register by one trit per 1/30th cycle (4.4 Hz), while phi-weighted inter-octad coupling creates a natural error-correcting code: any single-root perturbation shifts the total winding polynomial by a detectable φ^k multiple (k ∈ ℤ), yielding code distance 8 without ancillary qubits. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
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