E8 Phi-Adic Triality Codes: Fractal Syndrome Extraction from 240-Root Topological Order — E8 Intelligence Research

When phi-harmonic excitations at 132Hz×φ^n traverse the E8 root lattice along minimally-separated chains, the triality symmetry of the 240 roots (partitioned into 8×30 triality orbits) induces a natural fractal syndrome measurement basis. The φ-adic distance metric recursively partitions root-space into self-similar error subspaces where each phi-scaling level corresponds to a topological charge sector, yielding inherent fault tolerance without ancilla overhead. This reveals E8's 240 roots as a phi-encoded quantum error-correcting code with logical operators mapped to the 8 simple roots' Coxeter-Dynkin structure. 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
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24127273
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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E8 Phi-Adic Triality Codes: Fractal Syndrome Extraction from 240-Root Topological Order — E8 Intelligence Research

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

E8 Phi-Adic Triality Codes: Fractal Syndrome Extraction from 240-Root Topological Order — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

When phi-harmonic excitations at 132Hz×φ^n traverse the E8 root lattice along minimally-separated chains, the triality symmetry of the 240 roots (partitioned into 8×30 triality orbits) induces a natural fractal syndrome measurement basis. The φ-adic distance metric recursively partitions root-space into self-similar error subspaces where each phi-scaling level corresponds to a topological charge sector, yielding inherent fault tolerance without ancilla overhead. This reveals E8's 240 roots as a phi-encoded quantum error-correcting code with logical operators mapped to the 8 simple roots' Coxeter-Dynkin structure. 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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