E8 Error-Bundle Topological Charge Quantization on the φ-Hopf Torus — E8 Intelligence Research

The 429/402 period-locking ratio represents the minimal integer winding numbers (w₁, w₂) = (429, 402) of the error bundle's trajectory around the two fundamental cycles of the E8 torus T⁸ = ℝ⁸/Q(E8) that remain invariant under the Weyl group's φ-twisted action. Each Weyl-chamber wall crossing increments a topological charge vector in the weight lattice Λ_w(E8), and the observed lock occurs precisely when the bundle's holonomy around the 132Hz φ-harmonic loop satisfies exp(2πi⟨q, ρ⟩/φ) = 1, where ρ is the Weyl vector and q ∈ Λ_w is the accumulated charge. This quantization condition forces the parity-flip sequence across the 120 antipodal root-pair axes to encode the Coxeter element's spectral data, making the 429/402 lock a direct measurement of the E8 root system's φ-deformed modular invariant. 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
2026-11-08
DOI
https://doi.org/10.5281/zenodo.24049027
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

E8 Error-Bundle Topological Charge Quantization on the φ-Hopf Torus — E8 Intelligence Research

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

E8 Error-Bundle Topological Charge Quantization on the φ-Hopf Torus — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 429/402 period-locking ratio represents the minimal integer winding numbers (w₁, w₂) = (429, 402) of the error bundle's trajectory around the two fundamental cycles of the E8 torus T⁸ = ℝ⁸/Q(E8) that remain invariant under the Weyl group's φ-twisted action. Each Weyl-chamber wall crossing increments a topological charge vector in the weight lattice Λ_w(E8), and the observed lock occurs precisely when the bundle's holonomy around the 132Hz φ-harmonic loop satisfies exp(2πi⟨q, ρ⟩/φ) = 1, where ρ is the Weyl vector and q ∈ Λ_w is the accumulated charge. This quantization condition forces the parity-flip sequence across the 120 antipodal root-pair axes to encode the Coxeter element's spectral data, making the 429/402 lock a direct measurement of the E8 root system's φ-deformed modular invariant. 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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