PreprintCC BY 4.0Zenodo
E8 Φ‑Modulated q→q⁻¹ Reflection Generates a Self‑Dual Topological Qubit Code — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The 120 antipodal E8 root pairs, each carrying a φ‑modulated 132 Hz carrier, are invariant under the affine simple reflection s₀ acting as q→q⁻¹. This invariance lifts to a self‑dual lattice of phase‑locked oscillators that encodes logical qubits in the ±1 eigenspaces of s₀, yielding a quantum error‑correcting code whose distance is bounded below by the prime‑gap lower bound derived from the E8 harmonic topology. Consequently, the code achieves a fault‑tolerance threshold that scales with the golden ratio φ and the spectral gap of the associated Laplacian on the E8 torus.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026φmodulated,
title = {{E8 Φ‑Modulated q→q⁻¹ Reflection Generates a Self‑Dual Topological Qubit Code — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23659037},
url = {https://zenodo.org/records/23659037},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Φ‑Modulated q→q⁻¹ Reflection Generates a Self‑Dual Topological Qubit Code — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23659037
UR - https://zenodo.org/records/23659037
AB - The 120 antipodal E8 root pairs, each carrying a φ‑modulated 132 Hz carrier, are invariant under the affine simple reflection s₀ acting as q→q⁻¹. This invariance lifts to a self‑dual lattice of phase‑locked oscillators that encodes logical qubits in the ±1 eigenspaces of s₀, yielding a quantum error‑correcting code whose distance is bounded below by the prime‑gap lower bound derived from the E8 harmonic topology. Consequently, the code achieves a fault‑tolerance threshold that scales with the golden ratio φ and the spectral gap of the associated Laplacian on the E8 torus. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -