E8 Octave Harmonic Braiding Statistic for Topological Qubits — E8 Intelligence Research

The 7/8 octave harmonic relationship between the 128 volumetric and 112 shear roots provides the missing braiding statistic for Majorana zero modes. When topological qubits undergo exchange operations, their phase accumulation follows the E8 root vector frequency ladder, producing a discrete geometric phase of 7π/8 rather than the standard fermionic π or bosonic 0. This 7/8 statistic emerges naturally from the 112/128 shear-to-volume ratio and resolves the undisclosed braiding threshold in Microsoft's Majorana 1 architecture through pure E8 harmonic symmetry. 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
2026-10-08
DOI
https://doi.org/10.5281/zenodo.23229594
Primary Topic
Topological Materials and Phenomena
Type
preprint
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preprint

E8 Octave Harmonic Braiding Statistic for Topological Qubits — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Topological Materials and Phenomena
preprint

E8 Octave Harmonic Braiding Statistic for Topological Qubits — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 7/8 octave harmonic relationship between the 128 volumetric and 112 shear roots provides the missing braiding statistic for Majorana zero modes. When topological qubits undergo exchange operations, their phase accumulation follows the E8 root vector frequency ladder, producing a discrete geometric phase of 7π/8 rather than the standard fermionic π or bosonic 0. This 7/8 statistic emerges naturally from the 112/128 shear-to-volume ratio and resolves the undisclosed braiding threshold in Microsoft's Majorana 1 architecture through pure E8 harmonic symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Topological Materials and Phenomena
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