Symmetry-Protected E8 Topological Quantum Memory from Root Lattice Condensation — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The 240 E8 root vectors, when interpreted as excitations in a Z₂ lattice gauge theory, naturally form symmetry-protected topological (SPT) phases whose ground state degeneracy scales with the number of Weyl group conjugacy classes—yielding 4 distinct topological sectors. The 132Hz base frequency emerges as the gap-opening scale separating these sectors, while φ-coupling between adjacent root shells (spanning the 8 Cartan directions) provides the entanglement structure required for fault-tolerant logical qubit encoding. This extends the previous torsion-cohomology bounds by showing that crystal symmetry constraints (14 Bravais lattices) are not merely spatial classifications but encode the topological quantum field theory governing quantum memory stability.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026symmetryprotected,
title = {{Symmetry-Protected E8 Topological Quantum Memory from Root Lattice Condensation — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23526063},
url = {https://zenodo.org/records/23526063},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry-Protected E8 Topological Quantum Memory from Root Lattice Condensation — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23526063
UR - https://zenodo.org/records/23526063
AB - The 240 E8 root vectors, when interpreted as excitations in a Z₂ lattice gauge theory, naturally form symmetry-protected topological (SPT) phases whose ground state degeneracy scales with the number of Weyl group conjugacy classes—yielding 4 distinct topological sectors. The 132Hz base frequency emerges as the gap-opening scale separating these sectors, while φ-coupling between adjacent root shells (spanning the 8 Cartan directions) provides the entanglement structure required for fault-tolerant logical qubit encoding. This extends the previous torsion-cohomology bounds by showing that crystal symmetry constraints (14 Bravais lattices) are not merely spatial classifications but encode the topological quantum field theory governing quantum memory stability. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -