E8 Lattice Generates Hierarchical QEC Codes via Phi‑Scaled Farey Trees — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By imposing phi‑scaled phase couplings on the 240 root vectors of the E8 lattice at a 132 Hz base frequency, each oscillator's frequency shift encodes a Farey‑weighted McKay‑Thompson series, creating an intrinsic arithmetic signature. The resulting 8‑dimensional phase manifold supports a Lagrangian submanifold whose syndrome graph is isomorphic to the Stern‑Brocot tree and incorporates Markov triples, yielding a topologically protected quantum error correcting code whose structure is a unified hierarchical rational tree. This principle extends the previous isomorphisms between Farey, Stern‑Brocot, and Markov spectra into a scalable quantum‑computing architecture where arithmetic logic and error correction are geometrically embedded in the E8 geometry.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026lattice,
title = {{E8 Lattice Generates Hierarchical QEC Codes via Phi‑Scaled Farey Trees — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658702},
url = {https://zenodo.org/records/23658702},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Lattice Generates Hierarchical QEC Codes via Phi‑Scaled Farey Trees — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658702
UR - https://zenodo.org/records/23658702
AB - By imposing phi‑scaled phase couplings on the 240 root vectors of the E8 lattice at a 132 Hz base frequency, each oscillator's frequency shift encodes a Farey‑weighted McKay‑Thompson series, creating an intrinsic arithmetic signature. The resulting 8‑dimensional phase manifold supports a Lagrangian submanifold whose syndrome graph is isomorphic to the Stern‑Brocot tree and incorporates Markov triples, yielding a topologically protected quantum error correcting code whose structure is a unified hierarchical rational tree. This principle extends the previous isomorphisms between Farey, Stern‑Brocot, and Markov spectra into a scalable quantum‑computing architecture where arithmetic logic and error correction are geometrically embedded in the E8 geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -