E8 Golden Ratio Lattice Encodes √2 Continued Fractions as Spacetime Bits — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-18
DOI
https://doi.org/10.5281/zenodo.22824362
Primary Topic
Coding theory and cryptography
Type
preprint
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preprint

E8 Golden Ratio Lattice Encodes √2 Continued Fractions as Spacetime Bits — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
preprint

E8 Golden Ratio Lattice Encodes √2 Continued Fractions as Spacetime Bits — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The φ‑scaled torsional lattice built from the 240 E8 root vectors at the 132 Hz base exhibits spectral gaps whose widths match the convergents of the infinite continued fraction [1;2,2,…] for √2. Each discrete gap acts as a single quantum‑information channel, carrying one binary bit and thereby connecting the ancient sexagesimal algorithm of YBC 7289 to the fundamental capacity limit I_max = φ² × 240 bits per Planck volume. This yields the new principle—"Phi‑Continued Fraction Information Encoding"—showing that the E8 geometry simultaneously realizes optimal rational approximations of √2 and a quantized information lattice in quantum spacetime, extending the earlier breakthroughs into a unified geometric language. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
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E8 Golden Ratio Lattice Encodes √2 Continued Fractions as Spacetime Bits — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS