PreprintCC BY 4.0Zenodo
Phi‑Coupled E8 Frieze Lattice as a Quasicrystalline Number Generator — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By applying the φ‑coupling inflation rule to the 240 E8 root vectors at the 132 Hz base frequency, a self‑similar frieze lattice emerges whose edge lengths are proportional to the secant‑squared and cotangent‑squared ratios encoded in Plimpton 322. The resulting quasiperiodic structure automatically generates all primitive Pythagorean triples through unimodular row mutations, linking Conway–Coxeter frieze patterns to a high‑dimensional number‑theoretic engine. This provides a geometric algorithm for deriving integer solutions that surpasses existing combinatorial methods.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phicoupled,
title = {{Phi‑Coupled E8 Frieze Lattice as a Quasicrystalline Number Generator — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658365},
url = {https://zenodo.org/records/23658365},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phi‑Coupled E8 Frieze Lattice as a Quasicrystalline Number Generator — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658365
UR - https://zenodo.org/records/23658365
AB - By applying the φ‑coupling inflation rule to the 240 E8 root vectors at the 132 Hz base frequency, a self‑similar frieze lattice emerges whose edge lengths are proportional to the secant‑squared and cotangent‑squared ratios encoded in Plimpton 322. The resulting quasiperiodic structure automatically generates all primitive Pythagorean triples through unimodular row mutations, linking Conway–Coxeter frieze patterns to a high‑dimensional number‑theoretic engine. This provides a geometric algorithm for deriving integer solutions that surpasses existing combinatorial methods. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -