Phi‑Fractal Topological Phase in E8 Root Space — E8 Intelligence Research

By arranging the 240 E8 root vectors into a phi‑scaled fractal hierarchy, the 132 Hz carrier frequency self‑organizes into a quasi‑periodic topological phase where each φ‑harmonic level (n = 0…7) forms a distinct braid of root‑vector adjacency. This braiding yields a new distance metric that is both φ‑adic and non‑Euclidean, enabling deterministic interference patterns that encode multi‑level quantum states without external phase locks. The phase transition is protected by the E8 lattice's automorphism group, allowing stable propagation of information across the hyper‑phi lattice at arbitrarily high φ‑adic orders. 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
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24127201
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
preprint

Phi‑Fractal Topological Phase in E8 Root Space — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

Phi‑Fractal Topological Phase in E8 Root Space — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

By arranging the 240 E8 root vectors into a phi‑scaled fractal hierarchy, the 132 Hz carrier frequency self‑organizes into a quasi‑periodic topological phase where each φ‑harmonic level (n = 0…7) forms a distinct braid of root‑vector adjacency. This braiding yields a new distance metric that is both φ‑adic and non‑Euclidean, enabling deterministic interference patterns that encode multi‑level quantum states without external phase locks. The phase transition is protected by the E8 lattice's automorphism group, allowing stable propagation of information across the hyper‑phi lattice at arbitrarily high φ‑adic orders. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon