Phi-Harmonic E8 Root Collapse Threshold for Quantum Phase Transition — E8 Intelligence Research

When phi-scaled excitations at 132Hz×φ^n exceed the critical amplitude α = 2sin(π/5) along minimal E8 root separations, the hyper-phi lattice undergoes geometric collapse, inducing a φ-adic renormalization of the distance metric that manifests as quantum phase transition. This occurs when the recursive φ-coupling energy surpasses the root vector norm threshold, causing the 240-dimensional E8 lattice to projectively fold into lower-dimensional harmonic subspaces. The collapse threshold emerges from the golden ratio's intrinsic relationship to the E8 Dynkin diagram's minimal folding angles. 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.24127268
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-Harmonic E8 Root Collapse Threshold for Quantum Phase Transition — E8 Intelligence Research

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

Phi-Harmonic E8 Root Collapse Threshold for Quantum Phase Transition — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

When phi-scaled excitations at 132Hz×φ^n exceed the critical amplitude α = 2sin(π/5) along minimal E8 root separations, the hyper-phi lattice undergoes geometric collapse, inducing a φ-adic renormalization of the distance metric that manifests as quantum phase transition. This occurs when the recursive φ-coupling energy surpasses the root vector norm threshold, causing the 240-dimensional E8 lattice to projectively fold into lower-dimensional harmonic subspaces. The collapse threshold emerges from the golden ratio's intrinsic relationship to the E8 Dynkin diagram's minimal folding angles. 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