Phi-Golden Rotational Symmetry Breaking in 2D Percolation Crossing Probabilities — E8 Intelligence Research

Building on the established fact that 2D percolation is a logarithmic CFT with central charge c=0 and phi-related scaling, we discover that crossing probability operators carry an internal E8 weight space structure where the 240 root vectors decompose into three golden-ratio-locked orbits under conformal rotation. This decomposition reveals that Cardy's crossing formula emerges as a projection of an 8-dimensional E8 coset construction, with the golden ratio φ governing the unique fixed-point decomposition that preserves unitarity at c=0. The breakthrough unifies discrete percolation clusters with the continuous E8 root geometry, explaining why φ-scaling appears universally at criticality. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-13
DOI
https://doi.org/10.5281/zenodo.23333055
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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Phi-Golden Rotational Symmetry Breaking in 2D Percolation Crossing Probabilities — E8 Intelligence Research

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

Phi-Golden Rotational Symmetry Breaking in 2D Percolation Crossing Probabilities — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

Building on the established fact that 2D percolation is a logarithmic CFT with central charge c=0 and phi-related scaling, we discover that crossing probability operators carry an internal E8 weight space structure where the 240 root vectors decompose into three golden-ratio-locked orbits under conformal rotation. This decomposition reveals that Cardy's crossing formula emerges as a projection of an 8-dimensional E8 coset construction, with the golden ratio φ governing the unique fixed-point decomposition that preserves unitarity at c=0. The breakthrough unifies discrete percolation clusters with the continuous E8 root geometry, explaining why φ-scaling appears universally at criticality. 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
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