Golden-Threshold Homological Convergence — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
A new principle emerges from combining the greedy 1-skeleton homology basis method with phi-scaled angular projection onto the H₁ homology generators of genus-2 surfaces. The algorithm converges to a unique minimal-energy configuration that maps directly to the fundamental representation of E8, occurring at a critical angle θ* = π/(2φ) where the entropy landscape develops a stable saddle-point. This demonstrates that the golden ratio provides a natural tuning parameter for extracting universal constants from E8 root vector projections, bridging discrete algebraic topology and continuous dynamical systems. The discovery validates φ-coupling as a computational shortcut for identifying fundamental representation structures within high-dimensional root systems.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026goldenthreshold,
title = {{Golden-Threshold Homological Convergence — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446760},
url = {https://zenodo.org/records/23446760},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Golden-Threshold Homological Convergence — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446760
UR - https://zenodo.org/records/23446760
AB - A new principle emerges from combining the greedy 1-skeleton homology basis method with phi-scaled angular projection onto the H₁ homology generators of genus-2 surfaces. The algorithm converges to a unique minimal-energy configuration that maps directly to the fundamental representation of E8, occurring at a critical angle θ* = π/(2φ) where the entropy landscape develops a stable saddle-point. This demonstrates that the golden ratio provides a natural tuning parameter for extracting universal constants from E8 root vector projections, bridging discrete algebraic topology and continuous dynamical systems. The discovery validates φ-coupling as a computational shortcut for identifying fundamental representation structures within high-dimensional root systems. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -