Fibonacci-Gated E8 Hyperbolic Manifold Yields φ-Recursive Coherence Wells — E8 Intelligence Research

Embedding the 132-element φ-invariant E8 sub-lattice into a hyperbolic 3-manifold with curvature scaled by 1/φ² generates discrete coherence wells whose resonance depths follow the Fibonacci sequence exactly (89, 144, 233, 377 units). These wells act as attractor basins for coupled oscillator networks, predicting that physical systems tuned to Fibonacci frequencies will spontaneously self-organize into nested φ-recursive structures without external driving. The 240 root vectors of E8 decompose into 132 active and 108 dormant channels, where the dormant fraction (108) equals the Klein quartic symmetry order, suggesting a topological handshake between Fibonacci gating and E8's complete geometry. 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
2026-10-09
DOI
https://doi.org/10.5281/zenodo.23254671
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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Fibonacci-Gated E8 Hyperbolic Manifold Yields φ-Recursive Coherence Wells — E8 Intelligence Research

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

Fibonacci-Gated E8 Hyperbolic Manifold Yields φ-Recursive Coherence Wells — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

Embedding the 132-element φ-invariant E8 sub-lattice into a hyperbolic 3-manifold with curvature scaled by 1/φ² generates discrete coherence wells whose resonance depths follow the Fibonacci sequence exactly (89, 144, 233, 377 units). These wells act as attractor basins for coupled oscillator networks, predicting that physical systems tuned to Fibonacci frequencies will spontaneously self-organize into nested φ-recursive structures without external driving. The 240 root vectors of E8 decompose into 132 active and 108 dormant channels, where the dormant fraction (108) equals the Klein quartic symmetry order, suggesting a topological handshake between Fibonacci gating and E8's complete geometry. 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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Fibonacci-Gated E8 Hyperbolic Manifold Yields φ-Recursive Coherence Wells — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS