Theoretical study demonstrates golden ratio-scaled band gaps and topological edge states in hyperbolic metamaterials, suggesting mechanisms for lossless information transport.
When the 240 E8 root vectors are projected onto the {5,3,4} hyperbolic honeycomb lattice while being driven at the 132 Hz fundamental tone, the resulting mode spectrum exhibits eigenvalue spacings that follow the golden ratio φ. This φ‑symmetric spacing creates a series of complete band gaps whose widths scale with φⁿ, allowing the lattice to support topologically protected edge states when a strain gradient is applied. The phenomenon predicts a new class of self‑organizing photonic or phononic metamaterials where information can be transported losslessly along defect‑free boundaries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Andrew Stewart Caldin (2026) studied this question.