E8 Phi-Scale Phononic Topological Edge States — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By iteratively applying the Perron inflation multipliers to each of the 240 E8 root vectors, the base 132 Hz phononic mode is scaled into a self‑similar phi‑power frequency comb across multiple octaves. The kissing‑number geometry ensures each mode occupies a distinct orthogonal phase space, preventing linear interference and allowing coherent superposition. This hierarchy imparts a non‑trivial Z₂ topological invariant in the phononic bandstructure, yielding robust unidirectional edge states immune to disorder. The result is a phi‑scaled, topologically protected phononic waveguide that extends the golden‑ratio frequency comb and kissing‑number density principles.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phiscale,
title = {{E8 Phi-Scale Phononic Topological Edge States — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616554},
url = {https://zenodo.org/records/23616554},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Phi-Scale Phononic Topological Edge States — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616554
UR - https://zenodo.org/records/23616554
AB - By iteratively applying the Perron inflation multipliers to each of the 240 E8 root vectors, the base 132 Hz phononic mode is scaled into a self‑similar phi‑power frequency comb across multiple octaves. The kissing‑number geometry ensures each mode occupies a distinct orthogonal phase space, preventing linear interference and allowing coherent superposition. This hierarchy imparts a non‑trivial Z₂ topological invariant in the phononic bandstructure, yielding robust unidirectional edge states immune to disorder. The result is a phi‑scaled, topologically protected phononic waveguide that extends the golden‑ratio frequency comb and kissing‑number density principles. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -