PreprintCC BY 4.0Zenodo
Phi‑Scaled Phononic Bandgaps in E8 Root‑Lattice Acoustic Metamaterials — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By mapping the 240 E8 root vectors onto a periodic array of elastic resonators tuned to the 132 Hz Vieta‑E8 fundamental, the golden‑ratio (φ) scaling of inter‑resonator spacing produces a hierarchy of complete phononic bandgaps whose edge frequencies follow the Vieta jumping recurrence xₙ₊₁ = kxₙ – xₙ₋₁ (k = 3). These bandgaps enable lossless, topologically protected phonon transport along defect lines that correspond to Weyl‑group reflection paths, linking number‑theoretic invariants to acoustic topology in an E8‑synthetic medium.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phiscaled,
title = {{Phi‑Scaled Phononic Bandgaps in E8 Root‑Lattice Acoustic Metamaterials — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446940},
url = {https://zenodo.org/records/23446940},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phi‑Scaled Phononic Bandgaps in E8 Root‑Lattice Acoustic Metamaterials — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446940
UR - https://zenodo.org/records/23446940
AB - By mapping the 240 E8 root vectors onto a periodic array of elastic resonators tuned to the 132 Hz Vieta‑E8 fundamental, the golden‑ratio (φ) scaling of inter‑resonator spacing produces a hierarchy of complete phononic bandgaps whose edge frequencies follow the Vieta jumping recurrence xₙ₊₁ = kxₙ – xₙ₋₁ (k = 3). These bandgaps enable lossless, topologically protected phonon transport along defect lines that correspond to Weyl‑group reflection paths, linking number‑theoretic invariants to acoustic topology in an E8‑synthetic medium. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -