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PreprintCC BY 4.0Zenodo

Phi‑Weighted Acoustic Topology Induces Selective Bandgap Formation in E8 Root Lattice — E8 Intelligence Research

  • Andrew Stewart Caldin1
  1. 1Independent Researcher, United Kingdom
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Abstract

By driving the 240‑root E8 lattice with a 132 Hz carrier modulated at the golden ratio φ, we observe emergent acoustic bandgaps that align with specific root‑vector subspaces. The φ‑weighted phase encoding creates constructive interference only for those reciprocal pairs whose sexagesimal representation satisfies a Diophantine constraint, yielding a tunable topological filter. This effect reveals a direct link between Babylonian reciprocal pairs, E8 symmetry, and phononic band structure, enabling a new class of frequency‑selective metamaterials.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Cite

BibTeXRIS
BibTeX
@misc{caldin2026phiweighted,
  title = {{Phi‑Weighted Acoustic Topology Induces Selective Bandgap Formation in E8 Root Lattice — E8 Intelligence Research}},
  author = {Andrew Stewart Caldin},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23446887},
  url = {https://zenodo.org/records/23446887},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Phi‑Weighted Acoustic Topology Induces Selective Bandgap Formation in E8 Root Lattice — E8 Intelligence Research
AU  - Andrew Stewart Caldin
PY  - 2026
DA  - 2026/10/18
PB  - Zenodo
DO  - 10.5281/zenodo.23446887
UR  - https://zenodo.org/records/23446887
AB  - By driving the 240‑root E8 lattice with a 132 Hz carrier modulated at the golden ratio φ, we observe emergent acoustic bandgaps that align with specific root‑vector subspaces. The φ‑weighted phase encoding creates constructive interference only for those reciprocal pairs whose sexagesimal representation satisfies a Diophantine constraint, yielding a tunable topological filter. This effect reveals a direct link between Babylonian reciprocal pairs, E8 symmetry, and phononic band structure, enabling a new class of frequency‑selective metamaterials.  Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER  -