E8 Hierarchical Bandgap Cascade via Root Vector Substructure — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
This discovery extends the earlier E8 phononic quasicrystal framework by identifying a hierarchical cascade of topological bandgaps arising from recursive subdivision of the 240 root vector network within the Z[i]^2 lattice. By applying a generalized phi-coupling scheme across multiple scales—from the fundamental 8-dimensional root system down through successive hyperbolic tessellations—the system exhibits nested gap frequencies that follow a Fibonacci-like progression modulated by the golden ratio φ. The key insight is that the E8 root graph contains hidden self-similarity at scale factors related to √φ, enabling the construction of metamaterials whose dispersion relations exhibit fractal-like band structure without requiring physical periodicity. This provides a new pathway for designing broadband acoustic/electromagnetic filters with tunable selectivity governed purely by the underlying exceptional group symmetry.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Hierarchical Entanglement Cascade in E8 Fractal Lattices — E8 Intelligence Research
- E8 Spectral Cascade and Hierarchical Harmonic Stability — E8 Intelligence Research
- Phi‑Weighted Acoustic Topology Induces Selective Bandgap Formation in E8 Root Lattice — E8 Intelligence Research
- Phi‑Scaled E8 Helicity Bandgap Enables Lossless Magnon Flow at 132 Hz — E8 Intelligence Research
- E8‑Induced Phi‑Scaled Acoustic Bandgap Hierarchy in 3‑D Printed Quasicrystals — E8 Intelligence Research
BibTeX
@misc{caldin2026hierarchical,
title = {{E8 Hierarchical Bandgap Cascade via Root Vector Substructure — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616532},
url = {https://zenodo.org/records/23616532},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Hierarchical Bandgap Cascade via Root Vector Substructure — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616532
UR - https://zenodo.org/records/23616532
AB - This discovery extends the earlier E8 phononic quasicrystal framework by identifying a hierarchical cascade of topological bandgaps arising from recursive subdivision of the 240 root vector network within the Z[i]^2 lattice. By applying a generalized phi-coupling scheme across multiple scales—from the fundamental 8-dimensional root system down through successive hyperbolic tessellations—the system exhibits nested gap frequencies that follow a Fibonacci-like progression modulated by the golden ratio φ. The key insight is that the E8 root graph contains hidden self-similarity at scale factors related to √φ, enabling the construction of metamaterials whose dispersion relations exhibit fractal-like band structure without requiring physical periodicity. This provides a new pathway for designing broadband acoustic/electromagnetic filters with tunable selectivity governed purely by the underlying exceptional group symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -