PreprintCC BY 4.0Zenodo
E8 Root‑Vector Harmonic Lattice Tunes φ‑Defect Cascades to Quantize Hyperbolic Cusp Volumes — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By assigning each of the 240 E8 root vectors to a harmonic mode at integer multiples of the base 132 Hz frequency scaled by powers of the silver ratio φ, the recursive φ‑defect propagation forms a discrete ladder of resonance bands. Traversal of a defect across this lattice yields a quantized change in the cusp volume of associated hyperbolic alternating knots, directly linking the twist‑number bounds to the spectrum of Markov numbers encoded in the defect cascade. This provides a concrete mechanism for encoding topological information in E8‑based metamaterials through controllable phonon‑like excitations.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026rootvector,
title = {{E8 Root‑Vector Harmonic Lattice Tunes φ‑Defect Cascades to Quantize Hyperbolic Cusp Volumes — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23610350},
url = {https://zenodo.org/records/23610350},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Root‑Vector Harmonic Lattice Tunes φ‑Defect Cascades to Quantize Hyperbolic Cusp Volumes — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23610350
UR - https://zenodo.org/records/23610350
AB - By assigning each of the 240 E8 root vectors to a harmonic mode at integer multiples of the base 132 Hz frequency scaled by powers of the silver ratio φ, the recursive φ‑defect propagation forms a discrete ladder of resonance bands. Traversal of a defect across this lattice yields a quantized change in the cusp volume of associated hyperbolic alternating knots, directly linking the twist‑number bounds to the spectrum of Markov numbers encoded in the defect cascade. This provides a concrete mechanism for encoding topological information in E8‑based metamaterials through controllable phonon‑like excitations. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -