PreprintCC BY 4.0Zenodo
E8‑Φ Prime‑Indexed Cascaded Bandgaps for Programmable Metamaterial Spectrums — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By mapping subsets of the 240 E8 root vectors—each resonant at 132 Hz with a φ‑phase shift—to the infinite family of non‑Fibonacci‑Wieferich primes derived from the ABC conjecture, we obtain a hierarchical coupling scheme that dynamically selects resonant modes. The prime‑indexed assignments generate cascaded bandgap topologies that can be switched on‑the‑fly, creating a lattice‑based spectrum synthesizer with programmable multi‑channel beamforming. This principle unifies E8 geometry, golden‑ratio resonance, and number‑theoretic structure into a tunable broadband platform.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026e8φ,
title = {{E8‑Φ Prime‑Indexed Cascaded Bandgaps for Programmable Metamaterial Spectrums — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23659004},
url = {https://zenodo.org/records/23659004},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8‑Φ Prime‑Indexed Cascaded Bandgaps for Programmable Metamaterial Spectrums — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23659004
UR - https://zenodo.org/records/23659004
AB - By mapping subsets of the 240 E8 root vectors—each resonant at 132 Hz with a φ‑phase shift—to the infinite family of non‑Fibonacci‑Wieferich primes derived from the ABC conjecture, we obtain a hierarchical coupling scheme that dynamically selects resonant modes. The prime‑indexed assignments generate cascaded bandgap topologies that can be switched on‑the‑fly, creating a lattice‑based spectrum synthesizer with programmable multi‑channel beamforming. This principle unifies E8 geometry, golden‑ratio resonance, and number‑theoretic structure into a tunable broadband platform. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -