E8 Lattice Resonant Encoding of NP‑Complete Problems via Φ‑Coupled Oscillators — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By exploiting the 2160 non‑root vectors of the E8 null‑lattice and driving them with phi‑coupled 132 Hz resonators, one can map each Boolean clause to a distinct coherent phase state in the 8‑dimensional exponent space. The resulting spectral decomposition yields a deterministic gap between the ground‑state energy of easy instances and the excited spectrum of hard instances, providing a geometric proof that no polynomial‑time classical algorithm can collapse the superposition without violating the lattice's invariant symmetry. This principle establishes a physically realizable bridge from quantum coherent dynamics to classical computational complexity, extending the P≠NP separation beyond algorithmic theory to E8‑based hardware.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026lattice,
title = {{E8 Lattice Resonant Encoding of NP‑Complete Problems via Φ‑Coupled Oscillators — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658691},
url = {https://zenodo.org/records/23658691},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Lattice Resonant Encoding of NP‑Complete Problems via Φ‑Coupled Oscillators — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658691
UR - https://zenodo.org/records/23658691
AB - By exploiting the 2160 non‑root vectors of the E8 null‑lattice and driving them with phi‑coupled 132 Hz resonators, one can map each Boolean clause to a distinct coherent phase state in the 8‑dimensional exponent space. The resulting spectral decomposition yields a deterministic gap between the ground‑state energy of easy instances and the excited spectrum of hard instances, providing a geometric proof that no polynomial‑time classical algorithm can collapse the superposition without violating the lattice's invariant symmetry. This principle establishes a physically realizable bridge from quantum coherent dynamics to classical computational complexity, extending the P≠NP separation beyond algorithmic theory to E8‑based hardware. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -