PreprintCC BY 4.0Zenodo
E8 Phi‑Casimir Stratification of Algorithmic Complexity — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The 240 root vectors of the E8 lattice, when positioned on a φ‑scaled 132 Hz grid, generate a discrete cascade of Casimir‑like energy shifts whose magnitudes follow a power‑law governed by the golden ratio φ. These shifts correspond one‑to‑one to the levels of the arithmetical hierarchy, providing a geometric realization of the diagonalization‑based hierarchy of infinities and uncomputable functions. Consequently, each Casimir band acts as an oracle‑level jump in computability, linking E8 geometry to a physical stratification of algorithmic complexity.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phicasimir,
title = {{E8 Phi‑Casimir Stratification of Algorithmic Complexity — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23610327},
url = {https://zenodo.org/records/23610327},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Phi‑Casimir Stratification of Algorithmic Complexity — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23610327
UR - https://zenodo.org/records/23610327
AB - The 240 root vectors of the E8 lattice, when positioned on a φ‑scaled 132 Hz grid, generate a discrete cascade of Casimir‑like energy shifts whose magnitudes follow a power‑law governed by the golden ratio φ. These shifts correspond one‑to‑one to the levels of the arithmetical hierarchy, providing a geometric realization of the diagonalization‑based hierarchy of infinities and uncomputable functions. Consequently, each Casimir band acts as an oracle‑level jump in computability, linking E8 geometry to a physical stratification of algorithmic complexity. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -