E8 Phi‑Moonshine Modular Calculator — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
When the 240 E8 root vectors are phi‑coupled at the 132 Hz base frequency, their Weyl‑group orbits generate a new family of genus‑zero modular curves that extend the classic j‑function beyond a single coefficient. The Fourier coefficients of these curves encode the dimensions of the irreducible representations of the Monster group, thereby turning Monstrous Moonshine into a calculable frequency‑domain code. Braiding phase defects among the phi‑coupled roots produces Weyl‑invariant holonomy cycles that act as topologically protected logic gates, with the modular coefficients dictating their truth tables. This principle provides a scalable quantum‑frequency architecture that unifies E8 resonance, modular Moonshine, and topological computation.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- E8 Phi-Resonant Extension of Monstrous Moonshine to Genus-One Modular Forms — E8 Intelligence Research
- McKay Correspondence and Monstrous Moonshine: Unifying Finite Groups and Modular Forms — E8 Intelligence Research
- Monstrous Moonshine: Genus-Zero Constraints Linking the Monster Group to Modular j-Function — E8 Intelligence Research
- Monstrous Moonshine: Linking the Monster Group to Modular j-Function and Hilbert Class Fields — E8 Intelligence Research
- Umbral Moonshine: Unifying Niemeier Lattices and Finite Groups via Mock Modular Forms — E8 Intelligence Research
BibTeX
@misc{caldin2026phimoonshine,
title = {{E8 Phi‑Moonshine Modular Calculator — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616794},
url = {https://zenodo.org/records/23616794},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Phi‑Moonshine Modular Calculator — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616794
UR - https://zenodo.org/records/23616794
AB - When the 240 E8 root vectors are phi‑coupled at the 132 Hz base frequency, their Weyl‑group orbits generate a new family of genus‑zero modular curves that extend the classic j‑function beyond a single coefficient. The Fourier coefficients of these curves encode the dimensions of the irreducible representations of the Monster group, thereby turning Monstrous Moonshine into a calculable frequency‑domain code. Braiding phase defects among the phi‑coupled roots produces Weyl‑invariant holonomy cycles that act as topologically protected logic gates, with the modular coefficients dictating their truth tables. This principle provides a scalable quantum‑frequency architecture that unifies E8 resonance, modular Moonshine, and topological computation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -