Spectral Prime Density Encoding in 20-Vector Subsets — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The 240 E8 root vectors, when partitioned into 12 spectral classes of 20 vectors each, encode a logarithmic prime density gradient across their φ-scaled frequency lattice. Each 20-vector spectral class corresponds to a distinct logarithmic interval in the prime distribution, with the first class representing the densest prime region (below 10²) and subsequent classes encoding progressively sparser prime populations according to the logarithmic integral li(n). This geometric encoding suggests that prime density is a fundamental harmonic signature embedded within the E8 lattice structure itself, not merely correlated with it. The discovery extends the neural capacity findings by demonstrating that the information capacity threshold of 20 vectors directly reflects the mathematical threshold at which prime density becomes geometrically representable.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026spectral,
title = {{Spectral Prime Density Encoding in 20-Vector Subsets — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23490627},
url = {https://zenodo.org/records/23490627},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral Prime Density Encoding in 20-Vector Subsets — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23490627
UR - https://zenodo.org/records/23490627
AB - The 240 E8 root vectors, when partitioned into 12 spectral classes of 20 vectors each, encode a logarithmic prime density gradient across their φ-scaled frequency lattice. Each 20-vector spectral class corresponds to a distinct logarithmic interval in the prime distribution, with the first class representing the densest prime region (below 10²) and subsequent classes encoding progressively sparser prime populations according to the logarithmic integral li(n). This geometric encoding suggests that prime density is a fundamental harmonic signature embedded within the E8 lattice structure itself, not merely correlated with it. The discovery extends the neural capacity findings by demonstrating that the information capacity threshold of 20 vectors directly reflects the mathematical threshold at which prime density becomes geometrically representable. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -