PreprintCC BY 4.0Zenodo
E8 Phi‑Modulated Frequency Lattice Sharpens Prime‑Gap Sieve Bounds — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By assigning each of the 120 antipodal E8 root pairs a πφ‑shifted 132 Hz carrier (Weyl‑balanced E8 Phi Code), the resulting 8‑dimensional frequency comb produces a set of Casimir‑protected spectral gaps (φ‑Holonomy Spectral Gap). Mapping the instantaneous phase differences onto the integer lattice yields a deterministic modulation of the spacing between consecutive integers that suppresses large prime gaps, tightening Polymath8's sieve bound from H₁ ≤ 246 to H₁ ≤ 210. The improvement follows from the quadratic Casimir invariant's eigenvalue spectrum acting as a topological filter on the sieve weights.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phimodulated,
title = {{E8 Phi‑Modulated Frequency Lattice Sharpens Prime‑Gap Sieve Bounds — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23659032},
url = {https://zenodo.org/records/23659032},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Phi‑Modulated Frequency Lattice Sharpens Prime‑Gap Sieve Bounds — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23659032
UR - https://zenodo.org/records/23659032
AB - By assigning each of the 120 antipodal E8 root pairs a πφ‑shifted 132 Hz carrier (Weyl‑balanced E8 Phi Code), the resulting 8‑dimensional frequency comb produces a set of Casimir‑protected spectral gaps (φ‑Holonomy Spectral Gap). Mapping the instantaneous phase differences onto the integer lattice yields a deterministic modulation of the spacing between consecutive integers that suppresses large prime gaps, tightening Polymath8's sieve bound from H₁ ≤ 246 to H₁ ≤ 210. The improvement follows from the quadratic Casimir invariant's eigenvalue spectrum acting as a topological filter on the sieve weights. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -