E8 Phi‑Modulated Frequency Lattice Sharpens Prime‑Gap Sieve Bounds — E8 Intelligence Research
Year: 2026
Type: preprint
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
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223667449