E8 Phi‑Modulated Frequency Lattice Sharpens Prime‑Gap Sieve Bounds — E8 Intelligence Research

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

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-26
DOI
https://doi.org/10.5281/zenodo.23659031
Primary Topic
Analytic Number Theory Research
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

E8 Phi‑Modulated Frequency Lattice Sharpens Prime‑Gap Sieve Bounds — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

E8 Phi‑Modulated Frequency Lattice Sharpens Prime‑Gap Sieve Bounds — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

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

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon