The Lens of the Primes

How the lens of "The Fold and the Lens" connects to the Riemann zeros and the primes. Established results and proposals are kept separate throughout. Every number is reproducible from riemann_explicit.py, except where a figure is attributed to a companion paper and said to be so. Earned, and open — the one-line version. Earned: the primes→zeros reconstruction; the atomszeros GUE statistical link; the cavity's measured GOE fingerprint against its controls. Open: the Riemann Hypothesis itself, and any size→zero map. Closed against us: an "end of the zeros" — the zeros are proven infinite. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23848718
Primary Topic
Analytic Number Theory Research
Type
preprint
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The Lens of the Primes

James Norman Ibbotson
3 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

The Lens of the Primes

James Norman Ibbotson
preprint en

Abstract

How the lens of "The Fold and the Lens" connects to the Riemann zeros and the primes. Established results and proposals are kept separate throughout. Every number is reproducible from riemann_explicit.py, except where a figure is attributed to a companion paper and said to be so. Earned, and open — the one-line version. Earned: the primes→zeros reconstruction; the atomszeros GUE statistical link; the cavity's measured GOE fingerprint against its controls. Open: the Riemann Hypothesis itself, and any size→zero map. Closed against us: an "end of the zeros" — the zeros are proven infinite. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.

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