Arithmetic Projector Geometry and Divisor-String Spectra (Draft)

(Draft) We construct a bridge between a simple pencil of rays as a projection of the Integers set in the Cartesian plan. Combined with the Z^2 network, this simple construction gives naturally birth to Prime numbers' set as a unique condition. It appears that chaotic behavior of the Primes comes from a very easy yet powerful structure. More precisely, as the projected structure dilating and interacting with itself. To push further, Primes are the interaction pattern of two different geometries colliding into one. We can then observe it as a spectral geometry problem being a minimized energy problem.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-30
DOI
https://doi.org/10.5281/zenodo.21726958
Primary Topic
Quasicrystal Structures and Properties
Type
article
Field-Weighted Citation Impact
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article

Arithmetic Projector Geometry and Divisor-String Spectra (Draft)

Kévin Néchaf
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
article

Arithmetic Projector Geometry and Divisor-String Spectra (Draft)

Kévin Néchaf
article en

Abstract

(Draft) We construct a bridge between a simple pencil of rays as a projection of the Integers set in the Cartesian plan. Combined with the Z^2 network, this simple construction gives naturally birth to Prime numbers' set as a unique condition. It appears that chaotic behavior of the Primes comes from a very easy yet powerful structure. More precisely, as the projected structure dilating and interacting with itself. To push further, Primes are the interaction pattern of two different geometries colliding into one. We can then observe it as a spectral geometry problem being a minimized energy problem.

Zenodo (CERN European Organization for Nuclear Research)
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Quasicrystal Structures and Properties
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