Prime Distribution as Scalar Field Beyond Random Noise — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-21
DOI
https://doi.org/10.5281/zenodo.22873732
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Prime Distribution as Scalar Field Beyond Random Noise — E8 Intelligence Research

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

Prime Distribution as Scalar Field Beyond Random Noise — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Prime distribution may encode a scalar field structure beyond random noise, with new proofs of PNT via mean-value theorems | MATH: PNT π(x) ~ Li(x) ~ x/ln(x); zeta function ζ(s) critical line Re(s)=1/2; Dirichlet L-functions; mean-value theorem for arithmetic functions (arXiv:1510.03465v2) | CONNECTION: No explicit 0.382/0.618/0.786/1.618/2.618 or base-60 or crystallographic symmetry appears in the provided abstracts — only the "Prime Scalar Field" video title suggests a geometric framework, but no equations are given | DEPTH: 4/10 — the arXiv proof is rigorous but classical; the "scalar field" claim is unverified and likely speculative without formal math **Precise extraction:** 1. **Key mathematical insight:** - The arXiv paper (1510.03465v2) proves PNT and Dirichlet's theorem using only the mean value theorem for arithmetic functions and elementary zeta properties — a simplification of classical analytic number theory. - The "Prime Scalar Field" video claims hid 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
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Prime Distribution as Scalar Field Beyond Random Noise — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS