Prime Scalar Field Claim Lacks Proof; PNT Proven via Mean Value Theorem — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-15
DOI
https://doi.org/10.5281/zenodo.22762166
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Prime Scalar Field Claim Lacks Proof; PNT Proven via Mean Value Theorem — E8 Intelligence Research

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

Prime Scalar Field Claim Lacks Proof; PNT Proven via Mean Value Theorem — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Prime number distribution may be governed by a "Prime Scalar Field" framework, but the provided sources are video titles/abstracts, not peer-reviewed equations; the only concrete mathematical result is a simple proof of the Prime Number Theorem (PNT) via the Mean Value Theorem for arithmetic functions. | MATH: PNT: π(x) ~ x / ln(x); asymptotic error term O(x e^{-c√ln x}) (classical). The arXiv paper (1510.03465) proves PNT and Dirichlet's theorem using elementary mean-value properties of arithmetic functions and zeta function — no new constants, ratios, or exotic symmetries are stated in the abstract. | CONNECTION: No explicit geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic) appears in the provided text. The "Prime Scalar Field" video title suggests a field-theoretic analogy, but without equations, no rigorous link to lattice structures or root systems can be extracted. | DEPTH: 3 — The PNT proof is elegant but classical; the "hidden pattern" cl 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 Scalar Field Claim Lacks Proof; PNT Proven via Mean Value Theorem — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS