An extension of the Erd\H{o}s-Tur\'{a}n additive base conjecture via generalized circles of partition

TL;DR

This paper extends the concept of circles of partition and applies it to prove the Erdős-Turán additive base conjecture, advancing understanding of additive number theory.

Contribution

It introduces an extension of circles of partition and uses this to prove a longstanding conjecture in additive number theory.

Findings

Proves the Erdős-Turán additive base conjecture.

Develops an extended framework of circles of partition.

Provides new tools for additive number theory analysis.

Abstract

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.