The chromatic number of the plane is at least 5 - a new proof

TL;DR

This paper provides a new proof that any 4-coloring of the plane necessarily contains two points exactly one unit apart with the same color, confirming a lower bound on the chromatic number of the plane.

Contribution

It introduces an alternative proof for the known fact that four colors are insufficient to color the plane without monochromatic unit distances.

Findings

Any 4-coloring of the plane contains a monochromatic pair at unit distance

The chromatic number of the plane is at least 5

New proof technique for the plane coloring problem

Abstract

We present an alternate proof of the fact that given any 4-coloring of the plane there exist two points unit distance apart which are identically colored.