Karoński–Łuczak–Thomason 1-2-3 Conjecture

Let $G$ be a graph without isolated edges. An edge coloring $f:E\to\{1,2,\dots,k\}$ assigns a weight $\sigma(v)=\sum_{v\in e}f(e)$ to each vertex; adjacent vertices are distinguished when their weights differ, and $\chi_{\Sigma}(G)$ is the least $k$ for which such an edge coloring distinguishes every adjacent pair. 1-2-3 Conjecture. For every graph $G$ without isolated edges,

$$\chi_{\Sigma}(G)\leq 3.$$

The text states that Keusch confirmed this conjecture in 2024, so it is solved.