Czerwiński–Grytczuk–Żelazny's additive colouring conjecture

Let $G$ be a graph, let $\chi(G)$ be its chromatic number, and let $\chi_\Sigma^v(G)$ be the least $k$ for which a vertex weighting from $\{1,\ldots,k\}$ properly colours adjacent vertices by the sums of the weights on their neighbours.

Czerwiński–Grytczuk–Żelazny's conjecture. For every graph $G$,

$$\chi_\Sigma^v(G)\leq \chi(G).$$

This asks whether the additive colouring number is always bounded by the ordinary chromatic number. The source presents it as open, with partial results for trees and bipartite planar graphs in the list-setting discussion.