The list chromatic number versus list vertex arboricity conjecture

Let $G$ be a graph. Write $ch(G)$ for its choice number and $ch_{\mathcal F}(G)$ for its list vertex arboricity, where $\mathcal F$ is the family of forests.

List colouring conjecture.

$$ch(G)\leq 2ch_{\mathcal F}(G).$$

This conjecture was proposed in the cited literature and asks whether the ordinary choice number is always at most twice the list vertex arboricity. Its resolution status is not specified in the source.