List Erdős–Neumann-Lara conjecture

Let $G$ be a graph. Its list chromatic number $\chi_{\ell}(G)$ is the least integer $r$ such that every assignment of lists of $r$ colours to the vertices admits a proper list colouring. For an orientation $D$ of $G$, define its list dichromatic number $\vec\chi_{\ell}(D)$ analogously, using list colourings in which every colour class induces an acyclic digraph, and let

$$\vec\chi_{\ell}(G)=\max_D\vec\chi_{\ell}(D),$$

where the maximum is over all orientations $D$ of $G$.

List Erdős–Neumann-Lara conjecture. For every integer $k$ there is an integer $f(k)$ such that, for every graph $G$, $\chi_{\ell}(G)\geq f(k)$ implies $\vec\chi_{\ell}(G)\geq k$.

The paper states that it proves this list version of the Erdős–Neumann-Lara conjecture, so the claim is resolved by the source's results.