The degeneracy conjecture for proper conflict-free list coloring

A graph is $d$-degenerate if every nonempty subgraph has a vertex of degree at most $d$. A list assignment $L$ assigns a list of colors $L(v)$ to each vertex $v$; the graph is proper conflict-free $({\rm degree}+d)$-choosable if, for every such assignment satisfying $|L(v)|\geq \deg_G(v)+d$ for all vertices $v$, one can choose a color from each list to obtain a proper conflict-free coloring.

Degeneracy conjecture for proper conflict-free list coloring. If $G$ is a $d$-degenerate graph for some positive integer $d$, then $G$ is proper conflict-free $({\rm degree}+d)$-choosable.

The statement is motivated by the proved tree case, where the bound is $({\rm degree}+1)$, and by constructions showing that the corresponding bounds cannot generally be lowered. The supplied text gives no evidence that this conjecture has been resolved.