Five-list capital-colouring conjecture for plane graphs

Let $G$ be a plane graph, and assign to each vertex $v$ a list of five integers. A capital colouring is a colouring in which every face contains a unique vertex coloured with the maximal colour appearing on that face. Five-list capital-colouring conjecture. If each vertex of a plane graph is assigned a list of five integers, then there exists a capital colouring assigning each vertex a colour from its list. The ordinary five-choosability bound is known to be tight, whereas the corresponding capital-colouring list statement is proposed here and remains open.