Wong–Zhu's $(1,3)$-choosability conjecture

Let $G=(V,E)$ be a nice graph, meaning a graph without isolated edges. A graph is $(k,k')$-choosable if every assignment of a $k$-element list of real numbers to each vertex and a $k'$-element list to each edge admits a proper total weighting selecting each weight from its assigned list. Wong–Zhu's $(1,3)$-choosability conjecture. Every nice graph is $(1,3)$-choosable. This is presented as a strengthening of both the 1-2-3 conjecture and the edge-weight $3$-choosability conjecture; the source reports progress to $(1,5)$-choosability but does not state a resolution.