Bartnicki–Grytczuk–Niwczyk edge-weight $3$-choosability conjecture

Let $G=(V,E)$ be a nice graph, meaning a graph without isolated edges. A graph is edge-weight $3$-choosable if, for every assignment $L$ of a three-element set of real numbers to each edge, there is a proper edge weighting $w$ with $w(e)\in L(e)$ for every edge $e$. Bartnicki–Grytczuk–Niwczyk edge-weight $3$-choosability conjecture. Every nice graph is edge-weight $3$-choosable. The source explicitly states that this list variant of the 1-2-3 conjecture remains open.