Kündgen–Ramamurthi's weak 4-choosability conjecture for planar graphs

A list assignment $L$ of a graph is symmetric if its colours are integers and, for every vertex $v$ and integer $i$, $i\in L(v)$ implies that $-i\in L(v)$. A graph is weakly $k$-choosable if it is $L$-colourable for every symmetric list assignment $L$ in which each list has size $k$. Kündgen–Ramamurthi's conjecture. Every planar graph is weakly $4$-choosable. This is stated as a strengthening of the Four Colour Theorem and was proposed by Kündgen and Ramamurthi; it remains open.