Signed 4-choosability of planar graphs of girth at least 4

Let $(G,\sigma)$ be a signed planar graph, meaning that $G$ is a planar graph equipped with a signature $\sigma$. Its girth is the length of its shortest cycle. Girth-four signed choosability conjecture. Every signed planar graph of girth at least $4$ is signed $4$-choosable. This would improve the known upper bound for signed planar graphs of girth at least $5$, for which the source asks whether the signed list chromatic number is $3$; the conjecture itself is presented as an open problem.