The signed planar signature-packing conjecture

A signed graph is said to pack when its signature packing number attains the upper bound given by its negative girth. Let $\mathcal{C}_{10}$ and $\mathcal{C}_{11}$ be the classes of signed graphs described in the source; in particular, $\mathcal{C}_{10}$ is the class of signed bipartite graphs, while members of $\mathcal{C}_{11}$ can be switched to have all edges negative.

Signed planar signature-packing conjecture. Any signed planar graph in

$$\mathcal{C}_{10}\cup\mathcal{C}_{11}$$

packs.

This is listed as a conjecture equivalent or closely connected to the signed projective cube homomorphism conjecture. The general assertion remains open.