The local track-number conjecture for planar graphs

Let $G$ be a planar graph, and let its local track-number be the minimum number of tracks in an injective track cover such that every vertex belongs to at most that many tracks.

Local track-number conjecture. The local track-number of $G$ is at most $3$.

The source identifies this as the only unresolved entry in its table of covering-number questions. It notes that the bound is known for bipartite planar graphs and for planar graphs of treewidth at most $3$, while the general planar case remains open.