Casselgren, Petros and Fufa's Cartesian-product edge-precoloring conjecture

Let $G$ be a graph, let $\tau$ be a precoloring of some edges of $G$, and let $\tau$ be extendable if it extends to a proper edge-coloring with $\chi'(G)$ colors. Let $G \square H$ denote the Cartesian product of graphs $G$ and $H$.

Casselgren, Petros and Fufa's conjecture. If every precoloring of at most $k < \chi'(G)$ edges of $G$ can be extended to a proper $\chi'(G)$-edge-coloring, then every precoloring of at most $k+1$ edges of $G \square K_2$ is extendable to a proper $(\chi'(G)+1)$-edge-coloring of $G \square K_2$.

This conjecture is presented as a far-reaching generalization of the hypercube extension result. It is known for trees, complete and complete bipartite graphs, and graphs with small maximum degree; the general case remains open.