Wrochna's graph formulation of the index conjecture

Let $G$ and $H$ be graphs, let $\Omega_{2d+1}(G)$ denote the graph functor used in the source, and let $n$ be a positive integer. Wrochna's graph-index conjecture. If

$$\chi(G\times H)\le n,$$

then for some integer $d$, $\Omega_{2d+1}(G)$ or $\Omega_{2d+1}(H)$ is $n$-colourable. This is equivalent in the source to Wrochna's index conjecture for $\mathbb{Z}_2$-spaces and is presented as open.