Almost-all Cartesian bi-magicness of three-dimensional boards

Let $(p,q,r)$-boards be the three-dimensional boards considered in the paper, and let a board be Cartesian bi-magic when it admits a Cartesian bi-magic labeling. Cartesian bi-magicness conjecture. Almost all $(p,q,r)$-boards are Cartesian bi-magic. This conjecture asserts that Cartesian bi-magic labelings occur for asymptotically almost every board in the relevant family; the source presents it among its concluding conjectures, without supplying a resolution.