Divisibility conjecture for optimal hyperplane-cover weights

Let $A$ be an extremal multidimensional matrix with deficiency $\delta$, and let $\Lambda=(\lambda_{i,j})$ be an optimal hyperplane cover of $A$.

Divisibility conjecture. Every entry $\lambda_{i,j}$ is an integer multiple of $\delta$.

The conjecture would impose a discrete structure on optimal hyperplane covers and, as the source observes, would imply uniqueness of the optimal cover. It is presented as an open conjecture, although the paper proves related consequences in special settings.