The regular-mask conjecture for generic matrix completability

Fix a rank $r$ and let $G(n,n,2r,2r)$ denote a uniformly random $2r$-regular bipartite graph with $n$ vertices in each part. A mask is completable when its observed entries determine a generic rank-$r$ matrix. Regular-mask conjecture. With high probability, $G(n,n,2r,2r)$ is completable. Moreover, it remains completable with high probability after $r^2$ edges are removed uniformly at random. The paper gives experimental evidence for this behavior and notes its contrast with the incoherent setting, as well as its consistency with proved results for two-dimensional distance matrices.