The finite-basis conjecture for monotone grid classes

Let $M$ be a $0/\mathord{\pm}1$ matrix, and let $\operatorname{Grid}(M)$ be its monotone grid class, consisting of permutations whose entries in each nonzero cell are monotone with the sign prescribed by $M$.

Finite-basis conjecture for monotone grid classes. Every monotone grid class has a finite basis. The source notes that only limited cases are known, including skew-merged permutations and the monotone grid class of the $2\times2$ all-one matrix.