Characterization of strong singularity by a real submatrix

Let \text{\text{$\mathversion{bold}$ A }}$\in\mathbb{IR}^{n\times n}$ be an interval matrix. A submatrix is real when all of its entries are degenerate intervals, and \text{\text{$\mathversion{bold}$ A }}$is **strongly singular** when every point matrix contained in it is singular. **Strong-singularity submatrix conjecture.** The interval matrix$\text{\text{\mathversion{bold}$A$}} is strongly singular if and only if it has a real submatrix of size $k\times\ell$ whose rank is $k+\ell-n-1$. This would provide a structural characterization of strong singularity, complementing the preceding results and the open question of finding a simpler computationally cheaper test; the converse is described in the source as open and hard.