An n²-vertex characterization of inverse-M interval matrices

An interval matrix $[C-R,C+R]$ consists entirely of inverse-M matrices if and only if the $n^2$ vertices $C-D_iRD_j$ are inverse-M matrices, where $D_i$ is the diagonal matrix with $-1$ in position $i$ and $1$ elsewhere. This implies the conjectured $2n^2$-vertex criterion, which also tests $C+D_iRD_j$, and shows that half of those tests are unnecessary. The proof combines induction on principal submatrices, monotonicity of two-index Schur complements, and an adjugate lemma that rules out singularity without assuming regularity in advance. Zero entries, zero interval widths, and reducible matrices are allowed. Checking the $n^2$ vertices exactly takes $O(n^5)$ arithmetic operations.