Li et al.'s rational sign-pattern minimum-rank conjecture

Let $S$ be a sign pattern matrix, let $t$ be its term rank, and let $r$ be the minimum rank of $S$ over the reals. The term rank is the smallest number of rows and columns needed to include all nonzero entries of the matrix.

Li et al.'s conjecture. If $r\geqslant t-2$, then the minimum rank of $S$ over the rationals is also $r$.

The conjecture concerns when the minimum rank of a sign pattern over the rationals agrees with its minimum rank over the reals. The paper states that it proves this conjecture and gives examples showing the optimality of the result.