Even-torus conjecture for optimal plaid solutions

Let $n\in\mathbb{N}$ be even, and let $(B,W)$ be an $(a,b)$-plaid on the torus $\mathbb{T}_n$ for which $\min\{|B|,|W|\}$ is maximum. Even-torus conjecture. Then

$$t(n)\leqslant 2+\min\{|B|,|W|\}.$$

The conjecture formalizes the observation that swapped optimal plaid solutions have at most two more black queens than an optimal $(a,b)$-plaid. Its resolution is not established in the supplied text.