Positivity conjecture for the random-cluster polynomial $\mathcal{M}_{ef}(q)$

Let $G=(V,E)$ be a graph with positive edgeweights $x_e$, let $e,f\in E$ be distinct, and let $\mathcal{T}_A^B$ denote the random-cluster partition-function sums with edges in $A$ forced open and edges in $B$ forced closed. Define

$$\mathcal{M}_{ef}(q):=\frac{\mathcal{T}_e^f\mathcal{T}_f^e-\mathcal{T}_{ef}\mathcal{T}^{ef}}{x_ex_f(1-q)}.$$

Positivity conjecture for $\mathcal{M}_{ef}(q)$. For $0\leq q\leq1$ and positive edgeweights $x_e$, one has

$$\mathcal{M}_{ef}(q)\geq0.$$

The quantity is introduced by factoring the negative-correlation difference by $x_ex_f(1-q)$. The supplied text gives no resolution status.