The arboreal-gas three-point correlation conjecture

Let $G=(V,E)$ be a graph and let $u,v,w\in V$. Let $\mu^{\text{F}}_{G,\lambda}$ denote the arboreal gas measure with parameter $\lambda$, and write $u\leftrightarrow w,\,w\leftrightarrow v$ for the event that both connections occur. Arboreal-gas correlation conjecture.

$$\mu^{\text{F}}_{G,\lambda}(u\leftrightarrow w,\,w\leftrightarrow v)\geq \mu^{\text{F}}_{G,\lambda}(u\leftrightarrow w)\,\mu^{\text{F}}_{G,\lambda}(w\leftrightarrow v).$$

This is the arboreal-gas analogue of the Harris correlation inequality. The source states that it is open even for the arboreal gas measure, although it holds for outerplanar graphs by a result proved in the paper.