Signs-model conjecture for connectivity of the three-dimensional hypercube

For $p>0.55$, let $Q_3$ be the three-dimensional hypercube and let $\mathcal{D}_{\geq p}(Q_3)$ be the class of 1-independent percolation models on $Q_3$ in which every edge is open with probability at least $p$. In the signs model, vertices are independently assigned signs $+$ and $-$, and an edge is open exactly when its endpoints have the same sign.

Signs-model conjecture. Among models in $\mathcal{D}_{\geq p}(Q_3)$, the signs model minimises the probability that $Q_3$ is connected.

The statement is based on computational evidence and is presented as unknown in the supplied text.