Two-neighbor directed percolation in all dimensions conjecture

For each $d\in\mathbb{N}$, let the $2$-DnG be the directed $2$-neighbor graph on $\mathbb{Z}^d$, and let $\theta^{\rm D}(2,d)$ be its percolation probability. Two-neighbor directed percolation conjecture. The $2$-DnG percolates in all dimensions $d\in\mathbb{N}$. Numerical simulations support the claim, and it would settle the open two-dimensional case together with the higher-dimensional cases; it remains open.