The diamond-poset grid density conjecture

Let $D_2$ denote the diamond poset, and for $d\geq2$ let $\pi_{d,D_2}$ and $\pi^*_{d,D_2}$ be its weak and strong density parameters in the $d$-dimensional grid. The diamond-poset density conjecture. For every $d\geq2$,

$$\pi_{d,D_2}=\pi^*_{d,D_2}=2+\frac{1}{d}.$$

The paper identifies $D_2$ as the smallest poset for which the Boolean density conjecture has not been verified and gives the two-dimensional value, while the formula for larger dimensions remains conjectural.