Benevides–Griffiths–Przykucki conjecture on maximum percolation time

Let $M^d(n)$ denote the maximum percolation time in two-dimensional bootstrap percolation on the $d$-dimensional grid $[n]^d$. For fixed $d\geq 1$, the conjecture is

$$M^d(n)=\frac{6d^2-5d-1}{18}n^2+O(n).$$

Benevides–Griffiths–Przykucki conjecture. For all fixed $d\geq 1$,

$$M^d(n)=\frac{6d^2-5d-1}{18}n^2+O(n).$$

The lower bound is sharp for $d=2$, where it gives the constant $13/18$; the conjecture asserts that the same asymptotic formula gives the maximum percolation time in every fixed dimension.