Conjecture on the range of the percolation-time result

Let $T$ denote the percolation time in the $r$-neighbour bootstrap percolation model on $\mathbb{T}_n^d$, and let $t=t(n)$ be a time parameter. Range conjecture. Theorem~ holds for all $t$ in the range

$$t=o(\log n).$$

The preceding results establish the theorem only for a smaller range of $t$; extending it to $t=o(\log n)$ would determine the percolation time for all probabilities in the range $1-o(1)$.