The exact minimum percolating-set size conjecture for 4-neighbour bootstrap percolation on hypercubes

Let $Q_d$ be the $d$-dimensional hypercube, and let $m(Q_d;4)$ denote the minimum cardinality of a set that percolates under the $4$-neighbour bootstrap process on $Q_d$. Exact-size conjecture. For all $d\geq4$ with $d\neq5$,

$$m(Q_d;4)=\left\lceil\frac{d(d^2+3d+14)}{24}\right\rceil+1.$$

The paper states that this would extend the main theorem to all $d\geq4$ except $d=5$, which was ruled out by exhaustive computer search; the claim is presented as a conjectural extension because the authors have proved it only for some values of $d$.