Felsner–Reuter conjecture for the linear extension diameter of Boolean lattices

Let $B_n$ denote the $n$-dimensional Boolean lattice, namely the poset of all subsets of $[n]$ ordered by inclusion, and let $\textmd{led}(B_n)$ denote its linear extension diameter.

Felsner–Reuter conjecture.

$$\textmd{led}(B_n) = 2^{2n-2} - (n+1) \cdot 2^{n-2}.$$

The paper presents this as a conjecture from Felsner and Reuter. The supplied context does not state whether this Boolean-lattice formula has been resolved, so its status is recorded as open pending verification.