Odd-dimensional hypercube path-pairability conjecture

For $k\in\mathbb{N}$, let $Q_{2k+1}$ denote the $(2k+1)$-dimensional hypercube. A graph is path-pairable if every pairing of its vertices can be joined by pairwise edge-disjoint paths. Odd-dimensional hypercube conjecture. For every $k\in\mathbb{N}$,

$$Q_{2k+1}$$

is path-pairable. The source notes that even-dimensional hypercubes are not path-pairable, while $Q_1$ and $Q_3$ are path-pairable and the cases of odd dimension at least five were open.