Leader–Long antipodal geodesic conjecture

Let $Q_n$ be the $n$-dimensional hypercube, with antipodal vertices $v$ and $\bar v$ differing in every coordinate. Leader–Long conjecture. In every red-blue colouring of the edges of $Q_n$, there exists a geodesic path between antipodal vertices with at most one colour change. Equivalently, every antipodal edge-colouring, in which antipodal corresponding edges have different colours, contains a monochromatic geodesic path between antipodal vertices. This is presented as an open conjecture in the source.