Feder–Subi conjecture on antipodal paths with few colour changes

Let $Q_n$) be the $n$-dimensional hypercube, with edge set $E(Q_n)$, and consider a 2-colouring of its edges. Two vertices are antipodal if they differ in every coordinate.

Feder–Subi conjecture. Every 2-colouring of $E(Q_n)$ contains a path between some pair of antipodal vertices which changes colour at most once.

This strengthens Norine's conjecture, which asks only for a monochromatic path between some pair of antipodal vertices. The conjecture was proved in according to the supplied status evidence.