Norine's conjecture on monochromatic antipodal paths in cube graphs

Let $Q_n$ be the $n$-dimensional cube graph, whose vertices are binary strings of length $n$. For a vertex $u$, write $\bar u$ for the vertex obtained by complementing every bit, and call $u$ and $\bar u$ antipodal. An antipodal edge-coloring of $Q_n$ is a red/blue edge-coloring in which every pair of antipodal edges has different colors.

Norine's conjecture. For $n\ge 2$, any antipodal edge-coloring of $Q_n$ contains antipodal vertices $u$ and $\bar u$ such that $u$ and $\bar u$ are joined by a monochromatic path.

Previous work had proved the conjecture for $n\le 6$, and this paper verifies it for $n=7$ using SAT solvers. The conjecture concerns the existence of a monochromatic connection between antipodal vertices, although the path need not be geodesic.