Hypercube eigenfunctions with two strong nodal domains

Bıyıko{\u g}lu, Hordijk, Leydold, Pisanski, and Stadler conjectured that, for every $n\ge 3$ and $1\le i\le n-2$, the hypercube $Q_n$ admits a Laplacian eigenfunction with eigenvalue $2i$ and exactly two strong nodal domains. In this paper, we confirm this conjecture.