Stein's conjecture on oriented paths in graphs of large semidegree

Let $G$ be an oriented graph, let $\b7$ denote its minimum semidegree, and let $k$ be a nonnegative integer. An orientation of the $k$-edge path is an oriented graph obtained by assigning a direction to each edge of an undirected path with $k$ edges. Stein's conjecture. Every oriented graph $G$ with minimum semidegree $\b7(G)>k/2$ contains every orientation of the $k$-edge path.

Jackson's theorem proves the directed-path case. Stein and Trujillo-Negrete proved the conjecture for oriented graphs containing no oriented $4$-cycle, while the general statement remains open; the paper studies two-block paths as a step toward it.