Stein's path-orientation conjecture for oriented graphs

Let $G$ be an oriented graph, and let $4\delta^0(G)4$ denote its minimum semidegree, the minimum of the in-degree and out-degree over all vertices. An oriented path of length $\ell$ is an orientation of a path with $\ell$ edges. Stein's conjecture. Every oriented graph $G$ contains all oriented paths of length $2\delta^0(G)-1$. The bound is best possible by considering disjoint unions of regular tournaments on $2\delta^0(G)-1$ vertices. The conjecture is supported by several partial results, including the directed-path case and cases with one change in direction, but its arbitrary-orientation case is not resolved in the supplied text.