Stein's minimum-semidegree conjecture for oriented paths

Let $k\in\mathbb N$, and let $\delta^0(D)$ denote the minimum semidegree of an oriented graph $D$. Stein's conjecture. Every oriented graph with $\delta^0(D)>k/2$ contains every oriented path with $k$ edges. This would extend Jackson's result for directed paths to arbitrary orientations; it remains open.