Stein's pseudo-semidegree conjecture for long antipaths

Let $G$ be an oriented graph. Its minimum pseudo-semidegree $\bar{\delta}^0(G)$ is the minimum among all non-zero in-degrees and out-degrees of its vertices; equivalently, it is the maximum $k$ such that every vertex has either out-degree $0$ or at least $k$, and either in-degree $0$ or at least $k$. Stein's pseudo-semidegree conjecture. If $\bar{\delta}^0(G)\geq k$, then $G$ contains an antipath of length $2k-1$. Here an antipath is an oriented path in which every vertex has in-degree $0$ or out-degree $0$. The paper investigates this conjecture for antipaths and proves that every oriented graph with minimum semidegree at least $k$ contains an antipath of length $2k-1$, but the supplied text does not state that the full pseudo-semidegree conjecture is resolved.