The oriented-cycle minimum-out-degree conjecture

Let $C$ be an oriented cycle, and let $|V(C)|$ denote its order. Oriented-cycle conjecture. Every digraph $D$ with $\delta^+(D)\geq 2k-1$ contains a subdivision of any oriented cycle of order $k$. Equivalently, the source conjectures the upper bound $\operatorname{mader}_{\delta^+}(C)\leq 2|V(C)|-1$ for every oriented cycle $C$; the source does not give a resolution.