Anti-directed 2-factor conjecture for dense directed graphs

Let $D$ be a directed graph of even order $n \geq 8$, and let $\delta(D)$ denote its minimum total degree. An anti-directed 2-factor is a spanning 2-regular subgraph whose cycle edges, viewed as arcs of $D$, alternate in direction along each cycle.

Anti-directed 2-factor conjecture. If

$$\delta(D) \geq \frac{1}{2}n,$$

then $D$ contains an anti-directed 2-factor.

This conjecture is motivated by the paper's $\delta(D)>\frac{24}{46}n$ sufficient condition and by examples showing that the threshold cannot be lowered in general. The source does not state whether the conjecture has been resolved.