The threshold conjecture for arbitrary oriented Hamilton cycles in random digraphs

Let $D\sim\mathcal D(n,p)$ be a random directed graph on vertex set $[n]$, where each possible arc is present independently with probability $p$, and let $C$ be a Hamilton cycle with an arbitrary orientation. Threshold conjecture for arbitrary oriented Hamilton cycles. If

$$p=\frac{\ln n+\omega(1)}{n},$$

then $D$ contains a copy of $C$ with high probability. This conjecture seeks the exact appearance threshold for an arbitrary oriented Hamilton cycle; the corresponding threshold for consistently oriented Hamilton cycles is known, while the arbitrary-orientation case is presented here as open.