Ai–Guo–Freschi–Lo Ore-type conjecture for oriented Hamilton cycles

Let $G$ be an oriented graph, that is, a loopless directed graph with at most one edge between any two vertices. For a vertex, let its total degree be the number of incident edges, and let $\delta(G)$ be the minimum total degree. For an oriented cycle $C=v_1\ldots v_\ell v_1$, let $\sigma^+(C)$ and $\sigma^-(C)$ be the numbers of edges traversed in the forward and backward directions, respectively, and define

$$\sigma_{\max}(C)=\max\{\sigma^+(C),\sigma^-(C)\}.$$

For non-adjacent vertices $x,y$, meaning that there is no edge between them, define

$$\sigma_2(G)=\min\{d(x)+d(y)\mid x,y\in V(G)\text{ and }x,y\text{ are non-adjacent}\}.$$

Ai–Guo–Freschi–Lo conjecture. Let $G$ be an oriented graph on $n\geq 3$ vertices. If $\sigma_2(G)\geq n$, then $G$ contains a Hamilton cycle $C$ such that

$$\sigma_{\max}(C)\geq \frac{\sigma_2(G)}{2}.$$

This is an Ore-type extension of the oriented discrepancy analogue of Dirac's theorem. The supplied text says the problem was proposed as a conjecture by Ai et al.; the paper itself resolves the corresponding asymptotic result, but does not state that this exact conjecture has been solved.