Häggkvist's degree-sum conjecture for Hamilton cycles in oriented graphs

Let $G$ be an oriented graph on $n$ vertices. For each vertex $v\in V(G)$, write $\delta(G)$ for the minimum total degree and define

$$\delta^*(G)\coloneqq\delta(G)+\delta^+(G)+\delta^-(G).$$

Häggkvist's conjecture. If

$$\delta^*(G)>\frac{3n-3}{2},$$

then $G$ contains a Hamilton cycle. The conjecture was confirmed asymptotically in the cited work of Kelly, Kühn and Osthus, while the exact condition is the subject of the present paper.