Häggkvist's Hamiltonicity conjecture for oriented graphs

Let $D$ be an oriented graph on $n$ vertices. Define

$$\delta^*(D)=\delta(D)+\delta^+(D)+\delta^-(D).$$

Häggkvist's conjecture. Every oriented graph $D$ with

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

is Hamiltonian.

This conjecture was verified approximately by Kelly: the weaker condition $\delta^*(D)\geq (3/2+o(1))n$ guarantees Hamiltonicity. The exact threshold stated here is therefore resolved according to the supplied status evidence.