Hàn–Person–Schacht minimum degree conjecture for perfect matchings in hypergraphs

Let $H$ be an $r$-uniform hypergraph on $n$ vertices, where $n$ is divisible by $r$, and let $m_d(r,n)$ be the smallest integer $m$ such that every $r$-uniform hypergraph $H$ on $n$ vertices with minimum $d$-degree $\delta_d(H)\geq m$ contains a perfect matching. Here $1\leq d<r/2$.

Hàn–Person–Schacht conjecture.

$$m_d(r,n) \sim \max\left\{\frac{1}{2}, 1-\left(\frac{r-1}{r}\right)^{r-d}\right\}{n-d \choose r-d}$$

This conjecture predicts the asymptotic minimum $d$-degree threshold for perfect matchings in the range $d<r/2$, extending the known upper bound of Hàn, Person and Schacht. The surrounding text does not state whether the conjecture has been resolved.