Zhang–Lu matching extremal conjecture for 3-uniform hypergraphs

Let $H$ be a 3-graph of order $n$, let $\sigma_2(H)$ be the minimum of $\deg(u)+\deg(v)$ over adjacent vertices $u,v$, and let $H_{n,s}^2$ be the corresponding extremal 3-graph. Zhang–Lu matching extremal conjecture. There exists $n_0\in\mathbb{N}$ such that, for every 3-graph $H$ of order $n\ge n_0$ without isolated vertices, if

$$\sigma_2(H)>2\left(\binom{n-1}{2}-\binom{n-s}{2}\right)$$

and $n\ge3s$, then $H$ contains no matching of size $s$ if and only if $H$ is a subgraph of $H_{n,s}^2$. This extends the stated extremal matching result for the relevant degree-sum threshold; the supplied source gives no resolution of the conjecture.