Large sparse hypergraphs are lambda-perfect conjecture

Let $r\geq 3$. An $r$-graph $G$ has $m$ edges and is lambda-perfect when its Lagrangian density equals the natural complete-hypergraph lower bound determined by its number of vertices. Sparse lambda-perfectness conjecture. There exists $m_0$ such that for an $r$-graph $G$ with $m\geq m_0$ edges, if the number of vertices in $G$ is at least $m(r-1)+1$, then $G$ is lambda-perfect. The source presents this as a conjecture supported by several preceding theorems, but supplies no resolution.