Yan–Peng conjecture on large linear hypergraphs being lambda-perfect

Let $r\geq 3$. An $r$-graph is linear if any two edges have at most one vertex in common, and it is lambda-perfect when its Lagrangian density equals the natural complete-hypergraph lower bound. Yan–Peng's conjecture. There exists $n$ such that every linear $r$-graph with at least $n$ vertices is lambda-perfect. The conjecture proposes that sufficiently large linear hypergraphs have the simplest possible Lagrangian density; the source attributes it to Yan and Peng and gives no resolution.