Voisin's moving rational curve conjecture for projective IHS varieties

Let $X$ be a projective irreducible holomorphic symplectic variety of dimension $2n$. A primitive rational curve means a rational curve whose cohomology class is primitive. Voisin's moving rational curve conjecture. There is a primitive rational curve on $X$ which moves in a $(2n-2)$-dimensional family. The conjecture would provide a key geometric source of moving rational curves on projective irreducible holomorphic symplectic varieties and is used as a model for the argument in the paper; the source does not state that it has been resolved in this generality.