The rational curves conjecture for projective IHS manifolds

Let $(X,H)$ be a projective irreducible holomorphic symplectic manifold over the complex numbers, with $H$ a polarization. The rational curves conjecture for projective IHS manifolds. $X$ contains infinitely many integral rational curves $C$, each of which rules a divisor linearly equivalent to some multiple of $H$. The conjecture is an analogue of the rational-curves conjecture for projective K3 surfaces. It is known for very general projective IHS manifolds of $K3^{[n]}$ and generalized Kummer type, while the source states that the conjecture is not otherwise present in the literature and remains open.