Nodal rational curves conjecture for very general polarized K3 surfaces

Let $(X,L)$ be a very general polarized $K3$ surface. A rational curve in $|L|$ is a curve of geometric genus $0$. Nodal rational curves conjecture. All rational curves in $|L|$ are nodal. The case of rational curves is a genuine exception to the preceding nodality result in the source, which gives examples with cusps on special quartic sections; the conjecture predicts that such singularities do not occur for a very general polarized $K3$ surface and is important for enumerative formulas for rational curves.