Li–Ni conjecture on L-space-knot Floer homology and iterated torus knots

Let $K$ be a knot whose Floer homology agrees with that of an L-space knot, and suppose the Alexander polynomial of that L-space knot has all its roots on the unit circle. Li–Ni conjecture. Then $K$ is an iterated torus knot. This conjecture concerns a particularly restricted subclass of L-space knots and is presented as a more plausible coarse-detection statement than the unrestricted finiteness conjecture.