Hedden–Watson finiteness conjecture for knot Floer homology

Let $K$ be an L-space knot with knot Floer homology $\widehat{\operatorname{HFK}}(K)$. Hedden–Watson's finiteness conjecture. There are only finitely many other knots whose Floer homology is isomorphic to $\widehat{\operatorname{HFK}}(K)$ as bi-graded groups. The rational surgery formula implies that such knots are also L-space knots, and the Alexander polynomial determines the knot Floer homology of an L-space knot. The conjecture is therefore equivalent to finiteness of L-space knots of bounded genus, and remains open in general.