Heegaard Floer correction-term conjecture for finite knot surgeries

A finite manifold $Y$ is a rational homology sphere with finite fundamental group, and $d(Y,\mathfrak{t})$ denotes its Heegaard Floer correction term for a $b\mathfrak{t}d$ spin${}^c$ structure. Correction-term conjecture. The Heegaard Floer correction terms $d(Y,\mathfrak{t})$ are sufficient to distinguish which finite manifolds are knot surgeries. This would provide a complete Heegaard Floer obstruction to recognizing finite manifolds obtained by surgery on knots; the paper reports that the correction term was sufficient in all but one of the cases studied, but gives no resolution in general.