Boundedness conjecture for d-invariants on abelian Torelli subgroups

Let $S$ be a genus $g$ surface embedded in a homology sphere $Y$, and let $H$ be an abelian subgroup of the Torelli group. Boundedness conjecture. The set

$$\{d(Y_\phi) \mid \phi \in H\}$$

is bounded. This conjecture predicts that the Heegaard Floer correction terms of the homology spheres obtained from $Y$ by the mapping classes in an abelian Torelli subgroup remain uniformly bounded, strengthening the preceding boundedness result for abelian groups generated by separating twists and bounding pair maps.