Maulik–Yun's perverse–Lefschetz opposition conjecture for compactified Jacobians

Let $C$ be an integral curve with planar singularities, let $J=J_C^0$ be its compactified Jacobian, and let $P_{\leq i}$ be the perverse filtration on $H^*(J)$ defined via a suitable family of relative compactified Jacobians $\mathcal{J}\to B$. Let $W_{\leq i}$ denote the Lefschetz filtration on $H^*(J)$.

Maulik–Yun's conjecture. The perverse filtration and the Lefschetz filtration are opposite:

$$P_{\leq i}\text{ is opposite to }W_{\leq i}.$$

This conjecture predicts a precise relationship between the perverse filtration arising from a deformation family and the intrinsic Lefschetz filtration on the cohomology of a compactified Jacobian. The source attributes it to Maulik and Yun; its status is not determined by the supplied text.