Potent relative Langlands duality

Let $G\circlearrowright M$ be a polarized hyperspherical $G$-variety with $M=T^*X$, and let $\check G\circlearrowright\check M$ be its Langlands-dual polarized hyperspherical variety with $\check M=T^*\check X$. Denote by ${\mathbf D}^{pot}_G(X)$ and ${\mathbf D}^{pot}_{\check G}(\check X)$ the corresponding potent categorical representations. Potent relative Langlands duality. The potent Langlands duality conjecture matches

$${\mathbf D}^{pot}_G(X)\quad\text{with}\quad {\mathbf D}^{pot}_{\check G}(\check X).$$

This is a potent upgrade of the relative and unipotent Langlands correspondences for dual spherical varieties. The source notes that the underlying unipotent conjecture is known in many cases, while the potent statement is proposed as a stronger conjectural extension.