Quantum Hikita conjecture for Higgs–Coulomb duality

Let $X$ and $X^!$ be symplectically dual varieties arising respectively from Coulomb-branch and Higgs-branch constructions for the gauge theory $(G,N)$. Let $R$ be the coefficient ring and let $M_{eq}(X)$ and $M_{Kah}(X^!)$ denote the associated graded-trace and Calabi–Yau-specialized quantum $D$-modules. Quantum Hikita conjecture. There is an isomorphism of $R$-modules

$$M_{eq}(X) \cong M_{Kah}(X^!).$$

This is a categorical or module-theoretic expression of symplectic duality, relating Coulomb-branch graded traces to the quantum differential module of the dual Higgs branch. Its general validity is presented as conjectural.