BV compatibility for the mirror polyvector-field differential

Let $\mathcal{R}$ be a simple eigenray diagram, let $M_{\mathcal{R}}$ be the associated symplectic manifold, and let $\mathcal{Y}_{\mathcal{R}}$ be its proposed non-Archimedean mirror. Equip the polyvector fields in the polyvector-field conjecture with a differential by transporting the de Rham differential, and let the A-side carry its Batalin–Vilkovisky operator. BV compatibility conjecture. This differential is compatible with the BV operator on the A-side. The source presents this as a final expected compatibility in the mirror-symmetry framework and does not state that it is proved.