Family Floer mirror identification conjecture

Let $\pi_\mathcal{R}:M_\mathcal{R}\to B_\mathcal{R}$ be the symplectic fibration, let $p_\mathcal{R}:\mathcal{Y}_\mathcal{R}\to B_\mathcal{R}$ be the corresponding rigid analytic mirror, and let $\mathcal{Z}\to B_\mathcal{R}^{reg}$ be the rigid analytic space with analytic torus fibration constructed by Hang Yuan. Family Floer mirror identification conjecture. $\mathcal{Z}$ is isomorphic as a rigid analytic space to $p_\mathcal{R}^{-1}(B_\mathcal{R}^{reg})$ in a fiber-preserving way. A conceptual proof is expected to use closed-open string maps relating sections of the sheaf $\mathcal{F}_\mathcal{R}$ to functions on the Family Floer mirror.