The two-variable Hida deformation Iwasawa main conjecture

Let $\mathbf{f}$ be a Hida family of $p$-ordinary $p$-stabilized cusp newforms of tame level $N$, and let $\mathcal{T}$ be the nearly ordinary Hida deformation associated with $\mathbf{f}$. Fix an $\mathbf{I}^{\operatorname{n.ord}}_{\mathbf{f}}$-basis $\mathbf{B}^{\pm}_{\mathbf{f}}$ of the modules of $\mathbf{I}^{\operatorname{n.ord}}_{\mathbf{f}}$-adic modular symbols $\mathbf{MS}^{\pm}_{\mathbf{f}}$. Assume that the conditions $(\bf{NOR})$, $(\bf{IRR})$ and $(\bf{FIL})$ hold. Let $\operatorname{Sel}_{\mathbb{Q}}(\mathcal{T})$ denote the Selmer group and let $\operatorname{PD}$ denote Pontryagin duality. Then the Pontryagin dual $\operatorname{Sel}_{\mathbb{Q}}(\mathcal{T})^{\operatorname{PD}}$ is a finitely generated torsion $\mathbf{I}^{\operatorname{n.ord}}_{\mathbf{f}}$-module. Two-variable Hida deformation Iwasawa main conjecture. One has

$$\operatorname{char}_{\mathbf{I}^{\operatorname{n.ord}}_{\mathbf{f}}}\big(\operatorname{Sel}_{\mathbb{Q}}(\mathcal{T})^{\operatorname{PD}}\big)=\big(L_p(\{\mathbf{B}^{\pm}_{\mathbf{f}}\})\big),$$

where $L_p(\{\mathbf{B}^{\pm}_{\mathbf{f}}\})$ is a two-variable $p$-adic $L$-function attached to $\mathbf{B}^{\pm}_{\mathbf{f}}$. This is the Iwasawa main conjecture for the nearly ordinary Hida deformation associated with a Hida family; it predicts an equality between the characteristic ideal of the dual Selmer group and the principal ideal generated by the corresponding two-variable $p$-adic $L$-function. The supplied text does not state whether this conjecture has been proved or disproved.