Two-variable Iwasawa main conjecture for a Coleman family

Let $\mathbb{F}$ be a Coleman family over $\Lambda_{(k_0;r)}$ with slope $s\in\mathbb{Q}_{\geq 0}$, let $h\in\mathbb{Z}$ satisfy $h\geq s$, and let $\mathbb{T}\cong(\Lambda_{(k_0;r)})^{\oplus 2}$ be the associated Galois representation. Fix an $\Lambda_{(k_0;r),\mathcal{O}_K}$-basis $\Xi^\pm$ of $\mathbb{MS}(\Lambda_{(k_0;r),\mathcal{O}_K})^\pm$, and assume that the residual representation $\overline{\rho}:G_{\mathbb{Q}}\to\operatorname{GL}_2(\overline{\mathbb{F}}_p)$ associated to the family is irreducible on $G_{\mathbb{Q}_p}$. Let $\Lambda_{(k_0;r),\mathcal{O}_K}\widehat\otimes_{\mathbb{Z}_p}\Lambda_{\mathrm{cyc}}$ be the two-variable coefficient algebra, let $\mathcal{Z}(1)$ be the first Euler-system layer, and let $\mathbb{Q}_\Sigma$ be the maximal extension of $\mathbb{Q}$ unramified outside the specified finite set $\Sigma$. Two-variable Iwasawa main conjecture for a Coleman family. The module

$$H^2\left(\mathbb{Q}_\Sigma/\mathbb{Q},(\mathbb{T}\widehat\otimes_{\mathbb{Z}_p}\Lambda^\sharp_{\mathrm{cyc}})^*(1)\right)$$

is torsion, and

$$\operatorname{char}\left(H^1\left(\mathbb{Q}_\Sigma/\mathbb{Q},(\mathbb{T}\widehat\otimes_{\mathbb{Z}_p}\Lambda^\sharp_{\mathrm{cyc}})^*(1)\right)\big/\left(\Lambda_{(k_0;r),\mathcal{O}_K}\widehat\otimes_{\mathbb{Z}_p}\Lambda_{\mathrm{cyc}}\right)\mathcal{Z}(1)\right) = \operatorname{char}\left(H^2\left(\mathbb{Q}_\Sigma/\mathbb{Q},(\mathbb{T}\widehat\otimes_{\mathbb{Z}_p}\Lambda^\sharp_{\mathrm{cyc}})^*(1)\right)\right).$$

The conjecture is the two-variable analogue of the Iwasawa main conjecture for a Coleman family; the supplied text presents it after constructing the relevant Euler system, but gives no resolution.