The sharp/flat Beilinson–Flach element main conjecture

Let $K$ be as in the source, let $\Lambda_K$ be the corresponding two-variable Iwasawa algebra, and let $\mathcal X^{\hat\bullet\forall}$ and $\mathcal X^{\bullet0}$ be the dual Selmer modules with the indicated signed and coarse local conditions. Let $\Delta_\circ$ be the corresponding signed Beilinson–Flach element, viewed in $\mathcal X^{\hat\bullet\forall}$. The sharp/flat Beilinson–Flach element main conjecture. Given $\circ\in\{\sharp,\flat\}$,

$$\operatorname{Char}(\mathcal X^{\hat\bullet\forall}/\Delta_\circ\Lambda_K)=\operatorname{Char}(\mathcal X^{\bullet0}).$$

This conjecture is an algebraic main-conjecture formulation comparing the quotient by a signed Beilinson–Flach element with a Selmer module having a different local condition. The supplied text gives no resolution status.