The non-commutative main conjecture for a CM elliptic curve

In the notation above, let $\mathcal{L}_E\ \epsilon\ K_1(\Lambda(\mathcal{G})_{S^*})$ be the conjectural $p$-adic $L$-function, let $X(E/F_\infty)$ be the Pontryagin dual of the Selmer group, and let $[X(E/F_\infty)]_D$ denote its base change to $K_0(\mathfrak{M}_{D,\mathcal{H}}(\mathcal{G}))$. Let $\partial$ be the boundary map in the localization sequence. Main conjecture. The $p$-adic $L$-function is a characteristic element of the Selmer-group dual:

$$\partial\mathcal{L}_E=[X(E/F_\infty)]_D.$$

This is the non-commutative main conjecture, relating the analytic $p$-adic $L$-function to the algebraic Selmer module. The supplied text does not indicate that it has been proved.