Mazur's torsionness conjecture for the elliptic-curve Selmer group

Let $E$ be an elliptic curve over a number field $K$, let $K_\infty/K$ be the cyclotomic $\mathbb{Z}_p$-extension, and write $\Gamma=\operatorname{Gal}(K_\infty/K)\cong\mathbb{Z}_p$. Let $\Lambda=\mathbb{Z}_p[[\Gamma]]$, and let ${\rm Sel}_{E}(K_\infty)[p^\infty]^{\lor}$ be the Pontryagin dual of the $p$-primary Selmer group.

Mazur's conjecture. The $\Lambda$-module ${\rm Sel}_{E}(K_\infty)[p^\infty]^{\lor}$ is a finitely generated torsion $\Lambda$-module.

This is the basic torsionness assertion in the Iwasawa theory of elliptic curves. The supplied source does not state whether it is known or open in this generality.