$p$-adic Birch–Swinnerton-Dyer conjecture for elliptic curves

Let $p$ be an odd prime and let $E$ be an elliptic curve with good ordinary reduction at $p$. Let $L_p(E)$ denote its cyclotomic $p$-adic $L$-function, and let $\mathrm{cork}_{\mathbb{Z}_p}$ denote the corank over $\mathbb{Z}_p$.

$p$-adic Birch–Swinnerton-Dyer conjecture.

$$\mathrm{cork}_{\mathbb{Z}_p}\mathrm{Sel}(\mathbb{Q},E[p^\infty])=\mathrm{ord}_{\chi=\mathbf{1}}L_p(E).$$

The claim is described as a $p$-adic analogue of Birch–Swinnerton-Dyer and follows in the discussion from the Iwasawa main conjecture framework. Its resolution status is not specified in the source.