Mazur's growth number conjecture for Selmer groups over p-extensions

Let $E/Q$ be an elliptic curve, let $K$ be an imaginary quadratic field, and let $p$ be a prime at which $E$ has good ordinary reduction. Let $\mathcal{K}/K$ be a $\mathbb{Z}_p$-extension in which all primes of bad reduction for $E$ remain finitely decomposed. Write $\mathcal{K}_n$ for the degree-$p^n$ layer of $\mathcal{K}$, and let $\mathcal{K}_{\mathrm{ac}}$ denote the anticyclotomic $\mathbb{Z}_p$-extension of $K$. The pair $(E,K)$ is called generic if $E$ does not have complex multiplication by an order in $K$, and exceptional otherwise; its sign is the sign of the relevant functional equation.

Mazur's growth number conjecture. For all sufficiently large $n$,

$$\operatorname{corank}_{\mathbb{Z}_p}\operatorname{Sel}_{p^\infty}(E/\mathcal{K}_n)=cp^n+O(1),$$

where

$$c=\begin{cases}0&\text{if }\mathcal{K}\ne\mathcal{K}_{\mathrm{ac}}\text{ or }(E,K)\text{ has sign }+1,\\1&\text{if }\mathcal{K}=\mathcal{K}_{\mathrm{ac}},\ (E,K)\text{ is generic, and has sign }-1,\\2&\text{if }\mathcal{K}=\mathcal{K}_{\mathrm{ac}},\ (E,K)\text{ is exceptional, and has sign }-1.\end{cases}$$

The conjecture predicts the asymptotic growth of Selmer-group coranks in the finite layers of a $\mathbb{Z}_p$-extension, distinguishing the anticyclotomic extension and the generic or exceptional nature of the pair. Its resolution status is not specified in the supplied text.