Goldfeld's asymptotic rank conjecture for quadratic twists

Let $E:y^2=f(x)$ be an elliptic curve over $\mathbb{Q}$. For a squarefree integer $d$, let $E^{(d)}$ be the quadratic twist of $E$ by $d$, and let $n_{E,r}^{\ast}(X)$ count fundamental discriminants $d$ with $|d|<X$ for which the rank of type $\ast\in\{\operatorname{alg},\operatorname{an}\}$ equals $r$. For $r\in\{0,1\}$, the family is ordered by $|d|$. Goldfeld's conjecture.

$$n_{E,r}^{\ast}(X)\sim\frac{1}{2}\sum_{|d|<X}1,$$

where the sum runs over fundamental discriminants $d$. This is the precise rank-$0$ and rank-$1$ asymptotic formulation of Goldfeld's conjecture for quadratic twist families; the source presents it as unresolved in general.