Conjectural frequency of regular twists with a rational point

Let $C/\mathbb Q$ be a genus-one hyperelliptic curve, let $E$ be its Jacobian, and let $\mathcal F_b$ be the twist family specified by the local data $b$. Let $\mathcal F_b(X)=\{d\in\mathcal F_b:|d|\leq X\}$, let $n_b=\dim_{\mathbb F_2}\mathcal S_b$, let $m_b\in\{0,1\}$ satisfy $m_b\equiv1+n_b\pmod2$, and let $\alpha(k)$ be the distribution from the paper's main Selmer theorem. Regular-twist frequency conjecture. One has

$$\lim_{X\rightarrow\infty}\frac{\#\{d\in\mathcal F_b(X):\delta(P)\in\operatorname{im}\delta_d\}}{\#\mathcal F_b(X)}=\sum_{r=0}^{\infty}\frac{\alpha(2r+m_b)}{2^{n_b+2r+m_b}-1}.$$

This is obtained by modeling the relevant nonzero Selmer element as uniformly distributed; the source presents it as a heuristic consequence of the Selmer-distribution theorem, with resolution not established.