Asakura's characterization conjecture for the dlog image

Let $R$ be the ring of integers in an unramified extension $K$ of $\mathbb Q_p$, and let $\pi_R\colon X_R\to C_R$ be an elliptic surface over $R$ satisfying condition (Rat). Let $U^0_K$ and $U^0_{\overline K}$ denote the corresponding open elliptic surfaces over $K$ and an algebraic closure $\overline K$, and let $\Phi(X_R,D_R)_{\mathbb Z_p}$ be the subgroup defined in the preceding results. Characterization conjecture. The equality in the preceding inclusion should hold:

$$\operatorname{dlog}\varGamma(U^0_{\overline K},\mathcal{K}_2)\otimes_{\mathbb Z}\mathbb Q_p=\Phi(X_R,D_R)_{\mathbb Z_p}\otimes_{\mathbb Z_p}\mathbb Q_p.$$

This conjecture says that the dlog image is characterized by the numerical conditions on the Fourier coefficients. The source presents it as an expectation and gives no resolution status.