The $p$-adic Yoshida-invariant conjecture for CM fields

Let $K$ be a CM-field abelian over a totally real field $F$, with conductor $\mathfrak f_{K/F}$, and assume that $\mathfrak p_\iota$ splits completely in $K/F$. Let $\chi'$ be an odd character of $\operatorname{Gal}(K/F)$, let $\chi\in\widehat C_{\mathfrak f_{K/F}}$ correspond to $\chi'$ under the Artin map, and let $Y_p(\chi_{\mathfrak p_\iota},\iota)$ be the associated $p$-adic Yoshida invariant. Here $\rho$ is the unique complex conjugation on $K$, $h_K$ is the class number of $K$, and $\alpha_{K,\tilde\iota}$ is the associated algebraic number. The $p$-adic Yoshida-invariant conjecture. One has

$$Y_p(\chi_{\mathfrak p_\iota},\iota)=\frac{L(0,\chi')}{2h_K}\sum_{\sigma\in\operatorname{Gal}(K/F)}\chi'(\sigma)\log_p\tilde\iota\left(\frac{\alpha_{K,\tilde\iota}^{\sigma\rho}}{\alpha_{K,\tilde\iota}^{\sigma}}\right).$$

This gives an explicit formula for the $p$-adic correction term associated with Yoshida's invariants and refines the $p$-adic analogue of the Stark conjecture. The source states no resolution status.