Dasgupta's algebraicity and reciprocity conjecture

Let $\mathfrak{b}$ be an invertible $\mathcal{O}$-ideal that is $\mathfrak{f}$-integral, let $\mathfrak{n}$ be an invertible $\mathcal{O}$-ideal satisfying

$$\Gamma_{\mathfrak{b}}(\mathfrak{f})\supseteq\mathcal{O}(\mathfrak{n}\infty)^{\times},$$

and let $L=K(\mathfrak{n}\infty)^{\langle\sigma_{\wp}\rangle}$. Dasgupta's algebraicity conjecture. The invariant $u_{D,\widetilde{\delta}}(\mathfrak{b},\mathfrak{f})$ is a strong $p$-unit in $L$, and for $c\in C_K$ with $\operatorname{rec}(c)=\sigma$,

$$u_{D,\widetilde{\delta}}(\mathfrak{b},\mathfrak{f})^{\sigma^{-1}}=c\star u_{D,\widetilde{\delta}}(\mathfrak{b},\mathfrak{f}).$$

This is the main algebraicity and Shimura reciprocity prediction for Dasgupta's invariant; the source does not report a resolution.