Darmon's rationality conjecture with Shimura reciprocity for Darmon points

Fix an integer $c$ prime to $D\cdot N$, let $\mathcal{O}_c$ be the order of the real quadratic field $F$ of conductor $c$, and let $Q\in\mathcal{F}_{Dc^2}$ represent a class of quadratic forms defining $\tau_Q\in\mathcal{H}_p^{(Dc^2)}$. Let $H_c^+$ be the strict ring class field of $F$ of conductor $c$, let $G_c^+=\operatorname{Gal}(H_c^+/F)$, and fix the localization at the prime above $p$. Darmon's Shimura reciprocity conjecture. The Darmon point $P_{\tau_Q}$ is the localization of a global point $P_c\in E(H_c^+)$, and, for every $\sigma\in G_c^+$, if $P_c$ localizes to $P_{\tau_Q}$, then $P_c^\sigma$ localizes to $P_{\tau_{Q^\sigma}}$. This is the explicit Galois-equivariant form of the rationality conjecture. It describes not only the field of definition of the global point but also the action of the strict ring class field Galois group on its localizations. The source presents it as a conjectural Shimura reciprocity law.