Regulator image conjecture for mock plectic invariants

Let $E$ be an elliptic curve, let $K$ be an imaginary quadratic field, let $H_c$ be the relevant ring class field, and let $\chi$ be a character of $\Delta_c$. Let $\mathcal{K}\colon E(H_c)\to\operatorname{H}^1_f(H_c,V_p(E))$ be the Kummer map, and let $\mathcal{K}_p^{-a_p}$ be the $(-a_p)$-isotypic local Kummer map obtained from localization at $p$. The regulator is the map

$$\bigwedge^2 E(H_c)^\chi\longrightarrow \operatorname{H}^1_f(H_c,V_p(E))^\chi\otimes_{\mathbb{Q}_p}\operatorname{H}^1_f(K_p,V_p(E))^{-a_p},$$ $$P\wedge Q\longmapsto \mathcal{K}(P)\otimes\mathcal{K}_p^{-a_p}(Q)-\mathcal{K}(Q)\otimes\mathcal{K}_p^{-a_p}(P).$$

Regulator image conjecture. If $L(E/K,\chi,1)=0$, then $\mathcal{Q}^\chi$ belongs to the image of this regulator. This predicts a direct relation between the mock plectic invariant and global points in $E(H_c)^\chi$, via the global and local Kummer maps.