Jordán and Garamvölgyi's separator conjecture for globally linked pairs

Let $G=G_1\cup G_2$, where $|V(G_1)\cap V(G_2)|\leq d+1$, and let $u,v\in V(G_1)\cap V(G_2)$. A pair is $\mathcal{R}_d$-linked when it is contained in an $\mathcal{R}_d$-circuit. Jordán and Garamvölgyi's separator conjecture. If $\{u,v\}$ is $\mathcal{R}_d$-linked in both $G_1$ and $G_2$, then $\{u,v\}$ is globally linked in $G$ in $\mathbb{R}^d$. The conjecture concerns how global linkage behaves under unions with small separators and remains unresolved in the source.