The globally rigid graph bridge conjecture

Let $G$ be a globally rigid graph in $\mathbb{R}^d$, and let $e$ be an edge such that $G-e$ is not globally rigid. An edge is an $\mathcal{R}_{d+1}$-bridge when its deletion lowers the rank of the $(d+1)$-dimensional rigidity matroid. The globally rigid graph bridge conjecture. Under these hypotheses, $e$ is an $\mathcal{R}_{d+1}$-bridge in $G$. This is the globally rigid specialization of the linked-pairs dimension-dropping conjecture and remains open here.