The rigidity-matroid bridge conjecture

Let $d$ be a positive integer, let $G$ be an $\mathcal{R}_d$-connected graph, and let $e$ be an edge of $G$. An edge is an $\mathcal{R}_{d+1}$-bridge when its deletion lowers the rank of the $(d+1)$-dimensional rigidity matroid. The rigidity-matroid bridge conjecture. If $G-e$ is not $\mathcal{R}_d$-connected, then $e$ is an $\mathcal{R}_{d+1}$-bridge in $G$. The paper states that this is equivalent to the connectivity dimension-dropping conjecture, so it has the same significance and remains open in general.