The connectivity dimension-dropping conjecture for rigidity matroids

Let $G$ be a graph and let $d$ be a positive integer. A graph is redundantly $\mathcal{R}_d$-connected when deleting any edge leaves it $\mathcal{R}_d$-connected. The connectivity dimension-dropping conjecture. If $G$ is $\mathcal{R}_{d+1}$-connected, then $G$ is redundantly $\mathcal{R}_d$-connected. A positive answer would strengthen the paper's dimension-dropping theorem and could help establish the linked-pairs dimension-dropping conjecture. The paper proves the two-dimensional instance but leaves the general statement open.