The clique exclusion conjecture for minimally globally rigid graphs

Let $G$ be a minimally globally $d$-rigid graph, meaning that $G$ is globally $d$-rigid and deletion of any edge destroys global $d$-rigidity. Assume that $G$ has at least $d+3$ vertices.

Clique exclusion conjecture. The graph $G$ does not contain a copy of $K_{d+2}$.

The paper proves the analogous assertion for $d=2$ under the stronger hypothesis of $\mathcal{R}_2$-connected and $2$-stress-independent. It asks whether the corresponding statement holds for minimally globally $d$-rigid graphs in higher dimensions.