Whiteley's maximality conjecture for cofactor rigidity matroids

Let $\mathcal{C}_{d-1}^{d-2}(n)$ be the generic cofactor rigidity matroid on the edges of the complete graph, and let $K_{d+2}$ denote a complete graph on $d+2$ vertices. A matroid is freer than another when every independent set of the latter is independent in the former.

Whiteley's maximality conjecture. The matroid $\mathcal{C}_{d-1}^{d-2}(n)$ is the freest matroid in which every $K_{d+2}$ is a circuit. In particular, it is the freest among all abstract rigidity matroids of dimension $d$.

This is known for $d=2$ and was proved for $d=3$ by Clinch, Jackson, and Tanigawa. It remains open in higher dimensions.