Jackson–Tanigawa's rigidity maximality conjecture

Let $n$ be sufficiently large for the specified graphs to occur, and let $E$ be the edge set of the complete graph $K_n$. For a graph family $\mathcal{X}$, an $\mathcal{X}$-matroid is a matroid on $E$ in which every graph in $\mathcal{X}$ is a circuit; $\operatorname{val}_{\mathcal{X}}$ denotes the associated upper-bound function on subsets of $E$. The $d$-rigidity matroid $\mathcal{R}_n^d$ is the generic $d$-rigidity matroid on $n$ vertices.

Jackson–Tanigawa's rigidity conjecture. For $d\geq 3$ and $\mathcal{X}=\{K_{d+2},K_{d+2,d+2}\}$, $\mathcal{R}_n^d$ is the unique maximal $\mathcal{X}$-matroid, and $\operatorname{val}_{\mathcal{X}}$ is the rank function of $\mathcal{R}_n^d$.

The paper presents this as one of Jackson and Tanigawa's proposed maximality descriptions and studies counterexamples to such uniqueness claims. The supplied text gives no resolution status for this rigidity conjecture.