The edge-redundant rigidity conjecture for complete graphs in $\ell_\infty^d$

Let $d\geq 2$, let $n\geq 2d+2$, and let $K_n$ denote the complete graph on $n$ vertices. A graph is edge-redundantly rigid in a normed space if it has a framework that is infinitesimally rigid and remains infinitesimally rigid after deleting any edge. Edge-redundant rigidity conjecture. For every $d\geq 2$ and every $n\geq 2d+2$, the complete graph $K_n$ is edge-redundantly rigid in $\ell_\infty^d$.

The preceding proposition rules out $K_{2d+1}$, so the conjecture asserts that the stated threshold is sufficient as well as necessary. The supplied excerpt gives no evidence that the conjecture has been resolved.