Vertex-splitting conjecture for global rigidity

Let $G$ be a graph, let $d$ be a positive integer, and let $uv\in E(G)$. Suppose that $G$ is $(d+1)$-connected, $|N_G(u)\cap N_G(v)|=d-1$, and $G/uv$ is globally rigid in $\mathbb R^d$. Vertex-splitting conjecture. Then $G$ is globally rigid in $\mathbb R^d$. This is a long-standing question concerning whether the connectivity condition necessary for global rigidity is sufficient in the setting of vertex splitting; the source notes recent developments but does not establish the conjecture.