Borsuk's transversality conjecture

Let $K\subseteq\mathbb R^d$ be a set of points, let $D$ be the set of pairs of points in $K$ at the diameter distance, and call $(K,D)$ general if every continuous deformation of the distances on $D$ is realized by a deformation of $K$. Borsuk's transversality conjecture. If $(K,D)$ is general, then $K$ can be partitioned into $d+1$ sets of smaller diameter. The source proposes a stronger infinitesimal-deformation version, but gives no resolution status for the stated conjecture.