The crystalline kernel conjecture for Delone sets

Let $X\subset\mathbb R^3$ be a Delone set with parameter $R$. For each point $x\in X$, let $S_x(2R)$ be its local group, and let $K$ be the subset of points whose local groups contain axes only of orders $2$, $3$, $4$, or $6$. Crystalline kernel conjecture. The crystalline kernel $K$ is a Delone subset with some parameter $R'\leq kR$, where $k$ is a constant independent of $X$. This conjecture asserts that the points with only crystallographic rotational orders remain uniformly relatively dense; the source gives no resolution of the claim.