Open problem on realizing every chromatic number by interval distance graphs

Let $G_D$ be the distance graph on the plane whose vertices are the points of $\mathbb{R}^2$, with two points adjacent when their distance lies in $D$. For $b>1$, write $G_{[1,b]}$ for the graph with distance set $[1,b]$, and let $\chi$ denote chromatic number.

Realization problem. For any integer $k\ge 7$, there exists $b>1$ such that

$$\chi(G_{[1,b]})=k.$$

The problem asks whether interval distance graphs can realize every chromatic number at least $7$. The paper notes that several values, including $8$, $10$, and $11$, are not currently determined by the available constructions, so the question remains open.