{"schema":"vela.problem-packet.v0.1","problem":706,"statement":"Let $L(r)$ be such that if $G$ is a graph formed by taking a finite set of points $P$ in $\\mathbb{R}^2$ and some set $A\\subset (0,\\infty)$ of size $r$, where the vertex set is $P$ and there is an edge between two points if and only if their distance is a member of $A$, then $\\chi(G)\\leq L(r)$.Estimate $L(r)$. In particular, is it true that $L(r)\\leq r^{O(1)}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}