{"schema":"vela.problem-packet.v0.1","problem":704,"statement":"Let $G_n$ be the unit distance graph in $\\mathbb{R}^n$, with two vertices joined by an edge if and only if the distance between them is $1$.Estimate the chromatic number $\\chi(G_n)$. Does it grow exponentially in $n$? Does\\[\\lim_{n\\to \\infty}\\chi(G_n)^{1/n}\\]exist?","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)"}