{"schema":"vela.problem-packet.v0.1","problem":652,"statement":"Let $x_1,\\ldots,x_n\\in \\mathbb{R}^2$ and let $R(x_i)=\\#\\{ \\lvert x_j-x_i\\rvert : j\\neq i\\}$, where the points are ordered such that\\[R(x_1)\\leq \\cdots \\leq R(x_n).\\]Let $\\alpha_k$ be minimal such that, for all large enough $n$, there exists a set of $n$ points with $R(x_k)<\\alpha_kn^{1/2}$. Is it true that $\\alpha_k\\to \\infty$ as $k\\to \\infty$?","status":"solved","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)"}