{"schema":"vela.problem-packet.v0.1","problem":659,"statement":"Is there a set of $n$ points in $\\mathbb{R}^2$ such that every subset of $4$ points determines at least $3$ distances, yet the total number of distinct distances is\\[\\ll \\frac{n}{\\sqrt{\\log n}}?\\]","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)"}