{"schema":"vela.problem-packet.v0.1","problem":1082,"statement":"Let $A\\subset \\mathbb{R}^2$ be a set of $n$ points with no three on a line. Does $A$ determine at least $\\lfloor n/2\\rfloor$ distinct distances? In fact, must there exist a single point from which there are at least $\\lfloor n/2\\rfloor$ distinct distances?","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)"}