{"schema":"vela.problem-packet.v0.1","problem":655,"statement":"Let $x_1,\\ldots,x_n\\in \\mathbb{R}^2$ be such that no circle whose centre is one of the $x_i$ contains three other points. Are there at least\\[(1+c)\\frac{n}{2}\\]distinct distances determined between the $x_i$, for some constant $c>0$ and all $n$ sufficiently large?","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)"}