{"schema":"vela.problem-packet.v0.1","problem":654,"statement":"Let $f(n)$ be such that, given any $x_1,\\ldots,x_n\\in \\mathbb{R}^2$ with no four points on a circle, there exists some $x_i$ with at least $f(n)$ many distinct distances to other $x_j$. Estimate $f(n)$ - in particular, is it true that\\[f(n)>(1-o(1))n?\\]Or at least\\[f(n) > (1/3+c)n\\]for some $c>0$, for all large $n$?","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)"}