{"schema":"vela.problem-packet.v0.1","problem":1207,"statement":"Let $P_d(n)$ be such that in any set of $n$ points in $\\mathbb{R}^d$ there exist at least $P_d(n)$ many points which do not contain an isosceles triangle. Estimate $P_d(n)$ - in particular, is it true that\\[P_2(n)<n^{1-c}\\]for some constant $c>0$?","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)"}