{"schema":"vela.problem-packet.v0.1","problem":102,"statement":"Let $c>0$ and $h_c(n)$ be such that for any $n$ points in $\\mathbb{R}^2$ such that there are $\\geq cn^2$ lines each containing more than three points, there must be some line containing $h_c(n)$ many points. Estimate $h_c(n)$. Is it true that, for fixed $c>0$, we have $h_c(n)\\to \\infty$?","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)"}