{"schema":"vela.problem-packet.v0.1","problem":607,"statement":"For a set of $n$ points $P\\subset \\mathbb{R}^2$ let $\\ell_1,\\ldots,\\ell_m$ be the lines determined by $P$, and let $A=\\{\\lvert \\ell_1\\cap P\\rvert,\\ldots,\\lvert \\ell_m\\cap P\\rvert\\}$.Let $F(n)$ count the number of possible sets $A$ that can be constructed this way. Is it true that\\[F(n) \\leq \\exp(O(\\sqrt{n}))?\\]","status":"solved","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)"}