{"schema":"vela.problem-packet.v0.1","problem":116,"statement":"Let $p(z)=\\prod_{i=1}^n (z-z_i)$ for $\\lvert z_i\\rvert \\leq 1$. Is it true that\\[\\lvert\\{ z: \\lvert p(z)\\rvert <1\\}\\rvert>n^{-O(1)}\\](or perhaps even $&#62;(\\log n)^{-O(1)}$)?","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)"}