{"schema":"vela.problem-packet.v0.1","problem":230,"statement":"Let $P(z)=\\sum_{1\\leq k\\leq n}a_kz^k$ for some $a_k\\in \\mathbb{C}$ with $\\lvert a_k\\rvert=1$ for $1\\leq k\\leq n$. Does there exist a constant $c>0$ such that, for $n\\geq 2$, we have\\[\\max_{\\lvert z\\rvert=1}\\lvert P(z)\\rvert \\geq (1+c)\\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)"}