{"schema":"vela.problem-packet.v0.1","problem":973,"statement":"Does there exist a constant $C>1$ such that, for every $n\\geq 2$, there exists a sequence $z_i\\in \\mathbb{C}$ with $z_1=1$ and $\\lvert z_i\\rvert \\geq 1$ for all $1\\leq i\\leq n$ with\\[\\max_{2\\leq k\\leq n+1}\\left\\lvert \\sum_{1\\leq i\\leq n}z_i^k\\right\\rvert < C^{-n}?\\]","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)"}