{"schema":"vela.problem-packet.v0.1","problem":509,"statement":"Let $f(z)\\in\\mathbb{C}[z]$ be a monic non-constant polynomial. Can the set\\[\\{ z\\in \\mathbb{C} : \\lvert f(z)\\rvert \\leq 1\\}\\]be covered by a set of circles the sum of whose radii is $\\leq 2$?","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)"}