{"schema":"vela.problem-packet.v0.1","problem":1047,"statement":"Let $f\\in \\mathbb{C}[x]$ be a monic polynomial with $m$ distinct roots, and let $c>0$ be a constant small enough such that $\\{ z: \\lvert f(z)\\rvert\\leq c\\}$ has $m$ distinct connected components.Must all these components be convex?","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)"}