{"schema":"vela.problem-packet.v0.1","problem":1048,"statement":"If $f\\in \\mathbb{C}[x]$ is a monic polynomial with all roots satisfying $\\lvert z\\rvert \\leq r$ for some $r<2$, then must\\[\\{ z: \\lvert f(z)\\rvert <1\\}\\]have a connected component with diameter $>2-r$?","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)"}