{"schema":"vela.problem-packet.v0.1","problem":511,"statement":"Let $f(z)\\in \\mathbb{C}[z]$ be a monic polynomial of degree $n$. Is it true that, for every $c&#62;1$, the set\\[\\{ z\\in \\mathbb{C} : \\lvert f(z)\\rvert< 1\\}\\]has at most $O_c(1)$ many connected components of diameter $>c$ (where the implied constant is in particular independent of $n$)?","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)"}