{"schema":"vela.problem-packet.v0.1","problem":1040,"statement":"Let $F\\subseteq \\mathbb{C}$ be a closed infinite set, and let $\\mu(F)$ be the infimum of\\[\\lvert \\{ z: \\lvert f(z)\\rvert < 1\\}\\rvert,\\]as $f$ ranges over all polynomials of the shape $\\prod (z-z_i)$ with $z_i\\in F$.Is $\\mu(F)$ determined by the transfinite diameter of $F$? In particular, is $\\mu(F)=0$ whenever the transfinite diameter of $F$ is $\\geq 1$?","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)"}