{"schema":"vela.problem-packet.v0.1","problem":598,"statement":"Let $m$ be an infinite cardinal and $\\kappa$ be the successor cardinal of $2^{\\aleph_0}$. Can one colour the countable subsets of $m$ using $\\kappa$ many colours so that every $X\\subseteq m$ with $\\lvert X\\rvert=\\kappa$ contains subsets of all possible colours?","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)"}