{"schema":"vela.problem-packet.v0.1","problem":1177,"statement":"Let $G$ be a finite $3$-uniform hypergraph, and let $F_G(\\kappa)$ denote the collection of $3$-uniform hypergraphs with chromatic number $\\kappa$ not containing $G$.If $F_G(\\aleph_1)$ is not empty then there exists $X\\in F_G(\\aleph_1)$ of cardinality at most $2^{2^{\\aleph_0}}$.If both $F_G(\\aleph_1)$ and $F_H(\\aleph_1)$ are non-empty then $F_G(\\aleph_1)\\cap F_H(\\aleph_1)$ is non-empty.If $\\kappa,\\lambda$ are uncountable cardinals and $F_G(\\kappa)$ is non-empty then $F_G(\\lambda)$ is non-empty.","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)"}