{"schema":"vela.problem-packet.v0.1","problem":624,"statement":"Let $X$ be a finite set of size $n$ and $H(n)$ be such that there is a function $f:\\{A : A\\subseteq X\\}\\to X$ so that for every $Y\\subseteq X$ with $\\lvert Y\\rvert \\geq H(n)$ we have\\[\\{ f(A) : A\\subseteq Y\\}=X.\\]Prove that\\[H(n)-\\log_2 n \\to \\infty.\\]","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)"}