{"schema":"vela.problem-packet.v0.1","problem":1075,"statement":"Let $r\\geq 3$. There exists $c_r>r^{-r}$ such that, for any $\\epsilon>0$, if $n$ is sufficiently large, the following holds.Any $r$-uniform hypergraph on $n$ vertices with at least $(1+\\epsilon)(n/r)^r$ many edges contains a subgraph on $m$ vertices with at least $c_rm^r$ edges, where $m=m(n)\\to \\infty$ as $n\\to \\infty$.","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)"}