{"schema":"vela.problem-packet.v0.1","problem":161,"statement":"Let $\\alpha\\in[0,1/2)$ and $n,t\\geq 1$. Let $F^{(t)}(n,\\alpha)$ be the smallest $m$ such that we can $2$-colour the edges of the complete $t$-uniform hypergraph on $n$ vertices such that if $X\\subseteq [n]$ with $\\lvert X\\rvert \\geq m$ then there are at least $\\alpha \\binom{\\lvert X\\rvert}{t}$ many $t$-subsets of $X$ of each colour. For fixed $n,t$ as we change $\\alpha$ from $0$ to $1/2$ does $F^{(t)}(n,\\alpha)$ increase continuously or are there jumps? Only one jump?","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)"}