{"schema":"vela.problem-packet.v0.1","problem":128,"statement":"Let $G$ be a graph with $n$ vertices such that every induced subgraph on $\\geq \\lfloor n/2\\rfloor$ vertices has more than $n^2/50$ edges. Must $G$ contain a triangle?","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)"}