{"schema":"vela.problem-packet.v0.1","problem":268,"statement":"Let $X\\subseteq \\mathbb{R}^3$ be the set of all points of the shape\\[\\left( \\sum_{n\\in A} \\frac{1}{n},\\sum_{n\\in A}\\frac{1}{n+1},\\sum_{n\\in A} \\frac{1}{n+2}\\right) \\]as $A\\subseteq\\mathbb{N}$ ranges over all infinite sets with $\\sum_{n\\in A}\\frac{1}{n}<\\infty$.Does $X$ contain an open set?","status":"solved","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)"}