{"schema":"vela.problem-packet.v0.1","problem":337,"statement":"Let $A\\subseteq \\mathbb{N}$ be an additive basis (of any finite order) such that $\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert=o(N)$. Is it true that\\[\\lim_{N\\to \\infty}\\frac{\\lvert (A+A)\\cap \\{1,\\ldots,N\\}\\rvert}{\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert}=\\infty?\\]","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)"}