{"schema":"vela.problem-packet.v0.1","problem":344,"statement":"If $A\\subseteq \\mathbb{N}$ is a set of integers such that\\[\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert\\gg N^{1/2}\\]for all $N$ then must $A$ be subcomplete? That is, must\\[P(A) = \\left\\{\\sum_{n\\in B}n : B\\subseteq A\\textrm{ finite }\\right\\}\\]contain an infinite arithmetic progression?","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)"}