{"schema":"vela.problem-packet.v0.1","problem":333,"statement":"Let $A\\subseteq \\mathbb{N}$ be a set of density zero. Does there exist a $B$ such that $A\\subseteq B+B$ and\\[\\lvert B\\cap \\{1,\\ldots,N\\}\\rvert =o(N^{1/2})\\]for all large $N$?","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)"}