{"schema":"vela.problem-packet.v0.1","problem":35,"statement":"Let $B\\subseteq\\mathbb{N}$ be an additive basis of order $k$ with $0\\in B$. Is it true that for every $A\\subseteq\\mathbb{N}$ we have\\[d_s(A+B)\\geq \\alpha+\\frac{\\alpha(1-\\alpha)}{k},\\]where $\\alpha=d_s(A)$ and\\[d_s(A) = \\inf \\frac{\\lvert A\\cap\\{1,\\ldots,N\\}\\rvert}{N}\\]is the Schnirelmann density?","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)"}