{"schema":"vela.problem-packet.v0.1","problem":37,"statement":"We say that $A\\subset \\mathbb{N}$ is an essential component if $d_s(A+B)>d_s(B)$ for every $B\\subset \\mathbb{N}$ with $0<d_s(B)<1$ where $d_s$ is the Schnirelmann density.Can a lacunary set $A\\subset\\mathbb{N}$ be an essential component?","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)"}