{"schema":"vela.problem-packet.v0.1","problem":749,"statement":"Let $\\epsilon>0$. Does there exist $A\\subseteq \\mathbb{N}$ such that the lower density of $A+A$ is at least $1-\\epsilon$ and yet $1_A\\ast 1_A(n) \\ll_\\epsilon 1$ for all $n$?","status":"open","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)"}