{"schema":"vela.problem-packet.v0.1","problem":1145,"statement":"Let $A=\\{1\\leq a_1<a_2<\\cdots\\}$ and $B=\\{1\\leq b_1<b_2<\\cdots\\}$ be sets of integers with $a_n/b_n\\to 1$. If $A+B$ contains all sufficiently large positive integers then is it true that $\\limsup 1_A\\ast 1_B(n)=\\infty$?","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)"}