{"schema":"vela.problem-packet.v0.1","problem":1193,"statement":"Let $A\\subset \\mathbb{N}$ and let $g(n)$ be a non-decreasing function of $n$ which is always $>0$. Is the lower density of\\[\\{ n : 1_A\\ast 1_A(n)=g(n)\\}\\]always $0$? Is the upper density always $<c$ for some constant $c<1$?","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)"}