{"schema":"vela.problem-packet.v0.1","problem":328,"statement":"Suppose $A\\subseteq\\mathbb{N}$ and $C>0$ is such that $1_A\\ast 1_A(n)\\leq C$ for all $n\\in\\mathbb{N}$. Can $A$ be partitioned into $t$ many subsets $A_1,\\ldots,A_t$ (where $t=t(C)$ depends only on $C$) such that $1_{A_i}\\ast 1_{A_i}(n)<C$ for all $1\\leq i\\leq t$ and $n\\in \\mathbb{N}$?","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)"}