{"schema":"vela.problem-packet.v0.1","problem":1136,"statement":"Does there exist $A\\subset \\mathbb{N}$ with lower density $>1/3$ such that $a+b\\neq 2^k$ for any $a,b\\in A$ and $k\\geq 0$?","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)"}