{"schema":"vela.problem-packet.v0.1","problem":158,"statement":"Let $A\\subset \\mathbb{N}$ be an infinite set such that, for any $n$, there are most $2$ solutions to $a+b=n$ with $a\\leq b$. Must\\[\\liminf_{N\\to\\infty}\\frac{\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert}{N^{1/2}}=0?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_92c0892a649f28c8","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=weak) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}