{"schema":"vela.problem-packet.v0.1","problem":41,"statement":"Let $A\\subset\\mathbb{N}$ be an infinite set such that the triple sums $a+b+c$ are all distinct for $a,b,c\\in A$ (aside from the trivial coincidences). Is it true that\\[\\liminf \\frac{\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert}{N^{1/3}}=0?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_6b88c6c8889f58a4","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=partial) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}