{"schema":"vela.problem-packet.v0.1","problem":1,"statement":"If $A\\subseteq \\{1,\\ldots,N\\}$ with $\\lvert A\\rvert=n$ is such that the subset sums $\\sum_{a\\in S}a$ are distinct for all $S\\subseteq A$ then\\[N \\gg 2^{n}.\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_74921b8d9a4d3cd2","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=partial) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A276661","name":"Least k such that there is a set S in {1, 2, ..., k} with n elements and the property that each of its subsets has a distinct sum.","terms":"0,1,2,4,7,13,24,44,84,161,309","url":"https://oeis.org/A276661"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}