{"schema":"vela.problem-packet.v0.1","problem":312,"statement":"Does there exist some $c>0$ such that, for any $K>1$, whenever $A$ is a sufficiently large finite multiset of positive integers with $\\sum_{n\\in A}\\frac{1}{n}>K$ there exists some $S\\subseteq A$ such that\\[1-e^{-cK} < \\sum_{n\\in S}\\frac{1}{n}\\leq 1?\\]","status":"open","seam":"stone","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_66a291aa59ed36a6","kind":"transfer","claim":"Transfer from #306: exact distinct-semiprime certificates for 1/2,1/3,1/6 whose multiset union sums to 1; repeating the block gives arbitrary reciprocal mass (to 13) with an exact subset sum =1 (Opus-verified). Plus bounded-denominator extremal rows (D=10-14) and the prime-obstruction family.","grade":"obstruction_map","gateStatus":"needs_verification","superseded":false}],"velaLean":[{"file":"lean/Vela/Erdos312.lean","sorryFree":true,"url":"https://github.com/vela-science/vela-internal/blob/main/lean/Vela/Erdos312.lean"}],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}