{"schema":"vela.problem-packet.v0.1","problem":254,"statement":"Let $A\\subseteq \\mathbb{N}$ be such that\\[\\lvert A\\cap [1,2x]\\rvert -\\lvert A\\cap [1,x]\\rvert \\to \\infty\\textrm{ as }x\\to \\infty\\]and\\[\\sum_{n\\in A} \\{ \\theta n\\}=\\infty\\]for every $\\theta\\in (0,1)$, where $\\{x\\}$ is the distance of $x$ from the nearest integer. Then every sufficiently large integer is the sum of distinct elements of $A$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_623c15a88228ca3a","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=none) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}