{"schema":"vela.problem-packet.v0.1","problem":44,"statement":"Let $N\\geq 1$ and $A\\subset \\{1,\\ldots,N\\}$ be a Sidon set. Is it true that, for any $\\epsilon>0$, there exist $M$ and $B\\subset \\{N+1,\\ldots,M\\}$ (which may depend on $N,A,\\epsilon$) such that $A\\cup B\\subset \\{1,\\ldots,M\\}$ is a Sidon set of size at least $(1-\\epsilon)M^{1/2}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_34186a288295c43d","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 no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}