{"schema":"vela.problem-packet.v0.1","problem":1191,"statement":"Let $A\\subset\\mathbb{N}$ be an infinite Sidon set. Is it true that\\[\\liminf_{x\\to \\infty} \\frac{\\lvert A\\cap [1,x]\\rvert}{x^{1/2}}(\\log x)^{1/2}=0?\\]Does there exist an infinite Sidon set $A$ such that\\[\\liminf_{x\\to \\infty} \\frac{\\lvert A\\cap [1,x]\\rvert}{x^{1/2}}(\\log x)^c>0\\]for some $c>0$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}