{"schema":"vela.problem-packet.v0.1","problem":992,"statement":"Let $x_1<x_2<\\cdots$ be an infinite sequence of integers. Is it true that, for almost all $\\alpha \\in [0,1]$, the discrepancy\\[D(N)=\\max_{I\\subseteq [0,1]} \\lvert \\#\\{ n\\leq N : \\{ \\alpha x_n\\}\\in I\\} - \\lvert I\\rvert N\\rvert\\]satisfies\\[D(N) \\ll N^{1/2}(\\log N)^{o(1)}?\\]Or even\\[D(N)\\ll N^{1/2}(\\log\\log N)^{O(1)}?\\]","status":"solved","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)"}