{"schema":"vela.problem-packet.v0.1","problem":512,"statement":"Is it true that, if $A\\subset \\mathbb{Z}$ is a finite set of size $N$, then\\[\\int_0^1 \\left\\lvert \\sum_{n\\in A}e(n\\theta)\\right\\rvert \\mathrm{d}\\theta \\gg \\log N,\\]where $e(x)=e^{2\\pi ix }$?","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)"}