{"schema":"vela.problem-packet.v0.1","problem":527,"statement":"Let $a_n\\in \\mathbb{R}$ be such that $\\sum_n \\lvert a_n\\rvert^2=\\infty$ and $\\lvert a_n\\rvert=o(1/\\sqrt{n})$. Is it true that, for almost all $\\epsilon_n=\\pm 1$, there exists some $z$ with $\\lvert z\\rvert=1$ (depending on the choice of signs) such that\\[\\sum_n \\epsilon_n a_n z^n\\]converges?","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)"}