{"schema":"vela.problem-packet.v0.1","problem":225,"statement":"Let\\[ f(\\theta) = \\sum_{0\\leq k\\leq n}c_k e^{ik\\theta}\\]be a trigonometric polynomial all of whose roots are real, such that $\\max_{\\theta\\in [0,2\\pi]}\\lvert f(\\theta)\\rvert=1$. Then\\[\\int_0^{2\\pi}\\lvert f(\\theta)\\rvert \\mathrm{d}\\theta \\leq 4.\\]","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)"}