{"schema":"vela.problem-packet.v0.1","problem":317,"statement":"Is there some constant $c&#62;0$ such that for every $n\\geq 1$ there exists some $\\delta_k\\in \\{-1,0,1\\}$ for $1\\leq k\\leq n$ with\\[0< \\left\\lvert \\sum_{1\\leq k\\leq n}\\frac{\\delta_k}{k}\\right\\rvert < \\frac{c}{2^n}?\\]Is it true that for sufficiently large $n$, for any $\\delta_k\\in \\{-1,0,1\\}$,\\[\\left\\lvert \\sum_{1\\leq k\\leq n}\\frac{\\delta_k}{k}\\right\\rvert > \\frac{1}{[1,\\ldots,n]}\\]whenever the left-hand side is not zero?","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)"}