{"schema":"vela.problem-packet.v0.1","problem":1002,"statement":"For any $0<\\alpha<1$, let\\[f(\\alpha,n)=\\frac{1}{\\log n}\\sum_{1\\leq k\\leq n}(\\tfrac{1}{2}-\\{ \\alpha k\\}).\\]Does $f(\\alpha,n)$ have an asymptotic distribution function?In other words, is there a non-decreasing function $g$ such that $g(-\\infty)=0$, $g(\\infty)=1$,and\\[\\lim_{n\\to \\infty}\\lvert \\{ \\alpha\\in (0,1): f(\\alpha,n)\\leq c\\}\\rvert=g(c)?\\]","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)"}