{"schema":"vela.problem-packet.v0.1","problem":988,"statement":"If $P\\subseteq S^2$ is a subset of the unit sphere then define the discrepancy\\[D(P) = \\max_C \\lvert \\lvert C\\cap P\\rvert - \\alpha_C \\lvert P\\rvert \\rvert,\\]where the maximum is taken over all spherical caps $C$, and $\\alpha_C$ is the appropriately normalised measure of $C$.Is it true that\\[\\min_{\\lvert P\\rvert=n}D(P)\\to \\infty\\]as $n\\to \\infty$?","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)"}