{"schema":"vela.problem-packet.v0.1","problem":991,"statement":"Suppose $A=\\{w_1,\\ldots,w_n\\}\\subset S^2$ maximises\\[\\prod_{i<j}\\lvert w_i-w_j\\rvert\\]over all possible sets of size $n$. Is it true that\\[\\max_C\\lvert \\lvert A\\cap C\\rvert - \\alpha_C n\\rvert =o(n),\\]where the maximum is taken over all spherical caps $C$ and $\\alpha_C$ is the area of $C$ (normalised so that the entire sphere has area $1$)?","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)"}