{"schema":"vela.problem-packet.v0.1","problem":465,"statement":"Let $N(X,\\delta)$ denote the maximum number of points $P_1,\\ldots,P_n$ which can be chosen in a circle of radius $X$ such that\\[\\| \\lvert P_i-P_j\\rvert \\| \\geq \\delta\\]for all $1\\leq i<j\\leq n$. (Here $\\|x\\|$ is the distance from $x$ to the nearest integer.)Is it true that, for any $0<\\delta<1/2$, we have\\[N(X,\\delta)=o(X)?\\]In fact, is it true that (for any fixed $\\delta>0$)\\[N(X,\\delta)&#60;X^{1/2+o(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)"}