{"schema":"vela.problem-packet.v0.1","problem":95,"statement":"Let $x_1,\\ldots,x_n\\in\\mathbb{R}^2$ determine the set of distances $\\{u_1,\\ldots,u_t\\}$. Suppose $u_i$ appears as the distance between $f(u_i)$ many pairs of points. Then for all $\\epsilon>0$\\[\\sum_i f(u_i)^2 \\ll_\\epsilon n^{3+\\epsilon}.\\]","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)"}