{"schema":"vela.problem-packet.v0.1","problem":957,"statement":"Let $A\\subset \\mathbb{R}^2$ be a set of size $n$ and let $\\{d_1<\\ldots<d_k\\}$ be the set of distinct distances determined by $A$. Let $f(d)$ be the number of times the distance $d$ is determined. Is it true that\\[f(d_1)f(d_k) \\leq (\\tfrac{9}{8}+o(1))n^2?\\]","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)"}