{"schema":"vela.problem-packet.v0.1","problem":1083,"statement":"Let $d\\geq 3$, and let $f_d(n)$ be the minimal $m$ such that every set of $n$ points in $\\mathbb{R}^d$ determines at least $m$ distinct distances. Estimate $f_d(n)$ - in particular, is it true that\\[f_d(n)=n^{\\frac{2}{d}-o(1)}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A186704","name":"The minimum number of distinct distances determined by n points in the Euclidean plane.","terms":"0,1,1,2,2,3,3,4,4,5,5,5,6","url":"https://oeis.org/A186704"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}