{"schema":"vela.problem-packet.v0.1","problem":1133,"statement":"Let $C&#62;0$. There exists $\\epsilon&#62;0$ such that if $n$ is sufficiently large the following holds.For any $x_1,\\ldots,x_n\\in [-1,1]$ there exist $y_1,\\ldots,y_n\\in [-1,1]$ such that, if $P$ is a polynomial of degree $m<(1+\\epsilon)n$ with $P(x_i)=y_i$ for at least $(1-\\epsilon)n$ many $1\\leq i\\leq n$, then\\[\\max_{x\\in [-1,1]}\\lvert P(x)\\rvert >C.\\]","status":"open","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)"}