{"schema":"vela.problem-packet.v0.1","problem":50,"statement":"Schoenberg proved that for every $c\\in [0,1]$ the density of\\[\\{ n\\in \\mathbb{N} : \\phi(n)<cn\\}\\]exists. Let this density be denoted by $f(c)$. Is it true that there are no $x$ such that $f'(x)$ exists and is positive?","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)"}