{"schema":"vela.problem-packet.v0.1","problem":1115,"statement":"Let $f(z)$ be an entire function of finite order, and let $\\Gamma$ be a rectifiable path on which $f(z)\\to \\infty$. Let $\\ell(r)$ be the length of $\\Gamma$ in the disc $\\lvert z\\rvert<r$. Find a path for which $\\ell(r)$ grows as slowly as possible, and estimate $\\ell(r)$ in terms of $M(r)=\\max_{\\lvert z\\rvert=r}\\lvert f(z)\\rvert$.In particular, can such a path $\\Gamma$ be found for which $\\ell(r)\\ll r$?","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)"}