SOLVED, the site's label, with commentary recording a disproof by Gol'dberg and Eremenko. Their Theorems 1 and 2 give entire functions of order zero, growing barely above Hayman's logarithmic-square threshold, and of every finite order, such that no path on which $f\to\infty$ has length $O(r)$ inside the disc of radius $r$; the answer to the problem's question is therefore no, and the standing is solved, disproved (their claim page (Goldberg Eremenko, 1979)). The standing records a disproof where the label says only SOLVED, because the problem's definite question asks whether every entire function of finite order has a path with $\ell(r)\ll r$, and the accepted full claims refute that. Toppila's 1980 note proves the same theorem independently (Toppila's claim page (1980)), and Hayman's 1960 theorem, the yes-instances for functions with $\log M(r,f)=O((\log r)^2)$, is a partial claim (its claim page (Hayman, 1960)). The wider request for an optimal length estimate in terms of $M(r)$ is not supplied by that counterexample, and no optimal replacement bound for every growth class is asserted here.