Let $f:\mathbb{N} \to \{0,1\}$ be the Ehrenfeucht-Mycielski sequence. The first few digits of the sequence are: $$010011010111000100001111\ldots$$

For any $k\in\mathbb{N}$ let $s(k) = \sum_{i=0}^k f(i)$. It is conjectured that $\lim_{n\to\infty} s(n)/n = 1/2$.

Question. Is it known that $\liminf_{n\to\infty} s(n)/n = \limsup_{n\to\infty} s(n)/n$?