Knuth–Stolarsky conjecture on binary weight and addition-subtraction length

For a positive integer $n$, let $\nu_2(n)$ denote the number of $1$'s in its binary expansion, and let $s(n)$ denote the addition-subtraction chain length used in the paper. KnuthStolarsky conjecture. For all positive integers $n$,

$$s(n)\ge \log_2\nu_2(n).$$

Schnhage's inequality is described as a partial result toward this conjecture. The source gives no resolution status beyond identifying it as a conjecture of Knuth and Stolarsky.