Sing's generalized power-law conjecture for f-smooth-word complexity

Let $\mathpzc{A}=\{a,b\}$ be a binary alphabet, let $\mathcal{C}_f^\infty$ be the set of finite f-smooth words over $\mathpzc{A}$, and let $p_{\mathcal{C}_f^\infty}(n)$ denote its factor complexity. Define

$$\rho=\frac{\log(a+b)}{\log\left(\frac{a+b}{2}\right)}.$$

Sing's power-law conjecture. Over $\mathpzc{A}=\{a,b\}$,

$$p_{\mathcal{C}_f^\infty}(n)=\Theta(n^\rho).$$

The conjecture generalizes the original $\{1,2\}$ case; polynomial bounds and partial results are known, but the full asymptotic estimate is not established.