Asymptotic conjecture for prefix normal words and extension-critical words

For each $n$, let $\textit{pnw}(n)$ be the number of prefix normal binary words of length $n$, and let $\textit{crit}(n)$ be the number of extension-critical words of length $n$. Prefix-normal asymptotic conjecture. Based on empirical evidence,

$$\textit{crit}(n)=\textit{pnw}(n)\,\Theta\left(\frac{\ln n}{n}\right),$$

and

$$\textit{pnw}(n)=2^{n-\Theta((\ln n)^2)}.$$

These estimates refine the preceding conjecture about the extension-critical ratio and are presented as empirical predictions; no proof or resolution is supplied in the paper.