The normality conjecture for the limiting rational-base word

For each $k\geq 1$, let $\langle\operatorname{sat}(k)\rangle$ be the associated word, and define the infinite word

$$\langle\operatorname{sat}(\infty)\rangle=\lim_{k\to\infty}\langle\operatorname{sat}(k)\rangle.$$

An infinite word over a finite alphabet is normal if every word of length $\ell$ over that alphabet occurs with limiting frequency $1/b^\ell$, where $b$ is the alphabet size. The normality conjecture. The word $\langle\operatorname{sat}(\infty)\rangle$ is normal. This is stated as a stronger conjecture motivated by numerical evidence; its status is open.