Lexicographically least words in the orbit closure of the Rudin–Shapiro word

We give an effective characterization of the lexicographically least word in the orbit closure of the Rudin–Shapiro word having a specified prefix. In particular, the lexicographically least word in the orbit closure of the Rudin–Shapiro word is . This answers a question Allouche et al. (Theoretical Computer Science 2009).