Möbius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers

We show that the Möbius function is orthogonal to the Thue-Morse sequence $t(n)$ taken along the Piatetski-Shapiro numbers $\lfloor n^c\rfloor$ for any $1<c<2$. Previously this property was established for the subsequence along the squares $t(n^2)$. These are both examples of Möbius orthogonal sequences with maximum entropy.