Possible circular critical exponents for Rudin–Shapiro factors

Let the Rudin–Shapiro sequence be viewed as an infinite word, and consider each nonempty factor as a circular word. Its circular critical exponent is the largest exponent of a repetition occurring in that circular factor. Rudin–Shapiro exponent conjecture. Every nonempty factor of the Rudin–Shapiro sequence has a circular critical exponent lying in

$$\left\{1,2,\frac{5}{2},\frac{8}{3},3,\frac{10}{3},\frac{7}{2},\frac{11}{3},\frac{15}{4},4,\frac{21}{5},\frac{13}{3},\frac{14}{3},5,6,7,8\right\}.$$

The paper presents this only as something that might be provable in principle, and supplies no proof or resolution; it therefore remains open.