3 problems

Equal-logarithm global-boundedness conjecture. In this case, $T_0$ will necessarily be globally bounded and, assuming Christol's conjecture, will be the diagonal of a rational func…

Lower-logarithm non-global-boundedness conjecture. In the case $m<n$, the series $T_0$ cannot be globally bounded.

Highest-logarithm global-boundedness conjecture. The series $S_0$ will necessarily be globally bounded. Consequently, assuming Christol's conjecture, it will be the diagonal of a r…