4 problems

Critical-index divergence conjecture. For the exact solution of the master equation, the critical index $n^{\mathcal{S}}$ diverges for

Stieltjes-property conjecture. The function $a\mapsto G_{aa}$ is a Stieltjes function for

Stieltjes-equivalence conjecture. The function $a\to G_{aa}$ is Stieltjes if and only if the function $b\to G_{0b}$ is Stieltjes.

Stieltjes-function conjecture. The functions $G_{0b}$ and $G_{aa}$ are Stieltjes functions.