Definition of a boundary in the local Charzyński-Tammi conjecture

According to the Charzynski–Tammi conjecture, the symmetrized Pick function is extremal in the problem on the estimate for the $n$th Taylor coefficient in the class of holomorphic univalent functions close to the identical one. In this paper we find the exact value of $M_4$ such that the symmetrized Pick function is locally extremal in the problem on the estimate for the 4th Taylor coefficient in the class of holomorphic normed univalent functions, whose module is bounded by $M_4$.