Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation

[bo198214]

Theorem. There exists no entire pentation pen_b(z), for b>1, such that pen(0) = 1.

Either you have to specify that pen must use the principal branch of tetration (the cut is nothing god given, its just a choice to our human preference; the real function lives on Riemann manifolds), or you have to modify your proof and use the singularities of tetration at integers <=-2 (and show before that indeed every tetration has singularities there).