Can we get the holomorphic super-root and super-logarithm function?

[Ember Edison]

... So,Can we get the holomorphic super-root and super-logarithm function and all parameter is complex?

https://math.eretrandre.org/tetrationfor...p?tid=1017
fatou.gp implements Kneser's super-logarithm or inverse of tetration for complex bases and complex heights.

There is a proof of uniqueness of Kneser's slog if the slog between the two primary fixed points is defined, unique and one to one mapping in a region bounded by a sickle between the fixed points.  One side of the sickle is a curve connecting the two fixed points, and the other side is the exponent of the curve.  The algorithm for fatou.gp is a bit complicated, but it compute's Kneser's slog for a very wide range of real and complex bases.

I have reviewed other papers by the author, but not this one.  The results from the other paper match fatou.gp exactly (within error limits), so I'm pretty sure that my program would also be the inverse slog function matching the author's results for complex base tetration as well.  There is only one valid extension of Kneser's solution to complex tetration bases.

He use Cross Track method to evaluate tetration in real bases, larger than e^(1/e), Your's method to evaluate bases e^(1/e), Sword-Track to evaluate Shell Thron boundary, Double Dagger Track to Evaluate other complex bases.

I am reading your super-logarithm code,it look like can evaluate all complex bases. Thank you for your work.
So now what conclusion can get with complex super-root?