The ultimate sanity check

[Daniel]

My deep apologies but what was your own method again ?

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Im not sure what your analytic method is , what uniqueness it satisfies , what was proven or plotted etc.
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regards

tommy1729

Brute force, using Faa di Bruno's formula to construct what we call Schroder's iteration.

The software I wrote to validate my work begins by enumerating the combinatorial structure Schroeder's Fourth Problem (also hierarchies and total partitions) and assigning each enumerated structure a value in a manner similar to how Feynman graphs are evaluated. I can evaluate any derivative of \( f^n(z) \) without evaluating the prior derivatives. For example, \( D^4f^n(z) \) is represented by 26 trees whose values added together give the fourth derivative without knowing \( D^2f^n(z) \) or \( D^3f^n(z) \). 

As I have said in other postings, my methodology not only can use either Abel's or Schroeder's equations, it can be used to derive Abel's and Schroeder's functional equations AND THEIR PROPERTIES. My work explains why there is a Abel's and Schroeder's equation.