So, another version of this problem can be seen with our constructible functions. If we we define:
\[
\Psi(\chi(z)) = G\cdot\Psi(z)\\
\]
Where \(G = \beta'(0) \cdot \text{slog}'(1)\), then:
\[
\Psi(\beta(z))/G = \Psi(\text{sexp}(z))\\
\]
Where we get an absolutely beautiful graph:
We can define Kneser's tetration as the unique function to to satisfy this equation
\[
\Psi(\chi(z)) = G\cdot\Psi(z)\\
\]
Where \(G = \beta'(0) \cdot \text{slog}'(1)\), then:
\[
\Psi(\beta(z))/G = \Psi(\text{sexp}(z))\\
\]
Where we get an absolutely beautiful graph:
We can define Kneser's tetration as the unique function to to satisfy this equation