New tetration method based on continuum sum and exp-series

[bo198214]

Do I understand correctly, this quantity \( T=2\pi i/\ln(\ln \lambda) \) is the period of tetration? And what is lambda then? How to find it?

Yes, as I wrote \( \lambda \) is the fixed point of regular iteration.
For the detailed derivation see/google "Portrait of the four super-exponentials to base sqrt(2)" or the non-finished overview article.