Rank-Wise Approximations of Hyper-Operations

[Catullus]

Tetration for a global function doesn't necessarily behave like that. That's a uniqueness criterion you haven't defined though. All you've said with this is that:

\[
\text{Tet}(s-k) \approx L + e^{-Lk}\text{Tet}(s)\,\,\text{for}\,\,\Re(s) < -R\,\,\text{for}\,\,R\,\,\text{Large}\\
\]

Yes ABSOLUTELY THAT's TRUE!!!!! There are countably infinite solutions to that though...

A tetration function must do that about all of the fixed points. You could iterate from any of the fixed points, and continue back to where you want it. Like to calculate 2^^.5 you could use any of the fixed points. Tetration needs to be unique.