Regular "pentation"?

[mike3]

I think I finally understand what you're talking about here. There is an interval that plays the same role in pentation as \( (e^{-e}, e^{1/e}) \) plays in tetration. I talked about the upper bound of this interval here, but whether or not there is a lower bound to this interval is unknown.

Yes, without an extension to real/complex heights for \( b \le e^{-e} \) for tetration, determining the lower bound (if any) does not seem possible.