(06/19/2009, 05:17 PM)Tetratophile Wrote: "There exists only one holomorphic superlogarithm with b>e^1/e that maps G biholomorphically to *some* region with upper and lower unbounded imaginary part"Yes exactly. If you have one super-logarithm that maps G to *some* region and another super-logarithm that maps G to *some other* region , and both super-logarithms satisfies the other conditions of the proposition, then they must be equal. Hence this assumption of different images was already wrong: the images are equal .

That must mean that we still don't know WHAT region the superlogarithm must map G (the crescent moon thingy) to. So our different tetration methods might map G to different infinitely long strips of width 1.

Not sure why you think it wouldnt work. The only problem with our tetration methods may be the biholomorphy, the bijectivity of the super-logarithm on the initial region (or merely the holomorphy for some methods).