What's wrong with the predicting h-index paper.

_Editor’s Note: I recently posted about a paper in Nature that purported to predict the H-index. The authors contacted me to get my criticisms, then responded to those criticisms. They have requested the opportunity to respond publicly, and I think it is a totally reasonable request. Until there is a better comment generating mechanism at the journal level, this seems like as good a forum as any to discuss statistical papers.