Assuming it was written by her and not her adviser.

The writing doesn't sound like the same voice as her advisor's (e.g. arXiv:1402.1131). OTOH it is plausible that most of the original research in it was the latter's. Also, the fact that she doesn't seem to have ever published anything else is pretty suspicious. EDIT: also, she took ten years to finish it.

All in all, I'd guess her IQ is above 100 but below 130.

Two minutes' inspection of her thesis would, I think, lead any reasonable person to conclude that it was almost certainly not written by her adviser. The extremely unusual style is consistent with her adviser having, say, had all the actual clever mathematical ideas in it, but again the point here is merely that Piper is clearly intelligent, and being able to understand the material described in her thesis (which, again, I think it's clear she does if you actually look at the thesis) is itself indicative of a high IQ.

(PS. Hi, Eugine/Azathoth/Ra/Lion. This is your regularly scheduled reminder that I respond to mass-downvoting of my old comments, such as you've been engaging in very recently, by posting more, and that Less Wrong responds to it by banning you and forcing you to go to all the trouble of registering another identity.)