[impendia]

As I said in another comment, this research isn't about category theory. [Edit: Well, not about the foundations anyway.]

The use of moments as a method for understanding probability distributions isn't particularly new. What is new, is the introduction and adaptation of this framework for trying to understand the Cohen-Lenstra heuristics -- a smaller-scope problem in number theory that has seen a lot of attention recently.

The people quoted are among the world's leading experts in this topic, and I would say that Melanie Wood is the foremost expert. This is definitely novel.