Earlier quoted context omitted.
One small note on the paper itself. I love that the paper's author are in alphabetical orders, without any stupid jostling over first/last authorship. I think that's fantastic and wish academia went that way too (yeah right).
Why is alphabetical order great? It just only means that people with last names starting with z will get penalized every single time because of choosing wrong parents! I would think randomized order would be chosen - especially if you were mathematician.
(I can actually answer my own question to some degree: the "alphabetical authors" convention is also the norm in my own field of high energy physics. Only after I finally landed a tenure-track job and served on another search committee did I realize that folks from other fields of physics would see my lack of first-author publications as a black mark. But in principle, among those who know the convention, order ought to be unimportant, shouldn't it?)