As someone who was a research assistant in this field one summer back in college, I spent the day trying to check the proof, or at least the obvious places a mistake would be. It's surprisingly readable, so I guess we'll find out soon.

Lemma 2.2 specifically "feels" new to me. You can get part of the way by duct-taping several papers together (playing along at home: I found Tutte 1954, Bermond–Jackson–Jaeger 1983, Máčajová–Škoviera 2005, Zaslavsky 1982. interestingly, only Tutte appears in the works cited). But it's surprising you'd think to pick those, and surprising it works, because you still need a genuinely novel parity argument at the end. Those steps individually are all pretty simple, knowing to chain that chain together, isn't.

The guess-against the checker paradigm is real (ie AlphaProof), and something like that was probably involved here. But this area of graph theory isn't in mathlib, you need to write the proof checker first, and then you need to know what kind of proof checker you need to write (or just do a brute force search for new proof checkers). Probably how you got this result is have a recursive tree of agents until you divide into small enough subproblems.

At a certain point you need a philosopher to figure out what that "means", ie if you have a big enough tree of small enough subproblems, some of the "magic" so to speak moves out of the proof checkers and into the way the tree got structured.