alt Hacker NewsI was confused at first when you asked if the 8-flow is relevant, when like, the 8-flow is a key input that the cycle double cover is built out of. Then I realized, oh, I guess technically they're not using the 8-flow, they're using the Z_2^3-flow. But like. The existence of an 8-flow and the existence of a Z_2^3-flow are equivalent, and I gather most graph theorists are going to talk about it in terms of the existence of an 8-flow, so noting that having a Z_2^3-flow is equivalent to having an 8-flow helps the reader to put this information in context.
I'm not sure why you find this proof so hard to read. I found it mostly quite readable (and the definition of L is straightforward? I wouldn't have written it quite that way but it's hardly inscrutable), although I feel like some parts are maybe lacking some exposition to explain the reason for certain things -- it doesn't feel written "in order". I also don't like that it's not cleanly separated into theorems and proofs -- some of the proof occurs in parts that aren't set off, for instance, and there isn't even a proper main theorem statement! But overall I was able to get through it without a lot of trouble and I'm not even a graph theorist...
My issues with the definition of L are mostly about the order in which things are written.
L(t, epsilon)_e breaks down the range of L onto its component values indexed by edge, but this only really makes sense when you know that t and epsilon are. They are sort of defined in the middle of a sentence in the proof of 2.1, which IMO is asking a lot of the reader, and this sort of sloppiness is a way that errors can hide in a proof. (Not that I see an error here. But a formalization in Lean or whatever would not get away with this.)
And, in the same definition of L, for some reason the e=uv part comes at the end only after u and v are used.
What would be wrong with stating, in the definition, what sorts of objects t and epsilon are and with omitting e entirely in favor of just calling the edge uv everywhere?