Mathematicians Build Long-Awaited Graph Sandwich

Hilarious - a mathematical result that afaict has nothing whatsoever to do with AI, and 75% of the comments are about AI, including this one!

Actual meat: https://arxiv.org/abs/2510.20765

Wondering: if the process for the upper part of the sandwich is the complement of the process for the lower part, why was it so much more difficult? What would go wrong if you took one of the earlier lower-sandwich processes, and complemented it in a similar way? I have to assume it's something, but what?

I am not a mathematician but are most papers now accompanied by a lean proof?

Is there a central repository of lean proofs shared by mathematicians like an npm repository of JavaScript packages?

Does it all depend on a stupid is-odd package in the end?

Seems like this would have strong implications for distillation and/or smaller types of transformers!