Comment by jboggan

I went back to that Fable chat and showed it this new preprint. It coded up the new constructive algorithm and ran it against the existing test suite, that looks good at least.

It has been super helpful in delineating where the crucial concept came from. The proof is rather simple as graph theory proofs go, but it does seem to use some constructions that would only seem obvious if you had serious physics experience with partition function and calculating energy states that cancel out. It's not a wholly alien bolt from the heavens, but I can also see how there hasn't been a human being with the broad theoretical physics knowledge combined with the deep graph theory experience in planar graphs to come up with this idea. I don't know, I'm looking for precedents of this formulation and some old papers of Penrose counting the number of edge colorings of this same graph type are coming up, the line of argument at least rhymes.

But I agree with the thought that this sort of progress should not be siloed inside those companies. I propose a tax so that every slop cannon AI video pays for another hour of compute time for advancing mathematics.