What you're asking for is exactly the sort of thing that belongs in, and will appear in, a journal article. There will likely be a preprint on arxiv, so you might keep an eye out for that.

In any case, the fact that it was found by a commercial model means that the unfiltered reasoning trace isn't available even to the original author. So there are aspects of the problem-solving process we'll never see. Even if we did get access to the reasoning trace it wouldn't necessarily be definitive, given how these things work.

Hopefully it'll be possible to get the same solution from an open-weight model like one of the 3T heavyweights that are said to be coming up for release. If so, the chain of thought can be scrutinized in-depth.

No, I think it works the opposite way. Until there is an article somewhere that describes what happened, if there is one, all we have to go by is that some guy posted a counter-example for the Jacobian on X, with a vague allusion to using Fable and without any further information. Assuming and guessing anything about e.g. the method used at this point is just raising the noise level.

The original author works for Anthropic. And even without that, Anthropic might find this important enough to dig up the trace?