I can see this being important if you only care about the results as evaluations of AI progress, but if what you care about is the math itself why should you care about the prompt or anything other than the proof?

While you may want AI results to somehow "not count" if the methods weren't disclosed, that doesn't present these results from poisoning the well for others. Once a result (with verifiable proof object) is delivered, the problem is solved, regardless of whether methods were disclosed.

Methods are only really necessary for results at a meta level, about the design amd evaluation of AI math systems.

why is reproduceability the thing?

shouldnt the paper be the math of the argument? the reproduction is reading the following the proof

I think this is a bit optimistic compared to my view (wrt portability). There's a large stack of software that is involved in training and probably less so in inference. I'm not saying it's impossible but there are definitely different levels of reproducibility and the academic incentive structure doesn't really prioritize reproducibility in my experience. I'm sure it varies quite a bit, I'd be curious to know how those in this problem space are thinking about reproducibility and at what level.

If the proofs are formally verified by a proof assistant (Agda, Roq, Lean, ⋯), I see no reason we would need to know how these came about. All the information needed is in the proof.