I dunno, isn't a demonstration of a few factors proof that someone somewhere has broken RSA, or has a machine much more powerful than we'd expect to exist? It's not proof that any of the math in the paper is correct, but it doesn't have to be. Even if there's a subtle error in the proof-as-written it doesn't matter if the implementation actually works.

All that is true.

But if the author of the paper (or even someone else with a credible reputation) was to public factors and say they used this method then it's useful evidence.

I'd agree with that if he had merely tweeted about RSA. However, he put the claim to "destroy RSA" in the abstract. Claims made in the abstract do need to be substantiated, but RSA isn't discussed in the main text at all.

"Putting up" isn't proof that an RSA decryption algorithm exists, but it is proof that someone has found a way to reverse RSA either way.

The latter is much more important.

This is math claiming an algorithm that is faster.

For an algorithm, asking for results is not that weird. It certainly fits within the purview of a paper. Moreover, it would be really strong evidence for the claims made in the paper. It is much easier to check than the proofs.

I haven't looked into the details of the speed improvements... it's often the case that big-O improvements in complex problems come with bigger constant factors. It's entirely reasonable that this new algorithm is slower for factoring 384-bit numbers but faster for 4096-bit numbers.

I wouldn't be surprised if a demonstration that pushes the current publicly known record for largest factored RSA modulus costs hundreds of thousands or millions of dollars even with this new algorithm, and the algorithm is also slower than other methods for, say 384-bit RSA.

It may be difficult even for Peter Schnorr to get that kind of budget for a demonstration before his paper gets traction.