Additionally, if we do see an ASI, even if it is bound by a need for further physical testing and it stops at, say, twice the intelligence of our best minds, it may be able to prove many things about the physical world through experiments that have already been done.

Because not only would it be generally quite intelligent, it would specifically, as a computer, be far better at combing through massive amounts of research papers to look for connections. It's not a sure thing, but it's possible that it's able to find a connection between a paper on the elasticity of bubble gum and a paper on the mating habits of fruit flies to draw new proofs we never would have thought to look for. Not a certainty by any means, but one avenue for faster advancement than we might expect.