[throwawaymath]

Yes, hash functions only approximate one way functions since we haven't technically created one - your point here is what I was referring to by mentioning the random oracle model.

But the random oracle model is fully theoretically sound - I'm not sure where you got the impression it isn't. Do you think everything outside the standard model of cryptography isn't theoretically sound? What, then, is your definition of soundness?

[betterunix2]

ROM is not sound because there are constructions that are provably secure that cannot be securely instantiated. I do not deny that it is pragmatic or that the problems have not been relevant in practice, but the ROM is just a heuristic.