Are you saying that medicine makes no falsifiable predictions? It seems to me that ONLY empirical science has experimental verifiability. Maybe we have a disagreement about definitions - but falsifiability is what clinical drug trials (for example) is all about. Maybe I don't understand what you're saying.
I was splitting hairs a little, but Popper's solution to the problem of induction was that you could never verify something experimentally, you could only falsify it. So you have falsifiability, but never verifiability. By failing to falsify something you become more confident it's true, but you never verify it.
I love your constant attention to mathematical purity, and I thank you for it. Also, I have a draft I'm working on (RE: our discussion on AI), but who knows if I'll ever finish.