I agree, there are lots of outrageous claims out there about "provably secure software" which seem very dubious.

What are your thoughts on SEL4, is it really a breakthrough it is made to be in success of formal verification? Is there a way for users/administrators deploying it to verify themselves authors' claims? Or is it too difficult? I am afraid the latter...

In 2004 Peter Gutmann in his thesis/book criticized the hype around effectivity of formal methods in computer security [1]. Has the situation changed?

[1] https://archive.org/details/springer_10.1007-b97264