I just saw this video and I found the part about using interactive proof systems for proving computational correctness really interesting. I do not really know anything about the topic, but it seemed like a really cool possibility to apply this to the nix cache to somehow be able to prove that a build artifact is correctly built. Seems like a massive undertaking to try to implement something like this, though. But I think it would be really cool in some sci-fi future to be able to have a distributed peer-to-peer cache utilizing this kind of proof system. Then, if I understand everything correctly, you would not have to trust the cache server itself, but you can verify the build artifact using this kind of proof system.
Guix has something like that, you can build derivations locally and challenge a remote binary cache to see if they offer the same binaries, this only work if the derivation is reproducible.