I don't think that's possible at the moment. There are no deterministically built operating systems yet.

This is rather sad. I think FreeBSD has a project somewhere trying to move that way. Hopefully all of the unix-likes are at least aware of the concept, if not having an actual project for it. Also, none of the BSD's have any built-in integrity in their repositories, they just insist their infrastructure and committers are infallible among other escuses. (Excepting DragonFly which uses git, don't know if they sign it though. Monotone seems better at that sort of embedded pki thing.).