@CortAmmon Very interesting answer. I have to agree with the first post in this chat however on "The question of which religion is the "right" one is suddenly within our grasp.". I don't think this would be the case whatsoever. As he stated, once the search model "incorporates" entirely unpredictable, law breaking miraculous actions, the box certainly would not be able to discern that one of its computed possibilities for the universe is inconsistent with the observations given to it.

@CortAmmon Of course, at that point there really is no "search model" when the fallback could always be "miraculous action". Putting all of that aside though, there is still no reason why a deity could not simply go completely undetectable, or even perform miraculous unexplainable actions intended to fool the machine into incorrectly matching the universe to one religion.

What it could do is identify religions whose books are inconsistent with observed nature, which implies there are additional miracles which are required.