A God partition of the Universe, whatever its material or immaterial microscopic self-encoded nature, is in exactly the same boat as a human partition of the Universe as it attempts to ``know'' both the outside Universe and itself on top of its irreducibly self-encoded brain that is itself merely a part - a very small part compared to the Universe itself - of what it wants to know14.
Of course we can and do acquire a high-level, coarse-grained, approximate overview, a symbolic map that neglects most of the detail of the territory being mapped just so that it will fit in our limited storage and processing capacity, but this sort of knowledge can hardly be called ``omniscience'' whatever the scale of any real being that does the same. Furthermore, since any such map is necessarily self-referential, any being that relies on it can never make it into a complete and consistent system of knowledge, and cannot be certain that such knowledge as it thinks that it has is merely consistent, let alone complete. These are all mathematical results and are as close to a priori truths as it is possible to be in any system of symbolic reason, so I really don't think there is much chance that they will be refuted by any rational argument or empirical observation.
We are left with an inescable conclusion:
If God is real (and hence at least part of the Universe) and if God is omniscient and omnipresent, then God's knowledge cannot be any sort of symbolic map of the state of the Universe, it can only be the irreducibly self-encoded territory of the Universe itself.or
If God exists, God is necessarily the Universe itself!Q.E.D. Twice, even!
Those who wish to (for example) take the manifest existence of a non-empty Universe at all as de facto evidence of God should be somewhat relieved by this theorem as it provides them with a single way in which their belief can be consistent, and that is if the non-empty Universe and God are equivalent15. There is nothing logically or empirically inconsistent about the utter equivalence of Universe and God. Obviously the Universe is omnipresent, by definition. Obviously the Universe is omniscient (of its own self-encoded state), again by definition. The Universe may or may not be omnipotent in the naive sense of the word, but it is a simple identity of being that everything real is in some sense the ``will'' of God if God is equivalent to the Universe. God is not impossible, and it is up to each sentient being to make up their own mind concerning the extent to which sentient existence versus nonexistence constitutes ``evidence'' that makes the equivalence plausible16.
The consequences of this theorem are profound. If God exists, then everything is God: you are (a part of) God, I am God, a telephone pole is God, a speck of interstellar dust floating in intergalactic space is God, any hidden dimensions or alternative Cosmi are God - God is all that has being. Jesus (if he existed at all outside of myth and legend) was no more (nor less) God than you are - and said so on several occasions in the New Testament and Gnostics, all studiously ignored. Miracles become enormously implausible as they suggest that God's mind is inconsistent but the real is never inconsistent - to quote C. S. Lewis's Aslan (speaking as God): ``Do you think that I would break the Laws that I made?'' Physical Law throughout the visible and invisible Universe quite literally is the mind of God (where now ``mind'' and ``matter'' are indistinguishable - both are in the abstract and concrete merely self-encoded state information), and your actions, completely determined by the utterly mechanical operation of your component parts in that mind, are not morally good or bad any more than the Law of Universal Gravitation and consequent orbiting of the planets about the Sun is good or bad. We can immediately apply this theorem to most of the world religions and reject their theisms out of hand except to the extent that they capture this theorem (some do very much, in rare and beautiful parts interspersed with their extortionist threats of eternal torments for unbelievers and other nonsense).