Split the universe into energy and information.

Let positive and negative energy sum to nothing.

That leaves information. Large ensembles contain very little overall information because it takes little information to specify them, eg: "every real number". However, they can still seem complicated from the inside. An ultimate ensemble plausibly contains no information because there is no need to pinpoint it in EverythingPossibleSpace.

However, it is not clear that level IV is general enough, since the existence of non mathematical thingies is not obvioulsy impossible.