From previous discussions on this thread (as I recall) your worldview is that time is an illusion rather than a dimension, energy is an illusion, mass is an illusion. If that is the case, then the first question ought to be what do you consider to be physically real?
Also, when you speak of a “zero dimension universe” I will take it to mean a physical universe not a mathematical construct because you use the term “universe”. If you wish to discuss a “zero dimensional construct” then physics would not apply – then again, it would not have anything to do with the original subject, the void. Moreover, if that is to be the direction of the conversation, I would not be as interested since there are various instances where mathematical constructs do not translate well to physics. Constructs with less than 2 spatial and 1 temporal dimension are among these - as is the mathematical construct of infinity.
Black hole entropy is based on thermodynamics not information: black hole entropy.
We also need to make sure we are speaking of singularity theory and not the larger subject of mathematical singularity.
As a final issue, we need to agree to the difference between “zero” spatial and temporal dimensions and null spatial or temporal dimensions.
For Lurkers: the number 201 means there are no tens, the zero is a placemarker. The number would be written differently if tens do not exist at all, e.g. 2_1.
That would be the last question. As we are considering the nature of the ergod, we ought to realize we look for relevance, not relation. Geometry is metaphorical, as is the rest of mathematics. We need to agree that the ergod is the inverse of the void and then discover to nature of the inversion.
On the black hole, Hawking discovered that information can emerge from a black hole, thereby confusing thermodynamics with information theory through confusing entropy with entropy, two words with entirely different meaning, but spelled and pronounced the same and with the same mathematical form but different content: abstracting and mixing metaphors leads to bad science and worse morality.