First of all, thank you for taking the time to read my paper. I appreciate it very much. I agree with you about "Louis Sarwal's" comment. I knew this, but still want to show appreciation for all who take the time to read anyhow. Second of all, thank you for linking articles so I can read and better understand your question and learn myself.
Since the universe is expanding, I am positing that this is due to "new" atoms of space popping into existence and updating the relationships between the atoms of space. So, I am visualizing the universe (through the lens of the Wolfram Model) that everything that exists is a collection of these atoms of space, like water in a glass. As the volume of the water increases (more water goes into the glass) the dynamics of the molecules change because more molecules are added to the system which knocks around all the other molecules. Energy in their model, as you showed, is associated with the update events happening all over the place. To be completely honest I don't know enough about GR or cosmology to try and talk about the volume of the universe respecting the universe's total energy-density (the subtle points will kill me! that's why i love feedback). Now, the crucial point (I probably didn't define well) is that constant updates to the relationships of atoms of space conserve the information of their interactions in unique structures. That could be particles, unbelievably immense clusters of gas in space, stars, planets, solar systems, galaxies, so on...
Okay. So... I am declaring that just as organisms conserve the information of their interactions in geometric structures in the environment, we (organisms) are the information which has been conserved between interacting quantum systems in a local region of space in the universe, namely Earth. A biological system's unique structure and all its complexity arises from initial conditions which are the state of the environment that the organism is embedded in. My whole paper is really trying to say that all complexity (especially organisms) are the result of information being conserved amidst constant rewriting of the hypergraphs. If this does not make sense, please tell me your thoughts. Thanks again for your helpful feedback!
Ps. Please ignore the redundant post below this reply. I accidently posted that while not signed into my account and cannot delete it.