What can be interpreted with Wolfram et al's concepts is the existence of two main overall dimensions: an Updating Event dimension~ and a Relations Processing dimension~~
~ I am using the word dimension here to refer concisely to a set of n-subdimensions but supradimension or omnidimension would be most suitable too!! (Any universe is essentially an "Updating Event" isn't it!)
~~ This would be the complete Quantum Observer that is required for every Updating Event to happen coherently, here speculated to exist in the form of an "exotic extra" dimension (or possibly n-subdimensions) as often mentioned by Dr. Lisa Randall, that perhaps is the state-opposite of the Updating Event dimension, and having the full capacity to process every single updating event and its corresponding relations between distinct elements!
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It all begins with something very simple and very structureless. We
can think of it as a collection of abstract relations between abstract
elements. Or we can think of it as a hypergraph—or, in simple cases, a
graph. [...] And when we draw the graph, all that matters is what’s
connected to what; the actual layout on the page is just a choice made
for visual presentation. It also doesn’t matter what the elements are
called. Here I’ve used numbers, but all that matters is that the
elements are distinct.
Upon rereading the wonderful long article it also seems like the two overall dimensions could be described as the Hypergraphee and Hypergrapher dimensions!