Apologies for the extremely late answer. I haven't received any new notifications on this thread until a little while ago, for some reason. In any case:
I feel like this is a little misleading. Mathematics didn't originally exist, Uriel invented it and needed to work for an EXTREMELY long time to figure out how to alter the world from running on divinity to running on mathematics. This really doesn't seem like every divine object had some hidden platonic mathematical equivalent, it more seems like Uriel figured out the painstaking task of how to turn everything into something that abides by mathematical laws.
I wasn't really arguing that Unsong's mathematics operate on a Platonic Cosmology, though, and I actually think your explanation is closer to what I was trying to get across.
To elaborate on that, I was moreso saying that attempting to distinguish God from the Absolute Infinite is something that's not really supported by the text itself, even when taking into account the fact Uriel created mathematics as we know it. Remember that he also specifically states that only the underlying framework defining existence actually changed, while the world itself was pretty much the same, and even points to a tree and explains how it is functionally the same as before, with the only difference being that it's part of a self-sustaining reality, instead of one that needs to be constantly imbued with Divine Light to remain in existence.
Given how he goes on to state that every divine object has a mathematical equivalent (That is also close enough to it in nature to act as a replacement), even those residing in Yetzirah and the higher worlds, I think that it isn't too much of a reach to say this apply to God too, especially when the latter is already identified with a mathematical concept by the story itself.
But my argument is basically that I don't like rating "Above all hierarchies" as High 1-A because of allusions to mathematical objects that would have a 1-A size if they physically existed, but which don't actually exist. Its largest constructs (that don't backscale) only being rated at 1-C, without it ever being stated that they have potential to extend to a 1-A level (again, without backscaling) makes me not want to put it at High 1-A.
To complement this: My argument is that whether or not this hierarchy of cardinal numbers actually exists is largely a non-factor, since God (Himself a "physical" part of the verse's cosmology) is already defined as equal to a quantity which is greater than, and encompasses them, and the story saying that it's beyond the concept of "infinity" to begin with also hammers the point in even further.
I should also note that cardinalities shouldn't really be thought of as akin to layers, or higher realms of existence in an hierarchy, so much as quantities representing the amount of objects which a collection comprises, and these objects can be defined as being anything, really. In fact, spaces in mathematics are themselves thought of as uncountably infinite collections of 0-dimensional points (Called
"singletons", to be more specific)
Considering God is a physical, existent part of the cosmology, as mentioned above, then He could very well just be thought of as a space whose cardinality is equal to the absolute infinite/set of all sets (
The concept itself is problematic when formally defined, of course, but that's not relevant to the point), and it would naturally follow that said space would have subsets of any given cardinality, which would, again, do away with potential uncertainties over using these. At least in my view, obviously.
