Does your "principle which allows order" presume the existence of space and time, and more specifically the ordering of time? I would say that in a universe without time, "cause and effect" have little meaning.
I think I lost your train of thought when you say that numbers are qualities of Unit. Does your universe involve only "Unit", or are there other principles at play as well?
The Peano arithmetic hints at the proposition that numbers are gradations within a unified principle, in this case the principle of “succession”. If you start with nothing (zero) and recursively apply the same quality (succession) you get all integers. So we can rationally assume that all numbers are different qualifications of some primitive. As for time and space, they do not fundamentally exist and they do not configure a necessity within the universe. It takes a being able to record and internally persist events for time to appear. Space is similar, being also a referentiality. In essence, time and space are different framings of the same phenomenon. The length distance between two points is also a temporal ratio between the points. It is just two perceptions, two expediences, not grounded in singular reality. I believe “beings” are Unit juxtaposed over Unit, in the spirit of Wheeler ideas [1]. I don’t think there are fundamental necessities other than Unit. Unit is not causality, I have just used the terms for illustration. If there are other fundamental necessities other than Unit then one would need to explain how they came into being, and it would eventually recurse into Unit. From nucleosynthesis to procreation, it’s Unit all over. The way I grasp it, mathematics is a coloring of Unit, just like for seeing wind one need to sprinkle something over it. It boils down to the ascription of Parts within Wholes. Parts are mere subjections.
I think I lost your train of thought when you say that numbers are qualities of Unit. Does your universe involve only "Unit", or are there other principles at play as well?