Which is precisely what we see.
Yes, that's what I said. Pure randomness expects points of higher and lower density, not pure uniformity, as we see, which implies it's pure randomness.
every scientific and mathematical field is based on the universe having consistent, ordered rules of operation.
This has nothing to do with being random noise or not. In fact, random noise requires consistent ordered rules. If that isn't the case then you get something non-random where the rules change to achieve desired results, which isn't what we observe.