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As you could see I got some typos in my notation post. Like in the rules about the 1's there are bugs. I'm taking that one down when the formal notation is relased since I developed a faster growing, and non-buggy version. This notation was also the reason I was mainly inactive today. This notation made me dump 1/4 of my A4 paper storage :) Anyway, it'll be bugfixed and finished in 1-2 days.

The current growth rate (estimation) is

 $$f_{\omega^\omega}(n)$$ on linear arrays and $$f_{\omega^{\omega^\omega}}$$ on the simple dimensional ones. The linear array growth rates are more perfect because dimensional arrays aren't bugfixed yet beyond 3 dimensions. But it'll also be tweaked along with linear arrays. The arrays will always (with a few exception in advanced parts) be incased in {}'s. And I would like your opinion on whether [] or  html bracketrs are a more appropriate bracket for the dimensional seperators. The name was also decided two days ago, it'll be "Pete's Finite Arrays"