Quote Originally Posted by thehotelambush View Post
If you define it as a product of multiplication groups then it's basically abelian by definition and there is nothing to prove. The interesting part is that you can "multiply" the natural groupings of types (dichotomies) in such a way that they form a vector space.
If possible, I would like to write a long proof that does not take short cuts or apply laws only known to mathematicians to arrive at the answer. I'm assuming that almost everyone who reads this has not even heard of a graded vector spaces. Ideally, I would use only the most basic opperations and have a column next to each step explaining with words what I am doing and giving the appropiate background. If there is not a reasonable chance the layman could follow my proof, then it is not worth writing.

In school, I've been asked to recreate importaint proofs, like in physics and calculus. These proofs are facts, we know they work 100%, but the exercise shows "why" they work. I would like to include that "why" in all of my proofs.

Also, my final proof will be quite a bit more complex than just proving a single vectorspace or geometric projection. Eventually, I am going to take the direct product of multiple vector spaces. A great example is how the direct producted of the information elements and functions creates the 16 types or how the direct product of two types creates the intertype relations.

There is some nuance to this, as I think you have commented in your own article, because you can make the model appear unbalanced with out a full explanation. I think you define the supervisions rings as Dih4 if I remember right. This is unnecessary if you account for the rationality dichotomy, but i cannot just define the type dichotomies as z2 sign group and have that point understood.