AuT and the zero prime solution

Today I rode my bike in the terrible heat, then did two sets of weights, one fewer than a full work out, but perhaps enough so I'd be strong when we are together again.  AFter riding back, I swam long enough to cool down no more and it loosened me up a bit.
Tired I may be but I have soething to deal with here that is a continuing to evolves slowly but specifically.
And now I am back to deal with a different problem, the problem of folding which is the problem of zero prime.
As was stated, the most obvious way to deal with ct1 is with a 1,1,-1 and -1-1,1 solution.  But how do we get there?  2^n suggests a -1,1 solution which in pre AuT mathematics might be seen as a cancelling equation, but not with durable solutions.
The ansewr appears to both involve and ignore 0'.
The idea is that 0' is capable of yields a positive and a negative solution.  AuT means that these solutions, no matter what else happens with them, are durable.
Here is the general idea, for what is a concept piece building the universe from zero prime.
1) For every change in x there is a change in 0' yield an alternate -1 or 1 according to the representation in o-space of -1^x which is what we call 0'. These solutions are durable and independent and related only based on their solution order to one another.
2) The first 2^n equation (2^0 information arm) occurs when the solutions are folded "about" zero prime.  This yields an information state comprised of -1 and 1.  These "do not" cancel each other out because they are durable so you can imagine a circle with a 1 and a negative 1 together, it does not tend towards either a compression state or not, but it does have the f-series type combination.
3) The next change is the first true f-series solution (item 1 is an f-series solution but is unique because it involves both negative and positive values.  This solution is alternatively -1,1,1 or -1,1,-1 depending on which point quantum solutions are combined.  This process is reflected in this drawing:

The two 1's shown to form item 2 are in this example a postive 1 and a negative 1 which then combine with either a positive or negative solution to form (as 3) either -1,1,1 or -1,1,-1.  These then combine to form continuing f-series states that act as unstable carriers which, depending on their makeup, tend towards a compression or a decompression state.  

The multiple 1, or -1 net states can build on values to create carriers for the first time and these most fundamental carriers determine if the expansion state is compressive or decompressive based on the underlying makeup.  All of the states after this state will turn positive.

4) The next change is the first true carrier arm (2^n where n=1).  This is a true information set and is also creates a purely positive solution. Any number to the second comes out as a positive in our universe, but it still is made up of portions which are positve net or negative net and all have positive and negative elements that allow for alternatively compressive and decompressive solutions.

This process continues until you get to the current state.  But what happens to 0'.  Zero prime isn't combined with the other solutions in this model and it repeats the process of creating -1 or 1 with every change in x.  This model also allows for an increase of the denominator state from 2 or -2 as shown in the derivation equation of pi given earlier.
The point at which compression and decompression occur are governmened by the net compression solution and the necessary density for any given region defined by proximity of solution order.