Here we are again, reposted a little more clearly.  To do this I split this in half and I've gone from 3-5.  Another sleepless night, so you get this at 5:45 instead of some decent hour of the day.  It's the time of year and the stresses that keep me from where I'm supposed to be.
Today promises to be long and complicated, unlike this post.

AuT-Building an algorithm Calculus 1 of 5

When we look at dimensional elements we are automatically looking in the wrong direction.   Nevertheless, in predicting the “shape” of non-curved elements from a curved algorithm we also run into problems, but we do have averages where this works, otherwise we wouldn’t have a curved looking universe.

One difference from observed phenomena is that we actually have limits which changes the equation from a theoretical basis.

Dual limits:

xapproaches zero from right x-x0+; right hand limit or from leftx-x0-

In the case of NLC the answers were the same.  But this isn't the case in AuT and in fact there is a question as to whether it can be approached from the future event because there is nothing built and having built from the past, the changes that occurred to keep the future sold might be impossible to track backwards.  This is not so much a jump discontinuity where the limit from either side exists, it may be where the limit only exists from one side which would help explain why history only goes in one direction.

Another place where this issue comes up has to do with the inflection points.

limit as x-0 for 1/x is infinity; but x is finite at any point so that infinity isn't reached in the universe.  The limit as x approaches infinity from the negative position is negative infinity and this is a balanced equation that may have relevance with positive and negative spirals which do grow out in both directions towards infinity but achieve a quite different result because of their intersection.

WHY DOES AUT ARRIVE AT DIFFERENT SOLUTIONS THAN CALCULUS?

Perhaps one of the most significant features of this convergent/divergent, stacked, quantum universe is that when the relative change occurs, no two F-series carriers will be exactly the same length, no relative change will be the same and no SCT will be exactly the same as another.  

That being said, the leading contender feature of the math leading to compression is via the process of having like sized spirals that are generated at different times having sufficient alignment to move to the next compressed state by sharing at least one ct state carrier along sequential lengths of the carrier (since presumably no two points would occupy the same quantum length of the carrier.  Sequential in this case refers to sequential values of x, not standard clock time, since at any quantum value of x the universe is fixed but relative sct to ct1 allows for the perception of sufficient separation and perceived time from the non-dimensional origin.

To attempt this solution for ct1 to ct2 is so complicated that it is beyond what I want to tackle without some significant funding.  But the process is the same for changes in ct1 and so we're going to apply "dimensional" calculus to the non-dimensional calculus in order to show where the results come from and why the two give different results.

The spirals are generated as set forth herein, then the results are stacked in order to generate carrier spirals.  This process continues on so many different levels that it is possible that the compression states are generated when 256 ct1 spirals align at the same time to generate a single photon.

Alignment of space is an uncertain process but since it can occur based on any common feature, I'm going to start  and the same process occurs at the enormous values of x required to get similar concentrations of ct2 to get to ct3 and so on as x increases towards infinity.

Notations:

y=fx: dy=df

f' (newton for derivative) =df/dx=dy/dx=d/dx(f)=d/dy(y)

omits x(0)

fx=x^n; n=1,2,3 [in our case we're slightly modifying this by making it x^2^n

d/dx(x^n)=?; df/dx=[(x+dx)^n-x^n]/dx  could put in x0 at first x+dx

x is fixed, dx moves

binomial theorem: (x+dx)^n=(x+dx)*(x+dx) n times=x^n+n(x^n-1)dx+junk terms

Junk terms refers to O(big oh) O(dx)^2 where this is dx^2,dx^3 and higher are important because they don't go away in AuT because there is a specific limit (information) where you have quantum changes.  That is x can approach zero but never reach zero.

This is the same end point that allows pi to have a specific definition in AuT, the same that allows for there to be a quantum state beyond which there is no separation because it breaks down to pure information.

df/dx=1/dx((x+dx)^n-x^n)

=1/dx(x^n+nx^(n-1)dx+O(dx)^2-x^n)

=1/dx(nx^(n-1)dx+O(dx)^2)

=nx^n-1 + Odx

tends as dx goes to 0 to nx^n-1

=d/dx(x^n)=nx^(n-2)

So for our equation (f(x) is d/dx(x^2^n)=2^n(x^((2^n)-2) + O(dx)^2

Another difference is that we do not want to get a total or sum for the various answers or ignore O(dx).  Summing information gets rid of quantum relative changes to x (sct and dimension) and Odx is where the history of the equation resides, that is, obviously, the present is the derivative of the past in AuT since the F-series equation defines the present in that fashion (NOW=past 1 plus past 2).

We have a non-linear answer with discreet quantum units which assure that at a certain number of places we get an answer.