The evolving relationship of phi to pi to fpix

Not a word today?  Things must indeed be grim.
This goes into some weird.
You wonder what I do all day on my day off?
Aside from swimming 2000 yards while dodging storms
Working through this took some time
It isn't perfect, but this has to be addressed, not to understand the theory, but to prove it.
So here it is.

If science is unwilling to consider alternative hypothesis then science is not about real scientific method; but is about belief.  Put specifically, if a math based theory is called pseudo science, the standard model is being elevated to religion, or demoted in actuality.
When the astronomy group booted me for posting the first post in the series, one which is repeated at the bottom, they showed that they held their belief of astronomical theory supreme without a willingness to open the discussion to others.
Their prerogative.

This is a technical discussion.  AuT seeks to define the universe in terms of co-existing dimensional element from zero to at least 4 which are observed.  It eliminates time except as an effect, just as thermodynamic and therefore force and entropy are effects. It is highly predictive and that information has been repeatedly made available, but for the sake of being overly repetitive those sources are quoted again at the bottom of this post.

This is something of a brain twister, although the math is relatively simple and you can plug this into an excel spreadsheet (or ask for a copy of mine) and do all of the math shown here.  There are elements to this which I invite comment on.  These include the reasons for the failure of the quantum alignment at the ct4 level (see below); a cross check of the mathematics and general commentary on whether the conclusions reached by AuT are supported by this new way of tying together phenomena otherwise separated by infinity.

Everyone who wants can skip this section.  The point is to connect two things we know are connected intuitively, curvature and the Fibonacci number, but we're approaching that connection in a slightly different way.  We're assuming evolving curvature and that these two infinite series (fpix, the denominator of pi) and the golden ration of the Fibonacci number can be reconciled for discussion purposes in a way which further the theory of AuT.

The interesting historical part of this is that the relationship, the two dimensional relationship, between the golden ratio (Fibonacci's number discussed below) and pi has been known since the time that the pyramids were build, 5000 years ago.  Now that is something thing think about.
How is that defined;
1) There is a four sided pyramid (we can ignore the 8 sided features for this discussion since we are only interested in the base.
2) A circle insdie the base is defined by 2pi*r where r is the length from the middle of the pyramid to the edge of the pyramid.  If this circle is bent in half at 90 degrees, its height matches the height of the pyramid.
3) The ratio of the height of the pyramid to the half perimeter of the perfect square base (going half way or two sides worth of the base) you get the golden ratio^2.(half perimeter/height=phi^2)
Approximately.  No one can build to an infinitely small curve, fortunately, according to AuT you do not have to and that is the subject of this post, at least sort of.
length of a side: 440 and height 280; so you get 880/280^1/2; 3.142857^1/2 or 1.571429.

So what is the standard comparison of phi and pi?
2sin(pi/5)=(3-phi)^1/2.
Other ways exists of expressing this:
Phi=1-2cos(3pi/5)
https://www.goldennumber.net/pi-phi-fibonacci/
This however, requires that either pi or phi have a definite value and they are both infinite series.
Or are they?

If AuT is accurate, a quantum theory, there should be precise way of determining this relationship, a quantum way.  One way is limiting the number of points, that is saying that pi only goes to so many places or that the Fibonacci number only goes to so many places; one requires the other.  But maybe there is another way, and that is what this post is about.  That way is to limit the number of dimensions and thereby find precision in the comparison to a quantum amount.

Here are the simplified (we don't work with infinite series to infinity) equations we will work with:
pi is made up of an infinite series of fpix solutions along with a numerator that defines dimension.  This is not a simple process but it is mathematically covered by a few simple infinite series:
fpix=denominator of pi
Sin(piz)[the first place for sin for any value (z) of  the numerator of pi from -1 to whatever]sin=2*y/(pi2^(2n+1)
The Fibonacci compression equation: 2f(x)^2^x where f(x) is the Fibonacci number for x.

If you can define this relationship mathematically, then you can show how the universe turns fpix solutions into dimensions that compress according to Fibonacci compression, maybe.

Here is an interesting feature of Phi or the Fibonacci "golden ratio" (more precise) or the "golden number."
Phi plus 1=phi^2; or to use the vernacular of AuT where F(x)=1, the golden number^2=golden number plus 1=2f(x)^2^x where x =1. This is true only where 2f(x)=2*1/2 or where f(x)=-1+1+1.
Another feature is phi-1=1/phi.
We're going to get to this derivation eventually.

What does AuT add to this discussion?
Well AuT shows pretty convincingly that just as the ratio of F-series converges on phi and as ratio of pi converges on 1 there is a connection between f-series and pi convergence.

You may recall that the connection between pi and fseries was shown using pi(-1) to pi(1) to arrive at 256/27 comparing the sign results for the first answer.
On further examination, it shows that if you compare pi(1) for pi(2) for the same place and instead of going from -1 to 1; you go from 1 to 1 (dimension to next dimension) the result is the solution to this equation:
2f(x)^2^x]/1417176 for x=3; pi(2) [pi for a numerator of 2 in first place]
Where the sin (first place in an infinite series) for -1 and 1 were -.4444 (repeating) and .4444 (repeating) respectively.
To get the factor to generate 1 for the sin for a given y, that y is 256:27
This has been theorized at f(n)^2^n for n=2/3^3 which serves as a factor for converting fpix to f(x) according to an equation something like this:
1=sin(pi1) where y=2f(x)^2^x/27 or where y=2567 where x=2

Here, for pi2 (where the numerator=2), y is 1.7777(repeating).
Using 1=sinpi2 you get a different conversion factor:
for x=3 f(x)=1679616. To get 1, you have to divide f(x) by 1417176 (the denominator of y for pi2)
This denominator is 2^3 * 3^11
This represents a 8 fold increase.
It just so happens (and nothing just so happens) that 2^3 is 8.

We should, therefore, be able to predict that for pi3 the value of y to yield 1 might be
2f(x)^2^x/[2^4*3^11*3^16]=16*3^27 to yield a ration of 1.
If it does I haven't figured it out yet.
Instead, however we have the intriguing:
The numerator for y to yield 1 is: 10^16 for 2f(x)^2^x for x=4
When you use "4" for y (meaning the denominator is 10^16/4) you get:
1=sinpi3 2f(x)^2^x/this denominator(2.5x10^15).
y=10^16/2.5*10^15.
This denominator looks like 2^14 times 5^16
or y= 2f(x)^2^x/[2^{(2^4)-2} * 5^{(2^4)}] perhaps

This might suggest yet another ratio for y in the sin equation for pi(4):
where 7 is the abs value of -7 and the 3 earlier corresponds to the abs of -3.
This does not work.
There is a number to get the value of y to yield 1 which is around

9.481481479

which means that the ratio should be 3.40282x10^38/3.5889155895585600x10^37.

As close as I could get using fpix and F(x) for pi=3 was 9.5 to 9.48 using 7^25, 5^17,3^7 and 2^4 which might look close but is a million miles away for this type of analysis.

Do you need to have an evolving equation which gets you from one value of y in the sin equation to the next past fpix3 or 4?
I would argue yes and no.
You have a compression relationship between ct3 and ct4, so whether you have an exact ratio for fpix to f(x) at this point is critical for completion, but not required for the kind of cursory analysis that support the theory.
A bigger question is whether this ratio that yields y defines the amount of free matter within the matrix of the next higher ct state.
Using the numbers above we can theorize this "free" to "paired" ct state
For ct1-everything is free although there is the underlying fpix equation to deal with that changes charge.
CT2-256:27 indicating at ct2 you have 256 matched ct1 states for each ct2 state
Ct3-1679616:1417176
CT4-10^16:2.5^10^15 (neutron)
CT5-3.40282x10^38/3.5889155895585600x10^37 (black hole)

The evolving relationship of f(x) to fpix and its relationship to the amount of change that can occur without degrading a compression state is pretty important to understand more fully.  This is a working theory, not a finished theory.

While it is possible that the equation breaks down in its entirety, that is unlikely.  More likely the evolving relationship changes primarily based on the application of the finite solutions to otherwise infinite series which is fodder for another post.

You might also recall, that phi is determined by the infinite series of one fseries solution divided by the next.  That is f(x)/f(x-1)=phi where x=infinity.  We know from AuT that this number varies in terms of maximum curvature to align with the maximum value of pi which averages compression over several numerator and denominator values depending on the compression present.

The great pyramids reflect these features.
The 1,1,2,3,5,7 is not immediately shown but all of the floors are separated by precise fractions 1/2,1/3, etc although different bases are used for the 1/5 than the others.  The 1/6 is not ascribed to a specific feature that I am aware of but several internal features appear lined up.

If you are impatient Please see the author's Amazon page at: https://www.amazon.com/author/frzmn and the author's Facebook page for more links and articles at https://www.facebook.com/frzmn1 or @frzmn1 which include the blog which has 5 years of development of the theory is you feel like slogging through that.
Video overviews can be found on this Youtube Channel: www.youtube.com/channel/UCxK8BwhzafIi1Jd0yE8mQXQ

The videos are surprisingly up to date.  For the one on compression deals with how the folding occurs in detail.  And this is my blog which takes an often tongue in cheek approach. https://gmfbooks.blogspot.com/