Hi Friends, I recently published a paper that claims I have a Grand Unifying theory that unites all fields and forces into a single equation that can produce values for the Fine Structure Constant and others, using pure geometry.  
It was getting rejected by physicists and number theorists alike because we were talking past eachother when using words like Unit, Point Vector and the concept of dimensionality.

I now understand where the disconnect was between our language and the math.

In standard equations, the Metric : KG, meters, seconds is defined using Euclidian geometry  
by their fundamental relationships to eachother governed by that system.

Fundamentally in that system there are 3 squares, and 3 rotations.  Value is given to each of those units which is dependant on the other 2. Fix 2 in place, and it gives relationship to the third. That is the concept of building dimensionality from that system.

  
That concept of that relationship represents a 3 to 2 dimensional relationship of orthagonality and curvature.

What if we modeled it differently? What if we did a 1 to 1 relationship, of orthagonality and curvature.  Then, we created a second 1 to 1 relationship  which is orthagonal to the curvature of the first one, exactly as this picture shows.  
So x\^2 + y\^2 = 2 represents both x and y   
  
That way it is still modeling the same thing, except using only 2 relationships at a time to create the third relationship.

This allows dimensionless units to be created just like in Euclidian Geometry, except now the scale is given which ties them all together, yet still remains as a dimensionless unit ( in physics speak).  
  
That extra dimension which measures scale of all the units at the same time, comes from the weight of math itself. -Conjecture, Testable.  


Regardless on conjecture being true or not, it remains, that this is a valid way to model the Universe because I am following the exact same steps and principles of Euclidian Geometry.  
These are not arbitrary circles or functions, they represent the heart and core of real numbers and pi and root 2, the source of Algebra and therefor Geometry itself.  
  
What is the most deserving thing for that to represent ?  Ofcourse time.  
Then, if Time is what we are measuring as 2, what is the scale?

There is only one possible answer, it is the weight of math itself.  
The relative size of the numbers in the expanding polnomial represent scale, and so therefor by combinatorially expanding this polonomial so that it is balanced for whatever dimension you are measuring, gives you a scale at which to take measurement.

That scale can be used to measure the world.  
Since Gravity exists as a 3 2 curvature object  
Time and distance represent the two objects, which are the same, but also different, separated orthagonal to eachother. As a 1 2 Curvature orthagonal relationship.

Orthagonal/Curvature Beginning = x2 + y 2 = 2Pi  or  root2. adding together to equal 2

First Split = (x4 + y 4 )+ 2(x\^2 y\^2) =2

Second Split = (x\^8 + y\^8 ) + 6x\^4y\^4) + (4x\^6y\^2 + 4x\^2y\^6 ) = 2

It is a chain series of derivatives that never ends that all have relationship to eachother, and the combined summed total, must always be equal to the relationship x\^2 + y\^2 = 2 Where 2 represents two separate obects that cannot be reduced. Representing Orthagonality, and Curvature.

I say this to you as a number theorist first, This is a meaningless circle right? Unless, I thought of each curve as a weight value on top of the curve before it.... If I treated it that way, I could use it measure something. But what would I measure with it?  


Pi and Root 2 are the origin of reals themself, so what if expanding this polynomial was thought of as like, the weight of math itself... Then x\^2+y\^2 = 2 could have a meaning , in relation to its own weight, at the first level, compared to its own weight at the 2nd 3rd or 4th level, whatever level we wanted it would be easy we just keep multiplying by 2.

Then we could actually use that to represent the weight of math itself.

x = x\^2 = 1,-1 is the origin of alebra itself  
And root2 and pi are the origin of the real numberline together.  


I claim that: since orthagonality and curvature are the most fundamental objects in math, they must fundamentally explain the universe.  
Not because I say so, but because theres literally no other way to begin.   
 

I can prove it even more strongly from a purely number theoretical way, but I hope if at this point, you are still reading you will say... okay how?

Lets Take the equation x\^2+y\^2 = 2  
Then if x\^2  = 1 Then x =1  
Now consider x=1 ,  
Algebra forces y=1  
  
The algebra forces the real number line through i and pi  
Because x and y are just the same thing, and yet different .  
So therefor, it literally MUST  be modeling the real world. because theres no other way...  
Its a scale that defines itself by it's own definition. The weight of math and expanding polynomials. 

  
We didn't break Pythagoras, we followed it explicitly, we didn't break Mathematics, we followed the rules explicitly, the only thing we did that was arbitrary was choose a value for c\^2, and doing so forced us to view addition and multiplication as fundamentally different operations.  
  
Multiplication does not equal repeated addition, not as a convention, but because it's demanded by the relationship between 2 and 1.  
  
I realize I am not stating a new idea here, but I am attempting to conceptually align the ideas of mathematics, physics, real numbers infinitesimals all at the same time. Because these facts will be important in combining quantum physics and the standard model.  
The fact that choosing the value of 2 requires both terms x and y to represent it using fractions is the very source of the concept infinite, infinitesimal, and the the break between the standard model and quantum physics.  It's the source of boundary between layers.  


Consider the same equation using only x  
x\^2 + x\^2 = 2

It is impossible unless you include the idea of positive and negative numbers, then you get 2 possible solutions of +x\^2 and -x\^2  
But, Thats just another way of saying x + y , it's a dyadic splitting.  
Fundamentally, they are two different objects, because they are not the same, thats the underlying definition.  
They are orthagonal to eachother, therefor, logically, they are not the same.  
  
Now consider spin, what is the property that is logically not the same as orthagonal?  
Curvature ofcourse.  
Now with those two concepts in mind, it's possible to alternate back and forth between orthagonal and curvature in a way that aligns all of the symmetries between them at the same time, by simply expanding the full x\^2 + y\^2 =2  
So that is all squared, but still equals 2.  
So that you get  
Dimension 1 = x = 2  , y =1  
Dimension 2 = x\^2 + 2y = 2  
Dimension 3 = x\^4 + 4y + 2x\^2 + y2 = 2  
Dimension 4 = (x\^8 + 8y) + 6x\^4 +4y + 4x\^2 +2y  +4x\^2+ 6y) = 2  
  
Doing that, gives a perfect assymetry to all of the dimensions, so that they are all in a cycle of symmetry and assymetry on their own.

What if weight was literally, the weight of math itself.... Maybe Euler was on to that idea, but never formalized it.   
  
Calculating the infninite polynomial in my paper causes you to have to calculate enormously big and complex polynomials as you go up.... Doing so, is literally the weight of the universe, that is relevant at all scales, that weight... is curvature.... added continuallly over and over,  
until you have every single dimension represented as a curvature compared to an orthagonal.  
But to keep it on a simple level, just look at the first few dimensional properties of the polynomial expansions I have come up with in my paper.  
  
So if x\^2 + y\^2 = 2  
Then we square, that, we create a new orthagonality to this layer.  
Now it becomes  
x\^2 +y\^2 +2x\^2y\^2= 2

At first glance , that has no meaning, other than a perfect circle, just bigger than before....  
But a perfect circle means perfect balance, and the entire equation becomes x\^2+y\^2= 2  
All over again. Zero weight of math...

However, if you don't have perfect balance, it will give a relationship to eachother, through orthagonality and curvature.  
This time proportinately to the one before it, and a new, orthagonal and curvature relationship.

How do we measure that orthagonality? By continually expanding that fraction and keeping everything perfectly square. Then we have an equation of the form x\^2+y\^2 =2  
Where  it could have as many polynomially expanded forms as we want it to have, but it is still perfectly balanced.  

I had several pages of theory crafting proof regarding limits and infinites here, but let me skip all that and cut to the chase.

  
If we unbalance this equation, in a very specific way, by keeping all the exponents for X while treating all exponents of y simply as multipliers , then we get this very perfectly balanced series of curves, which is literally encoding the weighted values of x and y, through a relationship of pi and root 2.

Consider this graph and the points it crosses. [https://ibb.co/Ngj5SL8m](https://ibb.co/Ngj5SL8m)

This is made specifically from the equations I showed, when normalizing y vs x\^2.  
Dimension 1 = x = 2  
Dimension 2 = x\^2 + 2y = 2  
Dimension 3 = x\^4 + 4y + 2x\^2 + y2 = 2  
Dimension 4 = (x\^8 + 8y) + 6x\^4 +4y + 4x\^2 +2y  +4x\^2+ 6y) = 2

These curves represent orthagonality in 2 ways at the same time. Through stacked cuvature and orthagonality. By doing so, it curve generates.  
My conjecture, is that those curves are related to the physical world, because they have to be since they apply to math itself.

Therefore The red circle and the grey circle, must represent space and time.  
The curvature caused through that relationship corresponds to Gravity, it is the first and most fundamental force.   


In this equation the yellow circle represents acceleration, a continuuous function which trades between space and time according to this curve.  Therefor, velocity can be thought of as a property specifc to acceleration with this curve representing G the Scalar applied when trading along this curve.  


Due to crossing both x and y perfectly orthagonal to them,  this represents the connection between acceleration and time. Represented as G curvature. In one dimension.  


I am so sure that it models the Universe exactly, it is literally forced by the math, it is a circular proof in both logic in the funny haha way, and the geometric way.  
And when you think about it, any proof regarding time, must truly be a proof where it proves itself, in terms of itself.  
The weight of math, is literally the weight of the universe,

I am really hoping people can start checking into this with me, because its not an easy task to go forward from here. I have to rebuild scale for every unit, then use it to prove standard physics like electron orbitals.

I'm just a regular guy who loves physics and math, so thats going to take me time, so I am grateful for anyone that wants to pick this up from here and run with it  or help me ...

  
The picture of the equation in Thread post shows perfect assymetry. 

But if we adjust individual values by just a little bit, it produces more complex shapes, like this one here, which could represent electron orbitals, where the Grey circle is the equation worked out as far as momentum squared. [https://ibb.co/zTKpFPhk](https://ibb.co/zTKpFPhk)

Thanks for checking things out.   
Happy mathing.

By the way if you're interested heres the full paper, but I kinda just went over it all here already, [https://zenodo.org/records/18506210](https://zenodo.org/records/18506210) 

How To build Dimensions, Using Recursive Functions involving Pythagoras, translated into the Standard Understanding