First image.
Why are you including the [math]\pi[/math]s? They just cancel out.
On one side you have [math]\phi[/math] then an arrow and [math]\phi ^2[/math]. What is the meaning of the "1" under the arrow?
They would only cancel out as 1 if not building upon, but replacing pi with 1 is actually a mistake:
it assumes there are no identities which relies on the transcendental nature of pi, given pi contains
an intrinsic radius-to-circumference relationship. Once pi is dropped, the expression is geometrically meaningless.
The meaning of the '1' under the arrow is to indicate that by simply squaring phi,
recalling it is an irrational number, a natural '1' emerges such that you have phi,
which is irrational, giving rise to '1'. I don't understand how "mathematicians"
overlook the importance of that: transcendental becomes real and natural.
If not having started with pi, this transcendence would be meaningless, as
the '1' is already denoted by whoever decided to use '1' instead of allowing pi to produce it naturally.
Now the concerned '1' in any equation need not be the meaningless number/digit '1' but, say, unity.
Second image. Where did these numbers come from? They don't seem to have any relationship between this image and the first.
These numbers came from the concerned identity, when reducing the base by one power. For example, the identity is 1, phi^3, each over p^2. When setting p^1 reveals the numbers in the second image.
They are only related in that the concerned identity relates to the identity of phi^2, but has an intricate 3rd term ±c.
If you expect to have any conversation about this at all you are going to have to start explaining things. If you persist with confidentiality then you will have to get a Peer Review in order to try to win a Millenium Prize and you are nowhere near being able to do that. So you have a choice: Stay silent and not get anywhere here or open up and get some (badly needed) help. We simply can't help you if we don't know what you are talking about.
-Dan
It's not that you don't know, it's that you don't listen: I am asking a very simple question,
and everyone keeps diverting and focusing on things I'd rather not even talk about.
what is the correct "terminology" of the whatever-it-is in the top corners of the first image?
I am able to do it - I'm just not willing to write up a paper to submit to some journal
over verifying 1=1. If the mathematicians have to argue over that, I'm not interested.
Besides I found the solution to the number theory problem via pursuing a different problem entirely:
however at the roots they are related. It is the reason I came here: for "help" but all I am getting
is people who are full of enmity and generally bad attitudes. I just came here for help,
and this place is not unlike the rest: full of people who blame others for their own being angry.
So are we able to focus on the actual question I have been asking?