I hope you don’t mind me saying this but uploading a proof of this without even putting your name on the work invites theft. Someone else may easily rush into publishing this.
and if your proof is actually correct — i did not have time to read it yet — this would be sad.
I already submitted it with my name and address to Journal of the American Mathematical Society, who declined it for unknown reasons.
And I do have an identity here, technically, and I gave a copy to a lawyer with email headers and time stamps, so I can prove authorship.
To say nothing of notes and records of the derivations.
Definitely not cutting edge math, but if you are not familiar with the “Golden Ratio”
(Also identified by the Greek letter Psi), it is quite interesting. Check out some of the Youtube videos on the subject.