I understand what you're saying (in the first paragraph). I really do because I also went down this path. Self-reference is very tricky and it's way easier to trick yourself into proving things than to prove things.

You are referencing Godel and there is a reason why he only proved 'non-provability', namely Tarski's undefinability theorem[1]. In short, you cannot express the truthiness of a statement in the system within the system itself. This prohibits you to draw conclusions in a way you did above.

I'm of course no expert on the matter, and I might be wrong just as likely, but I'll encourage you not to make such strong, definitive statements. Maybe the reason for it is only that what you stated above would be a huge result in mathematics so one would think there is a mistake somewhere (especially since Liar's paradox is nothing new). And one would explore the subject further to find it rather than 'I post it on online forums because no one wants to accept my theory'

[1] https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theo...