Thats just a symbol mate. The actual text blows your theory out the window. Read your own scan.Kishi here points the focus on the Rinnegans here. He did that for a reason :-
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I don't think Shizen has any relevance here. That is the power of the Juubi. Yin and Yang is the power of Hagoromo. When Hagoromo became Jubbi Jin, I think those Three got muddled up and mixed.