You had a theory which stated based on certain arguments carrot will join....
Which means for us your theory was wrong because in manga she didn't join.
For example Carrot is still one of the background character who was linked the most with the strawhat. She is still the only character with a post besides the strawhat and is overall build like a strawhat. Those little things are not normal for a background character in One Piece. So there needs to be an explanation for their presence. My theory was first that Carrot is meant to join after Wano, this was proven wrong. Another theory that can't be disproven is that Oda changed is mindlast minute. I don't believe in that. I think that Carrot still has a shot, but later.
It's you who has to lay down proof regarding it
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Your theory and your conclusions and everything you say is wrong