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Since I don't know English very well, I can't understand everything from the end of the game.
However, inspired by the theory of Hirokey, I decided to build my own based on it. Quadatrum personally in my understanding is a world where all things and ideas that could not appear in the main world converge. (Where all the main action takes place)
Which makes it a parallel world by the standards of the world we know in the multiverse, but also distinguishes it from other worlds and makes it unique even among them.
Regarding the nature of Yozora and the Nameless Star, if Quadatrum is really a world in which all ideas that have not received a material shell in the world known to us are received in this, then Yozora can indeed be associated with at least Riku and possibly Sora. What if he's the failed nobody Sora and Riku? Regarding Riku, his body was taken over by Ansem and a little more and Riku could have had his own nobody, but it didn’t appear since Riku didn’t formally l his heart, so his is nothing more than an idea that got corporeality in Quadatrum nobody.
The same goes for Sora, when he freed his heart, his nobody was supposed to appear, however due to the fact that Sora had two hearts inside him including himself and the fact that he was heartless for too little, Roxas and Namine came out very unique. I mean Roxas is much more Ventus than Sora, and Namine is generally a unique creature that is neither Kairi nor Sora in full measure. Which essentially makes the real nobody Sora non-existent. So Yozora might be some sort of merger between nobody Riku and Sora. Ditto for the Nameless Star, she may very well be the real Kairi, for since Kairi is the princess of nobody's heart, she could not reproduce her therefore in the world of KH, its nobody is just an idea, while Quadatrum is a reality. The unnamed star actually looks very similar to Kairi (Eye color, hair color, full lips)
Regarding the origin of the Quadatrum, it is possible that it is a product of the creation of the Masters of Masters or the Book of Prophecy. For as far as I know (If I'm not mistaken) Dandelions also fled to the reality created with the help of the Book of Prophecy.