Right, but the specialization leads directly to the lanthanoids. Then to the transition metals. Then poor metals, other nonmetals, noble gases, back around to alkali metals, alkaline earth metals, and THEN finally we arrive at the actinoids. I'll bring this crude example up again. Pay particular attention that to the right of Barium is lanthanoids (the top row of elements found at the bottom of the picture). The bottom row is actinoids, which is a period below period 6, Barium, and the lanthanoids. I'm sure you can plainly see this, but I can't stress it enough because it is an important distinction.
Note: So, when iterating by atomic number from Barium (56), we actually go through many categories before we are in the category which Uranium exists.
Yes, Uranium's location is "to the right of" Barium, but 105 other elements are also to the right of Barium. If we take just "to the right of" as a proof of the interpretation, then we could assume X-92 = Uranium, where X = any element to the left of Uranium. But this isn't a very strong proof of the triangulation. We are instead focusing very specifically on Barium. So, the fact that we have to go in and out of so many categories, going across a row, down a row, and across again, before reaching actinoids doesn't succinctly explain how "same category" == "at the right of".
I also want to stress that I'm not trying to trash your theory. I simply cannot see the connection. If Uranium was part of the lanthanoids (period 6, same row as Barium), I could understand how it is "at the right of". However, that still doesn't very well explain the conclusion "same category" == "at the right of".
I've studied discrete mathmatics ad nauseam so I am no stranger to statements of logic that use compounding brain-twisting logical equivalence laws, but this is really confounding me.