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an Entity in Data Space: dbkwik.org

I want to understand the argument being made from equation 6.1 to 6.5 in this paper between pages 27-28 6.2, 6.4 and 6.5 are completely out-of-the-blue to me and I have no clue as to from where they come. My impression is that this part of the argument in the paper is self-contained and it would be great if someone can help me get these equations. If people want it then I can try to paraphrase here again as to what is written in the paper but I have actually nothing to add to what is already written in that paper..

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