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JSON Data Format

A widely used data format for storing and exchanging data in NoSQL document databases, offering flexibility and human readability.
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The statement of the theorem

Define the set of valid JSON structures J\mathcal{J} recursively over the following types: \begin{itemize} \item Primitive\text{Primitive}: The set of atomic values V={null,boolean,number,string}\mathbb{V} = \{\text{null}, \text{boolean}, \text{number}, \text{string}\}. \item Array\text{Array}: A finite ordered sequence of values, Array=⟨v1,v2,…,vk⟩\text{Array} = \langle v_1, v_2, \dots, v_k \rangle, where vi∈Jv_i \in \mathcal{J}. \item Object\text{Object}: An unordered mapping from keys (strings) to values, Object={k1:v1,k2:v2,…,km:vm}\text{Object} = \{k_1: v_1, k_2: v_2, \dots, k_m: v_m\}, where ki∈stringk_i \in \text{string} and vi∈Jv_i \in \mathcal{J}. \end{itemize} The set J\mathcal{J} is the smallest set satisfying J=V∪Array∪Object\mathcal{J} = \mathbb{V} \cup \text{Array} \cup \text{Object}. This structure allows for the representation of complex, nested data graphs.