A method of forming the structures of digital doubles of domain-oriented objects in the open source space based on the formalisms of the theory of sets, graphs, category theory and the theory of generating Chomsky languages

For the material of this article, open sources can be presented as information posted on the Internet for multiple and unlimited use in the form of machine-readable systematized data, in formats that allow their separate automated processing. Any of the open sources is partially structured content, characterized by the fact that it consists of fuzzy overlaps and connections formalized by a number of sustainable rules. Aim. The purpose of the study is to produce a mathematical description of the rules for the decomposition of links of virtual images of content based on statistical data of comparisons in order to formulate a digital analogue of the verbal structure. The research is accompanied by the development of a modular cross-platform predictive analytics system for distributed open sources of the social digital environment based on multi-stream data processing technologies. The system is based on the creation of a prototype of a digital twin, which allows monitoring and subsequent analysis of open sources. A cross-platform digital twin can be created for various open sources. Currently, among them, social networks are a priority for the analysis of the studied data. Materials and methods. Turning to the same type of code content, it becomes necessary to formalize the rules for categorizing the semantic meanings of the structure of connections of the object of study, which can be described in the language of graph theory, have a suitable structure in Lie matrices, obey the laws of transitivity and have properties that allow you to recreate connectivity in a quasi-projection. A method is proposed that makes it possible to produce sequential calculus that does not contradict each other according to the basic rules of axiomatics. Results. The method allows for real-time analysis of the data flow of open sources, identification of digital traces of research objects, identification of the structure of their connections. Conclusion. With the help of the proposed group of algorithmized mathematical iterations, it becomes possible to create a combination of local systems with feedback subsystems of predictive analytics of open sources of Internet resources and local systems for various purposes.