### State of the Art
It discusses the algorithmic principles of content-based, collaborative, knowledge-based, and hybrid filtering, with an emphasis on architectural features and implementation challenges. The authors address issues of scalability, data sparsity, integration into real-world user scenarios, and the necessity for recommendation diversity. The most commonly used datasets and application scenarios are also analyzed. While structural challenges are well described, the internal logic of algorithm operation is not detailed. Temporal aspects are likewise not discussed. The article [18] analyzes recommendation systems from the standpoint of fundamental mathematical approaches. The authors examine probabilistic algorithms and methods for measuring similarity between users or items, emphasizing how the choice of metrics influences accuracy and performance. A comparative analysis of the strengths and weaknesses of different similarity calculation approaches is provided. However, the article lacks a description of the system's architectural structure in terms of logical stages (categorization, validation, iteration), as well as the temporal dynamics of interaction. The article [19] proposes a formal method of collaborative filtering using production rules to estimate unknown similarity coefficients between users. The method is based on a graph structure, the application of fuzzy logic, and inference rules. The authors implement a software model and demonstrate improved system accuracy across several metrics. Although the study presents a clear inference structure, the logic of user model construction is limited to the matrix completion phase and does not include a more developed process architecture. The article [20] explores the use of Markov decision processes for building adaptive recommendation systems. The study highlights the limitations of static models and the necessity of considering the temporal dynamics of user interaction with the system. It presents the logic of an algorithm capable of responding to changes in user preferences based on iterative interaction, which is an important direction in the formalization of data processing algorithms. However, the article remains at the conceptual review level, not offering a formal structural model or assessment of probabilistic transitions between query processing stages, underscoring the relevance of further formalization of such approaches, for example, through the application of GERT models. The article [21] proposes the TSGNN architecture--a graph neural network model for recommending new items in session-based scenarios. The main contribution of the work lies in introducing a temporal structure into the session graph, enabling the modeling of user interest dynamics. Additionally, mechanisms of graph contrastive learning and temporal attention are implemented to mitigate data sparsity and bias. The work demonstrates a clearly formalized architecture and addresses tasks closely aligned with the logic of step-by-step user query processing. The architecture described in the paper is focused on training a neural network but does not formalize the processing logic in terms of probabilistic transitions or equivalent graphs, making the use of probabilistic network models relevant for the interpretation and quantitative analysis of algorithm structure. The authors of the article [22] present an analytical GERT model of a recommendation system operating in a decentralized P2P network. The focus is on formalizing probabilistic data transmission processes, taking into account the reliability and security of communication, which allows for the system to be modeled under dynamically changing topologies. The proposed model enables the analysis and comparison of various algorithmic schemes in the presence of stochastic factors. Despite its high degree of formalization, this model is primarily oriented toward transport and network aspects, while structural query processing, staged logic, and user behavioral adaptation are not modeled.