### State of the Art
Special attention is given to modern challenges, including increasing data volumes, the need for adaptability, and fair representation of recommendations. However, despite its broad scope, the authors barely touch on the internal logic structure of the systems. Therefore, there is no detailed step-by-step model of query processing. Furthermore, the authors do not consider temporal factors influence or system behavior cyclicity. The article [9] is a meta-review of recommendation system research covering the period from 2001 to 2010. The authors analyze 187 publications selected from 37 leading journals, categorizing them by subject areas (e.g., books, movies, and music) and by applied algorithms (kNN, neural networks, decision trees, etc.). The work highlights the growing interest in personalized recommendations while noting the field's immaturity and a lack of research applicable to practical problems. Specifically, it notes the underrepresentation of recommendations in visual arts and cultural heritage, as well as the limited application of social network analysis methods. The authors of the study [10] describe the implementation of a content-based recommendation system for creating personalized museum tours (based on the UCL Grant Museum of Zoology, London, UK). The paper presents features of user interaction with the system in a physical space, conducts pilot user tests, and identifies critical limitations. Despite the interesting case study, the system architecture remains simplified: there is no description of internal request processing logic, no modeling of decision-making step sequences, and no modeling of return or route refinement situations. Article [11] presents a prototype system called CHIP, designed for personalized access to digital museum collections. The authors address three fundamental tasks typical for recommendation systems in the open web environment. First, a content-based method is proposed for handling complex semantic relationships among objects, including both artworks and conceptual art topics. Second, attention is given to typical user modeling problems--the \"cold start\" effect, rating sparsity, and issues with feedback collection. Third, the visualization of recommendations through various representation channels is discussed, as follows: historical timelines, museum maps, and faceted navigation. The \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Reference(s)** & **Focus Area** & **Key Contributions** & **Identified Limitations** \\ \hline \multirow{2}{*}{[16; 17; 18; 19; 20; 21] algorithms} & Modeling of data processing algorithms & Analytical models (e.g., Markov chains, decision processes, and graph methods); early GERT use in networks & Mostly high-level or conceptual; lack of detailed probabilistic-time modeling of user request flows \\ \hline \multirow{2}{*}{[22; 23; 24; 25] system} & Intelligent recommendation system & Deep learning, knowledge graphs, semantic user models & Advanced architectures but missing explicit stage-wise logic and timing formalization \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._approach's effectiveness is confirmed by user testing results within a user-centered design cycle. Despite its high innovation and real-world application, the system architecture remains fragmented in terms of formal request processing modeling. There is no stage-wise processing logic, nor are probabilistic or temporal characteristics of user-system interactions specified. Preference refinement cycles, reverse transitions due to interest changes, or categorization errors are not considered. The article [12] examines the impact of user segmentation on the performance of recommendation algorithms. As a method of data structuring, the authors propose using a scheme similar to the recency-frequency-monetary (RFM) model, which is widely used in marketing.