## 2 Materials and Methods  
### Algorithmic Structure for Processing User Data in a Recommendation System  
The methodological foundation of this study lies in the use of probabilistic-time modeling for simulating the internal architecture of a personalized recommendation system. Central to this modeling approach is the application of GERT, which enables the representation of data processing flows that incorporate probabilistic transitions, return cycles, and time-distributed processing stages. This formalism was selected due to its capacity to capture the inherent uncertainty and cyclical nature of information refinement processes typical of personalized recommendation environments. Unlike classical modeling approaches such as Petri nets or queuing theory, GERT explicitly supports the inclusion of feedback loops and non-deterministic time delays, offering a more flexible and realistic description of user-system interaction in scenarios characterized by incomplete or evolving input data. In the course of the research, the user query processing procedure was decomposed into logically distinct stages, each corresponding to a semantically meaningful transformation of the data. For each of these stages, a GERT network was constructed to reflect the structure of transitions and branching logic. The associated transfer functions were then derived using Laplace transforms, which made it possible to describe the time behavior of the system in analytical form. To retrieve the actual temporal distributions, a numerical inversion of the transfer functions was carried out. This enabled the construction of time density and distribution functions, which in turn allowed for the computation of key statistical indicators such as the mathematical expectation, standard deviation, quantiles, and probability of exceeding specified time thresholds. Such formalization provides insight into how uncertainty and delays propagate through the recommendation process and how they influence the overall responsiveness of the system. Furthermore, this methodological approach facilitates the structural optimization of the recommendation system architecture through quantitative assessment, and it is adaptable to other domains where the logic of data processing involves probabilistic or iterative patterns. The process of response generation in the context of an intelligent recommendation system is a multi-stage procedure aimed at extracting, structuring, and interpreting user data. It is built on the principle of sequential filtering and information refinement, as follows: from receiving and categorizing the request to its formalization and the generation of a meaningful response. This architecture ensures high result accuracy, minimizes processing errors, and enables the consideration of both user-specific features and the specifics of global reference data. Input data can come from various sources. These include direct user queries, information about the user from external digital systems, and structured global knowledge bases. The initial textual formulation of the request may be either formal and well-structured or unstructured and ambiguous. External sources provide behavioral and demographic characteristics, activity history, and preferences. As a reference for global data, platforms like Europeana are used, which aggregates multimedia cultural resources with richly described metadata. The algorithmic structure is divided into three key stages, each implemented as a corresponding submodule formalized in the form of a GERT scheme. The first stage involves the reception and categorization of the user request. At this point, the system analyzes the initial input, identifies relevant conceptual domains, and attempts to assign the request to predefined categories. This stage also includes mechanisms for reformulation in cases of ambiguity or incorrect classification. The second stage is dedicated to the assignment and validation of semantic weights for the identified categories.