## 2 Materials and Methods
### GERT Model for User Data Processing in the Recommendation System  
#### 2.2.1. GERT Model of the First Stage of User Request Processing  
The first stage of user request processing is focused on structuring the incoming information, verifying the correctness of categorization, and resolving potential ambiguities. The logic of this process is formalized using a probabilistic graphical model, GERT (Graphical Evaluation and Review Technique), which is illustrated in Figure 4.  
In Figure 4, the process stages are schematically represented as a directed graph, where each node corresponds to a processing step, and the arcs represent probabilistic transitions between them. The model includes nodes and transitions. The list of nodes and their formal descriptions are shown in Table 2.  
After defining the main nodes of the GERT model for the first stage, it is necessary to examine the structure of transitions between them, reflecting the dynamics of request processing. The transitions between the model's nodes are probabilistic in nature and are governed by the logic of conditions for passing through or returning. The initial node (node 1) represents the moment the user's request is received. From this node, the process moves to node 2, which reflects the initial categorization of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Node** & **Stage** & **Purpose** \\ \hline
1 & Request reception & Initial entry point \\
2 & Categorization & Preliminary analysis of the data structure \\
3 & Category validation & Checking correctness of assigned category \\
4 & Reformulation & Correction and return to previous stages in case of error \\
5 & Weight assignment & Transition to the data prioritization stage \\
6 & Stage completion & Transfer to the next processing module \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The list of nodes and their formal descriptions. Figure 4: GERT scheme of the first stage of user request processing. request. This transition occurs via arc \(W_{12}\), which is characterized by a nearly certain probability of passage, as categorization is a mandatory step in processing any request. After the categorization is completed, the process transitions via arc \(W_{23}\) to node 3, where the assigned category is validated. At this stage, the category is checked for consistency with the user's request, the data structure, and the expected types of information. If validation is successful, the transition proceeds to node 5 via arc \(W_{35}\), corresponding to the next stage--assigning weights for further prioritization of information. If the validation fails (e.g., if the category is assigned incorrectly or the request turns out to be ambiguous), an alternative path is activated as follows: via arc \(W_{34}\), the system transitions to node 4, where the request is reformulated or corrected. The purpose of this step is to eliminate ambiguities and bring the request structure to a format suitable for repeated categorization. Then, via arc \(W_{42}\), the process returns to node 2, and the categorization is performed again. In the case of successful categorization and validation, the system reaches node 5, corresponding to the stage of weight assignment, and then proceeds via arc \(W_{56}\) to the final node 6, which completes the first stage of processing and hands control over to the next module of the system. Thus, the structure of the GERT graph enables multiple returns and iterations, particularly between nodes 2-3-4, providing flexibility in processing unstructured or erroneous requests and increasing the system's resilience to user errors. To analyze the temporal characteristics of the process, classical methods of GERT network analysis can be used. For example, the expected total processing time of a request, \(E[T]\), is defined as the sum of the weighted average times over all possible paths leading from the initial to the final node, taking into account the probabilities of traversing each path.