## 3 Results
### Propositional Stage  
In the propositional stage, the complete construction of the DTs is carried out based on the objectives, scope, and level of integration established in the contextual phase. This sequential stage aims to generate the DTs that will support decision-making related to the process, system, or product under study. To achieve this, a structured development project formulation is created, the studied system is interpreted, system coding and modeling are performed, along with connections to the real system, and finally, the obtained results are analyzed. In alignment with existing literature that differentiates between Digital Models (DM), Digital Shadows (DS), and DTs [50], this study proposes three practical levels of application for DTs implementations in production and service systems. These levels are structured to guide the progressive adoption of DTs according to the available infrastructure, integration capacity, and system complexity:  
* Level 1--Monitoring (Digital Model): At this level, the digital system receives data from the physical environment at predefined intervals. The representation is static or manually updated, and its main function is to support system observation and historical analysis. * Level 2--Diagnosis and Simulation (Digital Shadow): Here, data is automatically collected in real time and used to simulate or predict system behavior. Although the digital system does not influence the physical process directly, it offers valuable insights for operators, enabling decision support. * Level 3--Closed-Loop Optimization (DTs): This level enables bidirectional communication between the digital and physical environments. The virtual model performs predictive analysis and provides actionable outputs that are integrated into the operational workflow, either automatically or through operator-mediated execution. This dynamic feedback loop allows the system to adapt continuously and optimize performance in real time. The implementation presented in this study reaches Level 3, as it integrates real-time sensing, cloud-based processing, simulation, and a feedback mechanism that informs operational adjustments. This ensures continuous system adaptation, aligning with the core principles of fully functional DTs. Step 4: Validation of the Developed Methodology: The field validation was carried out in a rural composting facility located in Cajamarca, Tolima (Colombia), at an altitude of approximately 1700 m above sea level. The region is characterized by a temperate-humid climate with average daytime temperatures ranging from 18 \({}^{\circ}\)C to 26 \({}^{\circ}\)C and relative humidity between 70% and 85%, which can influence composite dynamics and sensor behavior. The composting process studied consists of a material reception area where the received organic material is homogenized, eight composting beds equipped with a forced aeration system operating in a linear arrangement with the product being rotated every eight days, and a packaging area. The control variables are the moisture and temperature of the compost piles, which are essential to ensuring high-quality compost. The DTs developed for composting in Cajamarca is a comprehensive system based on a three-layer architecture: physical, cloud, and virtual. In the physical layer, temperature and humidity sensors monitor the process conditions in real time, while operators adjust parameters such as ventilation and irrigation. The cloud layer processes and stores the collected data, feeding a predictive model in the virtual layer that simulates and optimizes the system's behavior. The DTs were developed following the methodology and architecture proposed in Table 2.  
The real system is operated by personnel responsible for executing the necessary actions. To integrate it with the DT, specific schedules were established for feeding the DT with data from the real system and implementing in the real system the actions recommended by the DT.