The article examines the concept of the digital thread in additive manufacturing as a foundation for improving the economic efficiency of the production cycle through intelligent support at the design stage. A mathematical model and algorithmic procedure for the "Search and Selection of Knowledge Fragments" stage are proposed within the framework of the authors' development of the MAPE-K adaptive control model by incorporating the stages of search, reuse, and evaluation. It is shown that the most significant potential for increasing the productivity of additive manufacturing is concentrated at the design stage of digital product models and technological processes, where the application of ontological modeling and machine learning methods can significantly reduce labor intensity and improve the quality of decisions made. The study formalizes the task of searching and selecting knowledge fragments based on a combination of semantic and embedding representations. A multi-stage candidate selection procedure is proposed, including attribute filtering, embedding search, re-ranking, constraint validation, and selection based on diversity criteria. This approach allows combining the interpretability of ontologies with the scalability and robustness of ANN mechanisms. The results of the work include a model of the digital thread for additive manufacturing, a detailed description, and a system of mathematical support for the stage of searching and selecting fragments. The obtained results form the basis for building a digital thread for additive manufacturing, oriented towards a self-learning knowledge base and continuous model improvement.