The learnware paradigm aims to enable users to leverage numerous existing well-trained models instead of building machine learning models from scratch. In this paradigm, developers worldwide can submit their well-trained models spontaneously into a learnware dock system, and the system helps developer generate specification for each model to form a learnware. As the key component, a specification should represent the capabilities of the model, enabling it to be adequately identified and reused, while preserving developer's original data. Recently, the reduced kernel mean embedding (RKME) specification was proposed and utilized as the foundation of learnware search algorithms and system construction. However, a theoretical analysis of the preservation ability of RKME specification for developer's training data remains open and challenging. In this paper, based on novel modeling and analysis, we prove that RKME specification can scarcely contain any of the developer's original data, and possess robust defense against common inference attacks, while preserving sufficient distribution information for effective learnware search.