The FAIR principles are globally accepted guidelines for improved data management practices with the potential to align data spaces on a global scale. In practice, this is only marginally achieved through the different ways in which organizations interpret and implement these principles. The concept of FAIR Digital Objects provides a way to realize a domain-independent abstraction layer that could solve this problem, but its specifications are currently diverse, contradictory, and restricted to semantic models. In this work, we introduce a rigorously formalized data model with a set of assertions using formal expressions to provide a common baseline for the implementation of FAIR Digital Objects. The model defines how these objects enable machine-actionable decisions based on the principles of abstraction, encapsulation, and entity relationship to fulfill FAIR criteria for the digital resources they represent. We provide implementation examples in the context of two use cases and explain how our model can facilitate the (re)use of data across domains. We also compare how our model assertions are met by FAIR Digital Objects as they have been described in other projects. Finally, we discuss our results' adoption criteria, limitations, and perspectives in the big data context. Overall, our work represents an important milestone for various communities working towards globally aligned data spaces through FAIRification.