This paper introduces Case-Enabled Reasoning Engine with Bayesian Representations for Unified Modeling (CEREBRUM). CEREBRUM is a synthetic intelligence framework that integrates linguistic case systems with cognitive scientific principles to describe, design, and deploy generative models in an expressive fashion. By treating models as case-bearing entities that can play multiple contextual roles (e.g. like declinable nouns), CEREBRUM establishes a formal linguistic-type calculus for cognitive model use, relationships, and transformations. The CEREBRUM framework uses structures from category theory and modeling techniques related to the Free Energy Principle, in describing and utilizing models across contexts. CEREBRUM addresses the growing complexity in computational and cognitive modeling systems (e.g. generative, decentralized, agentic intelligences), by providing structured representations of model ecosystems that align with lexical ergonomics, scientific principles, and operational processes. CC BY-NC-ND 4.0 at https://github.com/ActiveInferenceInstitute/CEREBRUM