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Categorical variants, or sets of genomic alterations constrained by shared properties, are pervasive across clinical, regulatory, and research domains in the biomedical ecosystem, yet their inconsistent and non-computable representation hinders data interoperability and clinical interpretation. We surveyed genomic knowledgebases spanning regulatory approvals and the biomedical literature and found that categorical variants underpin a substantial proportion of clinical genomics knowledge, but are largely described using incompatible bespoke models. To address this, we developed the GA4GH Categorical Variation Representation Specification (Cat-VRS), a constraint-based framework that provides a unified computable representation for both precise and intentionally broad categories across molecular and systemic variant domains. Cat-VRS enables harmonization of genomic knowledgebases, computable category-based search, and automated matching between assayed variants and categorical entities in clinical and research contexts. By providing a principled, extensible model for categorical variation, Cat-VRS enables computable reasoning over genomic variant categories and establishes a foundation for the standardized representation and exchange of genomic knowledge.