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Classification systems are the dark matter of social life: pervasive, structurally consequential, yet largely unmapped as relational systems. Despite a rich intellectual lineage from Durkheim and Mauss to Douglas and Bourdieu, sociological research on categories remains fragmented across cognition/institutions, boundary studies, and domain-specific case studies. This fragmentation has produced deep knowledge of particular categories but no shared toolkit for asking how classification systems are structurally similar or different across domains, or what functional consequences follow from their configurations. We develop a structural-functional framework, grounded in computational text analysis, that reveals the architecture of classification systems independently of their substantive content. We propose a three-axis theoretical model (relational structure, formation process, and boundary character) that generates functional properties including power, legitimacy, stability, and epistemic constraint. Structural comparison does not abstract from context and power; rather, it reveals precisely where power has deformed a system's architecture relative to systems with comparable histories. Our empirical strategy applies this framework across five institutionally grounded classification systems (U.S. Census racial categories, DSM-5 diagnostic classifications, NSF academic disciplines, musical genres, and Linnaean biological taxonomy) selected to vary along our three axes. We employ two complementary computational approaches: word embedding geometry, which maps how categories are organized in discourse and tracks structural change over time, and LLM-driven perturbation analysis, which stress-tests simulated institutional actors with structurally equivalent classificatory challenges. Together, these methods test whether structurally similar systems produce convergent behavioral responses even across unrelated domains. By treating classification as sociology's dark matter, amenable to indirect observation through its effects on language, we offer a shared conceptual vocabulary and demonstrate how computational text analysis can serve as a theoretical instrument for mapping the categorical scaffolding of social life.