• Computer Science > Databases [Submitted on 28 Jan 2026] Title:Topological Relational Theory: A Simplicial-Complex View of Functional Dependencies, Lossless Decomposition, and Acyclicity View PDF HTML (experimental)Abstract:We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex • This dependency complex exposes multi-attribute interactions and enables homological invariants (Betti numbers) to diagnose cyclic dependency structure • We define Simplicial Normal Form (SNF) as homological acyclicity of the dependency complex in positive dimensions, i • , vanishing reduced homology for all $n \ge 1$ • SNF is intentionally weaker than contractibility and does not identify homology with homotopy • For decompositions, we give a topological reformulation of the classical binary lossless-join criterion: assuming dependency preservation, a decomposition is lossless exactly when the intersection attributes form a key for at least one component

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  • Computer Science > Databases [Submitted on 28 Jan 2026] Title:Topological Relational Theory: A Simplicial-Complex View of Functional Dependencies, Lossless Decomposition, and Acyclicity View PDF HTML (experimental)Abstract:We develop a topological lens on relational schema design by encoding functional dependencies (FDs) as simplices of an abstract simplicial complex. This dependency complex exposes multi-attribute interactions and enables homological invariants (Betti numbers) to diagnose cyclic dependency structure. We define Simplicial Normal Form (SNF) as homological acyclicity of the depe

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