Zöget

Zöget is a term used in speculative mathematics and in certain works of fiction to denote an abstract class of structures intended to explore symmetry, duality, and computation. There is no single canonical definition, and different authors present zöget in distinct forms. In general, a zöget is treated as a finite, labeled object equipped with one or more relations that interact to reveal dual properties.

Formal sketches vary, but a common formulation describes a zöget as a finite set Z together with a family of relations {R1,...,Rk} on Z, satisfying informal axioms such as compatibility with a duality operation D, invariance under a symmetry group G, and a rule for composing relations. The exact axioms differ by treatment.

Variants of zögets include colored graphs, relational structures, or algebraic devices used in thought experiments about networks, information flow, or computation under symmetry constraints. Authors use zögets as illustrative tools rather than as standardized mathematical objects.

Origin and usage: The term appears in online discussions and pedagogical writings as a placeholder concept to discuss duality and symmetry. It has not achieved universal definition and remains an informal notion within a niche community.

Related concepts include dual graphs, symmetry, relational structures, and category-theoretic notions.