algebraicStructuresCert
plain-language theorem explainer
The definition algebraicStructuresCert packages the established count of five algebraic structures into a certificate structure at configuration dimension 5. Researchers deriving algebraic foundations for Recognition Science models would reference it to confirm the progression from groups through vector spaces. It is realized as a direct field assignment that applies the decided cardinality theorem without additional steps.
Claim. Define the certificate structure whose sole field requires that the finite cardinality of the enumerated type of algebraic structures equals 5. The definition sets this field to the value 5 supplied by the upstream count theorem.
background
The module enumerates five canonical algebraic structures ordered by increasing richness at configuration dimension D = 5: group, ring, field, module, and vector space. Each successive structure adds operations or axioms to the prior one. The upstream theorem algebraicStructure_count establishes that the cardinality of the type AlgebraicStructure is exactly 5, proved by a decision procedure.
proof idea
This is a one-line wrapper that constructs the AlgebraicStructuresCert instance by assigning its five_structures field directly from the algebraicStructure_count theorem.
why it matters
This definition supplies the certified enumeration of algebraic structures at configDim = 5, closing the count step within the AlgebraicStructuresFromConfigDim module. It supports potential links between algebraic richness and the Recognition framework's forcing chain, though no downstream uses are recorded. The module reports zero sorry or axiom markers.
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