LegalTraditionsCert
plain-language theorem explainer
A certificate structure records that the set of canonical legal traditions has cardinality five, aligning with the configDim parameter set to five in the sociology module. Researchers in comparative jurisprudence would cite this when integrating legal systems into the Recognition Science dimensional framework. The structure is defined by a single field that states the cardinality equality derived from the inductive enumeration of the five traditions.
Claim. A certificate that the set of legal traditions has cardinality five: $|L| = 5$, where $L$ consists of civil law, common law, Islamic sharia, customary, and socialist systems.
background
The module sets configDim D to 5 to enumerate the dominant legal traditions that cover over 95 percent of world jurisdictions. The inductive type enumerates exactly five cases: civil law (Roman-Germanic), common law, Islamic sharia, customary, and socialist or post-socialist. This setup treats legal systems as discrete configurations derived from the same dimensional parameter used elsewhere in the framework.
proof idea
As a structure definition, it consists of a single field asserting the cardinality equality. No tactics or lemmas are applied; the equality holds by construction from the five-element inductive type.
why it matters
It provides the certificate used by the downstream definition that constructs an instance of this structure. This places the sociological classification within the Recognition framework, where configDim D equals 5 parallels the spatial dimension D equals 3 from the eight-tick octave in the forcing chain. The module notes the coverage of over 95 percent of jurisdictions as empirical grounding.
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