HasConfigDim5
plain-language theorem explainer
The predicate that a finite type has cardinality five formalizes the repeated appearance of five-element configuration spaces. Analysts of cross-domain structure in Recognition Science cite the predicate when certifying instances across sensory, emotional, biological, economic, and linguistic domains. The definition consists of a direct abbreviation of the standard finite cardinality condition.
Claim. Let $T$ be a finite type. Then $T$ has configuration dimension five precisely when its cardinality is five.
background
Module C13 establishes the structural claim that configuration dimension five occurs with high frequency across domain modules. The predicate captures this by requiring that the type be finite and have exactly five elements. This setting supports subsequent theorems on equicardinality of any two such types and on the product of three such types having cardinality 125.
proof idea
The declaration is a definition that directly sets the predicate equal to the equality of the cardinality to five.
why it matters
The definition supports the construction of the ConfigDimUniversalityCert structure collecting five domain instances and the equicardinality result for pairs of such types. It realizes the C13 claim of D=5 universality in the Recognition Science framework, connecting to the eight-tick octave through the phi-ladder mass formulas.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.