civilizationalStageCount
plain-language theorem explainer
The theorem fixes the number of civilizational stages at five in the Recognition Science sociology model. Historians or sociologists formalizing phi-ladder cycle predictions would cite this cardinality when assembling the full certification object. The proof is a one-line decide tactic that exhausts the five constructors of the inductive stage type.
Claim. The finite type of civilizational stages has cardinality five: $|C| = 5$, where $C = $ {emergence, growth, consolidation, decline, transformation}.
background
The module models historical rise-and-fall cycles as recognition coherence fields whose timescales follow the phi-ladder. CivilizationalStage is the inductive type with exactly five constructors (emergence, growth, consolidation, decline, transformation) that derives Fintype, DecidableEq, and Repr. This supplies the stage count that the downstream certification object consumes to pair with the phi-ratio duration claim.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the equality Fintype.card CivilizationalStage = 5. The tactic succeeds because the inductive definition derives Fintype and the five constructors are decidably distinct.
why it matters
The result populates the five_stages field of the downstream civilizationCyclesCert definition, completing the minimal certificate that also carries the phi-ratio duration. It supplies the D = 5 stage count required by the sociology tier of the Recognition framework, consistent with the core eight-tick octave and phi-ladder structure (T7). No open scaffolding questions are closed by this declaration.
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