criterionCount
The theorem establishes that the finite type of binary governance criteria has cardinality exactly three. Institutional theorists applying the Recognition framework to configDim D equals five cite this when deriving the classical five-institution structure and the Arrow-like impossibility result. The proof is a one-line decision procedure that evaluates the Fintype instance generated by the three-constructor inductive type.
claimThe cardinality of the finite type of governance criteria equals three, where the criteria are the three binary conditions of accountability, effectiveness, and legitimacy.
background
The module Governance Design from ConfigDim E7 states that configDim D equals five forces five canonical institutions (executive, legislative, judicial, military, press) together with five failure modes. GovernanceCriterion is the inductive type whose constructors are accountability, effectiveness, and legitimacy; it derives DecidableEq, Repr, BEq, and Fintype. Upstream results supply the active-edge count A equal to one per fundamental tick and the actualization operator A that selects the realized configuration minimizing J-cost.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on Fintype.card applied to GovernanceCriterion. The tactic succeeds because the inductive type carries an automatically derived Fintype instance whose cardinality is the number of constructors.
why it matters in Recognition Science
This supplies the three_criteria field inside the governanceDesignCert definition that certifies the full governance design. It realizes the E7 step of the module where configDim D equals five implies the three-criteria structure, paralleling the social-choice impossibility that no single institution satisfies all three conditions simultaneously. The result sits downstream of the forcing chain that produces D equals three spatial dimensions and the Recognition Composition Law.
scope and limits
- Does not prove that no single institution satisfies all three criteria simultaneously.
- Does not enumerate or derive the five canonical institutions.
- Does not enumerate or derive the five institutional failure modes.
- Does not connect the criteria to the phi-ladder, J-cost, or mass formulas.
formal statement (Lean)
43theorem criterionCount : Fintype.card GovernanceCriterion = 3 := by decide
proof body
Term-mode proof.
44
45/-- A governance assignment. -/