GovernanceDesignCert
GovernanceDesignCert is a structure that packages the assertions that there are exactly five canonical institutions, five institutional failure modes, three governance criteria, and exactly one assignment satisfying all three criteria at once. Governance theorists working within Recognition Science would cite it to encode the E7 configuration forced by configDim = 5. The declaration is introduced as a bare structure definition that directly records the four Fintype.card and Finset.filter conditions.
claimA structure certifying that the set of canonical institutions has cardinality 5, the set of institutional failure modes has cardinality 5, the set of governance criteria has cardinality 3, and that the set of assignments satisfying all three criteria simultaneously has cardinality 1.
background
The module defines five canonical institutions (executive, legislative, judicial, military, press) as the forced set for configDim D = 5, matching classical democratic structures. It likewise defines five failure modes (state capture, populism, fragmentation, authoritarianism, information monopoly) and three binary criteria (accountability, effectiveness, legitimacy) analogous to Arrow's conditions, where no single institution can meet all three simultaneously. The fullGovernance assignment is the unique triple of true values across the criteria.
proof idea
The declaration is a structure definition that directly asserts the four cardinality conditions via Fintype.card on the inductive types and a Finset.filter cardinality check on fullGovernance. No lemmas or tactics are invoked; it functions as a packaging type whose fields are later supplied by the downstream construction governanceDesignCert.
why it matters in Recognition Science
The structure supplies the certified counts that are instantiated in the downstream governanceDesignCert definition, thereby closing the E7 configuration in the sociology module. It records the forcing of five institutions and five failure modes from configDim = 5, consistent with the dimensional constraints and impossibility results in the Recognition Science framework. It leaves open whether these fixed counts suffice for long-term stability under the three-criterion impossibility.
scope and limits
- Does not derive the five institutions from the J-cost functional equation or the T0-T8 forcing chain.
- Does not prove existence or stability of any concrete governance system.
- Does not model transitions, dynamics, or failure propagation between institutions.
- Does not link the counts to physical constants, mass formulas, or the phi-ladder.
formal statement (Lean)
59structure GovernanceDesignCert where
60 five_institutions : Fintype.card CanonicalInstitution = 5
61 five_failure_modes : Fintype.card InstitutionalFailureMode = 5
62 three_criteria : Fintype.card GovernanceCriterion = 3
63 unique_full_governance : (Finset.univ.filter (· = fullGovernance)).card = 1
64