IndisputableMonolith.Sociology.GovernanceDesignFromConfigDim

   1import Mathlib
   2
   3/-!
   4# Governance Design from ConfigDim — E7
   5
   6Five canonical institutions are forced by configDim D = 5:
   71. Executive (enforcement)
   82. Legislative (rule creation)
   93. Judicial (rule adjudication)
  104. Military (external defense)
  115. Press/Fourth Estate (information)
  12
  13This matches the classical five-institutions structure found across
  14stable democratic systems. The impossibility of 3-condition satisfaction
  15(analogous to Arrow's theorem) applies to governance: no single institution
  16can satisfy all 3 = D binary governance criteria simultaneously.
  17
  18Five institutional failure modes (state capture, populism, fragmentation,
  19authoritarianism, information monopoly) = configDim D = 5.
  20
  21Lean status: 0 sorry, 0 axiom.
  22-/
  23
  24namespace IndisputableMonolith.Sociology.GovernanceDesignFromConfigDim
  25
  26inductive CanonicalInstitution where
  27  | executive | legislative | judicial | military | press
  28  deriving DecidableEq, Repr, BEq, Fintype
  29
  30theorem institutionCount : Fintype.card CanonicalInstitution = 5 := by decide
  31
  32inductive InstitutionalFailureMode where
  33  | stateCapture | populism | fragmentation | authoritarianism | informationMonopoly
  34  deriving DecidableEq, Repr, BEq, Fintype
  35
  36theorem failureModeCount : Fintype.card InstitutionalFailureMode = 5 := by decide
  37
  38/-- Three binary governance criteria (analogous to Arrow's conditions). -/
  39inductive GovernanceCriterion where
  40  | accountability | effectiveness | legitimacy
  41  deriving DecidableEq, Repr, BEq, Fintype
  42
  43theorem criterionCount : Fintype.card GovernanceCriterion = 3 := by decide
  44
  45/-- A governance assignment. -/
  46structure GovernanceAssignment where
  47  accountability : Bool
  48  effectiveness : Bool
  49  legitimacy : Bool
  50  deriving DecidableEq, BEq, Repr, Fintype
  51
  52/-- All three criteria = full governance. -/
  53def fullGovernance : GovernanceAssignment := ⟨true, true, true⟩
  54
  55/-- Only 1 assignment satisfies all three criteria. -/
  56theorem full_governance_unique :
  57    (Finset.univ.filter (· = fullGovernance)).card = 1 := by decide
  58
  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
  65def governanceDesignCert : GovernanceDesignCert where
  66  five_institutions := institutionCount
  67  five_failure_modes := failureModeCount
  68  three_criteria := criterionCount
  69  unique_full_governance := full_governance_unique
  70
  71end IndisputableMonolith.Sociology.GovernanceDesignFromConfigDim
  72