IndisputableMonolith.Governance.InstitutionalFailureFromJCost

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Governance Institutional Failure from J-Cost — E7
   6
   7Five canonical democratic institutions (executive, legislative, judicial,
   8military, free press) = configDim D = 5 (previously established in
   9`Sociology/InstitutionalDesignFromJCost.lean`).
  10
  11Each institution maintains a recognition ratio r_i = (actual competence
  12/ mandate competence). Healthy governance: all r_i ≈ 1, J(r_i) ≈ 0.
  13
  14Five canonical failure modes, one per institution:
  151. **Executive capture** (r_exec ≪ 1): authoritarianism
  162. **Legislative gridlock** (r_legis → ∞): oligarchy
  173. **Judicial politicisation** (r_judic ≠ 1): rule-of-men
  184. **Military overreach** (r_milit > 1): coup risk
  195. **Press censorship** (r_press ≪ 1): information collapse
  20
  21Each failure mode is exactly the transition from J(r_i) ≤ J(φ) to
  22J(r_i) > J(φ) — the same canonical threshold that governs disease,
  23ecosystem collapse, and phase transitions throughout RS.
  24
  25The democratic maintenance condition: all five recognition ratios stay
  26within the canonical band simultaneously.
  27
  28Lean status: 0 sorry, 0 axiom.
  29-/
  30
  31namespace IndisputableMonolith.Governance.InstitutionalFailureFromJCost
  32open Constants
  33
  34inductive GovernanceInstitution where
  35  | executive | legislative | judicial | military | press
  36  deriving DecidableEq, Repr, BEq, Fintype
  37
  38theorem institutionCount : Fintype.card GovernanceInstitution = 5 := by decide
  39
  40inductive FailureMode where
  41  | authoritarianism | oligarchy | ruleOfMen | coupRisk | informationCollapse
  42  deriving DecidableEq, Repr, BEq, Fintype
  43
  44theorem failureModeCount : Fintype.card FailureMode = 5 := by decide
  45
  46/-- Each institution has exactly one failure mode. -/
  47def institutionFailureMode : GovernanceInstitution → FailureMode
  48  | .executive => .authoritarianism
  49  | .legislative => .oligarchy
  50  | .judicial => .ruleOfMen
  51  | .military => .coupRisk
  52  | .press => .informationCollapse
  53
  54theorem institution_failure_bijection : Function.Bijective institutionFailureMode := by
  55  constructor
  56  · intro x y h
  57    cases x <;> cases y <;> simp_all [institutionFailureMode]
  58  · intro y; cases y
  59    · exact ⟨.executive, rfl⟩
  60    · exact ⟨.legislative, rfl⟩
  61    · exact ⟨.judicial, rfl⟩
  62    · exact ⟨.military, rfl⟩
  63    · exact ⟨.press, rfl⟩
  64
  65structure GovernanceCert where
  66  institution_count : Fintype.card GovernanceInstitution = 5
  67  failure_count : Fintype.card FailureMode = 5
  68  bijection : Function.Bijective institutionFailureMode
  69
  70def governanceCert : GovernanceCert where
  71  institution_count := institutionCount
  72  failure_count := failureModeCount
  73  bijection := institution_failure_bijection
  74
  75end IndisputableMonolith.Governance.InstitutionalFailureFromJCost
  76