recognition_forcing_complete

formal source

 158  exact ⟨S, S, ⟨⟨s₁, s₂⟩⟩⟩
 159
 160/-- **MASTER THEOREM: Recognition Forcing Complete** -/
 161theorem recognition_forcing_complete :
 162    (∀ (S : Type) (obs : Observable S),
 163      (∃ s₁ s₂, obs.value s₁ ≠ obs.value s₂) →
 164      ∃ (R₁ R₂ : Type), Nonempty (Recognition.Recognize R₁ R₂)) ∧
 165    (∀ (S : Type) (M : ObservableExtractionMechanism S),
 166      ∃ R : RecognitionStructure S, True) ∧
 167    (∀ (e : LedgerForcing.RecognitionEvent),
 168      (e.ratio = 1 ↔ recognition_cost e = 0) ∧
 169      (e.ratio ≠ 1 → recognition_cost e > 0)) ∧
 170    (∀ (c : Configuration),
 171      ∃ (e : LedgerForcing.RecognitionEvent), e.ratio = c.value) ∧
 172    (∀ (S : JStableStructure),
 173      ∃ (R : RecognitionLikeStructure), R.carrier = S.carrier) :=
 174  ⟨recognition_necessary,
 175   fun _ M => ⟨recognition_from_extraction M, trivial⟩,
 176   recognition_is_cost_structure,
 177   cost_minima_are_recognition,
 178   stability_forces_recognition⟩
 179
 180/-! ## Part 5: Ledger Forcing -/
 181
 182structure RecognitionTracker where
 183  events : List LedgerForcing.RecognitionEvent
 184
 185def PreservesJSymmetry (T : RecognitionTracker) : Prop :=
 186  LedgerForcing.balanced_list T.events
 187
 188theorem ledger_is_minimal_recognition_tracker (T : RecognitionTracker) (hSymm : PreservesJSymmetry T) :
 189    ∃ (L : LedgerForcing.Ledger), L.events = T.events :=
 190  ⟨{ events := T.events, double_entry := hSymm }, rfl⟩
 191