reciprocity

formal source

  70noncomputable def event_cost (e : RecognitionEvent) : ℝ := J e.ratio
  71
  72/-- **Reciprocity**: Cost of event equals cost of reciprocal. -/
  73theorem reciprocity (e : RecognitionEvent) : event_cost e = event_cost (reciprocal e) := by
  74  simp only [event_cost, reciprocal]
  75  exact J_symmetric e.ratio_pos.ne'
  76
  77/-! ## Ledger Structure -/
  78
  79/-- A list of events is balanced if every event is paired with its reciprocal. -/
  80def balanced_list (l : List RecognitionEvent) : Prop :=
  81  ∀ e, l.count e = l.count (reciprocal e)
  82
  83/-- A ledger is a collection of recognition events with double-entry constraint. -/
  84structure Ledger where
  85  events : List RecognitionEvent
  86  double_entry : balanced_list events
  87
  88/-- The total cost of a ledger. -/
  89noncomputable def ledger_cost (L : Ledger) : ℝ :=
  90  L.events.foldl (fun acc e => acc + event_cost e) 0
  91
  92/-- A ledger is balanced if its event list is balanced. -/
  93def balanced (L : Ledger) : Prop := balanced_list L.events
  94
  95/-- Every Ledger is balanced by construction. -/
  96theorem ledger_balanced (L : Ledger) : balanced L := L.double_entry
  97
  98/-- The net flow at an agent. -/
  99noncomputable def net_flow (L : Ledger) (agent : ℕ) : ℝ :=
 100  L.events.foldl (fun acc e =>
 101    if e.source = agent then acc + Real.log e.ratio
 102    else if e.target = agent then acc + Real.log e.ratio
 103    else acc) 0