TimeReversalOp

formal source

  50  negate : ∀ i : Fin 3, ∀ x : ℝ, True  -- Placeholder
  51
  52/-- Time reversal operator: reverses time direction. -/
  53structure TimeReversalOp where
  54  /-- Reversal negates time. -/
  55  negate : ∀ t : ℝ, True  -- Placeholder
  56
  57/-! ## Ledger Structure and Symmetries -/
  58
  59/-- A ledger entry representing a recognition event. -/
  60structure LedgerEntry where
  61  /-- Position in 3D space. -/
  62  position : Fin 3 → ℝ
  63  /-- Time (tick number). -/
  64  tick : Phase
  65  /-- Charge/type indicator. -/
  66  charge : ℤ
  67  /-- Cost of this entry. -/
  68  cost : ℝ
  69  /-- Cost is non-negative. -/
  70  cost_nonneg : cost ≥ 0
  71
  72/-- A ledger is a collection of balanced entries. -/
  73structure Ledger where
  74  /-- The entries. -/
  75  entries : List LedgerEntry
  76  /-- Double-entry balance: charges sum to zero. -/
  77  balanced : (entries.map LedgerEntry.charge).sum = 0
  78
  79/-! ## C Symmetry: Charge Conjugation from J(x) = J(1/x) -/
  80
  81/-- Apply charge conjugation to a ledger entry. -/
  82def applyC (e : LedgerEntry) : LedgerEntry :=
  83  { e with charge := -e.charge }