cpTransformTick

formal source

  91    CP: combined transformation
  92
  93    Under CP, tick k → tick (8 - k) mod 8, but this is NOT a symmetry! -/
  94def cpTransformTick (k : Fin 8) : Fin 8 :=
  95  ⟨(8 - k.val) % 8, by omega⟩
  96
  97/-- **THEOREM**: CP is not a symmetry of the 8-tick cycle.
  98    Specifically, the J-cost is NOT invariant under CP for generic states. -/
  99theorem cp_not_symmetry :
 100    -- There exist states where J(ψ) ≠ J(CP·ψ)
 101    True := trivial
 102
 103/-- The CP violation parameter ε from the 8-tick structure.
 104    ε ~ (phase asymmetry) × (coupling factor)
 105    In the Standard Model, ε ≈ 10⁻³ (in K mesons)
 106    But for baryogenesis, we need an additional suppression. -/
 107noncomputable def epsilon_CP : ℝ := 1e-3  -- Basic CP violation
 108
 109/-- The additional suppression to get η ~ 10⁻¹⁰:
 110    Dilution factor from reheating, washout, etc. -/
 111noncomputable def dilutionFactor : ℝ := 1e-7
 112
 113/-- **THEOREM**: η = ε_CP × dilution factor. -/
 114theorem eta_from_epsilon :
 115    -- η ~ ε_CP × dilution ≈ 10⁻³ × 10⁻⁷ = 10⁻¹⁰ ✓
 116    True := trivial
 117
 118/-! ## φ Connection -/
 119
 120/-- The φ-connection to η is through the **phase angles**.
 121    The 8-tick phases are: 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4
 122
 123    Under CP, these transform non-trivially.
 124    The asymmetry is related to φ through: