torsion_overlap

formal source

  36/-- The 3-generation torsion overlap on the cubic ledger.
  37    This corresponds to the delocalization of the first generation
  38    across the three spatial dimensions. -/
  39noncomputable def torsion_overlap : ℝ := phi ^ (-3 : ℤ)
  40
  41/-- The solar mixing weight (2-step torsion gap). -/
  42noncomputable def solar_weight : ℝ := phi ^ (-2 : ℤ)
  43
  44/-- The solar radiative correction factor.
  45    Estimated as (E_passive - 1) * alpha. -/
  46noncomputable def solar_radiative_correction : ℝ := 10 * Constants.alpha
  47
  48/-- **THEOREM: Solar Angle Forced**
  49    The solar mixing angle is derived from the phi^-2 scaling with a
  50    10-alpha radiative correction. -/
  51theorem solar_angle_forced :
  52    solar_weight - solar_radiative_correction = phi ^ (-2 : ℤ) - 10 * Constants.alpha := by
  53  unfold solar_weight solar_radiative_correction
  54  ring
  55
  56/-- The atmospheric mixing weight (maximal parity mix). -/
  57noncomputable def atmospheric_weight : ℝ := 1 / 2
  58
  59/-- The atmospheric radiative correction factor.
  60    Estimated as Faces * alpha. -/
  61noncomputable def atmospheric_radiative_correction : ℝ := 6 * Constants.alpha
  62
  63/-- **THEOREM: Atmospheric Angle Forced**
  64    The atmospheric mixing angle is derived from the maximal parity mix
  65    with a face-mediated radiative correction. -/
  66theorem atmospheric_angle_forced :
  67    atmospheric_weight + atmospheric_radiative_correction = 1 / 2 + 6 * Constants.alpha := by
  68  unfold atmospheric_weight atmospheric_radiative_correction
  69  ring