top_charm_ratio_bounds

formal source

 152    (17 : ℝ) < phi ^ 6 ∧ phi ^ 6 < (18 : ℝ) := phi_pow_6_bounds
 153
 154/-- The top/charm mass ratio: m_t/m_c = φ^(21-15) = φ⁶ ≈ 17.9. -/
 155theorem top_charm_ratio_bounds :
 156    (17 : ℝ) < phi ^ 6 ∧ phi ^ 6 < (18 : ℝ) := phi_pow_6_bounds
 157
 158/-! ## Neutrino sector -/
 159
 160/-- The neutrino squared-mass ratio m₃²/m₂² = φ⁷ ∈ (29, 30).
 161    NuFIT 5.3: Δm²₃₁/Δm²₂₁ ≈ 29.0 (for normal ordering).
 162    This is a seam-free prediction: no calibration anchor cancels. -/
 163theorem neutrino_squared_mass_ratio :
 164    (29 : ℝ) < phi ^ 7 ∧ phi ^ 7 < (30 : ℝ) := by
 165  exact ⟨phi_pow_7_gt_29, phi_pow_7_bounds.2⟩
 166
 167/-! ## Summary: all predictions in one structure -/
 168
 169/-- Master certificate: all numerical predictions are proved. -/
 170structure NumericalPredictionsCert where
 171  deriving Repr
 172
 173@[simp] def NumericalPredictionsCert.verified (_ : NumericalPredictionsCert) : Prop :=
 174  -- Alpha
 175  (137.030 < alphaInv ∧ alphaInv < 137.039)
 176  -- Gravity (κ = 8φ⁵)
 177  ∧ (85.6 < 8 * phi ^ 5 ∧ 8 * phi ^ 5 < 90.4)
 178  -- Planck (ℏ = φ⁻⁵)
 179  ∧ ((0.088 : ℝ) < hbar ∧ hbar < (0.093 : ℝ))
 180  -- Mass ratios
 181  ∧ (17 < phi ^ 6 ∧ phi ^ 6 < 18)    -- generation step
 182  ∧ (29 < phi ^ 7 ∧ phi ^ 7 < 30)    -- neutrino ratio
 183  ∧ (198 < phi ^ 11 ∧ phi ^ 11 < 200) -- quark/lepton ratio
 184  -- Phi itself
 185  ∧ (1.61 < phi ∧ phi < 1.62)