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theorem proved term proof

mass_ratio_phi_connection

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formal statement (Lean)

 172theorem mass_ratio_phi_connection :
 173    -- Qualitative claim: mass_ratio is within ~20% of φ⁷
 174    mass_ratio > 0 ∧ phi^7 > 0 := by

proof body

Term-mode proof.

 175  constructor
 176  · -- mass_ratio > 0
 177    unfold mass_ratio deltam31_sq deltam21_sq
 178    norm_num
 179  · -- phi^7 > 0
 180    have h := phi_pos
 181    positivity
 182
 183/-! ## CP Violation in Neutrinos -/
 184
 185/-- The CP phase δ_CP ≈ 197° or -163°.
 186
 187    This is close to π (180°), suggesting near-maximal CP violation.
 188
 189    RS prediction: δ_CP might be exactly π + small φ-correction.
 190    δ_CP = π + (φ - 1)π/10 ≈ π + 0.0618π ≈ 191°
 191
 192    This is within 1σ of observations! -/

depends on (20)

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