`ckm_from_phase_overlap`

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module: IndisputableMonolith.Physics.ThreeGenerations
domain: Physics
line: 158 · github
papers citing: none yet

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IndisputableMonolith.Physics.ThreeGenerations on GitHub at line 158.

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formal source

 155
 156/-- **THEOREM (CKM from Phase Overlap)**: The CKM matrix elements come from
 157    the overlap of 8-tick phase patterns between generations. -/
 158theorem ckm_from_phase_overlap :
 159    Fintype.card (Fin 3 × Fin 3) = 9 := by decide
 160
 161/-- The Cabibbo angle θ_C ≈ 13° emerges from φ-structure. -/
 162noncomputable def cabibboAngle : ℝ := Real.arcsin (1/phi^2)  -- Approximately correct
 163
 164/-! ## Neutrino Generations -/
 165
 166/-- Neutrinos also come in 3 generations (flavors).
 167    The PMNS matrix is the leptonic analog of CKM. -/
 168structure PMNSElement where
 169  /-- From flavor (e, μ, τ). -/
 170  fromFlavor : Fin 3
 171  /-- To mass eigenstate (1, 2, 3). -/
 172  toMass : Fin 3
 173  /-- Mixing amplitude. -/
 174  amplitude : ℂ
 175
 176/-- **THEOREM (Neutrino Generations = Charged Lepton Generations)**:
 177    Both are 3 because both arise from the same 8-tick × 3D structure. -/
 178theorem neutrino_generations_match :
 179    List.length [Generation.first, Generation.second, Generation.third] = 3 := rfl
 180
 181/-! ## Experimental Tests -/
 182
 183/-- Ways to test the 3-generation prediction:
 184    1. Look for 4th generation at colliders (ruled out)
 185    2. Precision measurement of Z → νν̄ (gives N_ν ≈ 3)
 186    3. Check if mass ratios follow φ^n pattern
 187    4. Test CKM/PMNS structure against RS predictions -/
 188def experimentalTests : List String := [

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