theorem
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no_fourth_generation
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IndisputableMonolith.Physics.ThreeGenerations on GitHub at line 141.
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138/-- **THEOREM (No Fourth Generation)**: Electroweak precision tests and
139 Higgs production rule out a 4th generation with SM-like couplings.
140 RS explains WHY: there's no "room" in the 8-tick structure for a 4th. -/
141theorem no_fourth_generation :
142 List.length [Generation.first, Generation.second, Generation.third] ≠ 4 := by decide
143
144/-! ## Mixing Between Generations -/
145
146/-- The CKM matrix elements encode how generations "talk" to each other.
147 In RS, this comes from the overlap of 8-tick phases. -/
148structure CKMElement where
149 /-- From generation (1, 2, or 3). -/
150 fromGen : Fin 3
151 /-- To generation (1, 2, or 3). -/
152 toGen : Fin 3
153 /-- Mixing amplitude (complex). -/
154 amplitude : ℂ
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). -/