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hypothesis3
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IndisputableMonolith.StandardModel.WZMassRatio on GitHub at line 92.
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89 1.618 / √(2.618 + 1) = 1.618 / 1.902 ≈ 0.851
90
91 Getting closer! -/
92noncomputable def hypothesis3 : ℝ := phi / Real.sqrt (phi^2 + 1)
93
94/-- Hypothesis 4: cos(θ_W) = √(1 - 1/(φ² + 1))
95
96 √(1 - 1/3.618) = √(1 - 0.276) = √0.724 ≈ 0.851
97
98 Same as hypothesis 3. -/
99noncomputable def hypothesis4 : ℝ := Real.sqrt (1 - 1/(phi^2 + 1))
100
101/-- Hypothesis 5: cos(θ_W) = √(1 - 1/(2φ + 1))
102
103 √(1 - 1/4.236) = √(1 - 0.236) = √0.764 ≈ 0.874
104
105 Very close to observed 0.881! -/
106noncomputable def hypothesis5 : ℝ := Real.sqrt (1 - 1/(2*phi + 1))
107
108/-- Hypothesis 6: A more complex φ-expression.
109
110 cos(θ_W) = (φ³ - 1) / (φ³ + 1)
111 = (4.236 - 1) / (4.236 + 1) = 3.236 / 5.236 ≈ 0.618
112
113 This is too small. -/
114noncomputable def hypothesis6 : ℝ := (phi^3 - 1) / (phi^3 + 1)
115
116/-- **BEST FIT**: cos(θ_W) ≈ √(1 - 1/(2φ + 1))
117
118 Predicted: 0.874
119 Observed: 0.881
120 Error: ~0.8%
121
122 This is a promising φ-connection! -/