phi_23

formal source

 168def w_electron_ratio : ℝ := wBosonMass_GeV / electronMass_GeV
 169
 170/-- φ^23 is close to the W/e mass ratio scale. -/
 171def phi_23 : ℝ := phi ^ 23
 172
 173/-- φ^24 is close to the Z/e mass ratio scale. -/
 174def phi_24 : ℝ := phi ^ 24
 175
 176/-- VEV in units of electron mass. -/
 177def vev_electron_ratio : ℝ := vev_GeV / electronMass_GeV
 178
 179/-- VEV/m_e ≈ 4.8 × 10^5 ≈ φ^27. -/
 180def phi_27 : ℝ := phi ^ 27
 181
 182/-! ## Higgs Connection -/
 183
 184/-- Higgs boson mass in GeV. -/
 185def higgsMass_GeV : ℝ := 125.25
 186
 187/-- Higgs to W mass ratio. -/
 188def higgs_w_ratio : ℝ := higgsMass_GeV / wBosonMass_GeV
 189
 190/-- Higgs to W ratio ≈ 1.56 ≈ φ. -/
 191theorem higgs_w_near_phi : |higgs_w_ratio - phi| < 0.1 := by
 192  -- 125.25 / 80.3692 ≈ 1.5585, φ ∈ (1.61, 1.62)
 193  -- |1.5585 - 1.618| ≈ 0.06 < 0.1
 194  simp only [higgs_w_ratio, higgsMass_GeV, wBosonMass_GeV]
 195  have hphi_lo : phi > 1.61 := phi_gt_onePointSixOne
 196  have hphi_hi : phi < 1.62 := phi_lt_onePointSixTwo
 197  have h1 : (125.25 : ℝ) / 80.3692 > 1.55 := by norm_num
 198  have h2 : (125.25 : ℝ) / 80.3692 < 1.56 := by norm_num
 199  rw [abs_lt]
 200  constructor <;> linarith
 201