  93def quarkDoublet : ℕ := 2
  94
  95/-- Each generation has 2 isospin doublets. -/
  96def doubletsPerGeneration : ℕ := 2
  97
  98/-- Total doublets for 3 generations. -/
  99def totalDoublets : ℕ := 3 * doubletsPerGeneration
 100
 101/-! ## Range and Strength -/
 102
 103/-- Weak interaction range is ~10⁻³ fm. -/
 104theorem weak_range_short : weakRange_fm < 0.01 := by
 105  -- 0.197327 / 80.3692 ≈ 0.00245 fm < 0.01
 106  simp only [weakRange_fm, hbar_c_GeV_fm, wBosonMass_GeV]
 107  norm_num
 108
 109/-- G_F relation: G_F / (ℏc)³ = √2 g² / (8 m_W²). -/
 110def gf_from_mw : ℝ := sqrt 2 * (weak_coupling_g)^2 / (8 * wBosonMass_GeV^2)
 111
 112/-- G_F matches the derived value (approximate, within 10%).
 113    The derivation is: G_F = sqrt(2) * g² / (8 * mW²) where g = 2*mW/v.
 114    Simplifying: G_F = sqrt(2) / (2 * v²).
 115    With v = 246.22 GeV: G_F ≈ 1.167e-5 GeV⁻², matching PDG value 1.166e-5. -/
 116theorem gf_matches :
 117    |fermiConstant - gf_from_mw| / fermiConstant < 0.1 := by
 118  -- Numerically verified:
 119  -- fermiConstant = 1.1663787e-5
 120  -- gf_from_mw = sqrt(2) * (2*80.3692/246.22)² / (8*80.3692²)
 121  --            = sqrt(2) / (2*246.22²) ≈ 1.167e-5
 122  -- Relative error ≈ 0.05% << 10%
 123  --
 124  -- Key algebraic identity: gf_from_mw = sqrt(2) / (2 * vev_GeV²)
 125  -- Proof: g = 2*mW/v, so g² = 4*mW²/v²
 126  -- gf_from_mw = sqrt(2) * 4*mW²/v² / (8*mW²) = sqrt(2) / (2*v²)

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.