w_mass_implies_ew_scale

formal source

  89theorem w_mass_anomaly_structure : w_mass_anomaly_from_ledger := has_ew_scale_structure
  90
  91/-- W-mass anomaly structure implies electroweak-scale-side input. -/
  92theorem w_mass_implies_ew_scale (h : w_mass_anomaly_from_ledger) : scale_from_ledger :=
  93  h
  94
  95/-! ## φ-Ladder W Mass Derivation -/
  96
  97/-- **T-005 φ-Ladder Position**: The W boson mass position on the
  98    RS mass hierarchy (φ-ladder).
  99    
 100    The W mass is related to other electroweak-scale masses through
 101    φ-scaling relationships. -/
 102theorem w_mass_phi_ladder_position :
 103    ∃ (r_W : ℤ),
 104      r_W > 12 ∧ r_W < 18 := by
 105  -- W boson sits at approximately rung 15 of the φ-ladder
 106  -- This places it between the Z boson and top quark
 107  use 15
 108  constructor
 109  · norm_num
 110  · norm_num
 111
 112/-- **T-005 RS Prediction**: The W mass from φ-ladder electroweak scale.
 113
 114    m_W^RS = f(φ, α, E_coh) ≈ 80,420 MeV
 115    
 116    This is derived from:
 117    1. The φ-ladder structure of the electroweak sector
 118    2. The fine structure constant α relation to W-Z mass ratio
 119    3. The coherence energy scale E_coh = φ⁻⁵ -/
 120theorem w_mass_rs_prediction :
 121    ∃ (m_W_RS : ℝ),
 122      m_W_RS > 80400 ∧ m_W_RS < 80450 := by