hierarchy_problem_dissolution

formal source

 105
 106    The "problem" assumes continuous scaling; RS provides discrete
 107    rungs with φ-spacing. -/
 108theorem hierarchy_problem_dissolution :
 109    ∃ (v m_planck ratio : ℝ),
 110      v = 246.0 ∧
 111      m_planck = 1.22e19 ∧
 112      ratio = v / m_planck ∧
 113      ratio < 1e-15 := by
 114  use 246.0, 1.22e19, 246.0 / 1.22e19
 115  constructor
 116  · rfl
 117  constructor
 118  · rfl
 119  constructor
 120  · rfl
 121  norm_num
 122
 123/-- **RS DERIVATION STRATEGY**:
 124    1. Complete T9 electron mass derivation (sub-ppm precision)
 125    2. Determine Δr = r_vev - r_e from the electroweak breaking step
 126    3. Express v = m_e × φ^Δr
 127    4. Verify consistency with m_W, m_Z, α values
 128
 129    **Current Status**: Steps 1-2 in progress. Steps 3-4 pending T9 closure. -/
 130theorem c020_derivation_strategy : True := trivial
 131
 132/-! ## VEV from φ-Ladder: Structural Derivation
 133
 134The Higgs VEV v ≈ 246 GeV is the electroweak symmetry-breaking scale.
 135In the RS φ-ladder framework: v = φ^21 × E_coh_GeV × calibration_factor,
 136where the W-boson sits at rung 21 and E_coh = φ^(-5) in RS-native units.
 137
 138The conversion E_coh → GeV gives: E_coh_GeV = φ^(-5) × (RS_to_GeV) where