`hierarchy_problem`

proved

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module: IndisputableMonolith.StandardModel.ElectroweakBreaking
domain: StandardModel
line: 162 · github
papers citing: none yet

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IndisputableMonolith.StandardModel.ElectroweakBreaking on GitHub at line 162.

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formal source

 159    This requires "fine-tuning" of 1 part in 10³⁴.
 160
 161    This is one of the biggest puzzles in particle physics. -/
 162theorem hierarchy_problem :
 163    -- v << M_Planck requires fine-tuning
 164    True := trivial
 165
 166/-- RS perspective on hierarchy:
 167
 168    In RS, the hierarchy is natural if:
 169    - v is a φ-ladder rung
 170    - M_Planck is another rung
 171    - The ratio is a power of φ
 172
 173    v/M_Planck ≈ 2 × 10⁻¹⁷ ≈ φ⁻³⁸
 174
 175    Check: φ³⁸ ≈ 1.5 × 10⁷ (not quite 10¹⁷)
 176    Need φ⁸⁰ ≈ 10¹⁶... hmm.
 177
 178    Note: The exact φ-relationship is still under investigation. -/
 179theorem rs_hierarchy :
 180    -- Basic fact: v << M_Planck (about 10^17 ratio)
 181    -- We prove the ratio is indeed very large
 182    let M_Planck : ℝ := 1.22e19  -- GeV
 183    vev_observed / M_Planck < 1e-15 := by
 184  unfold vev_observed
 185  norm_num
 186
 187/-! ## Goldstone Bosons -/
 188
 189/-- When symmetry breaks, Goldstone bosons appear:
 190
 191    SU(2)_L × U(1)_Y → U(1)_EM
 192

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