renormalizationImplications

formal source

 160    2. **Finite theory**: All loop integrals converge
 161    3. **Predictive**: Cutoff-dependent terms are measurable
 162    4. **Hierarchy**: Explains why large scale separations exist -/
 163def renormalizationImplications : List String := [
 164  "UV divergences are artifacts of continuum approximation",
 165  "The true theory is discrete and finite",
 166  "Renormalization is correct effective description",
 167  "Cutoff effects could be observable at high enough energies"
 168]
 169
 170/-! ## The Hierarchy Problem Revisited -/
 171
 172/-- The Standard Model has a hierarchy problem:
 173    Why is the Higgs mass (125 GeV) << Planck mass (10¹⁹ GeV)?
 174    Loop corrections want to push m_H up to the cutoff.
 175    In RS, the hierarchy becomes a φ-cascade, not fine-tuning. -/
 176def hierarchyProblemDescription : String :=
 177  "m_H / m_Planck ~ 10^(-17), explained by φ-cascade"
 178
 179/-- Higgs mass in GeV. -/
 180def higgsMassGeV : ℚ := 125
 181
 182/-- Planck mass in GeV. -/
 183def planckMassGeV : ℚ := 1.22e19
 184
 185/-- The hierarchy ratio. -/
 186def hierarchyRatio : ℚ := higgsMassGeV / planckMassGeV
 187
 188/-- **THEOREM**: The hierarchy ratio is extremely small (~10⁻¹⁷). -/
 189theorem hierarchy_very_small :
 190    hierarchyRatio < 1 / 10^16 := by
 191  unfold hierarchyRatio higgsMassGeV planckMassGeV
 192  norm_num
 193