`hierarchyProblemDescription`

definition

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module: IndisputableMonolith.QFT.UVCutoff
domain: QFT
line: 176 · github
papers citing: none yet

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IndisputableMonolith.QFT.UVCutoff on GitHub at line 176.

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formal source

 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
 194/-! ## Predictions and Tests -/
 195
 196/-- Testable predictions from RS UV cutoff:
 197
 198    1. **No trans-Planckian modes**: Physics is regular at Planck scale
 199    2. **Modified dispersion relations**: E² = p² + m² gets corrections at high p
 200    3. **Cosmic ray spectrum**: GZK cutoff might be modified
 201    4. **Black hole formation**: Minimum mass related to τ₀
 202    5. **Loop corrections**: Finite and calculable with RS cutoff -/
 203def predictions : List String := [
 204  "Dispersion relation corrections at E ~ E0",
 205  "Modified loop corrections near cutoff",
 206  "Finite quantum gravity effects",

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