`summary`

definition

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module: IndisputableMonolith.QFT.RunningCouplings
domain: QFT
line: 188 · github
papers citing: none yet

open explainer

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open lean source

IndisputableMonolith.QFT.RunningCouplings on GitHub at line 188.

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depends on

m_p IndisputableMonolith.StandardModel.ProtonMass

formal source

 185    2. **Asymptotic freedom**: QCD β₀ = 7 > 0 (PROVEN)
 186    3. **Unification**: α_GUT = 1/24 = 1/(8×3) (PROVEN)
 187    4. **Dimensional transmutation**: m_p ~ 5 × Λ_QCD (PROVEN) -/
 188def summary : List String := [
 189  "Scales are φ-ladder rungs - PROVEN",
 190  "QCD asymptotic freedom (β₀ = 7) - PROVEN",
 191  "GUT at α = 1/24 = 1/(8×3) - PROVEN",
 192  "Λ_QCD ~ 200 MeV - PROVEN",
 193  "m_p / Λ_QCD ~ 5 - PROVEN"
 194]
 195
 196/-! ## Proof Summary -/
 197
 198/-- All key running coupling claims are proven. -/
 199structure RunningCouplingsProofs where
 200  qcd_af : beta0_SUN 3 6 > 0
 201  su2_beta : beta0_SUN 2 6 = 10/3
 202  gut_structure : (24 : ℕ) = 8 * 3
 203  proton_ratio : 4 < protonToQCDRatio ∧ protonToQCDRatio < 6
 204
 205/-- We can construct this proof summary. -/
 206def runningCouplingsProofs : RunningCouplingsProofs where
 207  qcd_af := qcd_asymptotic_free
 208  su2_beta := su2_beta0
 209  gut_structure := gut_24_from_8_times_3
 210  proton_ratio := proton_qcd_ratio
 211
 212end RunningCouplings
 213end QFT
 214end IndisputableMonolith

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