`mass_ratio`

proved

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module: IndisputableMonolith.Physics.MesonSpectrumFromPhiLadder
domain: Physics
line: 31 · github
papers citing: none yet

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IndisputableMonolith.Physics.MesonSpectrumFromPhiLadder on GitHub at line 31.

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formal source

  28
  29noncomputable def mesonMass (k : ℕ) : ℝ := phi ^ k
  30
  31theorem mass_ratio (k : ℕ) : mesonMass (k + 1) / mesonMass k = phi := by
  32  unfold mesonMass
  33  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  34  rw [div_eq_iff hpos.ne', pow_succ]
  35  ring
  36
  37theorem mass_pos (k : ℕ) : 0 < mesonMass k := pow_pos phi_pos k
  38
  39structure MesonSpectrumCert where
  40  five_families : Fintype.card MesonFamily = 5
  41  phi_ratio : ∀ k, mesonMass (k + 1) / mesonMass k = phi
  42  mass_always_pos : ∀ k, 0 < mesonMass k
  43
  44noncomputable def mesonSpectrumCert : MesonSpectrumCert where
  45  five_families := mesonFamily_count
  46  phi_ratio := mass_ratio
  47  mass_always_pos := mass_pos
  48
  49end IndisputableMonolith.Physics.MesonSpectrumFromPhiLadder

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