def
definition
mesonMass
show as:
view math explainer →
open explainer
Read the cached plain-language explainer.
open lean source
IndisputableMonolith.Physics.MesonSpectrumFromPhiLadder on GitHub at line 29.
browse module
All declarations in this module, on Recognition.
explainer page
used by
formal source
26
27theorem mesonFamily_count : Fintype.card MesonFamily = 5 := by decide
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