IndisputableMonolith.Physics.MesonSpectrumFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Meson Spectrum from φ-ladder — S2 Depth
   6
   7Five canonical meson families (= configDim D = 5):
   8  pseudoscalar (π, K, η), vector (ρ, ω, K*, φ), scalar (a₀, f₀),
   9  axial vector (a₁, b₁), tensor (a₂, f₂).
  10
  11Adjacent-family mass ratio on the φ-ladder.
  12
  13Lean status: 0 sorry, 0 axiom.
  14-/
  15
  16namespace IndisputableMonolith.Physics.MesonSpectrumFromPhiLadder
  17open Constants
  18
  19inductive MesonFamily where
  20  | pseudoscalar
  21  | vector
  22  | scalar
  23  | axialVector
  24  | tensor
  25  deriving DecidableEq, Repr, BEq, Fintype
  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
  50