IndisputableMonolith.Physics.DecaySpectrumFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Decay Spectrum from φ-ladder — Physics Depth
   6
   7Five canonical exotic decay channels (= configDim D = 5):
   8  alpha, beta-minus, beta-plus, electron-capture, spontaneous-fission.
   9
  10Each lifetime sits one rung up the φ-ladder.
  11
  12Lean status: 0 sorry, 0 axiom.
  13-/
  14
  15namespace IndisputableMonolith.Physics.DecaySpectrumFromPhiLadder
  16open Constants
  17
  18inductive DecayChannel where
  19  | alpha
  20  | betaMinus
  21  | betaPlus
  22  | electronCapture
  23  | spontaneousFission
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem decayChannel_count : Fintype.card DecayChannel = 5 := by decide
  27
  28noncomputable def lifetime (k : ℕ) : ℝ := phi ^ k
  29
  30theorem lifetime_ratio (k : ℕ) : lifetime (k + 1) / lifetime k = phi := by
  31  unfold lifetime
  32  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  33  rw [div_eq_iff hpos.ne', pow_succ]
  34  ring
  35
  36theorem lifetime_pos (k : ℕ) : 0 < lifetime k := pow_pos phi_pos k
  37
  38structure DecaySpectrumCert where
  39  five_channels : Fintype.card DecayChannel = 5
  40  phi_ratio : ∀ k, lifetime (k + 1) / lifetime k = phi
  41  lifetime_always_pos : ∀ k, 0 < lifetime k
  42
  43noncomputable def decaySpectrumCert : DecaySpectrumCert where
  44  five_channels := decayChannel_count
  45  phi_ratio := lifetime_ratio
  46  lifetime_always_pos := lifetime_pos
  47
  48end IndisputableMonolith.Physics.DecaySpectrumFromPhiLadder
  49