IndisputableMonolith.Physics.NeutrinoMassFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Neutrino Mass Hierarchy from Phi-Ladder — A1 SM Depth
   6
   7From RS, neutrino masses lie on the phi-ladder:
   8m_1 : m_2 : m_3 = phi^0 : phi^1 : phi^2 (normal ordering)
   9
  10This gives m_2/m_1 = phi ≈ 1.618, m_3/m_2 = phi.
  11
  12Three neutrino flavors = 3 mass eigenstates.
  13RS predicts normal ordering (m_1 < m_2 < m_3).
  14
  15Five-flavor extension (including sterile neutrinos) = 5 = configDim D.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Physics.NeutrinoMassFromPhiLadder
  21open Constants
  22
  23/-- Three active neutrino mass eigenstates. -/
  24noncomputable def neutrinoMass (k : ℕ) : ℝ := phi ^ k
  25
  26/-- Normal ordering: m_1 < m_2 < m_3. -/
  27theorem normal_ordering (k : ℕ) : neutrinoMass k < neutrinoMass (k + 1) := by
  28  unfold neutrinoMass
  29  have hphi_sq : phi ^ 2 = phi + 1 := phi_sq_eq
  30  have hpos := pow_pos phi_pos k
  31  rw [pow_succ]
  32  linarith [mul_lt_mul_of_pos_left one_lt_phi hpos]
  33
  34/-- Mass ratio between adjacent eigenstates = phi. -/
  35theorem mass_ratio (k : ℕ) : neutrinoMass (k + 1) / neutrinoMass k = phi := by
  36  unfold neutrinoMass
  37  have hpos := pow_pos phi_pos k
  38  rw [pow_succ, div_eq_iff hpos.ne']
  39  ring
  40
  41structure NeutrinoMassCert where
  42  normal_ordering : ∀ k, neutrinoMass k < neutrinoMass (k + 1)
  43  phi_ratio : ∀ k, neutrinoMass (k + 1) / neutrinoMass k = phi
  44
  45noncomputable def neutrinoMassCert : NeutrinoMassCert where
  46  normal_ordering := normal_ordering
  47  phi_ratio := mass_ratio
  48
  49end IndisputableMonolith.Physics.NeutrinoMassFromPhiLadder
  50