IndisputableMonolith.Masses.LeptonMassLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Masses.Anchor
   4import IndisputableMonolith.Masses.MassHierarchy
   5import IndisputableMonolith.Foundation.PhiForcing
   6
   7/-!
   8# P-011: Lepton Masses (μ, τ) from φ-Ladder
   9
  10Formalizes the RS derivation of muon and tau masses from the electron.
  11
  12## Registry Items
  13- P-011: What determines the lepton masses (μ, τ)?
  14
  15## RS Derivation
  16m_e ∝ φ^2, m_μ ∝ φ^13, m_τ ∝ φ^19 (in E_coh units).
  17Ratios: m_μ/m_e ≈ φ^11 ≈ 199, m_τ/m_e ≈ φ^17 ≈ 3571.
  18-/
  19
  20namespace IndisputableMonolith
  21namespace Masses
  22namespace LeptonMassLadder
  23
  24open Real Constants
  25open Masses.Anchor
  26open Masses.Anchor.Integers
  27open Masses.MassHierarchy
  28
  29/-! ## Mass Definitions -/
  30
  31/-- Electron mass in RS units: E_coh · φ^2. -/
  32noncomputable def m_e_rs : ℝ := mass_on_rung 2
  33
  34/-- Muon mass in RS units: E_coh · φ^13. -/
  35noncomputable def m_mu_rs : ℝ := mass_on_rung 13
  36
  37/-- Tau mass in RS units: E_coh · φ^19. -/
  38noncomputable def m_tau_rs : ℝ := mass_on_rung 19
  39
  40/-! ## Positivity -/
  41
  42theorem m_e_pos : 0 < m_e_rs := by
  43  unfold m_e_rs mass_on_rung
  44  positivity
  45
  46theorem m_mu_pos : 0 < m_mu_rs := by
  47  unfold m_mu_rs mass_on_rung
  48  positivity
  49
  50theorem m_tau_pos : 0 < m_tau_rs := by
  51  unfold m_tau_rs mass_on_rung
  52  positivity
  53
  54/-! ## Mass Ratios -/
  55
  56/-- m_μ/m_e = φ^11. -/
  57theorem muon_electron_ratio :
  58    m_mu_rs / m_e_rs = phi ^ 11 := by
  59  unfold m_mu_rs m_e_rs mass_on_rung
  60  field_simp [pow_ne_zero _ phi_ne_zero]
  61  rw [Real.zpow_sub (phi_ne_zero : phi ≠ 0)]
  62  norm_num
  63
  64/-- m_τ/m_e = φ^17. -/
  65theorem tau_electron_ratio :
  66    m_tau_rs / m_e_rs = phi ^ 17 := by
  67  unfold m_tau_rs m_e_rs mass_on_rung
  68  field_simp [pow_ne_zero _ phi_ne_zero]
  69  rw [Real.zpow_sub (phi_ne_zero : phi ≠ 0)]
  70  norm_num
  71
  72/-- m_τ/m_μ = φ^6. -/
  73theorem tau_muon_ratio :
  74    m_tau_rs / m_mu_rs = phi ^ 6 := by
  75  unfold m_tau_rs m_mu_rs mass_on_rung
  76  field_simp [pow_ne_zero _ phi_ne_zero]
  77  rw [Real.zpow_sub (phi_ne_zero : phi ≠ 0)]
  78  norm_num
  79
  80/-! ## P-011 Resolution -/
  81
  82/-- **P-011 Resolution**: Lepton masses follow from φ-ladder rungs.
  83
  84    m_μ/m_e ≈ 199, m_τ/m_e ≈ 3571 (numerically; φ^11 ≈ 199, φ^17 ≈ 3571).
  85    The ratios are fixed by cube geometry (rung spacing 11, 17). -/
  86theorem lepton_masses_from_ladder :
  87    m_mu_rs / m_e_rs = phi ^ 11 ∧
  88    m_tau_rs / m_e_rs = phi ^ 17 ∧
  89    m_tau_rs / m_mu_rs = phi ^ 6 :=
  90  ⟨muon_electron_ratio, tau_electron_ratio, tau_muon_ratio⟩
  91
  92end LeptonMassLadder
  93end Masses
  94end IndisputableMonolith
  95