IndisputableMonolith.Masses.MassHierarchy

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Masses.Anchor
   4import IndisputableMonolith.Foundation.PhiForcing
   5
   6/-!
   7# P-002: Fermion Mass Hierarchy from φ-Ladder
   8
   9Formalizes the RS derivation of the fermion mass hierarchy.
  10
  11## Registry Item
  12- P-002: What determines the fermion mass hierarchy?
  13
  14## RS Derivation
  15Each fermion sits on a specific rung of the φ-ladder. Mass ∝ φ^n where n
  16is the rung integer (from Anchor.Integers). The hierarchy spans orders of
  17magnitude because φ ≈ 1.618, so φ^11 ≈ 200, φ^17 ≈ 2200.
  18-/
  19
  20namespace IndisputableMonolith
  21namespace Masses
  22namespace MassHierarchy
  23
  24open Real Constants
  25open Anchor Integers
  26
  27/-! ## φ-Ladder Structure -/
  28
  29/-- Mass in RS units: E_coh · φ^r where r is the rung. -/
  30noncomputable def mass_on_rung (r : ℤ) : ℝ :=
  31  Anchor.E_coh * phi ^ r
  32
  33/-- Electron rung: r = 2. -/
  34theorem r_electron : r_lepton "e" = 2 := r_lepton_values.1
  35
  36/-- Muon rung: r = 13 (2 + 11). -/
  37theorem r_muon : r_lepton "mu" = 13 := r_lepton_values.2.1
  38
  39/-- Tau rung: r = 19 (2 + 17). -/
  40theorem r_tau : r_lepton "tau" = 19 := r_lepton_values.2.2
  41
  42/-! ## Hierarchy: Each Generation Heavier -/
  43
  44/-- **P-002 Resolution**: The mass hierarchy is geometric (powers of φ).
  45
  46    m_μ/m_e = φ^(13-2) = φ^11 ≈ 199
  47    m_τ/m_μ = φ^(19-13) = φ^6 ≈ 18
  48
  49    No Yukawa free parameters — each generation's mass ratio is determined
  50    by the rung spacing (τ(1)=11, τ(2)=17 from cube geometry). -/
  51theorem lepton_hierarchy_geometric :
  52    mass_on_rung (r_lepton "mu") / mass_on_rung (r_lepton "e") = phi ^ 11 ∧
  53    mass_on_rung (r_lepton "tau") / mass_on_rung (r_lepton "mu") = phi ^ 6 := by
  54  simp only [mass_on_rung, r_muon, r_electron, r_tau]
  55  have hE : Anchor.E_coh ≠ 0 := zpow_ne_zero (-5) phi_ne_zero
  56  constructor <;> field_simp [zpow_ne_zero 2 phi_ne_zero, zpow_ne_zero 13 phi_ne_zero,
  57    zpow_ne_zero 19 phi_ne_zero, hE]
  58
  59/-- Mass ratios are > 1 (each generation heavier). -/
  60theorem lepton_mass_increasing :
  61    phi ^ 11 > 1 ∧ phi ^ 6 > 1 :=
  62  ⟨one_lt_zpow₀ one_lt_phi (by norm_num : 0 < (11 : ℤ)),
  63   one_lt_zpow₀ one_lt_phi (by norm_num : 0 < (6 : ℤ))⟩
  64
  65end MassHierarchy
  66end Masses
  67end IndisputableMonolith
  68