IndisputableMonolith.Constants.ProtonElectronMassRatio

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Masses.Anchor
   4import IndisputableMonolith.Masses.MassHierarchy
   5
   6/-!
   7# C-009: Proton-to-Electron Mass Ratio
   8
   9Formalizes the RS derivation path for m_p/m_e ≈ 1836.15.
  10
  11## Registry Item
  12- C-009: What determines the proton-to-electron mass ratio m_p/m_e ≈ 1836.15?
  13
  14## RS Derivation Status
  15**STARTED** — Falls out from C-007 (electron mass) and C-008 (proton mass) once both
  16are derived. The electron mass is m_e = E_coh · φ^2 (LeptonMassLadder).
  17The proton mass follows from φ-ladder + confinement (QuarkMasses / C-008).
  18
  19When both masses are on the φ-ladder, m_p/m_e = φ^(r_p - r_e) where r_e = 2.
  20-/
  21
  22namespace IndisputableMonolith
  23namespace Constants
  24namespace ProtonElectronMassRatio
  25
  26open Real Constants
  27open Masses.Anchor Masses.MassHierarchy
  28
  29/-! ## Structural Formula -/
  30
  31/-- Electron mass in RS units: E_coh · φ^2 (from C-007, r_e = 2). -/
  32noncomputable def m_e : ℝ := mass_on_rung 2
  33
  34/-- The mass ratio m_p/m_e when both are on the φ-ladder has the form φ^k.
  35
  36    For electron: r_e = 2. For proton: r_p from C-008 (φ-ladder + confinement).
  37    This theorem states the structural form; the exponent k depends on the
  38    full proton derivation. -/
  39theorem m_e_pos : 0 < m_e := by
  40  unfold m_e mass_on_rung
  41  apply mul_pos
  42  · unfold Masses.Anchor.E_coh
  43    rw [zpow_neg, inv_eq_one_div]
  44    exact div_pos zero_lt_one (pow_pos phi_pos 5)
  45  · exact pow_pos phi_pos 2
  46
  47theorem mass_ratio_structural (r_p : ℤ) (m_p : ℝ)
  48    (hm_p : m_p = mass_on_rung r_p)
  49    (_hm_p_pos : 0 < m_p) :
  50    m_p / m_e = phi ^ (r_p - 2) := by
  51  rw [hm_p, m_e, mass_on_rung, mass_on_rung]
  52  field_simp [zpow_ne_zero _ phi_ne_zero]
  53  exact (zpow_sub₀ phi_ne_zero r_p 2).symm
  54
  55/-! ## C-009 Resolution Statement -/
  56
  57/-- **C-009 Status**: The ratio m_p/m_e is determined by the φ-ladder.
  58
  59    Once C-007 and C-008 give m_e and m_p, the ratio m_p/m_e = φ^(r_p - 2).
  60    No free parameters. The measured value 1836.15 constrains the effective r_p.
  61
  62    Full derivation: BLOCKED on C-008 (proton mass from confinement). -/
  63theorem proton_electron_ratio_from_ladder (r_p : ℤ) (m_p : ℝ)
  64    (hm_p : m_p = mass_on_rung r_p)
  65    (hm_p_pos : 0 < m_p) :
  66    m_p / m_e = phi ^ (r_p - 2) :=
  67  mass_ratio_structural r_p m_p hm_p hm_p_pos
  68
  69/-- Proton/electron ladder structure implies the stated ratio formula. -/
  70theorem proton_electron_ratio_implies_phi_gap (r_p : ℤ) (m_p : ℝ)
  71    (h : m_p / m_e = phi ^ (r_p - 2)) :
  72    m_p / m_e = phi ^ (r_p - 2) :=
  73  h
  74
  75end ProtonElectronMassRatio
  76end Constants
  77end IndisputableMonolith
  78