IndisputableMonolith.Masses.MassRatiosProved

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Foundation.PhiForcing
   4
   5/-! 
   6# Mass Ratios — Rigorous Proofs from φ-Ladder
   7
   8This module provides calculated proofs for mass ratios derived from
   9the φ-ladder structure. All ratios are expressed as φ-powers.
  10-/
  11
  12namespace IndisputableMonolith
  13namespace Masses
  14namespace MassRatiosProved
  15
  16open Constants
  17open Real
  18
  19/-! ## Section 1: Phi Power Bounds for Mass Ratios -/
  20
  21/-- **CALCULATED**: φ^6 bounds for mass ratios.
  22    
  23    From φ^3 = 2φ + 1, we have φ^6 = (2φ + 1)^2.
  24    With 1.5 < φ < 1.62, this gives 17 < φ^6 < 18. -/
  25theorem phi_6_bounds_mass_ratio : (17 : ℝ) < (phi : ℝ)^(6 : ℕ) ∧ (phi : ℝ)^(6 : ℕ) < (18 : ℝ) := by
  26  have h1 : (phi : ℝ)^(6 : ℕ) = ((phi : ℝ)^(3 : ℕ))^2 := by ring
  27  rw [h1]
  28  have h2 : (phi : ℝ)^(3 : ℕ) = 2 * phi + 1 := by
  29    have hphi2 : phi^2 = phi + 1 := phi_sq_eq
  30    calc
  31      (phi : ℝ)^(3 : ℕ) = phi * phi^2 := by ring
  32      _ = phi * (phi + 1) := by rw [hphi2]
  33      _ = phi^2 + phi := by ring
  34      _ = (phi + 1) + phi := by rw [hphi2]
  35      _ = 2 * phi + 1 := by ring
  36  rw [h2]
  37  have h3 : phi > (1.5 : ℝ) := phi_gt_onePointFive
  38  have h4 : phi < (1.62 : ℝ) := phi_lt_onePointSixTwo
  39  constructor
  40  · nlinarith
  41  · nlinarith
  42
  43/-! ## Section 2: Mass Ratio Structure Proofs -/
  44
  45/-- **PROOF**: Mass ratio formula from rung difference.
  46    
  47    If m₁ ∝ φ^r₁ and m₂ ∝ φ^r₂, then m₂/m₁ = φ^(r₂-r₁). -/
  48theorem mass_ratio_from_rung_difference (r1 r2 : ℤ) (E_coh : ℝ) (hE : E_coh > 0) :
  49    let m1 := E_coh * (phi : ℝ)^(r1 : ℝ)
  50    let m2 := E_coh * (phi : ℝ)^(r2 : ℝ)
  51    m2 / m1 = (phi : ℝ)^((r2 - r1 : ℝ)) := by
  52  intro m1 m2
  53  have h1 : m2 / m1 = (E_coh * (phi : ℝ)^(r2 : ℝ)) / (E_coh * (phi : ℝ)^(r1 : ℝ)) := rfl
  54  rw [h1]
  55  have h2 : E_coh ≠ 0 := by linarith
  56  have h3 : (phi : ℝ)^(r1 : ℝ) ≠ 0 := by
  57    have hphi : phi > 0 := phi_pos
  58    have h4 : (phi : ℝ)^(r1 : ℝ) > 0 := by positivity
  59    linarith
  60  field_simp
  61  rw [← Real.rpow_add]
  62  · congr
  63    simp
  64  · exact_mod_cast phi_pos
  65
  66/-! ## Section 3: Mass Ordering -/
  67
  68/-- **PROOF**: Mass ordering from rung ordering.
  69    
  70    Higher rung → higher mass since φ > 1. -/
  71theorem mass_ordering_from_rungs (r1 r2 : ℤ) (E_coh : ℝ) (hE : E_coh > 0) (hr : r1 < r2) :
  72    let m1 := E_coh * (phi : ℝ)^(r1 : ℝ)
  73    let m2 := E_coh * (phi : ℝ)^(r2 : ℝ)
  74    m1 < m2 := by
  75  intro m1 m2
  76  have h1 : m1 = E_coh * (phi : ℝ)^(r1 : ℝ) := rfl
  77  have h2 : m2 = E_coh * (phi : ℝ)^(r2 : ℝ) := rfl
  78  rw [h1, h2]
  79  have h3 : (phi : ℝ)^(r1 : ℝ) < (phi : ℝ)^(r2 : ℝ) := by
  80    apply Real.rpow_lt_rpow_of_exponent_lt
  81    · exact_mod_cast one_lt_phi
  82    · exact_mod_cast hr
  83  nlinarith [Real.rpow_pos_of_pos phi_pos r1, Real.rpow_pos_of_pos phi_pos r2]
  84
  85/-! ## Section 4: Mass Certificate -/
  86
  87/-- **CERTIFICATE**: Mass ratio predictions with bounds. -/
  88structure MassRatioCert where
  89  phi_6_lower : (17 : ℝ) < (phi : ℝ)^(6 : ℕ)
  90  phi_6_upper : (phi : ℝ)^(6 : ℕ) < (18 : ℝ)
  91
  92theorem mass_ratio_cert_exists : Nonempty MassRatioCert :=
  93  ⟨⟨phi_6_bounds_mass_ratio.1, phi_6_bounds_mass_ratio.2⟩⟩
  94
  95
  96end MassRatiosProved
  97end Masses
  98end IndisputableMonolith
  99