IndisputableMonolith.Verification.PDGComparison

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Constants.Alpha
   4import IndisputableMonolith.Constants.GapWeight
   5import IndisputableMonolith.Numerics.Interval.AlphaBounds
   6import IndisputableMonolith.Physics.LeptonGenerations.Defs
   7
   8/-!
   9# Machine-Verified PDG Comparison
  10
  11This module provides **rigorous, machine-verified** comparison between Recognition Science
  12predictions and Particle Data Group (PDG) / CODATA experimental values.
  13
  14## Epistemological Status
  15
  16This module is **QUARANTINED** from the certified surface because:
  171. It imports experimental values (which are not derived from RS)
  182. Numerical comparisons are informational, not part of the proof chain
  19
  20## Key Result
  21
  22**α⁻¹ (Inverse Fine-Structure Constant)**:
  23- RS Prediction: 137.030 < α⁻¹_RS < 137.039 (machine-verified interval)
  24- CODATA 2022: α⁻¹_exp = 137.035999177(21)
  25- **Status**: RS interval CONTAINS experimental value ✓
  26
  27## References
  28
  29- CODATA 2022: Tiesinga et al., J. Phys. Chem. Ref. Data 50, 033105 (2021)
  30- PDG 2024: Navas et al., Phys. Rev. D 110, 030001 (2024)
  31-/
  32
  33namespace IndisputableMonolith
  34namespace Verification
  35namespace PDGComparison
  36
  37open IndisputableMonolith.Constants
  38open IndisputableMonolith.Numerics
  39
  40/-! ## CODATA 2022 Experimental Values -/
  41
  42/-- CODATA 2022 inverse fine-structure constant (central value).
  43    α⁻¹ = 137.035999177(21) -/
  44def alphaInv_CODATA_2022 : ℝ := 137.035999177
  45
  46/-- CODATA 2022 uncertainty on α⁻¹ (1σ). -/
  47def alphaInv_CODATA_2022_sigma : ℝ := 0.000000021
  48
  49/-- CODATA 2022 lower bound (central - 3σ). -/
  50def alphaInv_CODATA_2022_lo : ℝ := 137.035999177 - 3 * 0.000000021
  51
  52/-- CODATA 2022 upper bound (central + 3σ). -/
  53def alphaInv_CODATA_2022_hi : ℝ := 137.035999177 + 3 * 0.000000021
  54
  55/-! ## PDG 2024 Particle Masses (MeV) -/
  56
  57/-- Electron mass: 0.51099895069(16) MeV -/
  58def mass_electron_PDG : ℝ := 0.51099895069
  59def mass_electron_PDG_sigma : ℝ := 0.00000000016
  60
  61/-- Muon mass: 105.6583755(23) MeV -/
  62def mass_muon_PDG : ℝ := 105.6583755
  63def mass_muon_PDG_sigma : ℝ := 0.0000023
  64
  65/-- Tau mass: 1776.86(12) MeV -/
  66def mass_tau_PDG : ℝ := 1776.86
  67def mass_tau_PDG_sigma : ℝ := 0.12
  68
  69/-! ## RS Predictions (Machine-Verified Intervals) -/
  70
  71/-- RS predicts: 137.030 < α⁻¹ < 137.039 -/
  72def alphaInv_RS_lo : ℝ := 137.030
  73def alphaInv_RS_hi : ℝ := 137.039
  74
  75/-! ## Main Verification Theorems -/
  76
  77section AlphaVerification
  78
  79/-- **THEOREM**: The RS α⁻¹ prediction lower bound is machine-verified. -/
  80theorem alphaInv_RS_lower_verified : alphaInv_RS_lo < alphaInv := alphaInv_gt
  81
  82/-- **THEOREM**: The RS α⁻¹ prediction upper bound is machine-verified. -/
  83theorem alphaInv_RS_upper_verified : alphaInv < alphaInv_RS_hi := alphaInv_lt
  84
  85/-- **THEOREM**: The RS prediction interval CONTAINS the CODATA central value.
  86
  87    This is the key result: the Recognition Science prediction
  88    137.030 < α⁻¹ < 137.039
  89    contains the experimental value
  90    α⁻¹ = 137.035999177(21)
  91-/
  92theorem alphaInv_RS_contains_CODATA :
  93    alphaInv_RS_lo < alphaInv_CODATA_2022 ∧ alphaInv_CODATA_2022 < alphaInv_RS_hi := by
  94  constructor
  95  · -- 137.030 < 137.035999177
  96    unfold alphaInv_RS_lo alphaInv_CODATA_2022
  97    norm_num
  98  · -- 137.035999177 < 137.039
  99    unfold alphaInv_CODATA_2022 alphaInv_RS_hi
 100    norm_num
 101
 102/-- The RS prediction interval width (precision). -/
 103def alphaInv_RS_interval_width : ℝ := alphaInv_RS_hi - alphaInv_RS_lo
 104
 105/-- The RS interval width is 0.009 (about 66 ppm relative precision). -/
 106theorem alphaInv_RS_interval_width_eq : alphaInv_RS_interval_width = 0.009 := by
 107  unfold alphaInv_RS_interval_width alphaInv_RS_hi alphaInv_RS_lo
 108  norm_num
 109
 110/-- Relative precision of RS prediction: interval_width / central ≈ 66 ppm. -/
 111noncomputable def alphaInv_RS_relative_precision : ℝ :=
 112  alphaInv_RS_interval_width / alphaInv_CODATA_2022
 113
 114/-- The RS relative precision is less than 100 ppm (1 part in 10,000). -/
 115theorem alphaInv_RS_precision_sub_100ppm :
 116    alphaInv_RS_relative_precision < 1 / 10000 := by
 117  unfold alphaInv_RS_relative_precision alphaInv_RS_interval_width
 118  unfold alphaInv_RS_hi alphaInv_RS_lo alphaInv_CODATA_2022
 119  norm_num
 120
 121end AlphaVerification
 122
 123/-! ## Error Analysis Summary -/
 124
 125/-- Structure capturing the comparison result for a single observable. -/
 126structure ComparisonResult where
 127  name : String
 128  rs_lo : ℝ
 129  rs_hi : ℝ
 130  exp_central : ℝ
 131  exp_sigma : ℝ
 132
 133/-- Check if RS interval contains experimental value. -/
 134def contains_exp (r : ComparisonResult) : Prop :=
 135  r.rs_lo < r.exp_central ∧ r.exp_central < r.rs_hi
 136
 137/-- Tension in sigma: how far is exp from RS interval center? -/
 138noncomputable def tension_sigma (r : ComparisonResult) : ℝ :=
 139  let rs_center := (r.rs_lo + r.rs_hi) / 2
 140  |r.exp_central - rs_center| / r.exp_sigma
 141
 142/-- α⁻¹ comparison result. -/
 143def alpha_result : ComparisonResult :=
 144  { name := "α⁻¹ (inverse fine-structure constant)"
 145  , rs_lo := 137.030
 146  , rs_hi := 137.039
 147  , exp_central := 137.035999177
 148  , exp_sigma := 0.000000021 }
 149
 150/-- **THEOREM**: α⁻¹ RS interval contains experimental value. -/
 151theorem alpha_result_contains_exp : contains_exp alpha_result := by
 152  unfold contains_exp alpha_result
 153  norm_num
 154
 155/-! ## Tension Analysis -/
 156
 157/-- RS α⁻¹ interval center. -/
 158noncomputable def alphaInv_RS_center : ℝ := (alphaInv_RS_lo + alphaInv_RS_hi) / 2
 159
 160/-- RS α⁻¹ interval center = 137.0345. -/
 161theorem alphaInv_RS_center_eq : alphaInv_RS_center = 137.0345 := by
 162  unfold alphaInv_RS_center alphaInv_RS_lo alphaInv_RS_hi
 163  norm_num
 164
 165/-- Deviation of RS center from CODATA central value. -/
 166noncomputable def alphaInv_deviation : ℝ := alphaInv_RS_center - alphaInv_CODATA_2022
 167
 168/-- The deviation is approximately -0.0015 (RS predicts slightly lower). -/
 169theorem alphaInv_deviation_approx : alphaInv_deviation < 0 ∧ |alphaInv_deviation| < 0.002 := by
 170  unfold alphaInv_deviation alphaInv_RS_center alphaInv_RS_lo alphaInv_RS_hi alphaInv_CODATA_2022
 171  constructor
 172  · norm_num
 173  · rw [abs_of_neg (by norm_num)]
 174    norm_num
 175
 176/-! ## Summary Report -/
 177
 178/-- Summary of α⁻¹ comparison. -/
 179def alpha_summary : String :=
 180  "α⁻¹ (Inverse Fine-Structure Constant)\n" ++
 181  "═══════════════════════════════════════════════════════════════\n" ++
 182  "RS PREDICTION (Machine-Verified):\n" ++
 183  "  Lower bound: 137.030 (proven: alphaInv_gt)\n" ++
 184  "  Upper bound: 137.039 (proven: alphaInv_lt)\n" ++
 185  "  Interval:    [137.030, 137.039]\n" ++
 186  "  Width:       0.009 (~66 ppm)\n" ++
 187  "\n" ++
 188  "CODATA 2022 (Experimental):\n" ++
 189  "  Central:     137.035999177\n" ++
 190  "  Uncertainty: ±0.000000021 (1σ)\n" ++
 191  "\n" ++
 192  "COMPARISON:\n" ++
 193  "  RS interval CONTAINS experimental value: ✓ (Theorem: alphaInv_RS_contains_CODATA)\n" ++
 194  "  RS center (137.0345) vs exp (137.0360): deviation ≈ -0.0015\n" ++
 195  "  Deviation is ~0.001% of value\n" ++
 196  "\n" ++
 197  "STATUS: RS prediction is CONSISTENT with experiment at ~0.001% level.\n" ++
 198  "        The theoretical uncertainty (interval width ~66 ppm) exceeds\n" ++
 199  "        the experimental uncertainty (~0.15 ppb) by a factor of ~400,000.\n" ++
 200  "        Tightening the RS interval requires more precise φ, π bounds.\n"
 201
 202end PDGComparison
 203end Verification
 204end IndisputableMonolith
 205