IndisputableMonolith.Physics.RecognitionCoupling

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Constants.Alpha
   4import IndisputableMonolith.RSBridge.Anchor
   5import IndisputableMonolith.Physics.RGTransport
   6import IndisputableMonolith.Physics.ElectronMass.Necessity
   7
   8/-!
   9# Recognition Coupling and the "Missing" Strength
  10
  11This module formalizes the "Missing Something" identified in the comparison between
  12perturbative RG transport and the geometric mass formula.
  13
  14## The Discrepancy
  15
  161. **Geometric Prediction**: The mass formula requires a large residue `F(Z)`:
  17   - Electron (Z=1332): F ≈ 13.95
  18   - Up-type (Z=276):   F ≈ 10.69
  19   - Down-type (Z=24):  F ≈ 5.74
  20
  212. **Perturbative RG**: Integrating Standard Model beta functions (literal SM \(\gamma_m\)) yields a small residue `f_RG`:
  22   - Electron: f_RG ≈ 0.05
  23   - Quarks:   f_RG ≈ 0.2 - 0.5
  24
  253. **The Gap**: The ratio `F(Z) / f_RG` is large (order 10² - 10³).
  26
  27## Interpretation: Recognition Strength
  28
  29We define the **Recognition Strength** `g_rec` as the ratio required to bridge this gap.
  30If the Standard Model forces (QED/QCD) are "shadows" of a stronger Recognition force,
  31this ratio quantifies that strength.
  32
  33Important: the “ratio” depends on what you mean by `f_RG` (endpoints, scheme, policy).
  34This file only **defines** the comparison; it does not assert universality of a single constant.
  35
  36-/
  37
  38namespace IndisputableMonolith
  39namespace Physics
  40namespace RecognitionCoupling
  41
  42open IndisputableMonolith.Constants
  43open IndisputableMonolith.RSBridge
  44open IndisputableMonolith.Physics.RGTransport
  45open IndisputableMonolith.Physics.ElectronMass.Necessity
  46
  47noncomputable section
  48
  49/-! ## Definitions -/
  50
  51/-- The Geometric Residue F(Z) defined by the structure. -/
  52def geometric_residue (f : Fermion) : ℝ := gap (ZOf f)
  53
  54/-- The Perturbative RG Residue f_RG (placeholder for the computed integral). -/
  55def rg_residue_value (f : Fermion) (val : ℝ) : Prop :=
  56  -- This is a predicate stating that the species f has perturbative residue 'val'.
  57  True
  58
  59/-- The Recognition Strength for species f: the factor by which the geometric
  60    structure exceeds the perturbative RG effect. -/
  61def recognition_strength (f : Fermion) (rg_val : ℝ) : ℝ :=
  62  geometric_residue f / rg_val
  63
  64/-! ## The Electron Case -/
  65
  66/-- For the electron, the perturbative residue is approx 0.0494. -/
  67def electron_rg_val_hypothesis : Prop :=
  68  -- Predicate for the specific electron value.
  69  True
  70
  71/-- The derived recognition strength for the electron. -/
  72def electron_strength (rg_val : ℝ) : ℝ := recognition_strength Fermion.e rg_val
  73
  74/-- Lower bound on the geometric residue for the electron (from the proven gap bounds). -/
  75theorem electron_geo_gt_13_953 : (13.953 : ℝ) < geometric_residue Fermion.e := by
  76  -- ZOf e = 1332, so this is exactly the lower bound on gap(1332).
  77  have hZ : ZOf Fermion.e = 1332 := by native_decide
  78  simpa [geometric_residue, hZ] using (gap_1332_bounds).1
  79
  80/-- A basic (non-universal) strength statement: if `rg_val = 0.04942583`,
  81then the ratio `F(Z)/f_RG` is certainly > 100 for the electron. -/
  82theorem electron_strength_gt_100 (rg_val : ℝ) (h_rg : rg_val = 0.04942583) :
  83    (100 : ℝ) < electron_strength rg_val := by
  84  unfold electron_strength recognition_strength
  85  -- rewrite rg residue value
  86  rw [h_rg]
  87  have hden_pos : (0 : ℝ) < (0.04942583 : ℝ) := by norm_num
  88  have hnum_gt : (13.953 : ℝ) < geometric_residue Fermion.e := electron_geo_gt_13_953
  89  -- It suffices to show 100 * 0.04942583 < 13.953.
  90  have h100 : (100 : ℝ) * (0.04942583 : ℝ) < (13.953 : ℝ) := by norm_num
  91  have hnum_gt' : (100 : ℝ) * (0.04942583 : ℝ) < geometric_residue Fermion.e :=
  92    lt_trans h100 hnum_gt
  93  -- divide by positive denominator
  94  exact (lt_div_iff₀ hden_pos).2 hnum_gt'
  95
  96/-! ## Structural Dominance -/
  97
  98/-- The "Zero Parameter" hypothesis: The mass is determined by the Geometric Residue,
  99    not the Perturbative Residue. The RG running is a small correction or shadow.
 100
 101    m_i = m_struct * φ^(F(Z))
 102
 103    The standard RG relation m = m_struct * φ^(f_RG) is **REPLACED** by the
 104    stronger geometric lock-in. -/
 105def structural_dominance_holds (f : Fermion) (rg_val : ℝ) : Prop :=
 106  geometric_residue f ≠ rg_val ∧
 107  recognition_strength f rg_val > 100
 108
 109end
 110
 111end RecognitionCoupling
 112end Physics
 113end IndisputableMonolith
 114