rg_residue_value

formal source

  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