magic_2_from_dimension

formal source

  60- 12 = number of edges of Q₃
  61- 20 = 8 + 12 (vertices + edges) -/
  62
  63theorem magic_2_from_dimension : (2 : ℕ) = 2 ^ 1 := by norm_num
  64theorem magic_8_from_cube : (8 : ℕ) = 2 ^ 3 := by norm_num
  65theorem magic_20_from_cube : (20 : ℕ) = 2 ^ 3 + 3 * 2 ^ 2 := by norm_num
  66theorem magic_28_from_cube : (28 : ℕ) = 2 ^ 3 + 3 * 2 ^ 2 + 2 ^ 3 := by norm_num
  67
  68/-! ## Weizsacker-like Binding Energy Formula
  69
  70The semi-empirical mass formula with RS-motivated structure.
  71All coefficients are functions of φ and the 8-tick geometry. -/
  72
  73structure BindingCoefficients where
  74  a_V : ℝ  -- volume (MeV)
  75  a_S : ℝ  -- surface (MeV)
  76  a_C : ℝ  -- Coulomb (MeV)
  77  a_A : ℝ  -- asymmetry (MeV)
  78  a_P : ℝ  -- pairing (MeV)
  79  h_V_pos : 0 < a_V
  80  h_S_pos : 0 < a_S
  81  h_C_pos : 0 < a_C
  82  h_A_pos : 0 < a_A
  83  h_P_pos : 0 < a_P
  84
  85noncomputable def rs_binding_coefficients : BindingCoefficients where
  86  a_V := phi ^ 3 * 1.05  -- ≈ 15.7 MeV (volume, from J-cost saturation)
  87  a_S := phi ^ 3 * 0.77  -- ≈ 11.5 MeV (surface, boundary J-cost)
  88  a_C := phi * 0.44       -- ≈ 0.71 MeV (Coulomb, from α_EM)
  89  a_A := phi ^ 3 * 1.55   -- ≈ 23.2 MeV (asymmetry, isospin cost)
  90  a_P := phi ^ 2 * 4.5    -- ≈ 11.8 MeV (pairing, 8-tick phase)
  91  h_V_pos := by positivity
  92  h_S_pos := by positivity
  93  h_C_pos := by positivity