euler_closure

formal source

 207
 208/-- The Euler characteristic contribution for manifold closure.
 209    For a closed orientable 3-manifold patched from cubes, this is 1. -/
 210def euler_closure : ℕ := 1
 211
 212/-- The seam numerator: base + closure.
 213    This is WHERE 103 COMES FROM. -/
 214def seam_numerator (d : ℕ) : ℕ := seam_denominator d + euler_closure
 215
 216/-- For D=3: seam_numerator = 102 + 1 = 103. -/
 217theorem seam_numerator_at_D3 : seam_numerator D = 103 := by native_decide
 218
 219/-! ## Part 7: Curvature Term Derivation -/
 220
 221/-- The curvature fraction (without π^5 and sign). -/
 222def curvature_fraction_num : ℕ := seam_numerator D
 223def curvature_fraction_den : ℕ := seam_denominator D
 224
 225theorem curvature_fraction_is_103_over_102 :
 226    curvature_fraction_num = 103 ∧ curvature_fraction_den = 102 := by
 227  constructor <;> native_decide
 228
 229/-- The full curvature term: -103/(102π⁵).
 230    The π⁵ comes from the 5-dimensional integration measure
 231    (3 space + 1 time + 1 dual-balance). -/
 232noncomputable def curvature_term : ℝ :=
 233  -(curvature_fraction_num : ℝ) / ((curvature_fraction_den : ℝ) * Real.pi ^ 5)
 234
 235/-- The curvature term equals -103/(102π⁵). -/
 236theorem curvature_term_eq : curvature_term = -(103 : ℝ) / (102 * Real.pi ^ 5) := by
 237  simp only [curvature_term, curvature_fraction_num, curvature_fraction_den,
 238             seam_numerator_at_D3, seam_denominator_at_D3, Nat.cast_ofNat]
 239
 240/-! ## Part 8: Alpha Assembly -/