faceCount_D3

formal source

 109theorem faceVertexCount_D3 : faceVertexCount 3 = 4 := by native_decide
 110
 111/-- In D=3, there are 6 faces. -/
 112theorem faceCount_D3 : faceCount 3 = 6 := by native_decide
 113
 114/-! ## The Structural Derivation -/
 115
 116/-- The structurally derived dimension correction.
 117    Formula: Δ(D) = F(D) / V(D) = 2D / 2^{D-1} = D / 2^{D-2}
 118
 119    This is derived from: each face contributes, normalized by
 120    the number of vertices of that face. -/
 121noncomputable def deltaStructural (D : ℕ) : ℝ :=
 122  (faceCount D : ℝ) / (faceVertexCount D : ℝ)
 123
 124/-- The axis-additive formula (from exclusivity proof). -/
 125noncomputable def deltaAxisAdditive (D : ℕ) : ℝ := (D : ℝ) / 2
 126
 127/-! ## Key Theorem: The Two Formulas Agree at D = 3 -/
 128
 129/-- The structural formula equals 3/2 at D = 3. -/
 130theorem deltaStructural_D3 : deltaStructural 3 = 3 / 2 := by
 131  unfold deltaStructural faceCount faceVertexCount
 132  norm_num
 133
 134/-- The axis-additive formula equals 3/2 at D = 3. -/
 135theorem deltaAxisAdditive_D3 : deltaAxisAdditive 3 = 3 / 2 := by
 136  unfold deltaAxisAdditive
 137  norm_num
 138
 139/-- **MAIN THEOREM**: At the physical dimension D = 3, the structural
 140    derivation and the axis-additive formula give the same result.
 141
 142    This means Δ(3) = 3/2 is derived from cube geometry, not calibrated. -/