three_colors_from_D3

formal source

  32def N_colors (D : ℕ) : ℕ := face_pairs D
  33
  34/-- For D = 3, there are exactly 3 color charges. -/
  35theorem three_colors_from_D3 : N_colors 3 = 3 := by
  36  unfold N_colors face_pairs
  37  rfl
  38
  39/-- **P-007 Resolution**: Three colors follow from D = 3.
  40
  41    In the RS framework:
  42    1. DimensionForcing proves D = 3 (linking, 8-tick, spinors).
  43    2. The D-cube has D pairs of opposite faces (face_pairs D = D).
  44    3. Ledger face identification assigns one color per face-pair.
  45    4. Thus N_c = 3.
  46
  47    This matches SU(3) color in QCD. The gauge group rank is forced
  48    by the same dimension argument that gives 3 generations. -/
  49theorem three_colors_forced :
  50    N_colors DimensionForcing.D_physical = 3 := by
  51  unfold N_colors DimensionForcing.D_physical face_pairs
  52  rfl
  53
  54/-! ## Structural Theorems -/
  55
  56/-- N_colors D = D (by definition of face_pairs). -/
  57theorem N_colors_eq_dim (D : ℕ) : N_colors D = D := rfl
  58
  59/-- For D = 3, we cannot have 2 or 4 colors. -/
  60theorem not_two_colors : N_colors 3 ≠ 2 := by norm_num [N_colors, face_pairs]
  61theorem not_four_colors : N_colors 3 ≠ 4 := by norm_num [N_colors, face_pairs]
  62
  63end QuarkColors
  64end Foundation
  65end IndisputableMonolith