`RoboticDOF`

definition

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module: IndisputableMonolith.CrossDomain.CubeFaceUniversality
domain: CrossDomain
line: 47 · github
papers citing: none yet

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IndisputableMonolith.CrossDomain.CubeFaceUniversality on GitHub at line 47.

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formal source

  44  | b1 | b2 | b3 | b4 | b5 | b6
  45  deriving DecidableEq, Repr, BEq, Fintype
  46
  47inductive RoboticDOF where
  48  | x | y | z | rollAxis | pitchAxis | yawAxis
  49  deriving DecidableEq, Repr, BEq, Fintype
  50
  51theorem quark_has_6 : HasCubeFaceCount Quark := by
  52  unfold HasCubeFaceCount; decide
  53theorem lepton_has_6 : HasCubeFaceCount Lepton := by
  54  unfold HasCubeFaceCount; decide
  55theorem cortical_has_6 : HasCubeFaceCount CorticalLayer := by
  56  unfold HasCubeFaceCount; decide
  57theorem braak_has_6 : HasCubeFaceCount BraakStage := by
  58  unfold HasCubeFaceCount; decide
  59theorem robotic_has_6 : HasCubeFaceCount RoboticDOF := by
  60  unfold HasCubeFaceCount; decide
  61
  62/-- The cube-face identity: 6 = 2 × 3 = face-binary × spatial-dim. -/
  63theorem cube_face_identity : (6 : ℕ) = 2 * 3 := by decide
  64
  65/-- Q₃ Euler: V - E + F = 8 - 12 + 6 = 2. -/
  66theorem q3_euler : (8 : ℤ) - 12 + 6 = 2 := by decide
  67
  68/-- Any two cube-face domains are equicardinal. -/
  69theorem cube_face_equicardinal
  70    {A B : Type} [Fintype A] [Fintype B]
  71    (hA : HasCubeFaceCount A) (hB : HasCubeFaceCount B) :
  72    Fintype.card A = Fintype.card B := by
  73  rw [hA, hB]
  74
  75/-- Standard Model total fermion count: 6 quarks + 6 leptons = 12. -/
  76theorem quark_lepton_sum :
  77    Fintype.card Quark + Fintype.card Lepton = 12 := by

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