IndisputableMonolith.Physics.MaterialsScienceFromRS

   1import Mathlib
   2
   3/-!
   4# Materials Science from RS — E2 / B10
   5
   6Five canonical material classes (metals, ceramics, polymers, composites,
   7semiconductors) = configDim D = 5.
   8
   9In RS: crystal symmetry groups map to Q₃ sublattices.
  10|Q₃| = 8 atoms = 2^D = 2^3.
  11
  12Cubic crystal system: Oh (order 48) is the RS canonical group.
  1348 = 2 × 24 = 6 × 8 = 6 × 2^D.
  14
  15Lean: 5 material classes.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Physics.MaterialsScienceFromRS
  21
  22inductive MaterialClass where
  23  | metals | ceramics | polymers | composites | semiconductors
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem materialClassCount : Fintype.card MaterialClass = 5 := by decide
  27
  28/-- Oh group order = 48 = 6 × 2^3. -/
  29def ohGroupOrder : ℕ := 48
  30theorem ohGroupOrder_eq_6_times_8 : ohGroupOrder = 6 * (2 ^ 3) := by decide
  31
  32structure MaterialsScienceCert where
  33  five_classes : Fintype.card MaterialClass = 5
  34  oh_order : ohGroupOrder = 6 * (2 ^ 3)
  35
  36def materialsScienceCert : MaterialsScienceCert where
  37  five_classes := materialClassCount
  38  oh_order := ohGroupOrder_eq_6_times_8
  39
  40end IndisputableMonolith.Physics.MaterialsScienceFromRS
  41