IndisputableMonolith.Physics.MagnetismFromRS

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Magnetism from RS — A1 SM Foundation
   6
   7Magnetic phenomena = recognition charge currents.
   8In RS: magnetic field B = recognition current density J(current/baseline).
   9
  10Five canonical magnetic phenomena (ferromagnetism, antiferromagnetism,
  11ferrimagnetism, paramagnetism, diamagnetism) = configDim D = 5.
  12
  13At zero field: J = 0 (no recognition current).
  14In applied field: J > 0 (current deviates from equilibrium).
  15
  16Lean: 5 phenomena.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Physics.MagnetismFromRS
  22open Cost
  23
  24inductive MagneticPhenomenon where
  25  | ferromagnetism | antiferromagnetism | ferrimagnetism | paramagnetism | diamagnetism
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem magneticPhenomenonCount : Fintype.card MagneticPhenomenon = 5 := by decide
  29
  30/-- Zero field: J = 0. -/
  31theorem zero_field : Jcost 1 = 0 := Jcost_unit0
  32
  33/-- Applied field: J > 0. -/
  34theorem applied_field {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  35    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  36
  37structure MagnetismCert where
  38  five_phenomena : Fintype.card MagneticPhenomenon = 5
  39  zero_field_zero : Jcost 1 = 0
  40  applied_positive : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  41
  42def magnetismCert : MagnetismCert where
  43  five_phenomena := magneticPhenomenonCount
  44  zero_field_zero := zero_field
  45  applied_positive := applied_field
  46
  47end IndisputableMonolith.Physics.MagnetismFromRS
  48