IndisputableMonolith.Materials.BatteryChemistryFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Battery Chemistry from φ-ladder — Energy Storage Depth
   6
   7Five canonical battery-chemistry families (= configDim D = 5):
   8  lead-acid, nickel-cadmium, nickel-metal-hydride, lithium-ion,
   9  solid-state (next-gen).
  10
  11Adjacent-family energy-density ratio on the φ-ladder.
  12
  13Lean status: 0 sorry, 0 axiom.
  14-/
  15
  16namespace IndisputableMonolith.Materials.BatteryChemistryFromPhiLadder
  17open Constants
  18
  19inductive BatteryChemistry where
  20  | leadAcid
  21  | nickelCadmium
  22  | nickelMetalHydride
  23  | lithiumIon
  24  | solidState
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem batteryChemistry_count : Fintype.card BatteryChemistry = 5 := by decide
  28
  29noncomputable def energyDensity (k : ℕ) : ℝ := phi ^ k
  30
  31theorem density_ratio (k : ℕ) :
  32    energyDensity (k + 1) / energyDensity k = phi := by
  33  unfold energyDensity
  34  have hpos : (0 : ℝ) < phi ^ k := pow_pos phi_pos k
  35  rw [div_eq_iff hpos.ne', pow_succ]
  36  ring
  37
  38theorem density_pos (k : ℕ) : 0 < energyDensity k := pow_pos phi_pos k
  39
  40structure BatteryChemistryCert where
  41  five_chemistries : Fintype.card BatteryChemistry = 5
  42  phi_ratio : ∀ k, energyDensity (k + 1) / energyDensity k = phi
  43  density_always_pos : ∀ k, 0 < energyDensity k
  44
  45noncomputable def batteryChemistryCert : BatteryChemistryCert where
  46  five_chemistries := batteryChemistry_count
  47  phi_ratio := density_ratio
  48  density_always_pos := density_pos
  49
  50end IndisputableMonolith.Materials.BatteryChemistryFromPhiLadder
  51