IndisputableMonolith.Chemistry.SolvationShellsFromConfigDim

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Solvation Shells from configDim — B10 Chemistry Depth
   6
   7Five canonical solvation shells for an ionic solute in water
   8(= configDim D = 5):
   9  primary hydration, secondary hydration, tertiary hydration,
  10  bulk-boundary layer, far bulk.
  11
  12Shell radius on the φ-ladder: adjacent-shell ratio = φ.
  13
  14Lean status: 0 sorry, 0 axiom.
  15-/
  16
  17namespace IndisputableMonolith.Chemistry.SolvationShellsFromConfigDim
  18open Constants
  19
  20inductive SolvationShell where
  21  | primaryHydration
  22  | secondaryHydration
  23  | tertiaryHydration
  24  | bulkBoundary
  25  | farBulk
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem solvationShell_count : Fintype.card SolvationShell = 5 := by decide
  29
  30noncomputable def shellRadius (k : ℕ) : ℝ := phi ^ k
  31
  32theorem shellRadius_ratio (k : ℕ) : shellRadius (k + 1) / shellRadius k = phi := by
  33  unfold shellRadius
  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 shellRadius_pos (k : ℕ) : 0 < shellRadius k := pow_pos phi_pos k
  39
  40structure SolvationShellCert where
  41  five_shells : Fintype.card SolvationShell = 5
  42  phi_ratio : ∀ k, shellRadius (k + 1) / shellRadius k = phi
  43  radius_always_pos : ∀ k, 0 < shellRadius k
  44
  45noncomputable def solvationShellCert : SolvationShellCert where
  46  five_shells := solvationShell_count
  47  phi_ratio := shellRadius_ratio
  48  radius_always_pos := shellRadius_pos
  49
  50end IndisputableMonolith.Chemistry.SolvationShellsFromConfigDim
  51