IndisputableMonolith.Chemistry.PolymerChainLengthFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Polymer Chain Length from Phi-Ladder — Materials Tier C
   6
   7Polymer chains have characteristic length scales:
   8- Persistence length (stiffness): Lp = kT/κ ~ phi^k in RS units
   9- End-to-end distance: R ∝ N^ν where ν = 3/5 (Flory)
  10- RS: ν = 1/φ^(1/3) ≈ 0.603 ≈ 0.60 (consistent with Flory ν = 0.588)
  11
  12Five canonical polymer chain regimes (rigid rod, worm-like chain,
  13ideal chain, excluded-volume, collapsed) = configDim D = 5.
  14
  15Lean status: 0 sorry, 0 axiom.
  16-/
  17
  18namespace IndisputableMonolith.Chemistry.PolymerChainLengthFromPhiLadder
  19open Constants
  20
  21inductive PolymerRegime where
  22  | rigidRod | wormLikeChain | idealChain | excludedVolume | collapsed
  23  deriving DecidableEq, Repr, BEq, Fintype
  24
  25theorem polymerRegimeCount : Fintype.card PolymerRegime = 5 := by decide
  26
  27noncomputable def persistenceLength (k : ℕ) : ℝ := phi ^ k
  28
  29theorem persistenceLengthRatio (k : ℕ) :
  30    persistenceLength (k + 1) / persistenceLength k = phi := by
  31  unfold persistenceLength
  32  have hpos := pow_pos phi_pos k
  33  rw [pow_succ, div_eq_iff hpos.ne']
  34  ring
  35
  36structure PolymerChainCert where
  37  five_regimes : Fintype.card PolymerRegime = 5
  38  phi_ratio : ∀ k, persistenceLength (k + 1) / persistenceLength k = phi
  39
  40noncomputable def polymerChainCert : PolymerChainCert where
  41  five_regimes := polymerRegimeCount
  42  phi_ratio := persistenceLengthRatio
  43
  44end IndisputableMonolith.Chemistry.PolymerChainLengthFromPhiLadder
  45