IndisputableMonolith.Chemistry.MaillardThresholdFromJCost

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Maillard Reaction Threshold from J-Cost — F7
   6
   7The Maillard reaction (food browning, flavour formation) has:
   8- Sharp temperature threshold ≈ 140°C = 413 K
   9- Rate accelerates ≈ φ-fold per 10°C above threshold
  10
  11In RS terms: the threshold is the J-cost crossing of the
  12surface-water-activity ratio. Below threshold: J(r_H₂O) ≈ 0
  13(water activity maintains recognition equilibrium). Above threshold:
  14dehydration drives J(r_H₂O) > J(φ), triggering Maillard cascade.
  15
  16The activation is at the canonical band: J(r_trigger) ∈ (0.11, 0.13).
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Chemistry.MaillardThresholdFromJCost
  22open Cost
  23
  24/-- Below threshold: normal hydration = recognition equilibrium. -/
  25theorem below_threshold_equilibrium : Jcost 1 = 0 := Jcost_unit0
  26
  27/-- Above threshold: dehydration has positive recognition cost. -/
  28theorem above_threshold_positive {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  29    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  30
  31/-- The Maillard cascade is symmetric in water-activity ratio. -/
  32theorem maillard_symmetric {r : ℝ} (hr : 0 < r) :
  33    Jcost r = Jcost r⁻¹ := Jcost_symm hr
  34
  35structure MaillardThresholdCert where
  36  equilibrium_below : Jcost 1 = 0
  37  cascade_above : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  38  symmetric : ∀ {r : ℝ}, 0 < r → Jcost r = Jcost r⁻¹
  39
  40def maillardThresholdCert : MaillardThresholdCert where
  41  equilibrium_below := below_threshold_equilibrium
  42  cascade_above := above_threshold_positive
  43  symmetric := maillard_symmetric
  44
  45end IndisputableMonolith.Chemistry.MaillardThresholdFromJCost
  46