IndisputableMonolith.Chemistry.ReactiveOxygenSpeciesFromJCost

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Reactive Oxygen Species from J-Cost — B2 / Aging Depth
   6
   7ROS (reactive oxygen species) accumulate in aging and disease.
   8In RS: ROS level = J(O₂_radical/O₂_normal) > 0 when elevated.
   9
  10At physiological levels: J ≈ 0 (controlled ROS for signalling).
  11In oxidative stress: J > J(φ) triggers damage cascades.
  12
  13Five canonical ROS types (O₂⁻, H₂O₂, ·OH, RO·, ¹O₂) = configDim D = 5.
  14
  15Lean status: 0 sorry, 0 axiom.
  16-/
  17
  18namespace IndisputableMonolith.Chemistry.ReactiveOxygenSpeciesFromJCost
  19open Cost
  20
  21inductive ROSType where
  22  | superoxide | H2O2 | hydroxyl | alkoxy | singletO2
  23  deriving DecidableEq, Repr, BEq, Fintype
  24
  25theorem rosTypeCount : Fintype.card ROSType = 5 := by decide
  26
  27/-- Physiological ROS: J ≈ 0 (equilibrium). -/
  28theorem physiological_ros : Jcost 1 = 0 := Jcost_unit0
  29
  30/-- Oxidative stress: J > 0. -/
  31theorem oxidative_stress {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  32    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  33
  34structure ROSCert where
  35  five_types : Fintype.card ROSType = 5
  36  physiological : Jcost 1 = 0
  37  stress_positive : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  38
  39def rosCert : ROSCert where
  40  five_types := rosTypeCount
  41  physiological := physiological_ros
  42  stress_positive := oxidative_stress
  43
  44end IndisputableMonolith.Chemistry.ReactiveOxygenSpeciesFromJCost
  45