IndisputableMonolith.Applied.UniversalEquilibriumResponseC7

   1import Mathlib
   2import IndisputableMonolith.Foundation.JCostHessianC7
   3
   4/-!
   5# C7: Universal Equilibrium Response
   6
   7Any RS equilibrium modeled by the same local J-cost kernel inherits the same
   8quadratic coefficient 1/2 and Hessian coefficient 1. This is the formal common
   9core behind the prose claim "Nash = market = health equilibrium" at r = 1.
  10
  11The empirical cross-field sensitivity comparison is not proved here; this file
  12proves the shared J-kernel that such a comparison must use.
  13
  14Lean status: 0 sorry, 0 axiom.
  15-/
  16
  17namespace IndisputableMonolith
  18namespace Applied
  19namespace UniversalEquilibriumResponseC7
  20
  21open Foundation.JCostHessianC7
  22
  23inductive EquilibriumDomain where
  24  | gameTheory
  25  | financialMarket
  26  | healthState
  27  deriving DecidableEq, Repr, Fintype
  28
  29theorem equilibriumDomain_count : Fintype.card EquilibriumDomain = 3 := by
  30  decide
  31
  32noncomputable def responseCoefficient (_ : EquilibriumDomain) : ℝ :=
  33  jcostHessianCoefficient
  34
  35theorem responseCoefficient_universal (D : EquilibriumDomain) :
  36    responseCoefficient D = 1 := by
  37  unfold responseCoefficient
  38  exact jcostHessianCoefficient_eq_one
  39
  40structure UniversalResponseCert where
  41  three_domains : Fintype.card EquilibriumDomain = 3
  42  universal_response : ∀ D : EquilibriumDomain, responseCoefficient D = 1
  43  kernel : JCostHessianCert
  44
  45noncomputable def universalResponseCert : UniversalResponseCert where
  46  three_domains := equilibriumDomain_count
  47  universal_response := responseCoefficient_universal
  48  kernel := jcostHessianCert
  49
  50end UniversalEquilibriumResponseC7
  51end Applied
  52end IndisputableMonolith
  53