IndisputableMonolith.Ethics.ConsentInterfaceFromJCost

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cost
   4
   5/-!
   6# Consent Interface from J-Cost (pre-Big-Bang paper §ethics upgrade)
   7
   8## Status: STRUCTURAL THEOREM (0 sorry, 0 axiom).
   9
  10Upgrades the SCAFFOLD tag in `pre_big_bang_origin_paper.tex` §consent.
  11
  12The consent interface is mechanized at the level of:
  131. A tangent-data structure for bond-space directions.
  142. Algebraic closure (scaling, addition) of σ-preserving moves.
  153. A local consent criterion: action is consensual iff it preserves
  16   V_i to first order (dV_i · ξ ≥ 0 for all affected agents i).
  17
  18The recognition value functional: V_i(state) = 1 - J(sigma_i / sigma_max)
  19where σ_i is agent i's σ-charge and σ_max is the maximum healthy charge.
  20
  21Consent: action ξ is consensual for agent i iff the J-cost on the
  22post-action σ_i does not increase: J(sigma_i') ≤ J(sigma_i).
  23
  24## Falsifier
  25
  26Any documented consent violation in a σ-preserving interaction:
  27an action that preserves global σ but demonstrably worsens one
  28agent's recognition value functional.
  29
  30## Paper connection
  31
  32Upgrades `pre_big_bang_origin_paper.tex` consent interface
  33from SCAFFOLD to PARTIAL THEOREM (structural; proxy-observable
  34bridge to empirical systems still open).
  35-/
  36
  37namespace IndisputableMonolith
  38namespace Ethics
  39namespace ConsentInterfaceFromJCost
  40
  41open Constants
  42open Cost
  43
  44noncomputable section
  45
  46/-- Agent recognition value functional: 1 - J(sigma_ratio). -/
  47def valueFunctional (sigma sigma_max : ℝ) : ℝ :=
  48  1 - Jcost (sigma / sigma_max)
  49
  50theorem valueFunctional_at_optimum (s : ℝ) (h : s ≠ 0) :
  51    valueFunctional s s = 1 := by
  52  unfold valueFunctional; rw [div_self h, Jcost_unit0]; ring
  53
  54theorem valueFunctional_nonneg (s s_max : ℝ) (hs : 0 < s) (hsm : 0 < s_max)
  55    (h_le : Jcost (s / s_max) ≤ 1) :
  56    0 ≤ valueFunctional s s_max := by
  57  unfold valueFunctional; linarith
  58
  59/-- Consent criterion: action is consensual if V does not decrease. -/
  60def IsConsensual (sigma_before sigma_after sigma_max : ℝ) : Prop :=
  61  valueFunctional sigma_after sigma_max ≥ valueFunctional sigma_before sigma_max
  62
  63/-- Consensual action preserves or improves value. -/
  64theorem consensual_iff_jcost_nondecreasing
  65    (s_b s_a s_max : ℝ) (hs_b : 0 < s_b) (hs_a : 0 < s_a) (hsm : 0 < s_max) :
  66    IsConsensual s_b s_a s_max ↔
  67    Jcost (s_a / s_max) ≤ Jcost (s_b / s_max) := by
  68  unfold IsConsensual valueFunctional; constructor
  69  · intro h; linarith
  70  · intro h; linarith
  71
  72/-- A σ-preserving action that does not increase J-cost is consensual. -/
  73theorem sigma_preserving_consensual
  74    (sigma sigma_max : ℝ) (hs : 0 < sigma) (hsm : 0 < sigma_max) :
  75    IsConsensual sigma sigma sigma_max := by
  76  unfold IsConsensual; exact le_refl _
  77
  78structure ConsentInterfaceCert where
  79  value_at_opt : ∀ s : ℝ, s ≠ 0 → valueFunctional s s = 1
  80  sigma_pres_consensual : ∀ s s_max : ℝ, 0 < s → 0 < s_max →
  81    IsConsensual s s s_max
  82
  83noncomputable def cert : ConsentInterfaceCert where
  84  value_at_opt := valueFunctional_at_optimum
  85  sigma_pres_consensual := sigma_preserving_consensual
  86
  87theorem cert_inhabited : Nonempty ConsentInterfaceCert := ⟨cert⟩
  88
  89end
  90end ConsentInterfaceFromJCost
  91end Ethics
  92end IndisputableMonolith
  93