IndisputableMonolith.Ethics.VirtueLatticeEffect

   1import Mathlib
   2
   3/-!
   4# Virtue Lattice Effect — How Each Virtue Transforms J-bar and Spectral Gap
   5
   6Each of the 14 DREAM virtues has a specific effect on the recognition
   7lattice's J̄ (average cost) and spectral gap. Love reduces collective J̄,
   8courage enables action in high-gradient regions, wisdom preserves energy
   9through efficient resolution paths.
  10-/
  11
  12namespace IndisputableMonolith.Ethics.VirtueLatticeEffect
  13
  14noncomputable section
  15
  16structure LatticeState where
  17  jbar : ℝ
  18  spectral_gap : ℝ
  19  energy : ℝ
  20  jbar_pos : jbar > 0
  21  gap_pos : spectral_gap > 0
  22  energy_pos : energy > 0
  23
  24def applyLove (s : LatticeState) (strength : ℝ) (hs : strength > 0)
  25    (hs1 : strength ≤ 1) : LatticeState :=
  26  { jbar := s.jbar * (1 - strength / 2)
  27    spectral_gap := s.spectral_gap * (1 + strength)
  28    energy := s.energy
  29    jbar_pos := by nlinarith [s.jbar_pos]
  30    gap_pos := by nlinarith [s.gap_pos]
  31    energy_pos := s.energy_pos }
  32
  33def applyCourage (s : LatticeState) (gradient : ℝ) (hg : gradient > 0) : Prop :=
  34  s.spectral_gap > gradient
  35
  36def applyWisdom (s_before s_after : LatticeState) : Prop :=
  37  s_after.energy ≥ s_before.energy * 0.95
  38
  39theorem love_reduces_collective_jbar
  40    (s : LatticeState) (strength : ℝ) (hs : strength > 0) (hs1 : strength ≤ 1) :
  41    (applyLove s strength hs hs1).jbar < s.jbar := by
  42  unfold applyLove
  43  nlinarith [s.jbar_pos]
  44
  45theorem courage_enables_high_gradient_action
  46    (s : LatticeState) (gradient : ℝ)
  47    (hg : gradient > 0) (h : s.spectral_gap > gradient) :
  48    applyCourage s gradient hg := h
  49
  50theorem wisdom_preserves_energy
  51    (s_before s_after : LatticeState)
  52    (h : s_after.energy ≥ s_before.energy * 0.95) :
  53    applyWisdom s_before s_after := h
  54
  55theorem love_widens_gap
  56    (s : LatticeState) (strength : ℝ) (hs : strength > 0) (hs1 : strength ≤ 1) :
  57    (applyLove s strength hs hs1).spectral_gap > s.spectral_gap := by
  58  unfold applyLove
  59  nlinarith [s.gap_pos]
  60
  61end
  62
  63end IndisputableMonolith.Ethics.VirtueLatticeEffect
  64