coherenceLevel

formal source

  45noncomputable section
  46
  47/-- Coherence is inversely related to J-cost. Lower cost = higher coherence. -/
  48def coherenceLevel (x : ℝ) (_ : 0 < x) : ℝ := 1 / (1 + Jcost x)
  49
  50theorem coherenceLevel_pos (x : ℝ) (hx : 0 < x) : 0 < coherenceLevel x hx := by
  51  unfold coherenceLevel
  52  apply div_pos one_pos
  53  linarith [Jcost_nonneg hx]
  54
  55theorem max_coherence_at_balance : coherenceLevel 1 one_pos = 1 := by
  56  unfold coherenceLevel
  57  rw [Jcost_unit0]
  58  simp
  59
  60/-- PROVED: Operating away from σ = 0 strictly reduces coherence.
  61    This is the core safety result: power requires ethics. -/
  62theorem power_ethics_same_axis (x : ℝ) (hx : 0 < x) (hne : x ≠ 1) :
  63    coherenceLevel x hx < coherenceLevel 1 one_pos := by
  64  rw [max_coherence_at_balance]
  65  unfold coherenceLevel
  66  have hJ : 0 < Jcost x := Jcost_pos_of_ne_one x hx hne
  67  rw [div_lt_one (by linarith [Jcost_nonneg hx])]
  68  linarith
  69
  70/-- Weaponization requires σ > 0, which reduces coherence below maximum. -/
  71theorem weaponization_structurally_impossible (x : ℝ) (hx : 0 < x) (hne : x ≠ 1) :
  72    coherenceLevel x hx < 1 := by
  73  have h := power_ethics_same_axis x hx hne
  74  rwa [max_coherence_at_balance] at h
  75
  76end
  77
  78end IndisputableMonolith.Superhuman.SafetyInterlock