self_ref_not_configuration

formal source

 100/-- **COROLLARY**: No consistent configuration can be a self-referential
 101    stabilization query. Such "configurations" are syntactically expressible
 102    but ontologically empty. -/
 103theorem self_ref_not_configuration :
 104    ∀ c : ℝ, ¬((defect c = 0) ↔ ¬(defect c = 0)) := by
 105  intro c h
 106  by_cases hd : defect c = 0
 107  · exact (h.mp hd) hd
 108  · exact hd (h.mpr hd)
 109
 110/-! ## The Extended Analysis: RSTrue, RSFalse, and Outside -/
 111
 112/-- RS-truth predicate (stabilization). -/
 113def RSStab (c : ℝ) : Prop := defect c = 0
 114
 115/-- RS-falsity predicate (divergence). -/
 116def RSDiverge (c : ℝ) : Prop := ∀ C : ℝ, defect c > C
 117
 118/-- Outside the ontology: neither stabilizes nor diverges. -/
 119def RSOutside (c : ℝ) : Prop := ¬RSStab c ∧ ¬RSDiverge c
 120
 121/-- A more general self-referential query: c encodes "I don't RSStab."
 122    We model this as: there's a function φ that tells us "what c asserts"
 123    and c asserts ¬RSStab(c). -/
 124structure GeneralSelfRefQuery where
 125  config : ℝ
 126  /-- c "asserts" a proposition -/
 127  asserts : Prop
 128  /-- That proposition is ¬RSStab(c) -/
 129  encodes_negation : asserts ↔ ¬RSStab config
 130  /-- c is "correct" if what it asserts matches its stabilization status -/
 131  correctness : RSStab config ↔ asserts
 132
 133/-- **THEOREM 2**: General self-referential queries are contradictory.