config_classification

formal source

 190  linarith
 191
 192/-- Every real configuration is either RSStab or RSOutside (never RSDiverge). -/
 193theorem config_classification (c : ℝ) : RSStab c ∨ RSOutside c := by
 194  by_cases hs : RSStab c
 195  · left; exact hs
 196  · right
 197    exact ⟨hs, diverge_impossible c⟩
 198
 199/-! ## The Gödel Dissolution -/
 200
 201/-- **THE GÖDEL DISSOLUTION THEOREM**
 202
 203    The Gödel phenomenon is dissolved, not denied:
 204    1. Self-referential stabilization queries are contradictory (can't exist)
 205    2. Gödel sentences translate to such queries
 206    3. Therefore Gödel sentences are "non-configurations" - outside the ontology
 207
 208    RS closure means "unique cost minimizer exists", not "all arithmetic true."
 209    These are different claims about different targets.
 210    Gödel constrains provability; RS constrains selection.
 211    Orthogonal. -/
 212structure GodelDissolutionTheorem where
 213  /-- Self-referential queries are impossible -/
 214  self_ref_impossible : ¬∃ q : SelfRefQuery, True
 215  /-- General self-ref queries are impossible -/
 216  general_self_ref_impossible : ¬∃ q : GeneralSelfRefQuery, True
 217  /-- Every real config has definite status -/
 218  definite_status : ∀ c : ℝ, RSStab c ∨ ¬RSStab c
 219  /-- RS closure is about unique minimizer, not arithmetic -/
 220  rs_closure_meaning : ∃! x : ℝ, RSExists x
 221
 222/-- The Gödel dissolution theorem holds. -/
 223theorem godel_dissolution_holds : GodelDissolutionTheorem := {