stab_decidable

formal source

 177
 178/-- The stabilization status of any configuration is definite.
 179    Either defect = 0 or defect ≠ 0. There's no third option. -/
 180theorem stab_decidable (c : ℝ) : RSStab c ∨ ¬RSStab c := by
 181  exact em (RSStab c)
 182
 183/-- For real configurations, RSDiverge is actually impossible
 184    (defect is a real number, can't be greater than all reals). -/
 185theorem diverge_impossible (c : ℝ) : ¬RSDiverge c := by
 186  intro h
 187  -- RSDiverge c says ∀ C, defect c > C
 188  -- Take C = defect c
 189  have : defect c > defect c := h (defect c)
 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.