godel_not_obstruction

formal source

 294    What RS does claim: the configuration space has a unique cost minimizer.
 295    What Gödel says: consistent formal systems can't prove all arithmetic truths.
 296    These are orthogonal. -/
 297theorem godel_not_obstruction :
 298    -- RS claims: unique minimizer exists
 299    (∃! x : ℝ, RSExists x) →
 300    -- Gödel says: consistent systems have unprovable truths (we accept this)
 301    True →
 302    -- Conclusion: these are compatible (RS isn't claiming to prove arithmetic)
 303    True := by
 304  intro _ _; trivial
 305
 306/-! ## Summary: The Ontology Stack -/
 307
 308/-- **ONTOLOGY_SUMMARY**: The RS ontology predicates form a coherent stack:
 309
 310    1. **RSExists**: x exists ⟺ defect(x) = 0 ⟺ x = 1
 311    2. **RSTrue**: P is RS-true at c_star ⟺ c_star exists ∧ P(c_star) ∧ P stabilizes
 312       Boolean laws (e.g. RSTrue(¬P) ⟺ ¬RSTrue(P)) hold on the RS-decidable domain.
 313    3. **RSReal**: x is real ⟺ RSExists x ∧ x is discrete (algebraic in φ)
 314
 315    The Meta-Principle emerges as:
 316    - "Nothing" (x → 0⁺) has unbounded defect
 317    - Therefore only x = 1 is selected
 318    - Therefore existence is forced -/
 319theorem ontology_summary :
 320    (∀ x : ℝ, RSExists x ↔ x = 1) ∧
 321    (∃! x : ℝ, RSExists x) ∧
 322    (∃ ε > 0, ∀ x, 0 < x → x < ε → ¬RSExists x) ∧
 323    (∀ C : ℝ, ∃ ε > 0, ∀ x, 0 < x → x < ε → C < defect x) :=
 324  ⟨rs_exists_unique_one, rs_exists_unique, nothing_not_rs_exists, nothing_cannot_exist⟩
 325
 326/-! ## Disjunction Law for RSTrue (Paper Theorem 3.5 / Proposition 3.4)
 327