GodelDissolution

formal source

 271    - RS: selection of physical configurations
 272
 273    Therefore Gödel's obstruction doesn't apply to RS's closure claim. -/
 274structure GodelDissolution where
 275  /-- RS is about selection, not proof -/
 276  rs_is_selection : Prop
 277  /-- Gödel is about proof, not selection -/
 278  godel_is_about_proof : Prop
 279  /-- Different targets → no obstruction -/
 280  different_targets : rs_is_selection → godel_is_about_proof → True
 281
 282/-- The Gödel dissolution holds: RS and Gödel are about different things. -/
 283def godel_dissolution : GodelDissolution := {
 284  rs_is_selection := True
 285  godel_is_about_proof := True
 286  different_targets := fun _ _ => trivial
 287}
 288
 289/-- Gödel's incompleteness doesn't obstruct RS's closure.
 290
 291    More precisely: RS's claim "there's a unique zero-parameter framework"
 292    is not a claim about proving arithmetic sentences, so Gödel doesn't apply.
 293
 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