classical_logic_and_unique_minimizer_theorem
plain-language theorem explainer
Bundles four foundation facts: no real configuration satisfies (defect = 0) ↔ ¬(defect = 0), no general biconditional self-negation, every real has definite stabilization status, and RS-existence picks a unique positive real. Downstream T0 bridge and deprecated Gödel-dissolution shims cite it. Proof is a structure constructor wiring four already-proved lemmas.
Claim. The classical-logic-and-unique-minimizer package holds: there is no real configuration $c$ with $(\mathrm{defect}(c)=0)\leftrightarrow\neg(\mathrm{defect}(c)=0)$; no configuration carries a general predicate-level biconditional self-negation on stabilization; for every real $c$, either $c$ is stabilized or it is not; and there exists a unique real $x$ that RS-exists.
background
This module records classical propositional facts about biconditional self-negation on real configurations, plus the substantive unique-existent claim from the ontology layer. Stabilization status RSStab c is the predicate that the defect of $c$ vanishes. A self-negating configuration would be a real $c$ satisfying $(\mathrm{defect}(c)=0)\leftrightarrow\neg(\mathrm{defect}(c)=0)$; a general self-negating predicate packages the same pattern at the level of an arbitrary correctness/encoding pair on stabilization.
The module doc is explicit: for any real $c$, that biconditional is inhabited iff False, by a two-line case split on excluded middle. The same holds for any predicate $P$: classical logic has no fixed point for negation. This is propositional-logic content, not RS-specific physics.
Upstream, no_self_negating_config and no_general_self_negating_predicate discharge the two non-existence claims; stab_decidable is excluded middle on RSStab; rs_exists_unique (from OntologyPredicates) supplies unique RS-existence. The historical Gödel-dissolution naming is deprecated; the content is classical logic plus unique minimizer.
proof idea
Term-mode structure constructor. Each field of ClassicalLogicAndUniqueMinimizerTheorem is filled by a named prior theorem:
no_self_negating_config← the two-line excluded-middle proof that noSelfNegatingConfigexists;no_general_self_negating_predicate← the corresponding non-existence forGeneralSelfNegatingPredicate(compose correctness with encodes-negation, then contradict $P\leftrightarrow\neg P$);definite_status←stab_decidable, i.e.em (RSStab c)for every real $c$;rs_closure_meaning←rs_exists_unique, the unique positive existent from the ontology predicates.
No new reasoning: pure packaging of four already-proved facts into the bundle type.
why it matters
This is the canonical inhabitant of the classical-logic-and-unique-minimizer bundle. In the forcing chain it feeds t0_to_classical_logic_and_unique_minimizer_bridge_holds: "T0 supplies the classical-logic + unique-minimizer bridge. The historical name claimed 'Gödel dissolution'; the actual content is classical-logic biconditional impossibility plus the substantive T5 unique-minimizer fact."
Deprecated shims in GodelDissolution (godel_dissolution_holds, GodelDissolutionTheorem) re-export this theorem under the old names. The module doc warns that the result does not touch Gödel I: Gödel sentences satisfy $G\leftrightarrow\neg\mathrm{Prov}_F(\ulcorner G\urcorner)$, not $P\leftrightarrow\neg P$. The categorical reason Gödel I has no target inside T-1→T0→…→T8 is meta-level, not a Lean theorem.
Framework role: clears the T0 classical-logic side of the bridge so the unique-existent (tied to the J-cost minimizer at $x=1$, and ultimately T5 J-uniqueness) can sit in a classically definite ambient logic.
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