SelfRefQuery
plain-language theorem explainer
A SelfRefQuery packages a real number c with the contradictory property that its defect vanishes if and only if it does not. Recognition Science authors working on cost-theoretic closure cite the structure to encode Gödel sentences as stabilization queries. The definition is a direct structural encoding of the biconditional on defect with no auxiliary lemmas required.
Claim. A real number $c$ is a self-referential stabilization query when its associated defect satisfies $(D(c)=0)↔¬(D(c)=0)$, where $D$ denotes the defect functional $D(x)=J(x)$ from the Law of Existence.
background
The GodelDissolution module translates Gödel sentences into RS by replacing proof-system self-reference with cost-minimization dynamics. Stabilizes(c) is the predicate defect(c)=0; Diverges(c) asserts that defect(c) exceeds every bound. The local setting is that RS selects configurations by unique cost minimizer rather than by arithmetic completeness, so self-referential queries become objects that assert their own non-stabilization.
proof idea
This is a structure definition that directly records the biconditional on defect; no tactics or upstream lemmas are invoked inside the declaration itself.
why it matters
The structure is the contradictory object consumed by self_ref_query_impossible, GodelDissolutionTheorem, and complete_godel_dissolution. It supplies the concrete translation step in the paper proposition that Gödel sentences become non-configurations outside the RS ontology. The definition therefore closes the gap between formal incompleteness and physical selection dynamics.
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