Stabilizes
plain-language theorem explainer
A real-valued configuration stabilizes exactly when its defect vanishes. Researchers formalizing the dissolution of Gödel sentences in Recognition Science cite this to separate stabilizing fixed points from diverging orbits under cost dynamics. The definition is a direct abbreviation that imports the upstream defect functional and sets it to zero.
Claim. A real number $c$ stabilizes when $J(c)=0$, where $J$ is the defect functional satisfying the Recognition Composition Law.
background
The Gödel Dissolution module models configurations as real numbers to translate self-referential queries into cost dynamics. Defect is defined as defect(x) := J(x), with J the cost function whose value is zero at unity. Upstream results supply the active-edge count A from IntegrationGap and the actualization operator from Modal.Actualization, both of which presuppose the same J-cost structure. The module's setting is that Gödel sentences become stabilization queries asserting non-stabilization, which must then be shown to lie outside the ontology of RS-true predicates.
proof idea
One-line definition that equates stabilization of a real configuration directly to the zero-defect condition imported from LawOfExistence.defect.
why it matters
This definition is the base case for the ontology predicates RSTrue, RSDecidable and rs_true_and in OntologyPredicates, which in turn feed the main dissolution argument that self-referential queries cannot be RSTrue or RSFalse. It closes the local step in the chain from T5 J-uniqueness to the claim that Gödel phenomena are non-configurations rather than truth gaps, supporting the cost-theoretic resolution of physical closure.
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