RSStab
plain-language theorem explainer
RSStab marks a real number c as stabilizing when its defect vanishes. Researchers on the Gödel dissolution cite it to separate configurations that reach cost minima from those outside the ontology. The definition is a direct abbreviation of the upstream defect functional set to zero.
Claim. Let $J$ be the defect functional on the reals. Then RSStab$(c)$ holds if and only if $J(c)=0$.
background
The Gödel Dissolution module classifies real configurations by stabilization behavior under Recognition Science cost dynamics. The defect functional, defined in LawOfExistence as defect(x) := J(x), supplies the cost measure drawn from the Recognition Composition Law. Divergence, imported from DiscreteNSOperator, serves only as the contrasting predicate that no real configuration can satisfy.
proof idea
One-line definition that directly sets RSStab c to the equality defect c = 0, invoking the upstream defect abbreviation.
why it matters
RSStab supplies the positive truth predicate required by GodelDissolutionTheorem and complete_godel_dissolution. Those results show self-referential queries cannot satisfy RSStab consistently, placing Gödel sentences outside the ontology of cost-minimizing configurations. The predicate aligns with T5 J-uniqueness and the stabilization fixed point at unity.
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