config_classification
plain-language theorem explainer
Every real configuration satisfies either stabilization (defect exactly zero) or lies outside the ontology (neither stabilizes nor diverges). Logicians and physicists studying cost-theoretic treatments of incompleteness theorems cite this trichotomy. The argument proceeds by case split on the stabilization predicate, then invokes the separate impossibility of unbounded real defects.
Claim. For every real number $c$, either the defect of $c$ equals zero or $c$ is outside the ontology, meaning its defect is neither zero nor greater than every real bound.
background
The module recasts Gödel incompleteness inside Recognition Science by translating self-referential sentences into stabilization queries under cost minimization. Stabilization holds precisely when defect vanishes; divergence requires the defect to exceed every real number; outside the ontology means failure of both predicates. The local setting treats RS closure as the existence of a unique cost minimizer rather than arithmetic completeness, so Gödel sentences become non-configurations that oscillate without fixed point.
proof idea
Case analysis on whether stabilization holds for the input real. The affirmative case yields the left disjunct directly. The negative case combines the negation of stabilization with the upstream result that divergence is impossible for any real defect, since an unbounded defect would exceed its own value.
why it matters
The classification supplies the exhaustive trichotomy required by the Gödel dissolution theorem, ruling out divergence for real configurations and forcing self-referential queries into the outside category. It thereby supports the paper claim that RS selection by cost is orthogonal to provability gaps. No downstream uses are recorded, but the result closes the logical space for diverging configurations in the foundation layer.
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