self_ref_not_configuration
plain-language theorem explainer
No real number c satisfies the biconditional that its defect vanishes if and only if it does not. This corollary shows self-referential stabilization queries cannot be consistent configurations in Recognition Science. The proof derives an immediate contradiction via case analysis on whether the defect is zero.
Claim. For every real number $c$, it is not the case that $J(c)=0$ if and only if $J(c)≠0$, where $J$ is the defect functional.
background
The module formalizes the claim that self-referential stabilization queries have no fixed point under RS dynamics. A configuration is RS-true only when its defect vanishes, the predicate holds, and the orbit stabilizes to that point. The defect functional is defined as $J(x)$ for positive $x$ and equals zero precisely at stable points.
proof idea
The term proof introduces arbitrary $c$ and assumes the biconditional for contradiction. Case analysis on whether defect $c$ equals zero is performed. Each branch applies one direction of the biconditional to obtain the negation of the case assumption, yielding the contradiction.
why it matters
The result supports the main theorem of the Gödel Dissolution module by showing self-referential queries lie outside the RS ontology. It contributes to reclassifying Gödel phenomena as non-configurations rather than gaps between truth and provability. The parent claim is that RS closure is achieved by unique cost minimization, not by proving arithmetic sentences.
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