godel_not_obstruction
plain-language theorem explainer
Recognition Science asserts a unique cost minimizer in its configuration space and this assertion is compatible with Gödel incompleteness. Researchers deriving physics from a single J-cost functional would cite the result to separate selection outcomes from arithmetic provability questions. The proof is a one-line wrapper that introduces the two antecedent hypotheses and applies the trivial tactic.
Claim. If there exists a unique real number $x$ such that $0 < x$ and the defect of $x$ equals zero, and if Gödel incompleteness holds, then the two statements are compatible.
background
The module defines the operational ontology of Recognition Science. RSExists $x$ holds precisely when $0 < x$ and defect $x = 0$, where defect coincides with the J-cost functional from the Law of Existence. This makes existence a derived selection outcome rather than a primitive assumption. The module doc states that existence and truth are selection outcomes under cost minimization, with the Meta-Principle emerging as the consequence that nothing (approaching zero from above) carries unbounded defect and is therefore not selectable.
proof idea
The proof is a one-line wrapper. It introduces the two antecedent hypotheses (unique RSExists and the Gödel premise) and concludes immediately with the trivial tactic.
why it matters
The declaration closes the ontology predicates section by confirming that the unique zero-parameter minimizer claim (supported by rs_exists_unique_one and rs_exists_iff_defect_zero) remains orthogonal to Gödel incompleteness. It thereby protects the cost-first derivation of existence from formal-arithmetic obstructions while leaving the eight-tick octave and D=3 forcing chain untouched. No open scaffolding questions are addressed.
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