exchange_invariance_status
plain-language theorem explainer
Exchange invariance status labels the symmetry requirement that the recognition cost between two entities is unchanged under their exchange. Researchers cataloging foundational postulates in Recognition Science reference it when classifying axioms that enforce reciprocity on the comparator. The declaration is a direct string assignment carrying no computational content or proof obligations.
Claim. The exchange invariance postulate asserts that the recognition cost satisfies $C(A,B)=C(B,A)$ for any pair of entities $A,B$.
background
The Meta.Axioms module functions as the central registry that classifies every axiom used in the Recognition Science formalization into physical postulates, standard mathematical facts, or open problems. Exchange invariance is entered as a physical postulate encoding the symmetry requirement on the recognition relation. Upstream, the Identity definition in LogicAsFunctionalEquation encodes the corresponding reciprocal symmetry clause: the cost of comparing $x$ to $y$ equals the cost of comparing $y$ to $x$, presented as the mathematical counterpart of non-contradiction.
proof idea
One-line definition that directly assigns the string label 'Physical Postulate (Symmetry)'.
why it matters
The declaration populates the axiom registry table shown in the module documentation, appearing next to the meta-principle and recognition identity axiom. It supplies the symmetry condition required for the J-cost function and the Recognition Composition Law to be well-defined. Within the forcing chain it aligns with T5 J-uniqueness by guaranteeing that the comparator remains single-valued under exchange.
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