optimal_transfer
plain-language theorem explainer
If two display channels are quality-equivalent, then a state is optimal for one exactly when it is optimal for the other. Researchers transferring optimality results between equivalent observation models in Recognition Science cite this result. The proof is a one-line wrapper applying the quality equivalence theorem directly to the given hypothesis and state.
Claim. Let $C_1$ and $C_2$ be display channels sharing a common state space. If $C_1$ and $C_2$ are quality-equivalent, then for any state $x$, $x$ minimizes the quality of $C_1$ if and only if it minimizes the quality of $C_2$.
background
The RRF order preservation module shows that the framework tracks ordering of states by strain or quality rather than absolute values. A display channel is a structure pairing an observation map from states to observations with a quality map from observations to reals. A state is optimal for the channel when its induced quality is minimal over the entire state space.
proof idea
The proof is a one-line wrapper that applies the optimal_iff theorem from the QualityEquiv namespace to the equivalence hypothesis and the state.
why it matters
This theorem supplies the basic transfer of optimality under quality equivalence, completing the channel_transfer claim listed in the module documentation. It reinforces the RRF principle that order-preserving operations preserve meaning without invoking the phi-ladder or T5-T8 forcing steps directly.
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