Walk me through what happens on a query where your eval...

A false negative costs you nothing you did not already have, as the pipeline simply degrades to naive RAG. A false positive is where the architecture is decided. By deriving the cost function, you can see the asymmetry between the penalty term and the gain term. This asymmetry motivates the use of an ambiguous band where the system might choose to abstain or hedge rather than force a retrieval that might be incorrect.