Definition. Verifier correctness indicator [ftip-0046]
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    For prompts and responses from Notation [ftip-002A], a deterministic verifier correctness indicator is a declared map

    \[ v:\{(x,y):x\in \mathcal X_{\mathrm {pr}},\ y\in \mathcal Y(x)\} \longrightarrow \{0,1\}, \]

    Here \(v(x,y)=1\) means that the response satisfies the checked predicate. The map includes the parsing and execution rules needed to reproduce the decision. A stochastic judge or learned reward model is a different feedback mechanism unless its randomness and decision procedure are separately exposed.