Definition. Finite declared feedback protocol [ftip-007Q]
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    Fix a horizon \(N\geq 0\), finite action sets \(\mathcal A_n\), finite feedback sets \(\mathcal F_n\), and a finite internal-seed set \(\mathcal U\) with a declared law \(\lambda \). A finite declared protocol \(\mathsf P\) consists of selection maps

    \[ a_n:\mathcal U\times \prod _{j<n}(\mathcal A_j\times \mathcal F_j) \longrightarrow \mathcal A_n \qquad (0\leq n<N). \]

    An action may specify the task, rollout record, feedback request, or sampling choice made at that round. The protocol can depend on earlier exposed feedback and its declared seed, but it cannot depend on a latent world field that has not entered those arguments.