Theorem. Capped retained context bounds finite exposure work [ftip-00DL]
Theorem. Capped retained context bounds finite exposure work [ftip-00DL]
Under the hypotheses of Lemma [ftip-00DK], every rollout with budget \(T\) satisfies
\[ E_T(\kappa ^{p,w})\leq T(p+w). \]Proof. Apply the pointwise bound in Lemma [ftip-00DK] to each of the \(T\) nonnegative summands in Definition [ftip-00DJ], then sum. This bounds token exposure, not wall-clock runtime or evaluation quality.