World-model predictions increasingly inform robot actions, yet instantaneous, model-internal reliability signals do not record where comparable imagination has failed. DreamLedger treats reliability as a persistent deployment object: execution-settled credit indexed by condition, region, and horizon, queried before use. Predictions consumed by the planner become claims settled against arriving reality without manual labels. Credit gates consumption; tickets and replayable logs preserve auditability. Persistent credit changes where the gate refuses rather than what the model gets wrong: 69% of denials occur in cells with prior failures, episode-local resets triple off-target denials in healthy conditions, and persistent credit halves burned imagination under localized recurrent degradation, at the cost of task completion. At matched refusal volume, every arm that removes the books or their persistence raises the per-spend burn rate, while a rate-matched random gate reduces task success without a burn-rate advantage in the healthy regimes; in a degraded regime with collapsed completion, random refusal regains a burn-rate advantage. We evaluate three simulated domains, unmodified DreamerV3, TD-MPC2, and V-JEPA 2-AC mounts, and a real Franka. Paired quadrotor evaluation shows credit gating reduces burned imagination by 62% (95% CI 43-81%) versus blind consumption. Settlement-grounded calibration yields moderate, seed-consistent operating points. In manipulation, the ledger completes +5.4pp more tasks than rate-matched random refusal, while trading success for verification against the no-books verifier (probes 0.55 vs. 1.00 at success 0.90 vs. 0.93). The trust layer spans decoder-, latent-, and token-space interfaces. On hardware, a failure loop is re-priced online, at 5 cm all counterfactual refusals land on the lowest-credit class, and all 1,062 registered spends replay from audit logs.

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