An inference budget is useful only when the system delivers an answer within it. We study a fixed-budget policy combining first-valid-box stopping with a charged finalization cue. On 100 fresh, independently audited GSM8K test questions per model, it improves delivered endpoint accuracy over first-box stopping by 8.0 percentage points for Qwen3-4B-Thinking-2507 and 7.0 for DeepSeek-R1-Distill-Llama-8B. A prelocked repeat on the same questions gives 7.0 and 10.0 points; neither seed shows a gross harm relative to first-box stopping. The point estimates of incremental physical-slot savings are below one percent. A finalization-only ablation separates cue recovery from stopping, and a fixed scalar reader tests extraction as an alternative explanation. The cue is prior art; the contribution is a component and readout analysis with charged injections and verified paths. Results cover two checkpoints, one task, one prompt family, and two fixed seed conditions.

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