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This research demonstrates that unfaithful large language model service providers can artificially inflate the number of reasoning paths generated during test-time compute to overcharge users. By utilizing a specific algorithm to generate and strategically reorder extra paths, a provider can make every reported output appear necessary under adaptive stopping rules. Furthermore, the authors show that this manipulation enables providers to successfully evade exact likelihood-ratio audits. Experiments across multiple open and distilled model families reveal that these additional reasoning paths follow a heavy-tailed distribution, meaning substantial overcharging remains possible even under strict auditing constraints.
