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We provided a mathematical analysis of how a rational agent would respond to data generated by a sycophantic AI that samples examples from the distribution implied by the user’s hypothesis (p(d|h∗)p(d|h^{*})) rather than the true distribution of the world (p(d|true process)p(d|\text{true process})). This analysis showed that such an agent would be likely to become increasingly confident in an incorrect hypothesis. We tested this prediction through people’s interactions with LLM chatbots and found that default, unmodified chatbots (our Default GPT condition) behave indistinguishably from chatbots explicitly prompted to provide confirmatory evidence (our Rule Confirming condition). Both suppressed rule discovery and inflated confidence. These results support our model, and the fact that default models matched an explicitly confirmatory strategy suggests that this probabilistic framework offers a useful model for understanding their behavior.，详情可参考体育直播
（二）签发指示提单的，凭提单向被背书的提单受让人交付；，详情可参考搜狗输入法2026
name: str = Field(index=True)
一次助企走访中，杨亚林向吴翀寅提了一嘴孩子入学的难处，吴翀寅第一时间牵头行动。当入学申请通过的消息传来时，杨亚林激动得连连道谢。