AI信誉标签影响公众判断，过度依赖可能固化错误信息。

Social media platforms increasingly use AI-based credibility indicators to help users judge misinformation. Unlike individual human-AI decision-making, these indicators are embedded in information spread: users see both an AI prediction and earlier judgments shaped by the same AI, and their own judgments may then enter the public history. Yet how to analytically characterize this process remains under-explored. We therefore introduce a social-learning lens for this setting by extending the classical Bayesian cascade model with the AI indicator as a shared public signal. The resulting Gateway condition compares the evidence from the AI prediction with users' private impressions. Through this view, we show that AI changes what public history means. Crowd agreement may reflect accumulated independent human evidence, or repeated dependence on the same AI prediction. This creates a preservation-correction trade-off: stronger reliance on AI can preserve correct predictions, but can also lock in incorrect ones by blocking corrective private impressions. We calibrate the model using human-subject data on news veracity judgments. Although the AI outperforms human users, the average user weights it below her own impression but above several peer judgments, while individual users vary from discounting the AI to relying on it enough to cascade. Simulations show that over-reliance on a weak AI is especially harmful, and that diversifying AI signals across users can better keep the crowd informative. We conclude with implications for understanding human-AI interaction in information spread and designing misinformation interventions.