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This dynamic creates a seductive trap for the user. Because the model provides data points that fit the user’s request, the interaction feels productive. In our specific task, the user is not driven to a state where they become unhinged from reality, as the model selects valid examples that fit the true rule. Nevertheless, the mechanism creates a false sense of verification. If a user’s prior is grounded in reality, the model simply narrows their view; but if a user is uncertain or exploring a misconception, the model’s tendency to affirm that misconception can manufacture certainty where there should be doubt. The result is that users become very strongly committed to a belief for which there may only be a small amount of evidence.777This mechanism provides an account of belief maintenance consistent with cognitive models of delusion [bell_explaining_2006].。关于这个话题，搜狗输入法下载提供了深入分析
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The fundamental group of \(X\) at \(x_0\) is \[\pi_1(X, x_0) \;:=\; \bigl\{[\gamma] \mid \gamma \text{ is a loop based at } x_0\bigr\}\] equipped with the group operation of concatenation: \[[\gamma] \cdot [\delta] := [\gamma * \delta], \qquad (\gamma * \delta)(s) := \begin{cases} \gamma(2s) & s \in [0,\tfrac{1}{2}] \\ \delta(2s-1) & s \in [\tfrac{1}{2},1] \end{cases}\] The identity element is the class of the constant loop \([c_{x_0}]\), and the inverse of \([\gamma]\) is \([\bar\gamma]\) where \(\bar\gamma(s) := \gamma(1-s)\).