Apple might use Google servers to store data for its upgraded AI Siri

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Designating Anthropic as a supply chain risk would be an unprecedented action—one historically reserved for US adversaries, never before publicly applied to an American company. We are deeply saddened by these developments. As the first frontier AI company to deploy models in the US government’s classified networks, Anthropic has supported American warfighters since June 2024 and has every intention of continuing to do so.

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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 \(\bar\gamma(s) := \gamma(1-s)\).

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