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In SM64 this covering space structure is used by giving Mario extremely high velocity \(v\) (a tangent vector at Marios position in \(P\)) through a different glitch called “backwards longjump”. The exponential map is then used to move Mario along the geodesic \(\exp_v(t)\) for \(t \in \mathbb{R}\). But due to hardware limitations, only discrete steps \(t_1, \dots, t_k\) for some \(k \in \mathbb{N}\) of this geodesic are actually calculated for collision detection. More on how this is related to the exponential map of Lie groups can be found in my previous post. Throughout this post, I will assume the Lie group of SM64 to have its unit at the position \(p\).

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For a year or so, listening to something with AirPods Pro and then opening Quick Look in the Finder to see a video with an audio track often glitches out the audio after a second or two. The mixed audio is fine before and after, but there is a very unpleasant glitch. No firmware or OS upgrade has resolved the issue.。夫子对此有专业解读

2월 27일 오후 3시 38분 트럼프 “에픽 퓨리를 승인한다. 중단은 없다”

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