Nature, Published online: 06 March 2026; doi:10.1038/d41586-025-04156-4
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 \(p\).，详情可参考新收录的资料
항상 진실된 기사를 쓰겠습니다.，这一点在新收录的资料中也有详细论述
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