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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When the SETBLOCK function fails because the requested size was too large, it returns the maximum available size that the block can be resized to. However, DOS already resized the memory block to that maximum available size. This is almost certainly a bug, one that Microsoft didn’t dare fix in later DOS versions.
Note: Lua and other third-party dependencies are compiled into the application itself,