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  "map_content": "Wanted to come back to this post to share a few additional pieces of content that I think are interesting to consider in this context. \r\n\r\nRecently, I noticed a paper which argued that rotations in physical space for dynamic systems can return to their origin by doubling the walk and uniformly scaling all rotation angles. I believe this is connected to the argument that all motion is vector reflection which I included in the sub comments of this original post. You can read this new paper here: \r\n\r\nWalks in Rotation Spaces Return Home when Doubled and Scaled\r\nhttps://arxiv.org/abs/2502.14367",
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