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Perhaps it is not obvious that getting the "root" signals (a set of points on an (n-1)D shell) from all of the signals (a set of points on an nD ball) is a matter of ignoring noise and phase distortion. Came up with a toy "wavelet" reconstruction of the continuous signal to show how this "dimensional reduction" is straightforward and natural (even for toy models). Will add it in soon. I got a job in construction! Should be indoors. Bonus.