Note that this simple scheme is independent of the atom ordering but it is neither translationally nor rotationally invariant. This is essential to allow the system to be used for storing pre-aligned conformers (e.g., for storing docking poses). If the user desires translational and/or rotational invariance, they should either standardize the orientation of conformers themselves before registering them or use the CanonicalizeOrientation step in the standardization pipeline to automate that process.