?? idea of instead of tweaking to close the gap between the two distributions, might be able to tweak the split octonion product by an elt of so(3,4) to get one whose nil subalgebra distribution matches the naive rolling distribution ..... ???? .....

?? (g,e) -> (g, g/e) .... ??? "homogeneous" .... ??? live at level of 1d isotropics ... 2d isotropics .... ???? ....... ???? .....