?? functor from _g2-torsor_ to _so(3,4)-torsor_ ... ?? projective light cone of imaginary part of split octonion algebra .... ???? ..... ?? what this looks like in rolling ball picture ??? .... ??? ....the "new lines" .... ????? .... 7d space thereof ... ??? i don't really suspect that it's the special split quaternion subalgebras, i don't think .... ???? ... [later that day : hmmmmm .... ???? .....] ..... ?? maybe do suspect that it's "the naive guess" ... ??? ignoring tweak map ..... ???? .... ???? ....

?? given pair of g2 configurations ..... ??? .... ?? not connected by geodesic rolling trajectory ..... ??? getting path between them via [?? split quaternion subalg ... ???? ....] vs by [linear subspace .... ??? ..... ???? ....] ... ??? .... ??? very different ??? ..... ???? .... ??? ....

?? wait ..... ???? dot vs cross here ??? .... ?? not generic configuration pair, but pair satisfying dot but not cross constraint ..... ???? ..... ?? is this "2 rolls away" ???? ..... ????? ..... ???? .....