?? "vertical" or "fiberwise" tangent bundle of map f : m -> n .... ?? as equalizer of t(f) : t(m) -> t(n) and t(m) -> m -> n -> t(n) ... ??? ....

?? special case where f is t(t(m)) -> [t(m) direct-sum t(m)] .... ?? vertical tangent bundle of this f as naturally equivalent to tangent bundle of m ... ???? ...

?? this as trying to get at heart of "lie bracket" from certain viewpoint ... ??? .... ?? maybe heart of some other things too ??? ...

?? torsors of tangent bundle here ?? ... ??? any interesting "cohomology" aspect here ??? ....

?? thinking about above in connection with ... ??? ... the "3" / "roll-spin" invariant distribution of the "2,3,5" of the g2 rolling ball geometry as not the tangent distribution of any invariant binary relation .... ??? ..... ?? and since not, then trying to systematize geometric process by which it _does_ arise (?? from "macroscopic" stuff ... ?? extent to which we've thought about / understood this before ?? ... ?? relationship to huerta's concerns / complaints ?? .... ??? .....

?? so ... ??? tangent cone of "2-rolls-away" schubert variety based at point of g2 configuration space ... ?? as some 4d cone ??? ..... ??? how related to 2,3,5 distributions ???? .... ?? ... again, seems pretty unfamiliar for some reason .... ???? ..... ?? if this _is_ what huerta's been complaining about then i don't think that they described it very well .... ??? .....

?? systematization mentioned above ... ??? "higher tangent spaces" and / or "auxiliary geometric figures" .... ?? relationship therebetween ... ???? ....

?? "there's an obvious way to identify the projective light cone of the imaginary split octonions with the configurations of a rolling ball ... ?? but the business of the "tweak map" means that we're _not_ using that obvious way, but a somewhat less obvious way ..." .... ??? .... ??? .... ?? still confused about this .... ?? and about what it might say about relationships of g2 to so(7) and so(8) and so forth .... ?????? ..... ????? does tweak map live in so(7) ?????? ..... ???? ..... split form, i mean ... ?? .....