Pushing battles in joseki 6
This variation of the 3-5 point low approach one-space low pincer isn't fully described in books in English. Ishida only gives it four diagrams, while what appears in Get Strong at Joseki volume 2 is somewhat misleading. This is a line often to be seen in current pro games, and used particularly by Chinese and Korean players. Black a and b are the usual ideas, while Black's placement at c has also been tried.
Since White is trying to build up power to attack the marked black stones on the upper side, the light jump Black 1 ought to be natural. White plays 2, usually, to get a base in the corner. White needs to be alert to the placement p, a thematic shape point for this joseki. It is also possible for White to connect at a, as played by Ryu Shikun recently.
The implication of the comment in Get Strong at Joseki vol. 2 p.73 is that Black 1 is no longer joseki; but that seems never to have applied to Chinese and Korean players' judgement of the sequence, and recent games in Japan go against it too.
Taking up the GSAJv2 line, this much is attested in pro games. White 6 can also be on the upper side to attack, but then Black 7 at 6 is a very good point for shape. There are numerous variations here: White 2 at 4, Black 3 jumps and so on. It all adds up to a joseki in a state of development.