13.k18 was a nice move, but black still has the option to play k16 as in the above variation.
After 4.o13 IMO white needs to block black's new threats across the middle of the board and 5.g16 doesn't do that. Instead |5.h12 makes use of white o17 as a potential ladder catcher. For example 6.i167.k15 or maybe 6.h107.r9
13.k18 was a nice move, but black still has the option to play k16 as in the above variation.
After 4.o13 IMO white needs to block black's new threats across the middle of the board and 5.g16 doesn't do that. Instead |5.h12 makes use of white o17 as a potential ladder catcher. For example 6.i16 7.k15 or maybe 6.h10 7.r9