gonuts has solved this subproblem too.
I have added some comments to his SGF file.
(;ST[2]SZ[19]CA[ISO8859-1]GM[1]AP[GOWrite:2.2.21]FF[4]PM[0]FG[259:]AW[br][bo][cl][bl][dq][dp][co][cn][bk][cm][ap]AB[cj][bj][aj][dl][cp][aq][an][bp][do][dn][ck][dm]
(
;C[May be best, but depends on the rest of the board?
*** Correct. It is almost always best, but that depends upon the rest of the board. ]W[am]
;B[ak]
;W[bn]
;C[Black ends in sente.]B[al]
;C[*** Right. Note that the net result is the same is the main line.]W[ao]
)
(
;C[Another possibility.]W[ao]
;C[White loses 3 points relative to the main line, and later loses 2 more points capturing the A3 stone. But Black ends in gote.So this line would be better for White, given at least a 5 point play elsewhere.
*** It is possible that this is best for White, but your conclusion does not follow. The position after the White connection is worth 1 point less for White, on average, than the position in the other line. But B2 gains only 4 points. If there were a play elsewhere that gained 5 points, Black should take it, as a rule.
Going back to the original problem, however, this line is not good for White, because White does not have the throw-in at A-07. If White is going to play at A-05, he should not play at A-04 first. ]B[al]
)
)
And that means that, along with his earlier work, gonuts has solved the original problem, as well.
Correct play for Black in it is the atari at A-03, which yields this subproblem.
The end result is the same as in the main line in
Gokyo Seimyo, so I did not find an improvement. And that line is cool for both players. However, I thought that the atari (A-03) was pretty cool. The cut (A-05), while it looks natural, loses a dame and, hence, 1 point by comparison.
in the variation?
also gives the same result as the main line.