Interesting question; I don't know the answer but here's how I'd approach it:
First take a look at normal joseki (and not) moves. So the idea of 8 is if black blocks immediately (a mistake) white can improve on an older joseki:
$$Wcm8 dia. 1: Joseki mistake
$$ ------------------
$$ | . . . . . . . . .
$$ | . b . . . . . . .
$$ | . a O . . 5 . . .
$$ | . 1 X 3 O . . X .
$$ | . 2 4 . X O . . .
$$ | . . X . X . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . c . . . . . .
- Click Here To Show Diagram Code
[go]$$Wcm8 dia. 1: Joseki mistake
$$ ------------------
$$ | . . . . . . . . .
$$ | . b . . . . . . .
$$ | . a O . . 5 . . .
$$ | . 1 X 3 O . . X .
$$ | . 2 4 . X O . . .
$$ | . . X . X . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . c . . . . . .[/go]
The exchange of 8 for 9 is good for white because now after black's capture at
a white
b is atari and white could then tenuki (probably) or defend (usually a bit slow). However black 9 is not totally useless, for example it means the jump to
c is connected (I used this on move 45 of my Gold Cup game here
http://www.lifein19x19.com/forum/viewto ... 92#p210292). Compare this to the old joseki below, now if black
a white can't block with atari but can only fall back to
b which feels slow, or tenuki but then black's follow-up is bigger (if white connects the atari black can tenuki, but in first diagram if he does so then white can capture one stone which is quite big points and eyes).
$$Bc dia. 2: old joseki
$$ ------------------
$$ | . . . . . . . . .
$$ | . . b . . . . . .
$$ | . a 8 . . 0 . . .
$$ | . . X 6 O . . 1 .
$$ | . . 9 . 3 4 . . .
$$ | . . 7 . 5 . . . .
$$ | . . . 2 . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc dia. 2: old joseki
$$ ------------------
$$ | . . . . . . . . .
$$ | . . b . . . . . .
$$ | . a 8 . . 0 . . .
$$ | . . X 6 O . . 1 .
$$ | . . 9 . 3 4 . . .
$$ | . . 7 . 5 . . . .
$$ | . . . 2 . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
So one joseki after the hane is for black to cut because at this moment white can only fall back so it's a good exchange (in dia.1 once white defends the cut in good shape it's self atari!) and although black sacrifices it the aji is useful for build the outside thickness). So white saves the outside stone and the corner is still up for grabs.
$$Bcm9 dia. 3: joseki
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . O . 2 . . . .
$$ | . O X 4 O 1 6 X .
$$ | . 3 5 . X O . 7 .
$$ | . . X . X . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bcm9 dia. 3: joseki
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . O . 2 . . . .
$$ | . O X 4 O 1 6 X .
$$ | . 3 5 . X O . 7 .
$$ | . . X . X . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
Another is where black cuts off the outside stone and white gets the corner. The outside stone still has significant aji and you quite often see pro games where white persuades black to add a netting move to reduce the outside. Worth noting
a is sente, and black is open on the side at
b. I don't seem to see this one so much these days, maybe they think it's locally good for white (and white doesn't do the corner attach of 6 if the outside is good for black).
$$Bcm9 dia. 4: another joseki
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . a . . .
$$ | . 4 O 1 6 7 . . .
$$ | . O X 2 O 5 . X .
$$ | . b 3 . X O . . .
$$ | . . X . X . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bcm9 dia. 4: another joseki
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . a . . .
$$ | . 4 O 1 6 7 . . .
$$ | . O X 2 O 5 . X .
$$ | . b 3 . X O . . .
$$ | . . X . X . . . .
$$ | . . . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
So based on the above joseki results, white losing the outside stone is not the end of the world if you get the corner. So here's a simple way to answer that solid connection. So how would I judge this? White has a bigger territory than dia 5 and can even slide at
a later. However there's no connection at
b so you can't monkey jump or use moves like
c as easily. Also black 13 means it's a lot harder to run out the cutting stone later, but it does still have aji. So my feeling is this is probably better for white than the joseki of dia 4.
$$Bcm9 dia 5: simple way
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . a .
$$ | . b O 2 . 4 . . .
$$ | . O X , O 3 5 X .
$$ | . . 1 . X O . . .
$$ | . . X . X . . . .
$$ | . c . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bcm9 dia 5: simple way
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . a .
$$ | . b O 2 . 4 . . .
$$ | . O X , O 3 5 X .
$$ | . . 1 . X O . . .
$$ | . . X . X . . . .
$$ | . c . O . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]
There is of course the question of if white can play 12 as atari at 13 but unless white can get that push Kirby showed in sente (which you probably can't) that looks doubtful.
Also I checked pro games for similar positions. Sometimes black crosscuts and you get white taking the corner and black the outside, but again white gets a result similar to dia. 4 and this solid connection result looks worse for black than those:
http://ps.waltheri.net/database/game/67827/.
in particular) to be a modern variation of the above joseki. The usual continuation I've seen in professional games is to cut at either A or B, with the result being that White eventually settles in the corner and Black gets some south-facing influence.
, then it seems Black will always get the cut.
So that makes me think that White shouldn't insist on capturing 
looks slow/questionable, and I'm really a bit lost. What am I missing?