All you need to know about Carpenter's Square - 34
Diagram 34.1: White to play
The corner is much stronger with the first-line hane at 
. Can white do anything?
Diagram 34.2: White fails
Because of , the solution for Shape 33 stops working. If white continues to play 'a', black is able to use 'oshi-tsubushi' to kill white.
Diagram 34.3: White fails
If 
occupies this key point first, 
is a good move.
Diagram 34.4: Seki
To continue from the previous diagram, the only thing white can do is to make 
/ 
exchange. Please confirm the corner is a seki.
Diagram 34.5: Can white form a ko?
Since white cannot kill the corner, an outcome of ko would be the next best. White hopes black to play 'a' so that Diagram 33.3 applies; or if black playes 'b', white can choose one of the ko options in Shape 7. However, black has better defence.
Diagram 34.6: Black alive
is a famous tesuji! If 
, black occupies the second 1-2 point and there is just enough room to make two eyes.
Diagram 34.7: Black alive
If occupies another 1-2 point, 
is good, recovering Diagram 34.2.
Diagram 34.8: Black alive
If , is good. Black makes the first eye in the corner, leaving miai point 'a' and 'b' for the second eye.
Diagram 34.9: Black alive
If 
, is the correct move, ensuring to recover Diagram 34.2 again.
Diagram 34.10: Black alive
If white makes / exchange first before blocking at , is still the tesuji, leaving 'a' and 'b' miai points to live.
Diagram 34.11: Black alive
To reply , 
is still the best move. White has a number of options. Clear 'a' and 'b' are miai points.
Diagram 34.12: Black alive
To reply 
, 
is calm, still leaving 'a' and 'b' as miai.
Diagram 34.13: Black alive
Finally, results in a double-ko. In most cases, black would be unconditionally alive.
To summarise: with the first-line hane, black corner is very safe. The best white can get is seki in Diagram 34.3 and 34.4. Black needs to know the 1-2 point tesuji. In very rare cases, white may consider Diagram 34.13 (see how a double-ko may be exploited in this pro game 
).
