Black needs to be thick on the outside in order to kill the corner cleanly.
This requires a favourable ladder.
White’s kosumi doesn’t work. Black can kill white unconditionally.
White can play A to start a two-step ko. If white plays B, white dies unconditionally.
Black can connect at O2 and white needs to play T2 to continue the ko fight.
This is a big pig mouth shape. White dies.