Let's continue on the 3-4 variations...
Let's see the knight move, first. The aim of such a move seems clear : lean on the corner, then counter-attack the pincer stone. Possible variations could be
$$c One space low pincer.
$$-----------
$$|..........
$$|..9.......
$$|.0815.7...
$$|...,46....
$$|..2.......
$$|..........
$$|..3.......
$$|..........
$$|..........
$$|..........
- Click Here To Show Diagram Code
[go]$$c One space low pincer.
$$-----------
$$|..........
$$|..9.......
$$|.0815.7...
$$|...,46....
$$|..2.......
$$|..........
$$|..3.......
$$|..........
$$|..........
$$|..........[/go]
Secure a base in the corner.
$$c One space low pincer.
$$-----------
$$|..........
$$|..........
$$|...157.9..
$$|...,468...
$$|..2.......
$$|..........
$$|..3.......
$$|..........
$$|..0.......
$$|..........
- Click Here To Show Diagram Code
[go]$$c One space low pincer.
$$-----------
$$|..........
$$|..........
$$|...157.9..
$$|...,468...
$$|..2.......
$$|..........
$$|..3.......
$$|..........
$$|..0.......
$$|..........[/go]
Counter-pincer.
Obviously, black might not answer this way. What happens if he push and cut?
$$c Cut first, think later.
$$-----------
$$|..........
$$|..........
$$|..018.....
$$|...54.....
$$|..267.....
$$|....9.....
$$|..3.......
$$|..........
$$|..........
$$|..........
- Click Here To Show Diagram Code
[go]$$c Cut first, think later.
$$-----------
$$|..........
$$|..........
$$|..018.....
$$|...54.....
$$|..267.....
$$|....9.....
$$|..3.......
$$|..........
$$|..........
$$|..........[/go]
The corner die. 9 is unreasonable.
$$c Cut first, think later.
$$-----------
$$|..........
$$|..........
$$|.9.18.....
$$|...54.....
$$|..267a....
$$|..........
$$|..30......
$$|..b.......
$$|..........
$$|..........
- Click Here To Show Diagram Code
[go]$$c Cut first, think later.
$$-----------
$$|..........
$$|..........
$$|.9.18.....
$$|...54.....
$$|..267a....
$$|..........
$$|..30......
$$|..b.......
$$|..........
$$|..........[/go]
I think the corner may still be killed, but white must first make sure that both of his group do live.
Black a threaten both the cut and capturing two white stone, but it's an acceptable exchange and white hane at b.
What about helping the other side?
$$c Cut first, think later.
$$-----------
$$|..........
$$|..........
$$|.9.18.....
$$|...54.0...
$$|..267.....
$$|..........
$$|..3.......
$$|..........
$$|..........
$$|..........
- Click Here To Show Diagram Code
[go]$$c Cut first, think later.
$$-----------
$$|..........
$$|..........
$$|.9.18.....
$$|...54.0...
$$|..267.....
$$|..........
$$|..3.......
$$|..........
$$|..........
$$|..........[/go]
$$c If :b3: one intersection below, black lose the capturing race.
$$-----------
$$|..........
$$|..980.....
$$|.X3XO.....
$$|.2.XO.O...
$$|..OOX....
$$|.6..1.....
$$|.4X.......
$$|.57.......
$$|..........
$$|..........
- Click Here To Show Diagram Code
[go]$$c If :b3: one intersection below, black lose the capturing race.
$$-----------
$$|..........
$$|..980.....
$$|.X3XO.....
$$|.2.XO.O...
$$|..OOX....
$$|.6..1.....
$$|.4X.......
$$|.57.......
$$|..........
$$|..........[/go]
I'm pretty sure that white win this.
The hane at D14 instead of

seems to lead to a similar outcome. So black can't capture either group. Black must come back to his corner or see it die. So, cutting here doesn't seems like a reasonable choice.
Edit : Well, apparently josekipedia consider

to be a trick play and the hane is the refutation. I guess not thinking about such moves is why I'm bad at this game

.