Jump stop vs "up and down"

[just another ref]

Originally Posted by Jurassic Referee

You can END a dribble with a jump stop. But if you do a jump stop AFTER a dribble has ended, you're traveling.

Is there a time limit?

4-44-2: A player ......... may stop and establish a pivot foot as follows.........


It never happens, but I don't see why the player couldn't catch the ball, then wait for any length of time before jumping off one foot and landing on two without a violation.