Ledgestall
The ledgedashstall is an advanced technique in Super Smash Bros. Melee that allows most of the cast to refresh the ledge invincibility infinitely. It is rarely used competitively because of the high amount of precision necessary and the risk of losing the stock if even one input is slightly off. Hax is one of the few players who have shown mastery of this technique.
Explanation
As soon as a character grabs the ledge, he goes into the CliffCatch animation that lasts 7 frames (3 for Link) and has complete invincibility. On the last frame of CliffCatch, he is granted another 30 frames of invincibility and can perform all ledge options except letting go (ledge attack, ledge roll, ledge climb, ledge jump). If he doesn't perform any of these, he enters the CliffWait animation during which he can also let go of the ledge. He now has 29 frames of invincibility left that he can use freely. It is not possible to grab the ledge again before the invincibility has ended.
By letting go of the ledge, jumping towards it and wavelanding away from it, the ledgegrab box overlaps the ledge again just when the ledge invincibility has ended for most of the cast. Some characters, like Marth, need to fastfall in order to get down far enough in time before the invincibility has run out while others, like Captain Falcon need to waste a few frames so they don't fall below the stage before the invincibility ends.