Where is Palming?

[rekent]

There is an NFHS mechanic for palming the ball, 4-15-4 b says: "The dribble ends when the dribbler palm/carries the ball by allowing it to come to rest in one or both hands," and 9-5 lays out when you can begin a dribble again without it being a violation.

Case 4.15.4 A describes a palming situation and says it is a violation, but where in the rules does it specify a "palming" violation rather than an illegal dribble?

I overheard an argument tonight where one official was saying that, strictly by the rulebook, "palming" should actually be double dribble and I found his points rather interesting. I know regardless it is violation and ball goes to the opposing team. This is just a semantic and mechanic issue, but what am I missing in the rulebook?