Landlord

Even though according to your perception of travelling, you can pick up your pivot foot and put it back down again. Right.

As long as you follow through continuously with a layup, yes you can. Your idea of how a pivot foot is first established is off base.

I'm no expert (although I have stayed at a HI Express) but when I reffed, we never considered the establishment of a pivot foot on a layup. You get two steps after picking up your dribble. Pivot foot doesn't come into play on a layup or continuing motion. But, I was taught this 30ish years ago. It might be technically different now but I don't think so.