Bismillahi Al-Rahmani Al-Rahim
Consecutiveness When Making Tayammum
The way you described the kayfiyyah of tayammum is confusing. How come in the first one (the obligatory acts of tayammum) you include wiping the hands/wrists but not in the description? And how come you included beating the ground in the description but not in the obligatory acts? What is the correct way of performing tayammum!?
You wrote ''consecutiveness in the minor ritual purity." as a condition for the validity of tayammum. What does consecutiveness mean here?
al-salamu `alaykum wa rahmatullahi wa barakatuhu
The text from the lessons is
As for beating the ground, while the substance used (pure, unburned earth) is an obligatory part of making tayammum, how this is gotten is not. The description lists the most common situation (getting it from the ground), but you could also get it off of the wall or your pet cat. The correct way of performing tayammum is largely dependent on where you are. If you're on a road trip through the Cascade mountains in the middle of winter, you'll probably end up wiping your hands over your car and not striking or slapping them on the ground.
As for consecutiveness, here it is determined by making it analogous to when making wudu.
And Allah knows best.
wa al-salamu `alaykum