I suspect it is the second of these that you have flowering purple. If so it was the only one we saw.
This one was at the spring where all those wasps lived.
I believe it was the second one of the three ball Coryphantha plants that
were collected. To me this one looks like a dasyacantha to me despite how many
heads are in that clump. It would be interesting to know if this is one
plant. I suspect not.
The next one was the first one that was collected that day.
It was rather small and ball-like.
It has different areoles and spination that cause me to wonder if this tiny thing is
not the purple flowering vivipara that you photographed.
Its incredible that it grew so fast if so.
OR
Did you collect yet another ball near the gate that I missed
photographing or that I am not recalling?
The Coryphantha dasyacanthus just
inside the gate was the last of the three ball Coryphanthas that were
collected that day. Photos of it can be seen
here