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Probably not Mammillaria muehlenpfordtii but it seems ...not like pilcayensis either. Too thick and upright. If I recall pilcayensis was a groundhugger that could hang upside down...
@mcvansoest please let us know if you have any thoughts here ... I can move the image to the species entry or the genus entry if there is some doubt about the current ID.
Could be. Hard to know - crosses between subspecies are generally not recognized as such but just ascribed to variability. There are huge areas in AZ where one could not tell what Agave parryi subspecies you are looking at because there is no abrupt transition - no matter how we would like for there to be one - but it is a slow gradual change from one to the next.
I guess when in doubt go with the most generic possibility so M. spinosissima is probably the way to go.