What is valid? I think that until such time as there is a major dna level study of the genus, there will be differing views as to how to divide it into species, subspecies etc. Those studies done so far all seem to agree that Mammillaria as we generally understand it is not a single genus, but that it isn't a simple matter just to split off those former genera like Cochemeia.
Until then, I think we amateur enthusiasts just have to accept that the varying classifications, and splitting or lumping, reflect different botanists view of the genus, done perhaps with different views of what defines a species or subspecies, or even genus!
Where a plant comes from helps to clarify its place in these classifications, which is what sometimes makes it really hard to identify a photo of a plant which doesn't conform to the "popular" view of a specific species. So, I urge everyone who wants to understand Mammillarias and grow them well, to understand where the specific plant comes from, ideally it should have a field collection reference, and also not be too distant in generations from the original collection (in case of accidental hybridisation).
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Chris43, moderator