The root is both deep and wide. In fact, most of the plant is the root. The green parts of the stem you see feed the root. Scroll down on this page to see some pictures of the root:
https://www.cactus-art.biz/schede/ARIOC ... etusus.htm
Because it has such a large, water-storing root, it is in fact easy to rot if the temperatures get below 50 degrees (10C) for very long and it's moist. In nature, it does get colder than this, but always during the dry parts of the year.
I have several Ariocarpus of different species, and they're easy as long as you give them a deep pot with highly inorganic substrate. I use about 80% grit with about 10% perlite and 10% soil.
I fertilize mine twice a year, in June and August. But you don't have to do this. In my area, no amount of indoor light is appropriate for an Ariocarpus year-round. They can be overwintered indoors if they're dormant, but don't plan on keeping it indoors during the summer. Remember that even the brightest south-facing window is still dimmer than being outside in Coahuila near a bush or boulder. In other words, even the "shade" that they grow in in nature is brighter than the fullest light indoors.
