So by the time you reached that sentence in the article you must have gone over the part where this is a result co-authored by a geophysicist, and that the paper has gone through peer review of at least three other geophysicists (whom all have been contacted to hear their opinion on the work, and they're very positive about it), and that the geology community in general seems excited to see what practical uses this model will have in practice.
But sure, the fact that this is a model that starts with making the least amount of assumptions[0] completely invalidates it as geology and makes it pure maths. Because as we all know, no useful model in physics was ever built up from the ground like that, only introducing complex caveats as required to make sense of empirical data as necessary.
[0] the simplest way that one can cut a shape is with a straight line (2D) or flat plane (3D). In this case no new concave shapes can be created unless a concave angle was a part of the initial shape. Ergo, if the starting shape is convex and we cut away parts randomly, then all shapes produced this way will be convex. If the initial shape has concave parts, then on average most shapes derived from it will be convex. This is even more true if we apply this "cutting away" recursively to the shapes that were cut away. This makes the assumption of shapes being (mostly) convex quite reasonable, unless there is a specific reason to expect concavity, like specific crystalline structures perhaps. Also, for the record, I just reasoned this out on the spot, it's not exactly difficult.
I appreciate the time you've taken to reply to my brief comment, though you admit it took little effort, assuming, as a sibling post here states, "spherical cows in a vacuum", or rather your own equivalents for the sake of reasoning. While I'll spare myself listing the several assumptions your post inserts on it's path to your conclusions, I would like to compliment you on your obvious passion for the subject.
I actually appreciated the explanation. Less so the heavy sarcasm. I'm glad it's boring, obvious cubes and not starfish or irreducible complexity, but not in the least surprised, and I still think atoms are concave.
I think what you're failing to see is that a sentence like "math; not geology" sounds incredibly condescending and snarky.
I don't know if that was your intent, but if not it might be worth reflecting on what you meant to say instead, and why you did not notice that what you wrote instead comes across so negative. Because then there would be no need for heavy sarcasm.
Math; not geology.