I think you might be more or less correct!
The density eigenvectors with the smallest eigenvalues are roughly spherical clumps around the centre of the sphere.
I was a bit confused by the fact that I can pretty much randomise the sample point locations and *still* get the same kind of immensely small determinant … but that doesn’t really negate your argument for the case where the sample points lie on the surface of the sphere. It’s just that any argument for other configurations would be more complicated and less intuitive.
