a small box I made a few years back has a finial with a captive ring.
The OD of the finial is about .015 and the thickness of the captive ring
is about .008. Does that count?

0.008" is a bit over 1/128" or about 4 strands of human hair. I'd say
your piece would qualify as "miniature". Now when you get down to a few
atoms, you'd get into nano pieces. Below that you're into The Emperor's
Tailor range.