It seems to be a vase held by a private collector -- and as for "precision", there are many ways of achieving it. It's essentially meaningless here.

Any time you turn something on a lathe, it comes out very even and with amazing precision. Leveling the top isn't that hard... just rub the mouth of the vessel on your sanding surface for awhile and if your sanding surface is level, you achieve an amazing precision there.

-- Byrd
Moderator, Hall of Ma'at