Ah yes! But also...
You are absolutely correct, and definitive up to a point. But there is more to the story. Let me start my response by saying that people are biased to understand all things in terms of the behavior of fermionic matter, and this is endemic to living in a world made of protons, neutrons, and electrons - not just a matter of human perception. I'll accede that within that realm, your answer makes perfect sense.
But why only uniqueness and oneness? I understand there is a balance there, or something that is preserved, but there is more. The next level up from unique would be completeness; in Physics this is preserved by Electricity that only flows when the circuit goes all the way around, and in Geometry the simplest figure with this property is the circle. Of course; the circle contains space and thus represents the next property which one could call nothingness.
Taking this to logical conclusion; I'd make enoughness or sufficiency the next preserved quality, and then a property that could be called agreement or equality is needed - which bespeaks the connection of such a hierarchy with oneness, or the totality of being. I spell out some of this in Physics terms, in my essay from the FQXi contest on What is ultimately possible in Physics.
More later,
Jonathan