Is there a word to describe the state of being the only one of something?

I need a word to describe the state of being the only one of something. For context, it's for the UI of a scientific device that detects and analyzes cells. In this particular case, we are talking about a particular cell that the device has judged to be the only one there.

The phrase needs to be short, so I want to use "Judgment of *". "Singularity" would appear to be the perfect word for what I am looking for -- if it hadn't already been taken for a very different meaning.

Any other suggestions? I really think there must be a word for this; it seems a pretty basic concept. I have a feeling that maybe I am simply not seeing an obvious choice...

Solution 1:

What about uniqueness, meaning the state of being the only if its kind?

(Dictionary.com)

Solution 2:

Singleton

a person or thing occurring singly, especially an individual set apart from others.

Solution 3:

Two root words that have not yet been suggested here are:

(Derived from) distinct: distinctiveness or distinction

(Derived from) exclusive: exclusiveness