You ask for a word that means being only one of something. That word is "the" -- the something. Whether this helps you here is another question.
You are not clear about how this cell is singled out. You say that it is identical to others of the same type, but it is the only one of its type in the given sample. If so, why not just refer to it as "the
____ cell", where
____ is the type? E.g., if it is the only blue cell then call it "the blue cell".
Does the the type have a name, or can you give it one? If you cannot name or at least characterize the type then it makes little sense to look for a word that specifies that this cell is the only one found to be of that type.
If the type is complex to describe, then do so first and then refer to this cell as the "target cell", the "targeted cell", the "cell found by the device", or some such.
You say that the characterization is that this is the "particular cell that the device has judged to be the only one there". But later you seem to say that it is not the only one there.
You say then that it is the only one in the sample that is of a particular type. It apparently has some property or passes some test, and that is what qualifies it. Define that property/test and you will have gone some way toward answering your question, I think.
My suggestion is to get the logic and thus the message clear first, without worrying about the wording. Ask yourself just what it is that you are trying to tell the reader about this cell (or about the device or about both...). Somehow, your device has targeted/identified/singled out this cell in this sample. Be clear about what that means and why it is important, and then you will find appropriate wording.
I'd also suggest that you avoid a noun phrase ("judgment of singularity" or whatever). Use a verb phrase instead. E.g., say what the device actually did: "determined that this cell is the only one that satifies XYZ."
Use judged instead of judgment of; determined instead of determination of; proved instead of proof of; demonstrated instead of demonstration of"... Stringing together noun phrases (especially latinate ones) is the curse of poorly written scientific papers. People often do it, oddly enough, because they think it makes them sound more authoritative. Especially if you are creating a UI or writing about one for its users, keep it simple. Put yourself in the place of the reader.