The observation that definitively proves a cell is a eukaryote is the presence of a membrane-bound nucleus.

Here's why:

* Eukaryotes are characterized by having their genetic material (DNA) enclosed within a membrane-bound nucleus. This separates the DNA from the rest of the cell's cytoplasm.

* Prokaryotes, on the other hand, lack a nucleus. Their DNA is located in a region called the nucleoid, which is not enclosed by a membrane.

Therefore, if you observe a cell with a clearly defined nucleus, you can confidently conclude that it is a eukaryote.