Certificate of analysis (COA)
A certificate of analysis is a laboratory report describing the tests performed on a sample, and their results.
It is a statement about the specific sample the laboratory received, on the date it was received. It is not a verdict on a product line, a seller, or the container you were sent.
Two things determine whether one means anything: which tests it actually contains, and who chose and sent the sample. A test that is absent has not been passed — it has simply not been done.
What it is not
A certificate is not proof that your vial matches it. If the lot number on the document does not match the lot on your container, the document describes different material. And a PDF is trivially editable — an altered certificate looks exactly like an unaltered one.