A certificate of analysis, or CoA, is the document that links a batch of material to the tests it passed. For research peptides it is the most important piece of paperwork you will receive, so it is worth knowing how to read it.
Start with the lot number. The lot on the certificate must match the lot printed on the box and on the vial label. If they do not match, the certificate does not describe the material you have.
Check the identity test. Identity is usually confirmed by mass spectrometry. The certificate should show the expected molecular mass and the mass that was measured. They should agree within a small margin.
Look at purity, and how it was measured. Purity is normally given as a percentage measured by HPLC (high performance liquid chromatography). A purity figure without a method is not very meaningful. Look for the method, the wavelength used and ideally the chromatogram itself.
Note who did the testing and when. A good certificate names the laboratory and the date of analysis. Testing should have taken place before the batch was released.
Read the appearance and content lines. Appearance (for example "white lyophilised powder") and net content per vial should match what you see.
A certificate that answers all of these points gives you a clear, checkable record of what is in the vial.