On the detail: the certificate is only as useful as the lot number, because without traceability it is gossip about someone else's material.
Lot number visibility is the first check, and it is the one most certificates fail — the number is not printed on the vial, or it is on the certificate but the vial is unmarked.
Concretely, writing the lot number on your vial in permanent marker is worth doing because it later proves that the certificate traces to your material.
The standards that exist in this space — ICH Q3A, Q3B and various pharmacopoeial chapters — are worth reading once even if nothing you test is obliged to meet them.
If the certificate does not trace to your vial, it is not evidence about your vial.