The lot number is the thread back
A lot or batch number identifies which production run a container came from. It is the only thing that connects a specific vial in your hand to any document written about it. A certificate of analysis whose lot number does not match your vial describes different material, however impressive the numbers on it look.
Write down what you have and when, from the container rather than from memory: product, supplier, lot number, and the date. Once a date is gone it cannot be reconstructed later from how something looks or from when you think you bought it — and an unresolvable record is of no use to a clinician you might later need to hand it to.