Accepted answer
three weeks is 21 days, and at 4 °C the ten-degree rule of thumb makes that roughly 20 refrigerated days of equivalent exposure. 4 °C is the condition the rule of thumb is anchored to, so it is the baseline rather than a multiplier: everything else in this thread is quoted relative to it. Compare that against what the certificate covers, which is the material as it left the laboratory on the date of analysis and nothing after it. That is short enough that a re-test is a stability study rather than a safety check — worth doing if you will publish the result, hard to justify if you will only reassure yourself. If you do re-test, send it for content as well as purity; the 21 days will have moved one of them further than the other.
Batch testing establishes what can be claimed about the lot as a whole, and the sample size determines how much you can actually claim.
Acceptance Sampling by Attributes defines the number of samples you need from a lot to claim a specified quality level at a specified risk — it is in ANSI standard Z1.4.
In practice, under AQL sampling plans, testing two vials from a fifty-vial lot gives you an operating characteristic curve that tells you what risks you are accepting.
Lyophilised peptide homogeneity studies show that vial-to-vial variation is usually small but occasionally large, depending on the distribution in the freeze-dryer.
I would treat a "complies with" statement without sampling details as a claim rather than as evidence.
The practical summary: a lot number without a sampling statement is a lot number without meaning.
edited 23 Nov 2024 by a_lindgren — removed a claim I could not source