A reference post rather than a discussion. Corrections are the point; I would rather this be right than mine. It is about certificates of analysis, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
The provenance questions are more useful than the numbers. Does the report name the batch on your vial. Is the date consistent with when that batch existed. Is it addressed to the vendor or to the person who paid for the test. Was the sample taken from general stock or supplied by the vendor. A perfect certificate for a different batch is worth nothing, and vendor-supplied samples are the most common way a genuine report ends up misleading.
The condition it depends on
One addition: an unstated method makes a report close to uninterpretable. "99% pure" without the technique, the standard and the conditions is a claim, not a measurement.
The practical version
The four things to check on any report, in order: does it name your batch, who commissioned it, what method was used, and does it report content as well as purity. A report failing any of those is weak evidence regardless of the percentage on it.
What I am not sure about
The question I want answered is whether a purity figure and a content figure can disagree without one of them being wrong. Tell me what I have not thought of.
— Dr.GastroMayo · corrections welcome and will be edited into this post with credit