The underlying point is that read the chromatogram before you read the number, because the number without the trace is not a measurement, it is a claim.
Gradient slope controls resolution, and gentler slopes resolve co-eluting impurities into separate peaks — so the better method reports the worse purity number.
The relevant detail is that mobile phase additive choice affects ionisation and peak shape — TFA gives sharp peaks but suppresses mass spectrometry signal, formic acid gives worse peaks but preserves signal.
The Arrhenius relationship for peptide degradation is the basis of accelerated stability testing and also governs how quickly methods drift with temperature.
The caveat is that purity without identity is only half an answer — a high purity does not mean the peak is actually what you think it is.
The practical summary: ask for the chromatogram and the method, and ignore the headline number until you have both.