So: I'd need a lot more detail about:
(1) The analytic methods used to measure K concentration, what are the errors, are there any confounders
(2) The methodology (to ensure complete homogeneity)
(3) How it is known there is no micro or nano precipitate
I'd want to know all the other ions in the liquid - because you need a cation I think? K2CO3?
If so, given K2CO3 is deliquescent, I'd want to be sure there was not some liquid that was very high in K2CO3 concentration balancing the lower concentration (if all other things check out and indeed the K ion concentration is lower).
Just a random thought - you never know - probably not relevant but google popped it up: