Several sahih hadiths command to leave/grow the beard in order not to be like the mushrikeen [who used to shave their beard altogether & grow big moustaches]. Many scholars concluded that the beard should be grown full-length.
However it seems that this opinion ignores the explicit reason behind the command, because if the purpose of the command is to not imitate people who shave their beard, then growing some beard or growing a beard seems sufficient to fulfill that command (while growing a full beard sounds like an overkill measure).
Ibn 'Umar used to trim his beard down to a fist-length. Many scholars concluded that this is the legal minimum. This strikes me as a serious problem: how can the action of one sahabi define the shari'ah? And this action doesn't prove he himself considered it the minimum length, it only proves he thought it's OK to do that (incidentally he's among the narrators of the hadiths used as evidence for the opinion that beard must be grown full-length...)
Note that narrations (authenticity not guaranteed) exist about Hasan al Basri, Ibn Abbas and Abu Huraira trimming their beard, and even Ibn Abbas expressing the permissibility of trimming the beard (without specifying a particular minimum length)
Although having a beard (vs. shaving it altogether) is explicitly commanded in several texts, I know of no authentic text setting a specific minimum length for the beard.
My question is: are there texts supporting the fist-length as legal minimum that I'm not aware of?