"Minutes" of a meeting: etymology?

What is the etymology of the term “minutes” refering to the record of a meeting?

WAG: the roots of the word “minute” has origins in “smallness,” not “time”

Thus the “minutes” are the “small notes” taken at a meeting.

Just a guess, though

That’s pretty much what our friends at M-W say, Mjollnir:

Main Entry: min·ute
Pronunciation: 'mi-n&t
Function: noun
Etymology: Middle English, from Middle French, from Late Latin minuta, from Latin minutus small, from past participle of minuere to lessen – more at MINOR
Date: 14th century
1 : a 60th part of an hour of time or of a degree : 60 seconds
2 : the distance one can traverse in a minute
3 : a short space of time : MOMENT
4 a : a brief note (as of summary or recommendation) b : MEMORANDUM, DRAFT c plural : the official record of the proceedings of a meeting

Although it never occurred to me that it was anything but literal, frankly; that it recorded what happened during the minutes that the meeting was in progress.