Minimum size

Minimum size is a hard number in the guidelines: the smallest width a given logo variant is allowed to be reproduced before it stops being legible. It is written per variant (the horizontal lockup needs far more width than the icon alone) and usually stated twice: millimeters for print, pixels for screen.

You set it by testing, not by taste, and you test once per medium. Reproduce the mark the way it will really be made (the cheap office laser, the uncoated stock, the screen at its actual device pixel ratio, the embroidery head, the pad print on a pen), then look at it from the distance people will actually stand at. Judge the whole chain: is the overall shape still recognizable, can you read the words, does the thinnest stroke survive, do the counters (the enclosed holes in letters like 'a' and 'e') stay open? Hairlines drop out on press and anti-alias into gray mush on screen, closed counters turn words into blobs, and a rough substrate eats both. Different media give different numbers, which is why the spec is written per variant and per medium.

Gotcha: the fix for a logo that keeps hitting its floor is not a bigger minimum, it is a different variant. Pen barrels, embroidery, favicons, and sponsor rows are where the full lockup dies, so give people an icon-only or simplified version to switch to and say exactly when to switch.