Source: the King Arthur Flour Baker's Companion, p. xi:

"At King Arthur Flour, we've held a long debate about what a "cup" of flour
weighs. In the past, for simplicity's sake, we called it 4 ounces. You
can, in fact, create a 4-ounce cup of flour by sifting the flour first. The
sifting process incorporates a lot of air into the flour, which is the first
source of leavening. Scooping flour, which can produce a much heavier cup
(up to 5 1/2 ounces), will obviously contain less air and more flour. You
can also fluff up flour in your flour bag, sprinkle it gently into your
measuring cup, scrape the top with a straight edge, and get close to 4
ounces, but you probably will get a little bit more.

Our preferred weight for a cup of flour is 4 1/4 ounces, and that's what
we've used throughout the book. This is closer to the standard weight that
bakers use. It makes calculating total ounces a little more difficult, but
in all of the recipes we've done the calculating for you. This discussion
would be much easier if we'd stop relying on measuring cups and start using
the scale. But since the old volume system of measurement is still pretty
standard, we're using it along with weight measurements."

p. xii:

"MEASURING BY VOLUME

When measuring flour by volume, fluff up the flour, sprinkle into your
dry-cup measure (the one that measures exactly a cup at the top), and scrape
off the excess with a straight edge (a metal flour scoop with a straight
edge allows you to scoop and sweep with one hand). This will get you
approximately 4 1/4 ounces."