I'm not qualified to judge code, but from a wordmonger who's all too often frustrated with documentation, congratulations.
Both your conversational style and clear content made reading this a pleasure.
I have just minor tics/suggestions (possibly pure taste issues: ignore at will):
you might want to use elipsis with a period in the graf beginning:
We can interpret it as saying,
assert that angdiff($a,$b) must be ..."
But there's a rub. It's that pesky "..." part.
-- this is not a punctuation-nazi suggestion. The fourth dot (in each case) would make locating the reference easier (and might argue for dropping the space, word and period after the closequote.
This, however, may be useage-nazi... but, risking that, I suggest it would be better to say
"so that's as far apart...."
"so that's the farthest apart...."
The problem is that we constrain our $diff to a 180-degree magnitude, so that's all the farther apart our input angles will ever be.
and, a minor typo:
because even though they have a 0% frequency, the fact that the show u
+p in the list at all means they were tested at least once.
where "the" before "show up" is probably intended to be "they...."