That's actually a great question!

CGEL says cannot "is hardly possible in pre-subject position: Can't/?Cannot we stay a little longer?; Not only can't/*cannot he find the key, he's not even sure the papers are in the office anyway!"

(p.1611)

That first question mark is supposed to be superscripted, but I can't do that in chat.

I typed up the cannot section

> The form cannot

> Can has an additional variant form cannot, unique in that not (the etymological source of the /nt/ suffix), complete with its vowel, is attached to the lexical base.

> This form is more common in the written language than in speech, though the distinction in writing between the single word cannot and the word sequence can is not matched by that between /ˈkænɒt/ (one /n/ and stress on the first syllable) and /kən ˈnɒt/ (two /n/'s and stress on the second syllable). In cannot, as in can't, the negative is invariably external, having scope over the modality, whereas this is not so with the analytic negative can not; see Ch. 3, §9.10.

> Cannot is more formal in style than can't. It is hardly possible in pre-subject position: Can't / ?Cannot we stay a little longer?; Not only can't / *cannot he find the key, he's not even sure the papers are in the office anyway!

That's the whole section.

Several auxiliaries are somewhat irregular when it comes to inversion.

I'm sure you'll recognize aren't as another example: Aren't I, but *I aren't

Yes, cannot is unique!

The negative form mayn't disappeared in the last hundred years.

corpus.byu.edu/coha/?c=coha&q=40625140

Me too. The English I speak has no mayn't.

But you'll find it in older English textbooks!

books.google.com/books?id=HYMZAAAAYAAJ&pg=PA144#v=onepage

books.google.com/books?id=NxHuNOvwt7wC&pg=PA197#v=onepage