grammaticality - Shortest correct sentence in English- use of contractions

I often hear people saying that "I am" is the shortest sentence in the English language. I know that there are also discussions about sentences using the imperative mood such as "Go." that would be shorter, but my question is this:

Why would we (the people saying "I am" is a full sentence) not accept "I'm" as a complete sentence? Is there some unwritten rule about contractions that says "I'm" wouldn't be correct?

Answer

In English, any clause has one mandatory stress slot: there must be at least one element that has stress (optionally more than one). That slot lies in the predicate of the clause, which must always be stressed. The subject (which stands outside the predicate) can receive stress, but does not necessarily have to, and even when it does receive stress, the predicate retains its stress.

Within the predicate, a verb that has one or more complements of a certain type (a generic object [i.e., one without an article], an adverbial phrase, a predicative expression, etc.) is unstressed (or at most secondarily stressed) unless it is emphasised for effect. In such a case, the predicate’s only stressed element(s) is/are the complement(s) that is/are considered most important.

Conversely, if the verb either does not have any compliments or has a non-generic object (i.e., an object with an article, a proper noun, etc.), it is stressed. Any following complements can also be stressed, but they do not have to be.

So for example (using the IPA character “ˈ” before a word to indicate stress, and the entirely ad hoc notation “ˣ” to specifically denote lack of stress):

He ˈran.
He ˣran ˈhome.
He ˈran a ˈmile.
He ˣran ˈfast.

As mentioned above, complements also include predicative expressions like subject and object complements—like what you have in ‘to be’ phrases. These follow the same rules (note that the distinction between generic and non-generic elements goes only for objects, not for predicative expressions):

He ˣis a ˈman.
He ˣis ˈgood.

Now very importantly: a stressed syllable cannot be syncopated. Only unstressed (or sometimes secondarily stressed) syllables can be syncopated away, leaving contractions in their wake. Of course, when you contract something, you are removing a syllable, and if that syllable is stressed, where would the stress go when you remove it? There has to be a stress somewhere.

As such, the following is possible:

He ˣis my ˈfather --> He’s my ˈfather.
I ˣcan ˈtell you ˈwhy --> I c’n ˈtell y’ ˈwhy.

– because the elements that are syncopated (is in the first, can and you in the second) are both unstressed. The following, however, is impossible, because here we’ve emphasised (= stressed) the verbs. Emphasising an element reduces other elements nearby to lose their stress entirely—it’s basically overriding the ‘natural’ assignment of stress—and the emphasised verbs end up being the only elements that carry any stress. If you syncopate those away, the stress would disappear entirely from the clause, which is not possible:

But he ˈis my ˣfather --> †But ˣhe’s my ˣfather.
I ˈcan tell you ˌwhy --> †I ˣc’n tell y’ ˣwhy.

Now recall that the predicate must be stressed. In a case like “I am” (with nothing more following the verb), where the verb has no complements at all, there is only one element that can be used to fill this stress slot: the verb itself, which is thus automatically stressed. And since the verb is stressed, it cannot be syncopated or contracted: that would remove the mandatory stress slot altogether, which is not an option.