A distich is defined as "two successive lines of verse regarded as a unit; a couplet." The shortest distich in the English language is very likely Strickland Gillilan's "Lines on the Antiquity of Microbes": Adam/Had 'em. Gillilan is probably better known, though, for his longer and more sentimental poem "The Reading Mother," which closes with the lines: Richer than I you can never be/I had a Mother who read to me. (I did too, and she started doing it pretty much as soon as I was born, which happens to have been the same year Strickland Gillilan died.) There were 44 cases of Distict* in OhioLINK this morning and, while it may be tempting to temporarily quarantine them into a sort of district for infectious typos, it would probably be better to just buckle down and, like Adam, get at 'em.
("Microbe" by Nevit Dilmen, 2009, from Wikimedia Commons.)