The person who hears that poem in circulation and records it in his notes has created literature; an anthology is literature but an original work isn't.
Sure they have, by virtue of writing it down. It becomes literature when it hits the paper (or computer screen, as it were).
(Unless you mean to imply that formulating an original poem in your mind counts as "writing", in which case I guess we illustrate the overarching point of value in shared symbols and language and the waste of time in stating our original definitions for every statement we want to make)
You're close. I'm making the point that, in modern English, no other verb is available for the act of creating a poem.
Here's a quote from the fantasy novel The Way of Kings that always appealed to me:
>> "Many of our nuatoma -- this thing, it is the same as your lighteyes, only their eyes are not light--"
>> "How can you be a lighteyes without light eyes?" Teft said with a scowl.
>> "By having dark eyes," Rock said, as if it were obvious. "We do not pick our leaders this way. Is complicated. But do not interrupt story."
For an example from reality, I am forced to tell people who ask me that the English translation of 姓 is "last name", despite the fact that the 姓 comes first.
Similarly, the word for writing a poem is "write", whether this creates a written artifact or not. And the poem is literature whether a written artifact currently exists, used to exist, or never existed.
(Though you've made me curious: if the Iliad wasn't literature until someone wrote it down, do you symmetrically believe that Sophocles' Sisyphus is no longer literature because it is no longer written down?)
Once someone writes it down, it is.