I think it's going to be hard to "document" the first monastery, unless you first define what you mean by it, and by "community."
I think you've got a good start.
Christian monastic life definitely began in the desert, with folks like St. Anthony, and Paul the Hermit - living alone. (or with helpful ravens, lions, etc.
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) Was that the first monastery? Or did it become a monastery when the first wannabees came to live "near" and learn from Anthony? Or perhaps was the first monastery the monks who lived in cells in the desert a couple miles from each other, but came together for "the Synaxis" and maybe on great feasts? Or was the first monastery when two monks decided to live in adjoining kellia, perhaps one as father and the other as disciple? Or was the first monastery when St. Pachomius gathered folks inside of one set of walls?
Christ gave us the measure of "where two or more are gathered." At what point does community commence?
I think your sources both have part of the answer.
St. Anthony is generally attributed with founding Christian monasticism. (If memory serves, in his later years he was not exactly alone in his part of the desert either.) His life of prayer and asceticism became the model for the Desert Fathers and Mothers who folowed him - some of whom eventually adopted the cenobitic life, which was pilot-tested by St. Pachomius, and eventually (down the road a piece) given a formal rule by St. Basil.
So what makes a monastery? One hermit monk? Two monks? How close together do they have to live? How often do they have to come together? Do they have to have a formally codified Rule? Community life?
I think if you define your parameters, you can answer the question. But you've got to decide what qualifies as a monastery.
Dunno if this helps at all.
Sharon