I am of the understanding—please correct if it's a misunderstanding—that those annotations denote the earliest known written source of the melody in question (in this case, 11th-13th century). The melody itself may be much older.
They are Roman numerals referring to the approximate century of the manuscript upon which the Vatican edition of a particular chant was based—which may or may not be the oldest known manuscript. The century indications should not be understood as the date of composition, which is oftener than not unknown.
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