The Vinaya account is that the Buddha refused the request to admit women three times, that Ananda intervened on their behalf, and that admission was granted on condition of eight garudhammas, rules of respect that place the nuns' order under the monks'.
The eight include that a nun ordained a hundred years must rise and pay respect to a monk ordained that day; that nuns may not admonish monks though monks may admonish nuns; that a nun must seek instruction from the monks' order twice monthly; and that ordination of a nun requires both orders.
Whether these are original is a live scholarly question and not a modern invention of convenience. The arguments against originality are textual: the eight rules appear in the Vinaya in a form that duplicates rules found elsewhere in the same collection, the narrative frame is of a type that scholarship treats as late, and the versions preserved in different Vinaya recensions do not agree on their number or order. Bhikkhu Analayo has argued the case in detail from the comparative Vinaya evidence. Others hold that the account is early and that the rules stand.
This is not an argument about history for its own sake. The eighth rule, that valid ordination requires a quorum of nuns as well as monks, is precisely the rule invoked to say the Theravada bhikkhuni order cannot be restarted once its line has lapsed. Whether that rule is the Buddha's or a later addition therefore decides a practical question about several thousand living women.
The atlas records the dispute rather than the verdict, because there is no verdict. Theravada has no central authority that could deliver one.