May wish to bring in the notion of sammatta-niyama, too.
22. The person who is affirmed in the eventual attainment of enlightenment (niyata) enters (okkamati) into affirmation (niyāma).387
There are two determinate states, i.e., states where the maturation is determined: determination on falsehood (micchattaniyama) resulting from unpardonable action (anantariyakamma) and the determination on correctness (sammattaniyama) which is the noble Path (ariyamagga). The Pubbaseliyas allude to another determination not recognoized by the Theravādins. Actually, the Buddhas can know, by means of their own power of consciousness (ñaṇabala), that such and such a being (satta) will attain (pāpuṇissati) awakening (bodhi) in the future (anāgata), and it is said: “The Bodhisatta is confirmed in the eventual attainment of enlightenment (niyata) due to the excellence of his own merit (puññussadattā).” Now the Bodhisatta who has come to his last lifetime (pacchimabhava), who is already fixed from this point of view, is able (bhabba) to understand completely (abhisametuṃ) [the Dharma] from the time of this birth (jāti) and thus is able to enter into the determination on correctness.
387 Kv, XIII, 4.
127. The person (puggala) attached to an immediate destiny (anantarāpayutta) cannot enter into the assurance of eventual attainment of enlightenment (sammattaniyāma).1305
1305 Kv, XIII, 3.
20. The individual (puggala) attached to an immediate destiny (anantarāpayutta) can enter into (okkameyya) the assurance of attaining eventual enlightenment (sammattaniyāma).1460
1460 Kv, XIII, 3.
I'll leave out other schools' ideas about this from non-Theravada sources.
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