The wisdom of liberation from the entanglements of birth and death within the three realms is identical. However, the Buddha attains ultimate liberation, having ended not only birth and death by stages but also birth and death through transformation, without even a trace of ignorance binding the mind; thus, it is complete liberation. The liberation of an Arhat is not yet ultimate, as residual ignorance remains, and birth and death through transformation have not been fully extinguished. A Wisdom-Liberated Arhat (Prajna-vimukti) must still await the exhaustion of worldly conditions to transcend the three realms and be liberated from birth and death, whereas a Both-Ways-Liberated Arhat (Ubhatobhaga-vimukti) does not need to await a specific time for liberation and can transcend the three realms and be liberated from birth and death at any moment.
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