[Tnzxovoz]

Does anyone know where the Buddha gave these specifications for a once returner in the Pali Canon?

Sakadāgāmī: 'Once returner'

A sakadagami (once-returner) has eradicated the first three hindrances of the 10 hindrances to enlightenment and greatly weakened the fourth and fifth; attachment to sense desires and ill-will. Such a person will be re-born to either the human or heavenly realm and will attain enlightenment there.

44. "Monks, in this Teaching that is so well proclaimed by me and is plain, open, explicit and free of patchwork, those monks who have abandoned three fetters and have reduced greed, hatred and delusion, are all once-returners, and, returning only once to this world, will then make an end of suffering.

Alagaddupama Sutta: The Snake Simile "In this community of monks there are monks who are arahants, whose mental effluents are ended, who have reached fulfillment, done the task, laid down the burden, attained the true goal, laid to waste the fetter of becoming, and who are released through right gnosis: such are the monks in this community of monks.

"In this community of monks there are monks who, with the wasting away of the five lower fetters, are due to be reborn [in the Pure Abodes], there to be totally unbound, destined never again to return from that world: such are the monks in this community of monks.

"In this community of monks there are monks who, with the wasting away of [the first] three fetters, and with the attenuation of passion, aversion, & delusion, are once-returners, who — on returning only once more to this world — will make an ending to stress: such are the monks in this community of monks.

"In this community of monks there are monks who, with the wasting away of [the first] three fetters, are stream-winners, steadfast, never again destined for states of woe, headed for self-awakening: such are the monks in this community of monks.

Anapanasati Sutta (Thanissaro Bhikkhu) "Bhikkhus, living in this community there are bhikkhus who are Worthy Ones (arahants) without eruptions (asavas), who have lived the sublime life, have done what is to be done, have dropped all burdens, have attained their purpose, have ended the fetters to existence, and are liberated through right understanding. Bhikkhus such as these are living in this community of bhikkhus.

"Bhikkhus, living in this community there are bhikkhus who are Non-Returners through having ended the five lower fetters, who are spontaneously arisen, who will realize perfect coolness in that existence and by nature will never return from that world. Bhikkhus such as these are living in this community of bhikkhus.

"Bhikkhus, living in this community there are bhikkhus who are Once-Returners through having ended the three fetters and lessened lust and hatred, who will come back to this world only once and then will put an end to dukkha. Bhikkhus such as these are living in this community of bhikkhus.

"Bhikkhus, living in this community there are bhikkhus who are Stream-Enterers through having ended the three fetters, who by nature never will full into evil again and are certain of future awakening. Bhikkhus such as these are in this community of bhikkhus.

Anapanasati Sutta (Santikaro Bhikkhu translating from Buddhadasa's Thai translation)