Which rūpa-kammaṭṭhāna did the Buddha practice when he was studying under Āḷāra Kālāma?

Which rūpa-kammaṭṭhāna did the Buddha practice when he was studying under Āḷāra Kālāma? On which meditation object did he practice the rūpa-jhānas in order to then transition to the arūpa-jhānas?

I am asking this because right before his enlightenment under the Bodhi tree, the Buddha recalled practicing ānāpānasati during his childhood—not during his time with Āḷāra Kālāma. Does this mean he was most likely using a kasiṇa to attain the rūpa-jhānas while training with Āḷāra Kālāma?

Additionally, is there any information about Āḷāra Kālāma’s doctrine and the methods he taught?

Yes it is a bit of a puzzle that. But I have never seen a clear answer.

"I found this excerpt in The Great Chronicle of Buddhas by Mingun Sayadaw:

Thereupon, it occurred to the Bodhisatta thus: ‘Not only does the sect-leader Āḷāra possess faith, firm enough to attain the absorptions, I, too, have faith firm enough to attain the absorptions. Not only does he possess energy, mindfulness, concentration and wisdom strong enough to reach absorption (appanā-jhāna), I, too, have energy, mindfulness, concentration and wisdom strong enough to reach it. Āḷāra says that he has himself realized the seven mundane absorptions attainments up to the sphere of nothingness with super knowledges (abhiññā) and abides blissfully therein. It would be good if I, too, were to strive to realize like him the seven mundane absorption attainments.’ With this intent, he strenuously practised the preliminary duties (kasiṇa-parikamma), and within two or three days he himself realized, like his teacher Āḷāra, the seven mundane attainments up to the absorption on the sphere of nothingness and dwelt blissfully therein.

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These are not related to rupa or kaya. I think they practiced breath meditation for jhana (not vipassana). Breath is rupa.

The Technique

The exact step-by-step instructions practiced by Āḷāra Kālāma are not fully detailed in the Pali Canon, but the texts specify the progression required to reach this state. The technique is a type of samatha (concentration meditation) rooted in early Upanishadic or proto-Sāmkhya yoga traditions. [1, 2, 3] [Āḷāra Kālāma - jhana technique]

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