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samadhi and ekaggata relationship


Formula in brief

noble-right-concentration + supports + requisites = mind-in-one-place equipped with [first] 7 factors [of noble eightfold path] 
to be precise note what the formula doesn't say

noble-right-concentration + supports + requisites = mind-in-one-place +  [first] 7 factors [of noble eightfold path] 

It's not saying

1) noble-right-concentration = mind-in-one-place +  [first] 7 factors [of noble eightfold path] 
and it's definitely not saying
2) right-concentration = mind-in-one-place +  [first] 7 factors [of noble eightfold path] 

You could say that (2) is a legitimate definition for right concentration even though a precise sutta reading does not say that, but I think how that differs from 4-jhana-right-concentration is that one could be only able to attain first jhana, and then not full develop jhana to 4th jhana quality level. By having samma-samadhi always mean 4 jhanas, it's implicit that one needs to develop jhana to the highest level one is able to.

from DN 18 , cst4

♦ 290. “‘taṃ kiṃ maññanti, bhonto devā tāvatiṃsā, yāva supaññattā cime tena bhagavatā jānatā passatā arahatā sammāsambuddhena satta samādhiparikkhārā sammāsamādhissa paribhāvanāya sammāsamādhissa pāripūriyā. katame satta? sammādiṭṭhi sammāsaṅkappo sammāvācā sammākammanto sammāājīvo sammāvāyāmo sammāsati. kho, bho, imehi sattahaṅgehi cittassa ekaggatā parikkhatā, ayaṃ vuccati, bho, ariyo sammāsamādhi saupaniso itipi saparikkhāro itipi. sammādiṭṭhissa bho, sammāsaṅkappo pahoti, sammāsaṅkappassa sammāvācā pahoti, sammāvācassa sammākammanto pahoti. sammākammantassa sammāājīvo pahoti, sammāājīvassa sammāvāyāmo pahoti, sammāvāyāmassa sammāsati pahoti, sammāsatissa sammāsamādhi pahoti, sammāsamādhissa sammāñāṇaṃ pahoti, sammāñāṇassa sammāvimutti pahoti. yañhi taṃ, bho, sammā vadamāno vadeyya ‘svākkhāto bhagavatā dhammo sandiṭṭhiko akāliko ehipassiko opaneyyiko paccattaṃ veditabbo viññūhi apārutā amatassa dvārā’ti idameva taṃ sammā vadamāno vadeyya. svākkhāto hi, bho, bhagavatā dhammo sandiṭṭhiko, akāliko ehipassiko opaneyyiko paccattaṃ veditabbo viññūhi apārutā amatassa dvārā


27.‘“This was the burden of Brahmā Sanankumāra’s speech. He went on: ‘What do my lords of the Thirty-Three think? How well has the Lord Buddha who knows and sees pointed out the seven requisites of concentration, for the development of perfect concentration and the perfection of concentration! What are they? They are right view, right thought, right speech, right action, right [217] livelihood, right effort, right mindfulness. 532 That one-pointedness of mind that is produced by these seven factors is called the Ariyan right concentration with its bases and requisites. From right view arises right thought, from right thought arises right speech, from right speech arises right action, from right action arises right livelihood, from right livelihood arises right effort, from right effort arises right mindfulness, from right mindfulness arises right concentration, from right concentration arises right knowledge, 533 from right knowledge arises right liberation.534 If anyone truthfully declaring: “Well-proclaimed by the Lord is the Dhamma, visible here and now, timeless, inviting inspection, leading onward, to be comprehended by the wise each one for himself”, were to say: “Open are the doors of the Deathless!” 535 he would be speaking in accordance with the highest truth. For indeed, my lords, the Dhamma is well-proclaimed by the Lord, visible here and now, timeless, inviting inspection, leading onward, to be comprehended by the wise, each one for him or herself, and, too, the doors to the Deathless are open!

also in MN 117

MN 117: "Now what, monks, is noble right concentration with its supports & requisite conditions? Any singleness of mind equipped with these seven factors — right view, right resolve, right speech, right action, right livelihood, right effort, & right mindfulness — is called noble right concentration with its supports & requisite conditions."
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