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Sutta Jhāna

abundant evidence of satipatthana in first Jhāna

There are numerous sutta passages in evidence of cases for doing satipattha while in the attainment of first jhana, so those are in the article above. The rest of the cases on this page mostly seeking evidence for fourth jhāna and higher attainments.


Evidence that satipatthana is the preferred method as the entry into jhana

http://www.accesstoinsight.org/tipitaka/sn/sn22/sn22.122.than.html

excerpt:

"An arahant should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. Although, for an arahant, there is nothing further to do, and nothing to add to what has been done, still these things — when developed & pursued — lead both to a pleasant abiding in the here-&-now and to mindfulness & alertness."

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"pleasant abiding in the here and now" is another way to state jhana absorption.


Strong evidence in favor of

mn 111

looking at mn 111:
phasso vedanā saññā cetanā cittaṃ chando adhimokkho vīriyaṃ sati upekkhā manasikāro

the words of particular interest are
cetana: intention, state of ceto in action, thinking as active thought, intention, purpose, will Defined as action (kamma

cittam: mind, thought
chando: will, impulse, wish

adhimokkho: firm determination

manasikaro: ideation, consideration

Those mental factors are in all the attainments 1-7, so it seems to more than cover enough mental activity to do thought, evaluation, comparison, vipassana, etc.

So if that's the case, one would have to deduce vitakka and vicara is just extraneous thinking, such as forming words that one is planning to speak, verbal sankhara, that one just chooses not to verbalize in the first jhana. In second jhana, extraneous thinking is mostly reduced, but is still a thorn of second jhana.

And if sari putta is contemplating each factor as they arise, cease, etc, then he's basically doing steps 13-16 of anapnasati, while in jhanas 1-4, and attainments 5-7.

regarding commentarial interpretation of jhaana, in that one attains jhaana, and has to emerge from jhaana attainment before being able to do vipassana, such as any of the exercises in the 4 satipatthaana, or steps 13-16 of anapana. In MN 111
Sariputta is doing vipassana (steps 13-16 of anapana) while in the attainment of jhaana. Not just in 1st jhana where vitakka and vicaara are still present, but in second jhana, all the way to 4th jhaana, and even the first 3 formless attainments. What really seals the deal in my mind is that in that sutta MN 111, only in the attainment of neither-perception-nor-
nonperception and the attainment of the cessation of perception and feeling does the sutta specifically say Sariputta had to emerge from those 2 attainments to be able to examine the mental factors that were active during the attainment.

 the presence of "sati and sampajaano" in the canonical def. of 3rd jhaana, looks exactly like the "sati and sampajaano" repeated 4 times in the canonical sammasati formula "ataapi sampajaano satima".
and the mental factors listed in jhanas 1-4 in MN 111 (thanissaro's translation in this excerpt)
contact, feeling, perception, intention, consciousness, desire, decision, persistence, mindfulness, equanimity, & attention — he ferreted them out one after another.
That seems to imply a fair amount of computing brain power, while absorbed in  jhaana attainment, to do vipassana, exercises in satipatthana, such as 4 elements which are pretty dynamic of intentionally redirecting one's attention to all parts of the anatomical body, observation of impermanence, etc.

As well as the sutta you referred to in your articles, where the Buddha comes to Moggallana to give pointers on jhaana, the way it is worded (at least the english translations i read), it really reads like Moggallana, while in jhaana attainment, he is actively dealing with the thorn of each particular jhaana, as opposed to having to first emerge from jhaana as Sariputta did only in attainments #8 and #9. 

AN 9.36 in each jhana, monk does satipatthana with 5 khandhas while in jhana

http://www.accesstoinsight.org/tipitaka/an/an09/an09.036.than.html
very similar to mn111 in that in attainments #8 and #9, while in those states one can not do satipatthana. mn111 is explicit in stating that one must emerge from #8 and #9 before doing satipatthana.
another interesting feature of an 9.36 is it implies first jhana is sufficient degree of concentration to attain full liberation, whereas other suttas seem to suggest 4 jhanas or necessary, and even other suttas suggest all 8 attainments are necessary.

MN64 mahamalunkya sutta - very similar to AN 9.36

“There is the case, Ānanda, where a monk... enters & remains in the first jhāna: rapture & pleasure born of seclusion, accompanied by directed thought & evaluation. He regards whatever phenomena there that are connected with form, feeling, perception, fabrications, & consciousness as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, empty, not-self…in the second jhāna…the third…the fourth jhāna…He regards whatever phenomena there that are connected with form, feeling, perception, fabrications, & consciousness as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, empty, not-self.”


AN 9.34 Nibbana sutta - the key phrase is "as he remains there" (in attainments 1-8)

http://www.accesstoinsight.org/tipitaka/an/an09/an09.034.than.html
AN9.34: “Now there is the case where a monk…enters & remains in the first jhana…If, as he remains there, he is beset with attention to perceptions dealing with sensuality, that is an affliction for him... Furthermore, there is the case where a monk…enters & remains in the second jhana…If, as he remains there, he is beset with attention to perceptions dealing with directed thought, that is an affliction for him...” Similar statements are made about all the remaining form and formless attainments, and how he should direct his mind to Unbinding "as he remains there."

Evidence from Agamas (pali nikaya sutta counterparts)

SA864: dwelling in jhānas, the meditator discerns the inconstancy, stress, insubstantiality, and not-self of all physical and mental experiences

Qiyi jing, an independent sutra as cited in T1537.493c28: insight takes place in all the four jhānas, and the three lower attainments of the formless bases (i.e. the only exception is the base of neither-perception-nor-non-perception)

Weak (inconclusive) evidence in favor of

sn 39 moggallana samyutta

http://www.metta.lk/tipitaka/2Sutta-Pitaka/3Samyutta-Nikaya/Samyutta4/39-Moggalana-Samyutta/01-Moggallanasamyuttam-e.html
from vism. point of view the thorn in each jhana was what knocked him out of that jhana (causing premature emergence instead of intended duration). AN 9.34 (see above under strong evidence) deals with similar topic, but uses a key phrase "while he remains there" [in the attainment]

MN 122 mahā suññata sutta

http://www.accesstoinsight.org/tipitaka/mn/mn.122.than.html
in sunnata attainment monk can do satipattjhana, walk and talk simultaneously

since sunnata is a higher attainment than 4th jhana, that if one can be in sunnata and walk and talk, then that meditator should be able to do so in 4th jhana. I can see your point, but I would only agree that's the case for the meditator who can do sunnata. If a meditator can only do 4th jhana and not sunnata, I don't know that he can necessarily walk and talk and do 4th jhana simultaneously.

Still investigating

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." In other words, jhanas (Right Concentration)=singleness of mind+the seven factors, including Right Speech. See also AN4.12 on this issue. Though it doesn't mention jhanas per se, it is clear that the meditation instructions are consistent with each other: http://www.buddhagautama.com/apps/blog/show/prev?from_id=16830025




DN2 describes jhanas and the imperturbility concentrations (jhana+a formless base) should be directed to the ending of the fermentations/outflows/asavas "as they have come to be." If access meditation is needed for this purpose, the Buddha really was grossly negligent to have failed to mention it here, which is absolutely a vital piece in practice instruction.
 
Most early commentaries differ from the Vism in that they assert jhanas NOT to be a samatha practice, but a practice that involves both samatha and vipassan. E.g. The Mahāvibhāṣā (Apidamo dapiposha lun):  “In the four dhyānas, śamatha and vipaśyanā are equal in strength, and thus they are named a pleasant dwelling.”
The Abhidharmakośabhāṣya (Apidamo jushe lun): “Samādhi is in fact excellent: it is a dhyāna filled with 'parts,' which goes by the means of the yoke of śamatha and vipaśyanā [that is to say, in which śamatha and vipaśyanā are in equilibrium], that is termed in the Sūtra 'happiness in this world' and 'the easy path,' the path by which one knows better and easily.”



SA609 (in Chinese) defines the "preliminary theme" to Right Concentration as "understanding." And "what is understanding?" "It is Satipatthana."