Polak's Reexamining Jhanas

There’s the panner sutta AN 3.101 which shows how thoughts are reduced and refined from mundane towards Supermundane, with the last type of thoughts remaining being about the dhamma, which I take to mean the awakening factor of dhamma-vicaya, which I also take to mean observing and ridding the mind of the 5 hindrances.

This is backed up by MN 48 about sotapannas:

And how does the view that is noble and emancipating lead one who practices it to the complete ending of suffering? It’s when a mendicant has gone to a wilderness, or to the root of a tree, or to an empty hut, and reflects like this, ‘Is there anything that I’m overcome with internally and haven’t given up, because of which I might not accurately know and see?’ If a mendicant is overcome with sensual desire, it’s their mind that’s overcome. If a mendicant is overcome with ill will, dullness and drowsiness, restlessness and remorse, doubt, pursuing speculation about this world, pursuing speculation about the next world, or arguing, quarreling, and disputing, continually wounding others with barbed words, it’s their mind that’s overcome. They understand, ‘There is nothing that I’m overcome with internally and haven’t given up, because of which I might not accurately know and see. My mind is properly disposed for awakening to the truths.’ This is the first knowledge they have achieved that is noble and transcendent, and is not shared with ordinary people.

Notice mundane view (pursuing speculation about this/next world) is abandoned as well.

This here is “thinking about the dhamma” aka dhamma-vicaya, which is again mirrored in “thoughts of a great man” sutta AN 8.30

“Good, good, Anuruddha! It’s good that you reflect on these thoughts of a great man: ‘This teaching is for those of few wishes, not those of many wishes. It’s for the contented, not those who lack contentment. It’s for the secluded, not those who enjoy company. It’s for the energetic, not the lazy. It’s for the mindful, not the unmindful. It’s for those with immersion, not those without immersion. It’s for the wise, not the witless.’ Well then, Anuruddha, you should also reflect on the following eighth thought of a great man: ‘This teaching is for those who don’t enjoy proliferating and don’t like to proliferate, not for those who enjoy proliferating and like to proliferate.’

First you’ll reflect on these eight thoughts of a great man. Then whenever you want, quite secluded from sensual pleasures, secluded from unskillful qualities, you’ll enter and remain in the first absorption, which has the rapture and bliss born of seclusion, while placing the mind and keeping it connected

edit:

Thanks for this, it aligns with the previous discussion we had about outsiders also telling the Buddha that they too overcome the 5 hindrances and develop the 7 factors of awakening. Were the 4 jhanas a unique discovery of the Buddha? - #14 by Thito