Explanation on the working of Abhiññā / Iddhi / Mind arising

If "based on science" means 'possible to do/follow/reproduce in real life', the answer appeared in Abhidhamma (as follows).

A person's mind arises and immediately vanishes more than trillions of times per second. And one person per one mind per time.

There are 2 types of mind by job:

1. mind which arises for life saving (sleeping mind; know only rebirth-kamma's object) and
2. mind which arises for knowing new object from a sense of 6 senses.

This 2 types arise switch each other whole life, from the rebirth to death. For example, while you reading this answer, these 2 types, included sleeping mind, still arise and vanish uncountable. And this sleeping mind drops human abilities, such as abhiññā.

And, there are 2 types of mind which knowing new object by job:

1. wholesome mind (kusala)
2. unwholesome mind (akusala)

Only unwholesome mind drops human abilities, such as abhiññā.

The trick of Abhiññā / Iddhi

The trick of jhāna is very simple and powerful: it is "how to pause sleeping mind and unwholesome mind", then "how to rising up wholesome mind continuously, development" (as much as sleeping mind/unwholesome mind can't arise, between the long period of wholesome minds arising).

Then the trick of abhiññā is very simple and powerful as well: it is "how to be professional of jhāna enough to get abhiññā which can adapting jhāna affects daily life more than the pure jhāna without abhiññā".

It's something like the professors of science/history/business/etc. They can see the future of their expertise and control it like what they want it be. But someone who never practice like them can't understand many of their speech. Similarly, the Abhiñño people can control their expert minds to do what they want, such as seeing the other minds, seeing the future, etc.

See citta-visuddhi-niddesa in path of purification.

It is impossible to attain wrong mindfulness and wrong concentration.

It is impossible to attain wrong mindfulness and wrong concentration. Because the uddhacca-cetasika (restlessness-mind-factor) arises with every unwholesome-mind, such as diṭṭhi-mind. This mind factor is the enemy of the main keyword of achievement, ekaggatā-cetasika (concentration-mind-factor). See the path of purification samādhiniddeso pathavīkasiṇaniddeso.

This is the reason that why in tipitaka the effects of unwholesome-minds have shorter period than the effects of wholesome-minds. And This is the reason that why the wholesome-minds have more mind factors than the unwholesome-minds.

Conceptual VS Perfect Anatta-understanding

The outsider ordinary people of Buddhism don't have anattā-understanding in any mind-moment. They never know, so they never do anything follow to it.
The buddhist ordinary people, the practitioners, have a conceptual anattā-understanding in some mind-moments, but it still being a concept. So, they do something follow to it sometime, but sometime they forget, not be mindful on, it and do some improper things, too.
The sotāpanna have the perfect anattā-understanding in every mind-moments, so they do everything follow to it.
If you understand like that, every sutta are the answer for your question.
And the reference sutta is the end of Sutta. Ma. Mū. Alagaddūpamasuttaṃ:

"In the Dhamma thus well-proclaimed by me — clear, open, evident, stripped of rags — those monks who have abandoned the three fetters, are all stream-winners, steadfast, never again destined for states of woe, headed for self-awakening. This is how the Dhamma well-proclaimed by me is clear, open, evident, stripped of rags.
...
"In the Dhamma thus well-proclaimed by me — clear, open, evident, stripped of rags — those monks who have a [sufficient] measure of conviction in me, a [sufficient] measure of love for me, are all headed for heaven. This is how the Dhamma well-proclaimed by me is clear, open, evident, stripped of rags."

What you did, is what you take. If you still understand anatta as a concept, then your fetters still going on. So, the effect is not the same as sotāpanna, who does every moments of his life by anattā-understanding.

Thai Forest tradition: thoughts like rain drop

Q: There is reference in the Thai Forest tradition to a teaching given to sāriputta by Buddha of thoughts like rain drop bubbles rising the mergie into the body of water?

A: Sāriputta enlightened as sotāpanna in Vinaya. Mahā (1) Mahākhandhaka, then he enlightened as arahanta in Sutta. Ma. Ma. Dīghanakhasuttaṃ, which it's atthakathā gave the similitude of vedanā arising and vanishing as bubbles.

Another, In sāriputta's cannons, KN Cūḷaniddeso Mogharājamāṇavakapañhāniddeso, used the similitude of viññāṇakhandha as bubble as well.

So, sāriputta maybe one of monks who listening Phena Sutta (SN 22.95), then he described his arahanta-enlightening-moments to his students. Then at 1st saṅgāyanā, his students put his description into that ancient atthakathā and into that KN Cūḷaniddeso which authored by sāriputta.

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Also, in KN Dhammapada's atthakatha Dha.A.6 atta-kodhavagga Buddhavaggavaṇṇanā 2. Yamakappāṭihāriyavatthu. (149), there are the sāriputta's conversation with the buddha about he is a genius who can count every rain's drops into the ocean, mountain, and the ground.

Whole pali canon focus on illusion analysis for purge illusion first

In tipitaka, only 121 minds, 52 mind-factors, 28 matters, and 1 nibbāna are not illusion. The other else are illusion. This is very important, because it is a start point to understand 3 characterizes.
12 paṭiccasamuppāda, both arising and cessation, are only the relativity of minds, mind-factors, matters, and nibbāna. They cause each other arise by themselves. If the practitioner still believe in an illusion, such as person, as the cause of 12 paṭiccasamuppāda, then he will not see the relativity of 12 paṭiccasamuppāda. Therefore, he can not meditate insight meditation in 3 characterizes in every second of life.

For the example, god is an illusion

1. When you still believe in god, do you understand 12 paṭiccasamuppāda of god?(no)
2. Then can you think God is impermanent, suffering, non-self? (no).
3. But if you understand how god can analysis as 12 paṭiccasamuppāda, then no god anymore right? (yes)
4. When no god anymore, 12 paṭiccasamuppāda, which you have been called it as god, can appear as impermanent, suffering, and non-self, right? (yes)

So whole pali canon focus on illusion analysis for purge illusion first

1. The first of all sutta, Sutta Pitaka Vol 1 : 1. Sutta. Tī. Sī Brahmajālasuttaṃ, is the biggest sutta which teaching about 62 self-illusion analysis. After buddha showed all 62 self-illusion, then buddha conclude them, 62 self-illusion analysis, as 12 paṭiccasamuppāda at the end.
2. The first fetter is sakkāya-diṭṭi, which have to destroyed by the practitioner first of all 10 fetters.
3. After jhāna meditation, whole tipitaka structure focus on diṭṭhi-analysis first for the insight meditation beginner, before comprehensions on "impermanent, suffering, and non-self".
4. Attavādupādāna-cessation, diṭṭhi-analysis/self purging, is taught only inside Buddhism according to MN Cūḷasīhanādasutta.
5. Sāriputta, the right-hand man of Buddha, described insight meditation by that same structure, in Sutta KN Paṭisambhidāmagga (whole structure).
6. 0 BE ancient commentary described insight meditation by that same structure.
7. 3th BE 3rd buddhist council members, arahanta, judge titthiya-monks by illusion analysis ability testing as well. See Abhidhamma Pitaka Vol 4 : Abhi. Kathāvatthu (whole structure).
8. 10th BE commentary, such as visuddhimagga (path of purification), described insight meditation by that same structure (whole structure).
9. 16th BE commentary, such as abhidhammatthasaṅgaha, described insight meditation by that same structure (whole structure).
10. Vimuttimagga described insight meditation by that same structure (whole structure).
11. Burmese monks, such as pa-auk monastery, described insight meditation by that same structure (whole structure).
12. Thai monks, such as Bh. Mun Bhuridatta who is the leader teacher of all thai forest monk, described insight meditation follow to abhidhammatthasangaha as well.

upekkhā-brahmavihāra

22:45 Q: How would you translate Ubekkha?
10:49 A: In this situation, upekkha means "keep seeing and caring in mind, then act only the proper, possible action/speech.
10:50 A: "keep seeing and caring in mind, then act only the proper, possible action/speech/thinking".
10:52 A: It is not over acting/ over thinking/ over speech.
10:55 Q: “Equality and indifference”?
10:55 Q: “Indifference with caring mind”?
10:56 A: Indifference of object.
10:56 Q: The Japanese monk in Chiangmai liked to talk about Upekkha a lot
10:57 A: If you think the object is indifference, then you will do just the proper action. But if you still think this is my son, wh difference from the other, you will be sad when he die.
10:58 Q: Chinese people translated it as 捨, means “throw away”
10:58 A: Nope.
10:59 Q: Not only “throw away” but they gave this character
10:59 Q: Chinese is symbolic language
11:00 A: Actually, it is very hard to translate even in thai language.
11:00 Q: 慈悲喜捨
11:01 Q: Metta Garuna Mutthita, Upekkha
11:01 Q: First meaning is Caring, sadness,joy, throw away
11:01 A: It's like when your son playing football you just see, not act. But if he try to jump from the mountain, you just act, not see.
11:04 Q: Monk in Chiangmai said, without Upekkha, other 3 don’t work
11:04 Q: Don’t function well
11:04 A: You act metta karuna mudita to the object, then you upekkha when you have not to do or you can't do anything to that object.
11:06 A: Your monk means upekkhā-ñāṇa, it is not upekkha-brahmavihāra.
11:07 Q: More example for Upekkha case?
11:07 Q: How do you use it
11:08 A: upekkhā-ñāṇa=vipassanā paññā mind-factor, upekkhā-brahmavihāra=tatramajjhattatā mind-factor
11:09 Q: I mean in our life
11:09 Q: Actual example
11:09 Q: When do you use it
11:09 Q: When should we use it
11:10 A: When you feel good, I just know you are there, but I have not to do anything to you. But when you sad, I have to ask and try to help.
11:11 A: And if I can't help, I will just know I can't help you and do not anything to you again.
11:12 A: Both texts are upekkhā-brahmavihāra
11:12 Q: When people compare Christianity and Buddhism, they often mention charity
11:13 Q: Christian Churches try to help poor people by giving foods etc more than Buddhist temples
11:13 Q: Maybe this difference is from Upekkha?
11:14 A: Yes, it is difference.
11:15 Q: Even if you give them food, their situation is same, poor
11:17 A: Upekka means keeping to look, by the direct defination.
11:18 A: It's same taking care.
11:19 A: taking care by metta karuna mudita or upekkha
11:22 A: And that taking care must done by proper, appropriate.
11:22 A: Upekkha will not done by bias.
11:23 Q: It’s like “to know the limitation of helping”?
11:23 Q: We can’t do some things in some situation
11:23 A: That is a part of it. It is the end of helping.
11:24 A: It’s like “to know the limitation of helping”? is what I wrote "And if I can't help, I will just know I can't help you and do not anything to you again".
11:24 A: But I also wrote "When you feel good, I just know you are there, but I have not to do anything to you. But when you sad, I have to ask and try to help."
11:25 A: All of those are upekkha.
11:26 A: However, we have 4 types of upekkha in tipitaka. And what we talking is just one of them, upekkhā-brahmavihāra.
11:27 Q: “To know limitation of our helping ability, and try not to be too nosy”
11:27 Q: “And help only at appropriate situation”
11:28 A: You can be nosy if you have enough ability.
11:29 Q:  Yes, so have to know our ability(limitation) first
11:29 A: The main keyword is "Do  the appropriate action for each case".
11:30 A: The main keyword is "Do  the appropriate action/speech/thinking for each case".
11:31 A: Some case you can metta karuna mudita upekkha, but some case you may can do just upekkha.
11:32 A: And for chiangmai monk speech, it is upekkhā-ñāṇa.
11:37 Q:  At work I tell myself “just be useful for somebody at least”
11:38 Q:  I can’t help the drown kid’s brain but I can be helpful for something else at least
11:40 A: If you still keep try to do what you can't you will lose the chance to do what you can do. This is called "proper/appropriate"

What is meant by statement “the one who sees Dhamma sees dependent origination”?

Dhamma in this clause is fourth Noble truth in meditating minds, the fold-eight-paths-noble-truth of the ordinary practitioner, lokiya-khandha.  Because the sutta conclusion is 'you have to comprehend your meditation-minds as well, because your comprehending-minds are grasping-aggregates in paṭiccasamuppāda, too.Then you will giving up and getting rid of desire and greed for these five grasping aggregates is the cessation of suffering.'
The readers have to connect this sutta with KN paṭisambhidāmagga, especially bhaṅgañāṇaniddesa, because both place are the same sāriputta's teaching. You can see in the same chapter of the path of purification as well.
The introduction part of this sutta said "all skillful qualities-all kusala-dhamma":

“The footprints of all creatures that walk (such as paṭiccasamuppāda, catudhātu, ) can fit inside an elephant’s footprint, so an elephant’s footprint is said to be the biggest of them all.
“Seyyathāpi, āvuso, yāni kānici jaṅgalānaṃ pāṇānaṃ padajātāni sabbāni tāni hatthipade samodhānaṃ gacchanti, hatthipadaṃ tesaṃ aggamakkhāyati yadidaṃ mahantattena;
In the same way, ...all skillful qualities... can be included in the four noble truths.
evameva kho, āvuso, ...ye keci kusalā dhammā... sabbete catūsu ariyasaccesu saṅgahaṃ gacchanti.

And what you asking is answered already in the explanation of that introduction.

But the Buddha has said:
Vuttaṃ kho panetaṃ bhagavatā:
“One who sees dependent origination sees the teaching.
“yo paṭiccasamuppādaṃ passati so dhammaṃ passati;
One who sees the teaching sees dependent origination.”
yo dhammaṃ passati so paṭiccasamuppādaṃ passatī”ti.
And these five grasping aggregates are indeed dependently originated.
Paṭiccasamuppannā kho panime yadidaṃ pañcupādānakkhandhā.
The desire, clinging, attraction, and attachment for these five grasping aggregates is the origin of suffering.

And this part showing "all ..skillful **qualities..." is the fold-eight-paths-noble-truth which enlightening the cessation-noble-truth:**

Yo imesu pañcasu upādānakkhandhesu chando ālayo anunayo ajjhosānaṃ so dukkhasamudayo.
Giving up and getting rid of desire and greed for these five grasping aggregates is the cessation of suffering.’
Yo imesu pañcasu upādānakkhandhesu chandarāgavinayo chandarāgappahānaṃ, so dukkhanirodho’ti.
At this point, much has been done by that mendicant.
Ettāvatāpi kho, āvuso, bhikkhuno bahukataṃ hoti.

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The long sutta often already included the answer, because "svākkhāto bhagavatā dhammo-buddha's teaching was the best teaching (because buddha [and his ariya students] connects these 4 subjects of genius [4 paṭisambhidā] together for each listener personally when he taught everything: causes & effects & linguistics of causes+effect & talents of these 4)".
So, when your question is appear almost at the end of Sutta Pitaka Vol 4 : Sutta. Ma. Mū. Mahāhatthipadopamasuttaṃ, you have to search for the answer at the previous paragraphs first. It is a proving tool you understand or not of each sutta, then you can search for the reference with the other sutta/part/nikāya/piṭaka. By this way, I can connects whole tipitaka together without conflicts.

Sāriputta used HetuPaccaya to avoid to conflict mula with sutta

Paccaya/hetu/āhāra = Whole Condition (Lead&Supporting Condition) in paṭiccasamuppāda.
Mūla = Lead Condition/Root Condition in paṭiccasamuppāda.
Mūla = "Root" in pāli language. Life is similar to a tree, lobha&dosa&moha&whole unwholesome are the seed & root of life. When you want to kill this tree you have to destroy whole seed&root. Because if you destroy just the top of tree, new trees can grow up again and again by the left seeds&roots. This is the reason which pali often use mūla as Lead Condition. See the quote sutta below for more explanation.
HetuPaccaya is used by sāriputta-mahāsāvaka in paṭṭhāna-abhidhammapiṭaka because he have to avoid to conflict mūla with Sutta Pitaka Vol 4 : Sutta. Ma. Mū. {285.1} (English translation). if he use mūla in this context instead of hetu, all other unwholesome saṅkhāra can't be mūla, so paṭṭhāna will conflict with that sutta. That's the reason why sāriputta chose hetu instead of mūla for paṭṭhāna.

Paccaya/hetu/āhāra = Whole Condition (Lead&Supporting Condition)

Playing as lead condition in paṭiccasamuppāda

Tasmātihānanda eseva hetu etaṃ nidānaṃ esa samudayo esa paccayo upādānassa yadidaṃ taṇhā. --Sutta Pitaka Vol 2 : Sutta. Tī. Ma. {58.3} / (English translation)

Playing as supporting condition in paṭiccasamuppāda

tasmātihānanda eseva hetu etaṃ nidānaṃ esa samudayo esa paccayo vedanāya yadidaṃ phasso. --Sutta Pitaka Vol 2 : Sutta. Tī. Ma. {58.3} / (English translation)
Kavaḷīkāro āhāro oḷāriko vā sukhumo vā phasso dutiyo manosañcetanā tatiyā viññāṇaṃ catutthaṃ . ime kho bhikkhave cattāro āhārā bhūtānaṃ vā sattānaṃ ṭhitiyā sambhavesīnaṃ vā anuggahāyāti. --Sutta Pitaka Vol 8 : Sutta. Saṃ. Ni. [31] / (English translation)

Mula = Lead Condition/Root Condition

{79.7} Katamo ca sīha pariyāyo yena maṃ pariyāyena sammā vadamāno vadeyya tapassī samaṇo gotamo tapassitāya dhammaṃ deseti tena ca sāvake vinetīti . tapanīyāhaṃ
sīha pāpake akusale dhamme vadāmi kāyaduccaritaṃ
vacīduccaritaṃ manoduccaritaṃ yassa kho sīha tapanīyā
pāpakā akusalā Dhammā pahīnā ucchinnamūlā tālāvatthukatā anabhāvaṃ katā āyatiṃ anuppādadhammā tamahaṃ tapassīti
vadāmi tathāgatassa kho sīha tapanīyā pāpakā akusalā
dhammā pahīnā ucchinnamūlā tālāvatthukatā anabhāvaṃ katā
āyatiṃ anuppādadhammā ayaṃ kho sīha pariyāyo yena maṃ pariyāyena sammā vadamāno vadeyya tapassī samaṇo gotamo tapassitāya dhammaṃ deseti tena ca sāvake vinetīti.
{79.8} Katamo ca sīha pariyāyo yena maṃ pariyāyena sammā vadamāno vadeyya apagabbho samaṇo gotamo apagabbhatāya
dhammaṃ deseti tena ca sāvake vinetīti . yassa kho sīha āyatiṃ gabbhaseyyā punabbhavābhinibbatti pahīnā ucchinnamūlā
tālāvatthukatā anabhāvaṃ katā āyatiṃ anuppādadhammā tamahaṃ
apagabbhoti vadāmi tathāgatassa kho sīha āyatiṃ gabbhaseyyā punabbhavābhinibbatti pahīnā ucchinnamūlā tālāvatthukatā anabhāvaṃ katā āyatiṃ anuppādadhammā ayaṃ kho sīha pariyāyo yena maṃ
pariyāyena sammā vadamāno vadeyya apagabbho samaṇo gotamo apagabbhatāya dhammaṃ deseti tena ca sāvake vinetīti. -- Sutta Pitaka Vol 4 : Sutta. Ma. Mū. {285.1} / (English translation)