How does Theravada practice to obtain the direct knowledge of anatta?

In this comment it is stated that the Pali Suttas contain the correct method for manifesting direct knowledge of anatta.

The method to attain direct knowledge of anatta is to make the mind quiet (samadhi) so "self" thoughts diminish & also disappear. When this occurs, at the same time, the aggregates such as breathing/body, feelings of rapture, mental defilements and consciousness will be seen directly to be merely those elements/dhatu (breathing, body, feelings, defilements, consciousness, etc).

Its like observing a computer. It can be easily seen there is no 'self' in a computer; that a computer is just metal, plastic, paint, wires, glass, etc.

I agree, but I wonder what Theravada adherents would regard as the precise suttas that definitively explain?

The Eightfold Path explains, namely, abandoning wrong thoughts (2nd factor); abandoning covetousness & distress (7th factor); abandoning unwholesome and developing wholesome/supramundane (6th factor); developing samadhi (8th factor), which makes subtle thoughts naturally disappear. When samadhi develops by "letting go" (SN 48.10), direct knowledge of anatta occurs without an act of will (AN 11.2).

In particular, is SN 5.10 included: “Why do you believe there’s such a thing as a ‘sentient being’? Māra, is this your theory? This is just a pile of conditions, you won’t find a sentient being here.

The above is just intellectual. It might help abandon self-thoughts but it takes a prolonged cleansing of self-thoughts for direct knowledge of anatta to arise towards everything.

When the parts are assembled we use the word ‘chariot’. So too, when the aggregates are present ‘sentient being’ is the convention we use.

This is just intellectual, again. It is the words of an arahant disciple to the evil Mara who believes "a being" is an thing rather than merely a "view".

Dependent Origination explains in its 11th condition about the "birth" ("jati") of these views or ideas or superstitions of "a being".

"A being" is also explained in SN 23.2; as merely an idea born from craving & attachment. In other words, there are no such thing as "sentient beings" apart from views, concepts & ideas.

This is what Venerable Sariputta teaches Yamaka in SN 22.85; that a Tathagata is not a "sentient being" that "dies" or that is "annihilated".

But it’s only suffering that comes to be, lasts a while, then disappears. Naught but suffering comes to be, naught but suffering ceases.”

The arising of the idea of "a being" (SN 5.10) or "self" (SN 12.15) is merely the arising of suffering; born from craving & ignorant contact (SN 22.81).

I ask because the Analysis of the Chariot expounded by Chandrakirti is highly praised as one of the best methods for quickly using analysis to confirm that things lack inherent nature.

No. This is wrong. If the Analysis of the Chariot expounded in SN 5.10 was the best method for quickly realising anatta then Mara in SN 5.10 would have realised anatta.

It is said that conducting this analysis in meditation when combined with serenity meditation is the method to achieve the direct knowledge of anatta.

No. AN 11.2 says the method to achieve the direct knowledge occurs without an act of will. The very craving to analyze the aggregates itself produces "self".

The "self" cannot realise "anatta" by engaging in intellectual Mahayana analysis. The "self" must be subsumed with samadhi. Analytical analysis alone won't work.

In the Pali suttas, the intellectual analytical analysis is called YONISO MANASIKARA, which is used preliminary to the Path.

Just as the chariot lacks an inherent nature of "chariot" and is merely a convention, just so the person lacks inherent nature and is merely a convention.

The above is merely intellectual. The realisation of anatta in confirmed when all craving and all defilements are destroyed in the mind. The realisation of anatta results in the IMPOSSIBILITY of suffering ever occurring again.

So is this a Sutta upon which Theravada agrees as source for the analysis necessary to manifesting direct knowledge of anatta?

No. Theravada does not agree with Mahayana.

How about the conversation between the Arahant Nagasena and the King?

There is no evidence Nagasena was an arahant because he says many wrong things that even a child can refute.

In this answer you wrote that, according to Mahayana,

What is an Arya being? Someone who has directly perceived emptiness in a completely unmistaken and non-conceptual way while in meditative equipoise.

My opinion is that, per the Pali suttas, people tend to "enter the stream" at a time when they must have been aware of all three characteristics (i.e. dukkha and anicca as well as anatta).

For example, there's the story of Skinny Gotami -- who is (if I can paraphrase) looking for the atta of her dead son -- from doing which she gains insight into her own (its saying "confirmed in the fruit of stream-entry" implies she has abandoned sakkaya ditthi).

Or from the comment which you quoted, which said:

Actually, a conceptual understanding of anatta is insufficient in Theravada. One has to "see it through wisdom" using vipassana. This is explained in the Khemaka Sutta (SN 22.89).

I didn't understand that comment's saying One has to "see it through wisdom" using vipassana but the SN 22.89 (which it references) starts with,

And at that time Ven. Khemaka was staying at the Jujube Tree Park, diseased, in pain, severely ill.

I am not getting better, my friend. I am not comfortable. My extreme pains are increasing, not lessening. There are signs of their increasing, and not of their lessening.

IOW I think that means he's dying.

Perhaps this (i.e. saying that you see all three characteristics) is consistent with doctrine too -- since "doubt about the dhamma" is also associated with stream entry, and the dhamma includes "the three characteristics".

Also since self-view is a cause of (or associated with, or conditions, gives rise to) dukkha, you may perceive self-view if and when you perceive dukkha -- and conversely perceive anatta when you perceive non-dukkha.

So is this a Sutta upon which Theravada agrees as source for the analysis necessary to manifesting direct knowledge of anatta?

I don't think "direct knowledge" comes only from reading any sutta. The suttas (and/or the Dhamma) may be needed to explain experience, to describe experience, to guide practice.

Remember that for what it's worth a "human" birth is said to be more propitious/conducive to enlightenment than birth in a higher (i.e. less suffering) realm.

What is the precise method for generating direct knowledge as opposed to mere conceptual or inferential understanding?

I'm not sure there's a single "precise method":

I learned 82,000 from the Buddha,
And 2,000 from the monks;
These 84,000
Are the teachings I have memorized.

— the Venerable Ananda, in Theragatha 17.3

The four noble truths, perhaps; or compassion.

A sentient being is not the same as the self. Please see this answer which explains why plants are not sentient beings, unlike animals. "Sentient beings" is the convention used to denote the presence of the five aggregates.

So is this a Sutta upon which Theravada agrees as source for the analysis necessary to manifesting direct knowledge of anatta? Are there other Suttas which take precedence?

Conversations between Nagasena and the king (Milindapanha) is not part of the Pali Canon. So, it is considered a secondary text.

My favourite sutta on the self is the Vina Sutta (SN 35.205):

"Suppose there were a king or king's minister who had never heard the sound of a lute before. He might hear the sound of a lute and say, 'What, my good men, is that sound — so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling?' They would say, 'That, sire, is called a lute, whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' Then he would say, 'Go & fetch me that lute.' They would fetch the lute and say, 'Here, sire, is the lute whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' He would say, 'Enough of your lute. Fetch me just the sound.' Then they would say, 'This lute, sire, is made of numerous components, a great many components. It's through the activity of numerous components that it sounds: that is, in dependence on the body, the skin, the neck, the frame, the strings, the bridge, and the appropriate human effort. Thus it is that this lute — made of numerous components, a great many components — sounds through the activity of numerous components.'

"Then the king would split the lute into ten pieces, a hundred pieces. Having split the lute into ten pieces, a hundred pieces, he would shave it to splinters. Having shaved it to splinters, he would burn it in a fire. Having burned it in a fire, he would reduce it to ashes. Having reduced it to ashes, he would winnow it before a high wind or let it be washed away by a swift-flowing stream. He would then say, 'A sorry thing, this lute — whatever a lute may be — by which people have been so thoroughly tricked & deceived.'

"In the same way, a monk investigates form, however far form may go. He investigates feeling... perception... fabrications... consciousness, however far consciousness may go. As he is investigating form... feeling... perception... fabrications... consciousness, however far consciousness may go, any thoughts of 'me' or 'mine' or 'I am' do not occur to him."

Using a musical instrument you can play nice music. But if you break it down to its constituent parts, you cannot find music. Music cannot be isolated from the musical instrument. Similarly, the self arises from the inter-working of the five aggregates. You cannot isolate the self from the five aggregates.

Perhaps, you can look at it in this way: The musical instrument is the sentient being. The music coming out of the musical instrument is the self. The musical instrument is composed of various parts which are analogous to the five aggregates. When these parts work together, they make music. The way they work together is dependent origination.

I think the dependent origination of the Pali Suttas are more complex than a mere assembly of parts. It describes a far more complex interaction. The Buddha stated that if you understand dependent origination, you understand the Dhamma in MN 28.

The Upanisa Sutta (SN 12.23) describes dependent origination and also the path to understanding it using the water flow allegory - this is more like a chain of processes where each link in the chain depends on each other - it's not an assembly of parts:

"Just as when the gods pour rain in heavy drops & crash thunder on the upper mountains: The water, flowing down along the slopes, fills the mountain clefts & rifts & gullies. When the mountain clefts & rifts & gullies are full, they fill the little ponds. When the little ponds are full, they fill the big lakes. When the big lakes are full, they fill the little rivers. When the little rivers are full, they fill the big rivers. When the big rivers are full, they fill the great ocean. In the same way:

"Fabrications have ignorance as their prerequisite, consciousness has fabrications as its prerequisite, name-&-form has consciousness as their prerequisite, the six sense media have name-&-form as their prerequisite, contact has the six sense media as its prerequisite, feeling has contact as its prerequisite, craving has feeling as its prerequisite, clinging has craving as its prerequisite, becoming has clinging as its prerequisite, birth has becoming as its prerequisite, stress & suffering have birth as their prerequisite

Conviction has stress & suffering as its prerequisite. Joy has conviction as its prerequisite, rapture has joy as its prerequisite, serenity has rapture as its prerequisite, pleasure has serenity as its prerequisite, concentration has pleasure as its prerequisite, knowledge & vision of things as they actually are present has concentration as its prerequisite, disenchantment has knowledge & vision of things as they actually are present as its prerequisite, dispassion has disenchantment as its prerequisite, release has dispassion as its prerequisite, knowledge of ending has release as its prerequisite."

Another description of the dependent origination based on the allegory of reeds leaning on each other from the Sheaves of Reeds Sutta (SN 12.67) - this is also not an assembly of parts:

"Very well then, Kotthita my friend, I will give you an analogy; for there are cases where it is through the use of an analogy that intelligent people can understand the meaning of what is being said. It is as if two sheaves of reeds were to stand leaning against one another. In the same way, from name-&-form as a requisite condition comes consciousness, from consciousness as a requisite condition comes name-&-form. From name & form as a requisite condition come the six sense media. From the six sense media as a requisite condition comes contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of suffering & stress.

"If one were to pull away one of those sheaves of reeds, the other would fall; if one were to pull away the other, the first one would fall. In the same way, from the cessation of name-&-form comes the cessation of consciousness, from the cessation of consciousness comes the cessation of name-&-form. From the cessation of name-&-form comes the cessation of the six sense media. From the cessation of the six sense media comes the cessation of contact. From the cessation of contact comes the cessation of feeling. From the cessation of feeling comes the cessation of craving. From the cessation of craving comes the cessation of clinging/sustenance. From the cessation of clinging/sustenance comes the cessation of becoming. From the cessation of becoming comes the cessation of birth. From the cessation of birth, then aging & death, sorrow, lamentation, pain, distress, & despair all cease. Such is the cessation of this entire mass of suffering & stress."

What is the precise method for generating direct knowledge as opposed to mere conceptual or inferential understanding?

From the Kimsuka Sutta (SN 35.204):

"Suppose, monk, that there were a royal frontier fortress with strong walls & ramparts and six gates. In it would be a wise, experienced, intelligent gatekeeper to keep out those he didn't know and to let in those he did. A swift pair of messengers, coming from the east, would say to the gatekeeper, 'Where, my good man, is the commander of this fortress?' He would say, 'There he is, sirs, sitting in the central square.' The swift pair of messengers, delivering their accurate report to the commander of the fortress, would then go back by the route by which they had come. Then a swift pair of messengers, coming from the west... the north... the south, would say to the gatekeeper, 'Where, my good man, is the commander of this fortress?' He would say, 'There he is, sirs, sitting in the central square.' The swift pair of messengers, delivering their accurate report to the commander of the fortress, would then go back by the route by which they had come.

"I have given you this simile, monk, to convey a message. The message is this: The fortress stands for this body — composed of four elements, born of mother & father, nourished with rice & barley gruel, subject to constant rubbing & abrasion, to breaking & falling apart. The six gates stand for the six internal sense media. The gatekeeper stands for mindfulness. The swift pair of messengers stands for tranquillity (samatha) and insight (vipassana). The commander of the fortress stands for consciousness. The central square stands for the four great elements: the earth-property, the liquid-property, the fire-property, & the wind-property. The accurate report stands for Unbinding (nibbana). The route by which they had come stands for the noble eightfold path: right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration."

I think the above quote should be self-explanatory. Also, please see the Upanisa Sutta quote above, which I quote again below:

Conviction has stress & suffering as its prerequisite. Joy has conviction as its prerequisite, rapture has joy as its prerequisite, serenity has rapture as its prerequisite, pleasure has serenity as its prerequisite, concentration has pleasure as its prerequisite, knowledge & vision of things as they actually are present has concentration as its prerequisite, disenchantment has knowledge & vision of things as they actually are present as its prerequisite, dispassion has disenchantment as its prerequisite, release has dispassion as its prerequisite, knowledge of ending has release as its prerequisite."

Well the goal of the practice is not the direct knowledge of anatta. That already does not bode well. The goal of the practice for the puthujjana is the nibbidā, which is the disenchantment, the viraga, the dispassion, and the nibbana which is the cessation of dukkha.

The disciple must always have sati, which is having in mano and ideally in the citta the teaching and if there is only one paragraph to remember is the famous sequence that what is annica is dukkha, what is dukkha is anatta, what is anatta is worthy of disappointment and once there is disappointment or dispassion there is the cessation of dukkha and its knowledge. The few puthujjanas who are obsessed with atta and anatta and atman do not talk about the end of the sequence. Their usual sequence is what is anicca is dukkha, what is dukkha is anatta and they stop here. Just like The Anatta-lakkhana Sutta where the conclusion is

"O monks, the well-instructed noble disciple, seeing thus, gets wearied of form, gets wearied of feeling, gets wearied of perception, gets wearied of mental formations, gets wearied of consciousness. Being wearied he becomes passion-free. In his freedom from passion, he is emancipated. Being emancipated, there is the knowledge that he is emancipated. He knows: 'birth is exhausted, lived is the holy life, what had to be done is done, there is nothing more of this becoming.'"

And the usual way to go beyond understanding annica, which is called Aniccānupassī, is precisely the method of the anapanasati sutta. The beginning is the usual rise of samadhi for the citta and calming all the Shankaras that are still here. Just like for the jahnas. This is as far as a puthujana go without the teaching.

Of course, for the good puthujjanas, they want to go beyond the usual samadhi and want to stop being puthujjanas. Once the citta has samadhi or is in samadhi, then it is time to Aniccānupassī, which again means "deeply see impermanence" so it is the vipassana that so many puthujjanas crave and manage to claim they got and do.

Now the sutta does not talk about dukkha and anatta of the sequence, since that's not really the goal, and jump form the annica to the goal, which is the Virāgānupassī, meaning the dispassion, and paṭinissaga, which is the "rejection of the things" and that's nibanna.

So again, the disciple begins with sati, but of course sati is not really an action. What is done for and with the rise of sati and the development of sati is the anapanasati or the Satipatṭhāna. THe easiest way to have sati is the be around good people and to avoid bad people. The good people are the kalyāṇamitta who are the good friends meaning they show sagacity for the dhamma and do not cause drama over material things and rules, conventions and norms.

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.

There's no cutting corners nor shortcuts in Theravada. SN 5.10 speaks the truth. But to actually attain direct knowledge to this truth as opposed to mere conceptual understanding, one has to perfect the Gradual trainings of Sila-Samadhi-Panna, which Ven. Bodhi did a great job of explaining in his "Noble Eightfold Path". And to each aspect of the gradual trainings, there are many different suttas one'd need to read, study, contemplate, and put into practice (ie: for Sila: AN 8.39-43, 3.70, Sn 2.4, SN 3.5; for Samadhi: Anapanasati Sutta, Satipatthana Sutta; for Panna: MN 43, AN 8.2, AN 3.73, AN 7.6, and many more as detailed in Ven. Bodhi's "In the Buddha's Words"). There're no shortage of teachers in the world who can eloquently speak at great length about all the ins and outs of anatta/shunyata and stuff. But when facing some young voluptuous beautiful women, some title, some power, some cash, etc. then the number start dropping like flies! Why? Because they're the experts of Anatta who fail the basics of Sila-Samadhi-Panna.