What is the relationship between signless samadhi, emptiness and cessation of perception & feeling?

I will analyse two discourses, the maha & cula sunnata suttas https://suttacentral.net/mn122/en/sujato https://suttacentral.net/mn121/en/sujato

I will also add some excerpts from udana 9.x, a verse appearing in khajjaniya sutta, and an excerpt from mn43

But there is this dwelling discovered by the Tathagata where, not attending to any themes, he enters & remains in internal emptiness. If, while he is dwelling there by means of this dwelling, he is visited by monks, nuns, lay men, lay women, kings, royal ministers, sectarians & their disciples, then — with his mind bent on seclusion, tending toward seclusion, inclined toward seclusion, aiming at seclusion, relishing renunciation, having destroyed those qualities that are the basis for mental fermentation — he converses with them only as much as is necessary for them to take their leave

• As i see it, the meaning here is that by means of not attending to themes [attaining cessation of perception & feeling as a turning the mind to the deathless property aka destruction of taints] Tathagata has entered into & remains in internal emptiness which is empty of the perception of the defilements of sensuality, desire to be reborn, and ignorance, iow attained nibbana with residue, arahantship, the foremost unprovoked release.

Furthermore, a mendicant—ignoring the perception of the dimension of nothingness and the perception of the dimension of neither perception nor non-perception—focuses on the oneness dependent on the signless immersion of the heart. Their mind becomes eager, confident, settled, and decided in that signless immersion of the heart. They understand: ‘Here there is no stress due to the perception of the dimension of nothingness or the perception of the dimension of neither perception nor non-perception. There is only this modicum of stress, namely that associated with the six sense fields dependent on this body and conditioned by life.’ They understand: ‘This field of perception is empty of the perception of the dimension of nothingness. It is empty of the perception of the dimension of neither perception nor non-perception. There is only this that is not emptiness, namely that associated with the six sense fields dependent on this body and conditioned by life.’ And so they regard it as empty of what is not there, but as to what remains they understand that it is present. That’s how emptiness is born in them—genuine, undistorted, and pure.

• Note that Buddha doesn't say "There is only dukkha of the oneness dependent on the signless immersion of the heart". Why is that? Because signless release is a release from all dukkha as it is attained in dependence on the signless truth & reality, namely the unmade and nothing else;

"There is, bhikkhus, a not-born, a not-brought-to-being, a not-made, a not-conditioned. If, bhikkhus, there were no not-born, not-brought-to-being, not-made, not-conditioned, no escape would be discerned from what is born, brought-to-being, made, conditioned. But since there is a not-born, a not-brought-to-being, a not-made, a not-conditioned, therefore an escape is discerned from what is born, brought-to-being, made, conditioned."

The escape from that [from the conditioned], the peaceful, beyond reasoning [ineffable?], Constant, The not-born, the unproduced, The sorrowless state that is void of stain, The cessation of states associated with suffering, The stilling of the conditioned — bliss.

• Is the signless element the same thing as the signless samadhi? No, signless samadhi refers to entering into & emerging from samadhi in dependence on the signless base, whereas the signless element is that unmade base in dependence on which one is absorbed. If there was no signless truth & reality then there would be no attainment of samadhi based on it.

"And to the monk whose mind is thus released, the devas, together with Indra, the Brahmas, & Pajapati, pay homage even from afar:

'Homage to you, O thoroughbred man. Homage to you, O superlative man — you of whom we don't know even what dependent on which you're absorbed.'"

“How many conditions are there, your reverence, for the attainment of the freedom of mind that is signless?” “There are two conditions, your reverence, for the attainment of the freedom of mind that is signless: paying no attention to any signs, and paying attention to the signless realm. These, your reverence, are the two conditions for the attainment of the freedom of mind that is signless.”

“How many conditions are there, your reverence, for the persistence of the freedom of mind that is signless?” “There are three conditions, your reverence, for the persistence of the freedom of mind that is signless: paying no attention to any signs, and paying attention to the signless realm, and a preceding preparation. These, your reverence, are the three conditions for the persistence of the freedom of mind that is signless.”

“How many conditions are there, your reverence, for emergence from the freedom of mind that is signless?” “There are the two conditions, your reverence, for emerging from the freedom of mind that is signless: paying attention to all signs, and not paying attention to the signless realm. These, your reverence, are the two conditions for emergence from the freedom of mind that is signless.”

• This is akin to turning the mind away from form, consciousness feeling, perception, sankhara and towards the deathless element.

Furthermore, a mendicant—ignoring the perception of the dimension of nothingness and the perception of the dimension of neither perception nor non-perception—focuses on the oneness dependent on the signless immersion of the heart. Their mind becomes eager, confident, settled, and decided in that signless immersion of the heart. They understand: ‘Even this signless immersion of the heart is produced by sankhara and intentions.’ They understand: ‘But whatever is produced by sankhara and intentions is impermanent and liable to cessation.’ Knowing and seeing like this, their mind is freed from the defilements of sensuality, desire to be reborn, and ignorance. When they’re freed, they know they’re freed.

• Note the entering into & emerging from the samadhi & the samadhi faculty are sankhara, these states are fabricated & willed whereas that in dependence on which one enters into & emerges is not sankhara.

• Note that it ought not be said that one enters into the unmade because the unmade is the ayatana wherein there is no coming nor going, neither a here nor there, therefore it ought to be said that one enters samadhi.

There is, bhikkhus, that base where there is no earth, no water, no fire, no air; no base consisting of the infinity of space, no base consisting of the infinity of consciousness, no base consisting of nothingness, no base consisting of neither-perception-nor-non-perception; neither this world nor another world nor both; neither sun nor moon. Here, bhikkhus, I say * there is no coming, no going, no staying, no deceasing, no uprising*. Not fixed, not movable, it has no support. Just this is the end of suffering.

• Is the signless samadhi the same thing as 'cessation of perception & feeling"? No, and neither is 'the samadhi based on the cessation of perception & feeling' the same thing as 'the cessation-principle [of perception & feeling]'.

• Is the signless property the same thing as the nirodha property in sannavedananirodha? Yes it is the same principle truth & reality by which an escape from the conditioned is discerned.

• Is sannavedananirodhasamadhi the same thing as animittosamadhi? Yes, the difference in name emphasises different aspect of the same truth & reality.

• Perception is 'perception of something', it is conjoined with feeling born of contact and always has an object which is the sign produced by attention. Cessation of perception is therefore a cessation of contact and is thus signless.

They understand: ‘Rebirth is ended, the spiritual journey has been completed, what had to be done has been done, there is no return to any state of existence.’

They understand: ‘Here there is no stress due to the defilements of sensuality, desire to be reborn, or ignorance. There is only this modicum of stress, namely that associated with the six sense fields dependent on this body and conditioned by life.’ They understand: ‘This field of perception is empty of the perception of the defilements of sensuality, desire to be reborn, and ignorance. There is only this that is not emptiness, namely that associated with the six sense fields dependent on this body and conditioned by life.’ And so they regard it as empty of what is not there, but as to what remains they understand that it is present. That’s how emptiness is born in them—genuine, undistorted, and pure.

Whatever ascetics and brahmins enter and remain in the pure, ultimate, supreme emptiness—whether in the past, future, or present—all of them enter and remain in this same pure, ultimate, supreme emptiness. So, Ānanda, you should train like this: ‘We will enter and remain in the pure, ultimate, supreme emptiness.’ That’s how you should train.”

That's how i understand it.

I am not fully sold on the commentary take on kamabhu sutta, it isn't clear that one doesn't apprehend all three characteristics

"When a monk has emerged from the cessation of perception & feeling, three contacts make contact: contact with emptiness, contact with the signless, & contact with the undirected.[3]

[3]Emptiness, the signless, & the undirected are names for a state of concentration that lies on the threshold of Unbinding. They differ only in how they are approached. According to the commentary, they color one's first apprehension of Unbinding: a meditator who has been focusing on the theme of inconstancy will first apprehend Unbinding as signless; one who has been focusing on the theme of stress will first apprehend it as undirected; one who has been focusing on the theme of not-self will first apprehend it as emptiness.

As i understand it contact is then at the mind base and the objects of ideation are the signless, emptiness, undirected, but it is not merely the ideas of it that are apprehended, it is the knowledge & vision of release which is possesed only by those who have attained it.

i have some notes from the wiki that might help. Note, these are not my experiences.

First, śūnyatā ("emptiness") can be taken three ways: "(1) as a meditative dwelling, (2) as an attribute of objects, and (3) as a type of awareness-release."

In regards to the third category - the state just after emerging from the final formless jhana, "cessation of perception and feeling" - this is said:

Emptiness, the signless, & the undirected are names for a state of concentration that lies on the threshold of Unbinding. They differ only in how they are approached. According to the commentary, they color one's first apprehension of Unbinding: a meditator who has been focusing on the theme of inconstancy will first apprehend Unbinding as signless; one who has been focusing on the theme of stress will first apprehend it as undirected; one who has been focusing on the theme of not-self will first apprehend it as emptiness.

Thag 1.92 The Verse of Arahant Vijaya corroborates:

92. All the taints in his life were destroyed. Now he doesn’t have any desire, even for food. His mind now is only focused on the meditation objects of emptiness, signlessness, and non-establishment. That monk’s Dhamma path is impossible to find, just as the paths of birds are impossible to find in the air.

hopefully, this gets you started on the right track

According to Theravadin commentaries signless release is an ariyan attainment of samadhi entailing cessation of perception & feeling and all conditioned phenomena (nibbananirodha) as a directing the mind to the Deathless.

When the Tathāgata—not attending to any theme at all, and with the cessation of certain feelings—enters & remains in the theme-less concentration of awareness, that is when his body is more at ease. - Dn16

Comy. explains this term here as referring to the fruition-attainment of arahatship (phalasamapatti), in which the Buddha becomes absorbed in the direct experience of Nibbana and no longer attends to external objects or feels mundane feelings. tipitaka/dn/dn.16.1-6.vaji.html#fn-19

Cessation attainment is a pleasure apart from the feelings of pleasure

"It may happen, Ananda, that Wanderers of other sects will be saying this: 'The recluse Gotama speaks of the Cessation of Perception and Feeling and describes it as pleasure. What is this (pleasure) and how is this (a pleasure)?'

"Those who say so, should be told: 'The Blessed One describes as pleasure not only the feeling of pleasure. But a Tathagata describes as pleasure whenever and whereinsoever it is obtained.'" - mn59

I have heard that on one occasion Ven. Sariputta was staying near Rajagaha in the Bamboo Grove, the Squirrels' Feeding Sanctuary. There he said to the monks, "This Unbinding is pleasant, friends. This Unbinding is pleasant."

When this was said, Ven. Udayin said to Ven. Sariputta, "But what is the pleasure here, my friend, where there is nothing felt?"

"Just that is the pleasure here, my friend: where there is nothing felt. - an9.34

This is essentially the same eventuality as here

“Whatever exists therein of material form, feeling, perception, formations, and consciousness, he sees those states as impermanent, as suffering, as a disease, as a tumour, as a barb, as a calamity, as an affliction, as alien, as disintegrating, as void, as not self. He turns his mind away from those states and directs it towards the deathless element thus: ‘This is the peaceful, this is the sublime, that is, the stilling of all formations, the relinquishing of all attachments, the destruction of craving, dispassion, cessation, Nibbāna.’

Not giving attention to all signs is essentially a turning away from all conditioned dhammā because dhammā come into being through attention

They come into being through attention. - an10.58

This is the commentarial Theravada interpretation.

Note that according to the commentaries the Animittacetovimutti is not the same thing as Animittanupassana. This is very important because nowadays many people confuse these two and explain signless samadhi as contemplation of the signless.

Here i quote Mahasi Sayadaw's Manual of Insight to present the classical comy interpretation, although here merely in part as i will leave out the path attainments focusing only on fruition.

Contemplation of the signless (animittānupassanā) is actually the same as contemplation of impermanence, as I explained in the summary above. Nevertheless, this different term should be defined, so I will explain it in brief. “Sign” (nimitta) means the sign of conditioned phenomena or formations.808 “The sign of conditioned phenomena” (saṅkhāranimitta) refers to phenomena that seem to be solid [to a nonmeditator] due to the concepts of solidity of mass and so on. But the sign of conditioned phenomena appears [to a meditator] due to the discernment and separation of their individual functions and so on. Bodily activities and movements that are conditioned physical phe- nomena—such as walking, standing, sitting, lying, bending, stretching, and so on—conditioned mental phenomena—such as seeing, hearing, smelling, tasting, touching, thinking, and so on—and the objects that appear at the six sense doors—such as visible form, sound, smell, taste, touch, and mental objects—do not appear to be mere activities and phe- nomena, or to be distinct from each other, or to only exist momentarily. Actually, they appear to have solid forms, to be one single entity, and to be permanent. This concept of solidity is also referred to as “the sign of permanence,” “the sign of stability” (dhuvanimitta), or “the sign of eternity” (sassatanimitta). Contemplation of impermanence, which sees conditioned phenomena as impermanent, is called “the signless” because it is opposite to the sign of permanence, the sign of stability, and the sign of eternity. It is called “contemplation” because it observes impermanence. When we compound the two terms we have “contemplation of the signless,” which means to observe the opposite of the signs of solidity in conditioned phenomena. When one constantly observes mental and physical phenomena at the time of their occurrence, the conditioned phenomena that arise at the six sense doors do not appear to have solid forms, to be one single entity, to be permanent, or to be enduring and stable. Actually they appear to be mere activities and phenomena, to be different from each other, to only exist momentarily, and to disappear a moment after they have arisen. Because they appear in this way when one attains insight knowledge of dissolution, one sees conditioned phenomena as disappearing, ending, being destroyed, vanishing, or impermanent. When one sees conditioned phenomena this way, they cannot appear as permanent and solid entities, and the defilements that develop based on seeing things to be permanent and solid can no longer arise. Because one can abandon the sign of solidity in conditioned phenomena, the Visuddhimagga says:

Thus it is called the signless, because the sign of permanence, the sign of stability, and the sign of eternity are abandoned after breaking through the concept of solidity by means of contem- plation of impermanence.810

If one uninterruptedly observes the signs of conditioned phenomena, each of the different functions of these conditioned phenomena will become apparent. Not only this, but their unique characteristics, their momentariness, and their objects (in the case of mental conditioned phe- nomena), will become apparent. For a detailed description of how they appear see the section dealing with the four types of concept of solidity under the heading “Contemplation of not-self.” The way conditioned phenomena appear when one is distinguishing between their function, characteristic, momentariness, and object is the sign of conditioned phenomena. When one can distinguish them by means of their function, characteristic, momentariness, and object, one sees these signs of conditioned phenomena and takes them as one’s object at the same time. Thus contemplation of impermanence is neither the opposite of the signs of conditioned phenomena nor is it able to be free of them. This is why this contemplation is called contemplation of the signless: because it is the opposite of the signs of solidity (permanence, stability, and eternity) in conditioned phenomena and because its object is free from these signs of solidity in conditioned phenomena. When contemplation of the signless, which is contemplation of imper- manence, is well established, conditioned phenomena only appear by means of the nature of their dissolution. As a result, one will rightly understand the signs of conditioned phenomena that previously appeared to be solid and lasting entities.

Here as to animittacetovimutti as fruition attainment of cessation (nirodhasamapatti) aka phalasamapatti.

Entering the attainment of fruition

Friend, there are two conditions for the attainment of the sign- less deliverance of mind698: non-attention to all signs and atten- tion to the signless element. These are the two conditions for the attainment of the signless deliverance of mind.699

The procedure for entering the state of attainment of fruition is as follows: A noble disciple who seeks to attain fruition retreats to a solitary place and observes conditioned phenomena. Beginning from knowledge of arising and passing away, one should develop the various insights until the change-of-lineage that takes a condi- tioned phenomenon as its object arises. Immediately afterward, one’s mind will enter the state of cessation [of conditioned phe- nomena] in the form of the attainment of fruition. In this case, only the fruition consciousness arises, rather than a new path consciousness, even if one is still a trainee, [that is, one who has attained one of the first three stages of enlightenment]. This is because the mind has previously determined to enter the attain- ment of fruition.700 Note that the Visuddhimagga here refers to the [peak] insight that takes a conditioned phenomenon as its object as “change-of-lineage.” This is based on the description given in the Paṭisambhidāmagga. However, this insight is called “insight knowledge of adaptation” in the Paṭṭhāna [and is referred to by that name in this book]. Based on the above passage, understand that a noble person begins his or her insight practice from insight knowledge of arising and passing away. That is, if a noble disciple practices insight, he or she is immediately able to see phenomena arising and passing away. Thus in order to enter the attainment of fruition, one is able to develop the sequence of insight knowledges quite rapidly, quickly moving from insight knowledge of arising and pass- ing away to insight knowledge of equanimity toward phenomena in due course. If the noble one has previously made the determination to become absorbed in fruition, and his or her insight knowledge of equanimity toward phenomena is mature, it is then followed by the insight knowledge of adaptation that leads directly to the cessation of the conditioned phe- nomena that she or he has been observing.

As you can see according to the classical commentary tradition the nirodha attainment is the signless samadhi.

Afaik, when spoken of as a cessation-extinguishment attainment it is said that one surmounts the other ayatanas (eg the base of neither perception nor non- perception) whereas when spoken of as the signless release it is said that one ignores the other ayatanas, that is the only difference.

All things in dhamma are elements (dhatu; MN 115). MN 115 summarises all elements into two types: (i) conditioned element (saṅkhatādhātu); and (ii) unconditioned element (asaṅkhatādhātu). The unconditioned element, namely, Nibbana, is permanent (SN 43.14-43). Also, the laws of nature such as anatta/not-self are 'fixed' thus permanent (ṭhitāva sā dhātu dhammaṭṭhitatā; AN 3.136), which also includes 'sunnata' (described in SN 35.85).

The signless element (animittāya ca dhātuyā) is found in MN 43 as one of five types of liberation of mind. However MN 43 says, in itself, the signless is not the supreme or unprovoked liberation of mind, which is the mind empty of greed, hate & delusion.

Signless samadhi (animitte cetosamādhimhi) is mentioned in MN 121. Obviously it means concentration on the signless element.

There is no inherent relationship between the 'signless samadhi/signless property' and 'emptiness' & 'the cessation of perception & feeling'.

Based on MN 121, signless samadhi is a way to gradually come to realise emptiness. However, the signless element, itself, is not emptiness. MN 121 says the signless samadhi is mentally formed by intention and subject to impermanence & cesssation (yaṁ kho pana kiñci abhisaṅkhataṁ abhisañcetayitaṁ tadaniccaṁ nirodhadhamman’ti) and realising this about the signless element results in attaining Nibbana via the ending of [signless & all other] becoming & ignorance. Therefore, MN 121 refers to the "supreme emptiness" (paramānuttaraṁ suññataṁ) as when the fermentations (asava) of sensuality, becoming & ignorance are not present. In other words, the signless samadhi can be a type of becoming (bhava), namely, an arupabhava.

The same applies to the cessation of perception & feeling. It is conditioned, impermanent & subject to cessation, therefore it is not emptiness/sunnata or Nibbana, which are permanent.

MN 44 mentions when the mind emerges from the cessation of perception & feeling, it first experiences emptiness & then the signless. However, apart from this, these three phenomena are not the same.

MN 122 contains the vague statement: "The Realized One woke up to this meditation, namely, to enter and remain in emptiness internally by not focusing on any signs." This can only mean the Buddha used the signless to help realize emptiness (of self), as explained in MN 121. It cannot mean the signless & emptiness are the same things because they are not, per the other suttas and per basic Dhamma principles.

In summary, a Buddha or Arahant (for their entire remaining lifetime) permanently has the perception of emptiness (absence of self; refer to SN 35.85) towards all things & experiences. However, the cessation of perception & feeling and the signless can never be a permanent abiding for a Buddha or Arahant. This is why these two conditioned impermanent states are not emptiness.

To add: DN 16 offers an example of the Buddha temporarily entering the signless concentration:

Sometimes the Realized One, not focusing on any signs, and with the cessation of certain feelings, enters and remains in the signless immersion of the heart. Only then does the Realized One’s body become more comfortable.

Yasmiṁ, ānanda, samaye tathāgato sabbanimittānaṁ amanasikārā ekaccānaṁ vedanānaṁ nirodhā animittaṁ cetosamādhiṁ upasampajja viharati, phāsutaro, ānanda, tasmiṁ samaye tathāgatassa kāyo hoti.

To add, also a footnote to DN 16 by the translator:

The suttas say little about this meditation state. Its defining characteristic is that consciousness does not “follow after signs” (nimittānusāri viññāṇaṁ, eg. AN 6.13:5.3). This is explained in MN 138:10.2 as not being distracted or affected by the features of sense impressions. The mental unification (ekattaṁ) based on this practice is listed after the form (and formless) jhānas, so it is very advanced. It is nonetheless a conditioned state (MN 121:11.4), so it is possible that a mendicant might fall from it and disrobe (AN 6.60:8.10). However it may also be used to describe the meditation of an arahant (SN 41.7:6.12). It seems that the Buddha [in DN 16] relied on his mastery of this practice to focus attention away from the pain in his body.