user23662: This seems to be a very baffling Sutta passage where he describes a seemingly contradictory state where one is in a special Samadhi beyond neither perception nor non perception but is still percipient.
What is this Samadhi attainment called?
AN 10.7

Then Ven. Ananda went to Ven. Sariputta and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there, he said to Ven. Sariputta, "Friend Sariputta, could a monk have an attainment of concentration such that he would neither be percipient of earth with regard to earth, nor of water with regard to water, nor of fire... wind... the dimension of the infinitude of space... the dimension of the infinitude of consciousness... the dimension of nothingness... the dimension of neither perception nor non-perception... this world... nor of the next world with regard to the next world, and yet he would still be percipient?"
"Yes, friend Ananda, he could..."
"But how, friend Sariputta, could a monk have an attainment of concentration such he would neither be percipient of earth with regard to earth... nor of the next world with regard to the next world, and yet he would still be percipient?"
"Once, friend Ananda, when I was staying right here in Savatthi in the Blind Man's Grove, I reached concentration in such a way that I was neither percipient of earth with regard to earth... nor of the next world with regard to the next world, and yet I was still percipient."
"But what, friend Sariputta, were you percipient of at that time?"
"'The cessation of becoming — Unbinding — the cessation of becoming — Unbinding': One perception arose in me, friend Ananda, as another perception ceased. Just as in a blazing woodchip fire, one flame arises as another flame ceases, even so, 'The cessation of becoming — Unbinding — the cessation of becoming — Unbinding': One perception arose in me as another one ceased. I was percipient at that time of 'The cessation of becoming — Unbinding.'"


user2282: 
This seems to be a very baffling Sutta passage where he describes a seemingly contradictory state where one is in a special Samadhi beyond neither perception nor non perception but is still percipient. What is this Samadhi attainment called?

It does seem baffling because this state is only available to those who already attained one of the four Paths, according to the Commentary:

Mp identifies this with the concentration of fruition attainment (phalasamapattisamadhi). This attainment is not the fruition that occurs for a few moments immediately following the path, but a special meditative state accessible only to those who have already attained one of the four paths and its subsequent fruition. The attainment, as shown in this sutta, does not take any of the mundane, conditioned meditation objects as its support; its support is the unconditioned nibbana, experienced directly and immediately. The commentaries hold that this attainment is graded as fourfold according to the four stages of realization (from stream-entry to arahantship).


user8157: AN 10.7 appears to literally say the perception is of Nibbana (Unbinding).

But what, friend Sariputta, were you percipient of at that time?"
"'The cessation of becoming — Unbinding — the cessation of becoming —
Unbinding': One perception arose in me, friend Ananda, as another
perception ceased. Just as in a blazing woodchip fire, one flame
arises as another flame ceases, even so, 'The cessation of becoming —
Unbinding — the cessation of becoming — Unbinding': One perception
arose in me as another one ceased. I was percipient at that time of
'The cessation of becoming — Unbinding.'"

Ud 8.1 defines Nibbana as follows:

There is, bhikkhus, that base [ayatana; sense object] 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.


23662: <p>This seems to be a very baffling Sutta passage where he describes a seemingly contradictory state where one is in a special Samadhi beyond neither perception nor non perception but is still percipient.
What is this Samadhi attainment called?</p>
<p><a href="https://www.accesstoinsight.org/tipitaka/an/an10/an10.007.than.html" rel="nofollow noreferrer">AN 10.7</a></p>
<blockquote>
<p>Then Ven. Ananda went to Ven. Sariputta and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings &amp; courtesies, he sat to one side. As he was sitting there, he said to Ven. Sariputta, &quot;Friend Sariputta, could a monk have an attainment of concentration such that he would neither be percipient of earth with regard to earth, nor of water with regard to water, nor of fire... wind... the dimension of the infinitude of space... the dimension of the infinitude of consciousness... the dimension of nothingness... the dimension of neither perception nor non-perception... this world... nor of the next world with regard to the next world, and yet he would still be percipient?&quot;
&quot;Yes, friend Ananda, he could...&quot;
&quot;But how, friend Sariputta, could a monk have an attainment of concentration such he would neither be percipient of earth with regard to earth... nor of the next world with regard to the next world, and yet he would still be percipient?&quot;
&quot;Once, friend Ananda, when I was staying right here in Savatthi in the Blind Man's Grove, I reached concentration in such a way that I was neither percipient of earth with regard to earth... nor of the next world with regard to the next world, and yet I was still percipient.&quot;
&quot;But what, friend Sariputta, were you percipient of at that time?&quot;
&quot;'The cessation of becoming — Unbinding — the cessation of becoming — Unbinding': One perception arose in me, friend Ananda, as another perception ceased. Just as in a blazing woodchip fire, one flame arises as another flame ceases, even so, 'The cessation of becoming — Unbinding — the cessation of becoming — Unbinding': One perception arose in me as another one ceased. I was percipient at that time of 'The cessation of becoming — Unbinding.'&quot;</p>
</blockquote>
 2282: <blockquote>
<p>This seems to be a very baffling Sutta passage where he describes a seemingly contradictory state where one is in a special Samadhi beyond neither perception nor non perception but is still percipient. What is this Samadhi attainment called?</p>
</blockquote>
<p>It does seem baffling because this state is only available to those who already attained one of the four Paths, according to the Commentary:</p>
<blockquote>
<p>Mp identifies this with the concentration of fruition attainment (phalasamapattisamadhi). This attainment is not the fruition that occurs for a few moments immediately following the path, but a special meditative state accessible only to those who have already attained one of the four paths and its subsequent fruition. The attainment, as shown in this sutta, does not take any of the mundane, conditioned meditation objects as its support; its support is the unconditioned nibbana, experienced directly and immediately. The commentaries hold that this attainment is graded as fourfold according to the four stages of realization (from stream-entry to arahantship).</p>
</blockquote>
 8157: <p>AN 10.7 appears to literally say the perception is of Nibbana (Unbinding).</p>
<blockquote>
<p>But what, friend Sariputta, were you percipient of at that time?&quot;</p>
<p>&quot;'The cessation of becoming — Unbinding — the cessation of becoming —
Unbinding': One perception arose in me, friend Ananda, as another
perception ceased. Just as in a blazing woodchip fire, one flame
arises as another flame ceases, even so, 'The cessation of becoming —
Unbinding — the cessation of becoming — Unbinding': One perception
arose in me as another one ceased. I was percipient at that time of
'The cessation of becoming — Unbinding.'&quot;</p>
</blockquote>
<p><a href="https://www.accesstoinsight.org/tipitaka/kn/ud/ud.8.01.irel.html" rel="nofollow noreferrer">Ud 8.1</a> defines Nibbana as follows:</p>
<blockquote>
<p>There is, bhikkhus, that base [<em>ayatana</em>; sense object] 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.</p>
</blockquote>
