If you go by the sutras, then he entered paranirvana. Some of his remains were kept, as relics. But he said to his followers not to take on anyone else as leader of the community but rather to take his words themselves, his sutras as their teacher. He had already realized cessation of dukkha as a young man when he entered nirvana, and taught the path through his life for decades. As to what paranirvana is, well he was asked if he exists, doesn’t exist, or both or neither after death and this is how he replied:
Buddha was asked if he holds any of these views:
"...'after death a Tathagata exists'...
"...'after death a Tathagata does not exist'...
"...'after death a Tathagata both exists & does not exist'...
"...'after death a Tathagata neither exists nor does not exist'
To all of those he answered
"Vaccha, the position that ''after death a Tathagata exists' is a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. It is accompanied by suffering, distress, despair, & fever, and it does not lead to disenchantment, dispassion, cessation; to calm, direct knowledge, full Awakening, Unbinding.
He uses the analogy of a fire going out and goes on to say
"Even so, Vaccha, any physical form by which one describing the Tathagata would describe him: That the Tathagata has abandoned, its root destroyed, made like a palmyra stump, deprived of the conditions of development, not destined for future arising. Freed from the classification of form, Vaccha, the Tathagata is deep, boundless, hard to fathom, like the sea. 'Reappears' doesn't apply. 'Does not reappear' doesn't apply. 'Both does & does not reappear' doesn't apply. 'Neither reappears nor does not reappear' doesn't apply.
"Any feeling... Any perception... Any fabrication...
"Any consciousness by which one describing the Tathagata would describe him: That the Tathagata has abandoned, its root destroyed, made like a palmyra stump, deprived of the conditions of development, not destined for future arising. Freed from the classification of consciousness, Vaccha, the Tathagata is deep, boundless, hard to fathom, like the sea. 'Reappears' doesn't apply. 'Does not reappear' doesn't apply. 'Both does & does not reappear' doesn't apply. 'Neither reappears nor does not reappear' doesn't apply."
In another sutra he uses the analogy of someone shot by an arrow when Malunkyaputta came to him and said he wouldn’t live the holy life until he answered questions like this:
"It's just as if a man were wounded with an arrow thickly smeared with poison. His friends & companions, kinsmen & relatives would provide him with a surgeon, and the man would say, 'I won't have this arrow removed until I know whether the man who wounded me was a noble warrior, a brahman, a merchant, or a worker.' He would say, 'I won't have this arrow removed until I know the given name & clan name of the man who wounded me... until I know whether he was tall, medium, or short... until I know whether he was dark, ruddy-brown, or golden-colored... until I know his home village, town, or city... until I know whether the bow with which I was wounded was a long bow or a crossbow... until I know whether the bowstring with which I was wounded was fiber, bamboo threads, sinew, hemp, or bark... until I know whether the shaft with which I was wounded was wild or cultivated... until I know whether the feathers of the shaft with which I was wounded were those of a vulture, a stork, a hawk, a peacock, or another bird... until I know whether the shaft with which I was wounded was bound with the sinew of an ox, a water buffalo, a langur, or a monkey.' He would say, 'I won't have this arrow removed until I know whether the shaft with which I was wounded was that of a common arrow, a curved arrow, a barbed, a calf-toothed, or an oleander arrow.' The man would die and those things would still remain unknown to him.
He ends it by saying.
"So, Malunkyaputta, remember what is undeclared by me as undeclared, and what is declared by me as declared. And what is undeclared by me? 'The cosmos is eternal,' is undeclared by me. 'The cosmos is not eternal,' is undeclared by me. 'The cosmos is finite'... 'The cosmos is infinite'... 'The soul & the body are the same'... 'The soul is one thing and the body another'... 'After death a Tathagata exists'... 'After death a Tathagata does not exist'... 'After death a Tathagata both exists & does not exist'... 'After death a Tathagata neither exists nor does not exist,' is undeclared by me.
"And why are they undeclared by me? Because they are not connected with the goal, are not fundamental to the holy life. They do not lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are undeclared by me.
"And what is declared by me? 'This is stress,' is declared by me. 'This is the origination of stress,' is declared by me. 'This is the cessation of stress,' is declared by me. 'This is the path of practice leading to the cessation of stress,' is declared by me. And why are they declared by me? Because they are connected with the goal, are fundamental to the holy life. They lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are declared by me.
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