The closest things we can observe to what happens at the singularity of a black hole are neutron stars, as there’s such a fine line between them in their formation.
In neutron stars, the matter is squeezed so tightly that the atoms themselves disintegrate into their constituent particles and merge into a sort of paste, to vastly oversimplify things. It’s likely that what happens inside a black hole is similar, though probably much weirder in practice.
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