This gave confirmation that we understand what is going on. The core of the star remains. It is made almost exclusively of neutrons, and held up by the degeneracy pressure of the neutrons. Like white dwarfs, the more massive neutron stars are, the smaller they are. Note these stars are typically 10-15 km in radius.
Density is unbelievable - typically one quadrillion times that of water.
This means that a cubic centimeter weighs as much as a mountain. Neutron stars have a Chandrasekhar mass too. Probably bigger - in the range 1.5 to 2 Solar masses. Neutron stars probably spin about 1000 times a second when they are first born. Magnetic field gets concentrated by the shrinking.