How Do We Know That Pulsars Must Be Neutron Stars

How do we know that pulsars must be neutron stars?

A) Pulsars have the same upper mass limit as neutron stars do.
B) Telescopic images of pulsars and neutron stars look exactly the same.
C) No massive object, other than a neutron star, could spin as fast as we observe pulsars to spin and remain intact.
D) We have observed massive- star supernovae produce pulsars.
E) This is only a theory that has not yet been confirmed by observations.

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