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General relativity predicts formation of a black hole if the core material is compressed into a singularity, but the real state of such compressed baryonic matter (CBM) before an event horizon of black hole appears is not yet well understood because of the non-perturbative nature of the fundamental strong interaction. Certainly, the rump left behind after a supernova explosion could manifest as a pulsar if its mass is less than the unknown maximum mass, $M_{\\rm max}$. 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