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That's not a core, that's hard core.
It can burn a hole in the space-time continuum fabric.
should be okay up to about 1.36 × 10^50 bits per second per kilogram (as per Bremmerman's limit)
However cache memory would be limited by the Bekenstein bound - assuming a spherical cpu, approximately 2.57 x 10^43 x mR bits (m is the mass of the system in kilograms, R is radius expressed in meters.)
Information density exceeding this limit would indeed cause the system to collapse into a black hole.