A core is a general term for one of the icosohedral objects obtained from an AI vessel.
Quantum Computer
A quantum computer (QC for short) is an object appearing almost icosohedral, and holds no special effects.
Obtained from the Edgerunner ships, and will sell on Enceladus Prime for 250 000 E$.
Singularity
A singularity appears as a blue icosohedron, and causes EMP effects and gravitational distortions, visible from it's poles. It is harder to capture than a Quantum Computer, but will reward you higher with a sell price of 1 000 000 E$ at Enceladus Prime.
Obtained from either the Hybrid ship or randomly in the rings. Touching it grants the "A Touch of Singularity" achievement.