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It is shown that the Di\'osi-Penrose criterion of gravity-induced quantumcollapse may be inconsistent with the discreteness of space-time, which isgenerally considered as an indispensable element in a complete theory ofquantum gravity. Moreover, the analysis also suggests that the discreteness ofspace-time may result in rapider collapse of the superposition of energyeigenstates than required by the Di\'osi-Penrose criterion.

On Di\'osi-Penrose criterion of gravity-induced quantum collapse