We characterize the infall rate onto protostellar systems forming in self-gravitating radiation-hydrodynamic simulations. Using two dimensionless parameters to determine disks' susceptability to gravitational fragmentation, we infer limits on protostellar system multiplicity and the mechanism of binary formation. We show that these parameters give robust predictions even in the case of marginally resolved protostellar disks. We find that protostellar systems with radiation feedback

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... form binaries via turbulent fragmentation, not disk instability, and we predict turbulent fragmentation is the dominant channel for binary formation for low-mass stars. We clearly demonstrate that systems forming in simulations including radiative feedback have fundamentally different parameters than those in purely hydrodynamic simulations.