Both the core mass function (CMF) and filament line mass function (FLMF) observed in the California GMC follow power-law distributions at the high-mass end, consistent with the Salpeter initial mass function (IMF). Current results strongly support the existence of a connection between the FLMF and the CMF/IMF, demonstrating that this connection holds at the level of an individual cloud, specifically the California GMC. The FLMF presented is a distribution of local line masses for a complete, homogeneous sample of filaments within the same cloud. It is the local line mass of a filament that defines its ability to fragment at a particular location along its spine, not the average line mass of the filament. This connection is more direct and provides tighter constraints on the origin of the CMF/IMF.