  Recent studies suggest that filamentary structures are representative of the
initial conditions of star formation in molecular clouds and support a filament
paradigm for star formation, potentially accounting for the origin of the
stellar initial mass function (IMF). Using Herschel imaging observations of the
California giant molecular cloud, we aim to further investigate the filament
paradigm for low- to intermediate-mass star formation and to better understand
the exact role of filaments in the origin of stellar masses. Using the
multiscale, multiwavelength extraction method getsf, we identify starless
cores, protostars, and filaments in the Herschel data set and separate these
components from the background cloud contribution to determine accurate core
and filament properties. Both the prestellar core mass function (CMF) and the
distribution of filament masses per unit length or filament line mass function
(FLMF) are consistent with power-law distributions at the high-mass end,
$\Delta N/\Delta {\rm log}M\propto M^{-1.4 \pm 0.2}$ at $M > 1\,M_\odot$ for
the CMF and $\Delta N/\Delta {\rm log} {M}_{\rm line} \propto {M}_{\rm
line}^{-1.5\pm0.2}$ for the FLMF at $M_{\rm line} > 10\,M_\odot {\rm pc^{-1}}$,
which are both consistent with the Salpeter power-law IMF. Based on these
results, we propose a revised model for the origin of the CMF in filaments,
whereby the global prestellar CMF in a molecular cloud arises from the
integration of the CMFs generated by individual thermally supercritical
filaments within the cloud. Our findings support the existence a tight
connection between the FLMF and the CMF/IMF and suggests that filamentary
structures represent a critical evolutionary step in establishing a
Salpeter-like mass function.
