We report ALMA observations in 0.87 mm continuum and $^{12}$CO ($J$ = 3--2) toward a very low-luminosity ($<$0.1 $L_{odot}$) protostar, which is deeply embedded in one of the densest core MC27/L1521F, in Taurus with an indication of multiple star formation in a highly dynamical environment. The beam size corresponds to $sim$20 AU, and we have clearly detected blueshifted/redshifted gas in $^{12}$CO associated with the protostar. The spatial/velocity distributions of the gas show there is a rotating disk with a size scale of $sim$10 AU, a disk mass of $sim$10$^{-4}$ $M_{odot}$ and a central stellar mass of $sim$0.2 $M_{odot}$. The observed disk seems to be detached from the surrounding dense gas, although it is still embedded at the center of the core whose density is $sim$10$^{6}$ cm$^{-3}$. The current low-outflow activity and the very low luminosity indicate that the mass accretion rate onto the protostar is extremely low in spite of a very early stage of star formation. We may be witnessing the final stage of the formation of $sim$0.2 $M_{odot}$ protostar. However, we cannot explain the observed low luminosity with the standard pre-main-sequence evolutionary track unless we assume cold accretion with an extremely small initial radius of the protostar ($sim$0.65 $R_odot$). These facts may challenge our current understanding of the low mass star formation, in particular the mass accretion process onto the protostar and the circumstellar disk.
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