  We have analyzed archival ASCA data on the soft X-ray transient source V404
Cyg in quiescence. We find that in the energy range 0.7 to 8.5 keV the spectrum
is a hard power-law with a photon spectral index between 1.8 and 2.6 (90%
confidence limits). We present a model of V404 Cyg in which the accretion flow
has two components: (1) an outer thin disk with a small annular extent, and (2)
a large interior region where the flow is advection-dominated. Nearly all the
radiation in the infrared, optical, UV and X-ray bands is from the
advection-dominated zone; the thin disk radiates primarily in the infrared
where it contributes about ten percent of the observed flux. The spectrum we
calculate with this model is in excellent agreement with the ASCA X-ray data
presented here, as well as with previous optical data. Moreover, the fit is
very insensitive to the choice of parameters such as black hole mass, orbital
inclination, viscosity coefficient $\alpha$, and magnetic field strength. We
consider the success of the model to be strong support for the
advection-dominated accretion paradigm, and further evidence of the black hole
nature of V404 Cyg. We discuss strategies whereby systems with
advection-dominated accretion could be used to prove the reality of event
horizons in black holes.
