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 .