  We present sensitive, arcsecond-resolution Submillimeter Array observations
of the 12CO J=2-1 line emission from the circumstellar disk orbiting the
double-lined spectroscopic binary star V4046 Sgr. Based on a simple model of
the disk structure, we use a novel Monte Carlo Markov Chain technique to
extract the Keplerian velocity field of the disk from these data and estimate
the total mass of the central binary. Assuming the distance inferred from
kinematic parallax measurements in the literature (d is approximately 73 pc),
we determine a total stellar mass M_star = 1.75^{+0.09}_{-0.06} solar masses
and a disk inclination i_d = 33.5^{+0.7}_{-1.4} degrees from face-on. These
measurements are in excellent agreement with independent dynamical constraints
made from multi-epoch monitoring of the stellar radial velocities, confirming
the absolute accuracy of this precise (~ few percent uncertainties) disk-based
method for estimating stellar masses and reaffirming previous assertions that
the disk and binary orbital planes are well aligned (with |i_d - i_star|
\approx 0.1\pm1 degree). Using these results as a reference, we demonstrate
that various pre-main sequence evolution models make consistent and accurate
predictions for the masses of the individual components of the binary, and
uniformly imply an advanced age of ~5-30 Myr. Taken together, these results
verify that V4046 Sgr is one of the precious few nearby and relatively evolved
pre-main sequence systems that still hosts a gas-rich accretion disk.
